Chapter 3 Preliminaries II: Data Formatting
The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents.
Note: The example code in this chapter relies on code executed in previous chapters. This code is available in a ready-to-run block in Appendix II (19.0.1).
Matrix projection models are estimated with demographic data. Regardless of whether the goal is a set of raw (empirical) or function-based matrices, the dataset used needs to follow a particular format to make the estimation of elements or vital rate models possible. Package lefko3 utilizes a standardized format similar to formats required by other protocols, such as the projection.matrix() function in package popbio. However, unlike other packages, lefko3 includes functions that can standardize a variety of starting dataset formats into the right format. These functions likely do not cover all possibilities, but deal with most of the interesting differences among the protocols that different demographers use.
The format used in analysis is similar to what one would expect in setting up a data frame for a linear model in R or another statistical analysis environment. If we start with a record of observations of a single individual across several years, where each observation was conducted during a single monitoring session per time interval (such as year), then our data should be formatted to allow us to assess at the very least whether the state of an individual at some time depends on the state at the previous time. For a historical model, this dependence extends one further time step back, so that we have to be able to assess demographic patterns across groups of three consecutive monitoring times.
In order to analyze these patterns of dependence, we break the data up into groups of two or three consecutive observation times, depending on whether the analysis will be ahistorical or historical, respectively. These broken up groups are then stacked together into a data frame. For example, if we have data for an individual in years 2010, 2011, 2012, and 2013, then we can break up these data into consecutive year pairs, starting with years 2010 and 2011, followed by years 2011 and 2012, followed by years 2012 and 2013 (if historical, then we would group together 2010-2011-2012, followed by 2011-2012-2013). In terms of the language of matrix projection models, these standardized datasets are arranged with time t followed by time t+1 if ahistorical, and time t-1, followed by time t, followed by time t+1 if in historical format. In terms of the language of linear modeling, individual status in the final time in each group can be viewed as the response variable, while status in the previous one or two times can be seen as causal. We refer to this stacked format as vertical format, because it stretches the data for a single individual vertically across data frame rows. This format can be further divided into historically-formatted vertical (hfv) format (Shefferson et al. 2021), in which groups of three consecutive monitoring times are stacked, and ahistorically-formatted vertical (ahfv) format, in which pairs of consecutive years are stacked. Note that analysis in lefko3 requires historically-formatted vertical (hfv) format.
The different aspects of the states of individuals can be described by different variables per observation time. There may be one or more measures of size, an age metric, a measure of reproductive status, and perhaps fecundity, among other variables. Each monitoring occasion should have the same variables for use in analysis. Thus, concatenating states for consecutive pairs or triplets of times in this way will generally result in data frames with many more than two or three columns. Stacking the data in this fashion also typically yields multiple rows of data originating from the same individual. Until recently, these rows were typically treated as independent data points, and the simplest analyses still assume independence. However, if a separate variable is created to record the identity of the individual across rows within the dataset, then the non-independence of data points can be dealt with statistically by treating individual identity as a random factor in mixed modeling of vital rates (more on this in chapter 5).
3.1 Kinds of individual state variables that may be included
What sorts of variables can be handled in MPM analysis through lefko3? Because this package was originally developed to handle historical size-classified Lefkovitch models, it can of course handle size variables. From version 4.0.0 onward, up to three different size variables can be included in a single analysis. However, lefko3 can handle many more variables. At the very least, variables denoting reproductive status and fecundity can be included. These three groups of variables - size, reproductive status, and fecundity - are the classic three variable types used for classification purposes in stage-based models. Wildlife demographers may be more interested in age than size, and so age at each time can also be included. In fact, lefko3 automates the estimation of age and related variables, such as observed age at time t and observed lifespan, and can be used to estimate both Leslie (age-based) and age-by-stage MPMs. Plant demographers may be interested in variables denoting observation status, which is a binomial variable used to denote whether an individual is in an observable stage (lefko3 can automate the identification of these occurrences within the dataset). Some ecologists may also be interested in using multiple measures of reproductive status and fecundity, since many plants and animals have multiple modes of reproduction, and often fecundity cannot be accurately known and so must be estimated.
Identity variables may be included and used in analysis. Such variables include population identity, patch identity or subpopulation identity, individual identity, and monitoring occasion or time (denoting the time at time t). Package lefko3 can use these to subset the data accordingly, and also to estimate variables such as observed age at time t and observed lifespan. If the user has already determined stages for all individuals at all times, then these data may be incorporated as well (although lefko3 can automatically assign stages).
Demographers commonly include censoring variables to denote data points that are suspect. These can also be included in lefko3, and censored data points can also be easily removed from analysis. For example, individuals with damaged tags from which identity cannot be properly read can be marked differently in a censor variable, and analyses can then be performed with and without these potentially biasing data. Alternatively, ornithologists may mark individuals with partially missing bands with censor variables. Censor data can be added once per individual, or for each individual in each monitoring occasion.
Spatial coordinates can be included in datasets. When used, spatial coordinates should be Cartesian, and so paired as X-Y coordinates. Package lefko3 includes automated density estimation, and so these coordinates can be used to estimate spatial density.
Finally, variables can be included covering status as alive or dead, status as observed or unobserved, and up to three separate individual or environmental covariates that can be numeric or categorical. Individual covariates may be particularly useful as a means to include environmental variables, or further information on status, such as management regime or presence of injury.
3.2 Formatting demographic data properly for analysis
Regardless of how the dataset should be structured for analysis, demographers themselves often have their own ways of structuring data. In general, most demographers keep their data either in some variant of vertical format (explained above), or in some variant of horizontal format, in which the data for each single individual spans only a single row that contains all data on state across all monitoring occasions. In figure 3.1, we see an example of an ahistorically-formatted vertical dataset. In figure 3.2, we see an example of a horizontally-formatted dataset.
Every demographer has his or her own way of keeping data, and I personally do not feel it is up to me to judge (the level of chaos in my own record-keeping prevents me from making any harsh judgments). Therefore, lefko3 includes two powerful functions that can take most datasets falling into these two general types and standardize them into formats that can be analyzed by the package. These functions are verticalize3() and historicalize3(). We will start by describing the former.
3.3 Function verticalize3()
Many demographers (including the author) prefer horizontal data formats for demographic record-keeping. Here, individual life histories are recorded in a spreadsheet with each unique individual’s data organized within a single row. The columns then correspond to descriptor variables and to condition at different times. This format has the advantage of making an individual’s resighting history easier to analyze even by eye, since it must occur all within a single row. In these circumstances, the verticalize3() function can standardize these data into hfv format.
Function verticalize3() takes a number of inputs. Naturally, it needs the data frame being used for analysis (the data field). It also requires input corresponding to the number of monitoring occasions that the dataset covers (field noyears), and which columns identify the population, patch or subpopulation, and individual (fields popidcol, patchidcol, and individcol, respectively).
After these most basic of fields have been entered, the columns conveying each kind of demographic variable need to be identified (this is a very flexible function, so only those variables that actually occur in the dataset need be identified and all others can be ignored). Up to three separate size variables can be identified (sizeacol, sizebcol, and sizeccol), as can up to two reproductive status variables (repstracol and restrbcol), and up to two fecundity variables (fecacol and fecbcol). These variables will naturally repeat across monitoring occasions, and so each variable represents as many actual columns as monitoring occasions covered by the dataset.
To ensure that R finds all columns corresponding to a variable, the user may take one of two approaches. The most flexible is to treat each input field as a vector, and to input the name or column number of each variable in order of monitoring occasion. For example, if we decided to use only one size variable, perhaps the height of a plant in centimeters, and this variable is labelled ht.2010, ht.2011, ht.2012, and ht.2013 for the years 2010, 2011, 2012, and 2013, then we can input the following.
sizeacol = c("ht.2010", "ht.2011", "ht.2012", "ht.2013").
All other variables covering status across time can be input in the same way, yielding equal length vectors in the same temporal order.
Alternatively, if the data are arranged such that each monitoring occasion has its variables arranged in a strictly repeating order, then we can use the blocksize argument to simplify our function call. Here, each variable in our dataset should be a fixed number of columns away from the equivalent variable in the preceding time and in the next time. Then, only the first column of each core variable group needs to be designated in verticalize3(), and the blocksize field can be set to the number of columns separating these entries. In the plant height example, if each size variable is 10 columns after the previous size variable and this pattern holds for all other variable types, then this would mean entering only the following.
noyears = 4, blocksize = 10, sizeacol = "ht.2010"
Note that the use of the blocksize option absolutely requires that each variable group occurs exactly blocksize columns after the previous instance, with absolutely no exceptions. Users who occasionally add empty or extra columns here and there in their dataset will find mistakes in the resulting standardization if they do not make sure that the exact number of columns between instances is always the same.
While standardizing the data, function verticalize3() can also assign stage designations if given a proper stageframe (the stageassign field). For this purpose, lefko3 also needs the proper size variable designations. Currently, the options include:
sizea,sizeb, orsizecif only one of these size metrics determines stagesizeab,sizeac, orsizebcif stage assignment is based on a pair of size metricssizeabcif stage assignment should utilize three size metrics; orsizeadded, if stage assignment should proceed on the basis of the sum of all used size metrics.
Stage assignment is automated using these size metrics as well as reproductive status, observation status, and status as propagule, immature, and mature. Stage assignment will yield warnings and unassigned stages if any combination of variables is found in the demographic dataset that does not fit exactly one stage in the stage frame. We also encourage the use of this function without stage assignment on the first pass, since this will allow users to explore the data more fully prior to the development of a life history model and stageframe.
Function verticalize3() includes a few more fields of interest. The repstrrel and fecrel fields provide means of equalizing reproductive status variables and fecundity variables, respectively, that are set on different scales. For example, if two reproductive status variables are used, the first covering the presence of single-flowered stems and the second covering the presence of double-flowered stems, then setting repstrrel = 2 will tell R that the second variable counts for twice the reproductive status of the first. The same applies to fecundity with the fecrel field, if two different fecundity measures are used.
Demographers using censoring variables will find powerful options in this function. First, censorcol can be set to a static censor variable covering an individual’s entire resighting history, or to censor variables that vary across time. This can be set with the censorRepeat field, which defaults to FALSE and so assumes that censor values do not vary across time. The value of the censor variable used to denote which individuals to keep can be set to any numeric value (the censorkeep option). The default is censorkeep = 0, meaning that any data points marked 0 are considered OK and kept, while any other value is assumed to be subject to removal. Any character or numeric value may be used to mark data to keep, even NA. Finally, if all options are set as described, then function verticalize3() will format the data with censor variables in place but will not remove any data points. To force verticalize3() to remove censored data points, set censor = TRUE (the default is censor = FALSE).
Function verticalize3() can handle spatial coordinates, and can even estimate spatial density. Cartesian coordinates for each individual are assumed to be a single set. However, if coordinates can change across time and each time point has its own set of coordinates for each individual present, then users can set coordsRepeat = TRUE. If the intent in using these coordinates is to estimate spatial density, then this function will calculate the number of individuals within some radius of each focal individual in each monitoring time if given the length of the radius to use via option spacing (e.g. spacing = 1 sets the distance radius to check for other individuals nearby at one unit of distance).
This function includes further parameters handling miscellaneous cases. First, demographers often treat missing data as blanks within their spreadsheets. Setting NAas0 = TRUE tells R to interpret missing data as zeros. This can be useful in many circumstances. For example, if fecundity is estimated as the number of flowers per individual in a plant demographic study, but the number of flowers per individual is only recorded if flowers actually exist, then setting NAas0 = TRUE can allow 0 values to be incorporated in analyses of fecundity when no data were entered for flower number. Second, the NRasRep option allows stage classification to proceed without matching stage reproductive characteristics to the data. For example, if stages are defined such that mature stages are reproductive but it is nonetheless possible for fecundity to equal 0, then setting NRasRep = TRUE tells R not to use reproductive status in stage classification. Otherwise, R will assume that a mature individual that produces offspring is in a different stage than a mature individual that does not. Third, the NAasObs option provides a means of telling R that unobservable stages should be treated as observed during stage classification, if set to TRUE (the default is FALSE). Fourth, the reduce option, if set to TRUE, will tell R that any columns in the output dataset with a single constant value across all rows should be removed, as invariant variables yield no influence on response variables in statistical modeling. Fifth, the a2check field should generally be kept to FALSE (the default), but if set to TRUE, then the resulting standardized dataset will include data for individuals not alive in time t (these instances are removed automatically under the default, since it is only individuals alive in time t that can transition to anything in time t+1). This function also assumes that monitoring studies are conducted using pre-breeding life history models, making 1 the earliest observed age. To use a post-breeding model, set prebreeding = FALSE. Finally, the age_offset option can be used to add a specific number to all ages, as might happen if the first few years of life cannot be monitored.
3.3.1 An example of verticalize3()
Now that we have explained the options, let’s standardize data frames for the stageframes created in the last chapter (chapter 2). Let’s first standardize the vertical dataset for the raw MPM. Because we are lumping reproductive and non-reproductive individuals into the non-dormant adult classes, we will set NRasRep = TRUE. Otherwise, verticalize3() will attempt to use the reproductive status of individuals in classification, and will fail due to the presence of non-reproductive adults. We will also set NAas0 = TRUE to make sure that NA values in size are turned into 0 entries where necessary, and so aid in the assignment of the vegetative dormancy stage. Note that we will set up three different size variables here, as sizea, sizeb, and sizec, and that we will tell R that we want overall stage classification size to be the sum of these (stagesize = "sizeadded"). Finally, since the individuals in this dataset must be at least 5 years old when they are first seen as adults, we will use the age_offset option to adjust the estimated age.
cypraw_v1 <- verticalize3(data = cypdata, noyears = 6, firstyear = 2004,
patchidcol = "patch", individcol = "plantid", blocksize = 4,
sizeacol = "Inf2.04", sizebcol = "Inf.04", sizeccol = "Veg.04",
repstracol = "Inf.04", repstrbcol = "Inf2.04", fecacol = "Pod.04",
stageassign = cypframe_raw, stagesize = "sizeadded", NAas0 = TRUE,
NRasRep = TRUE, age_offset = 4)
Let’s now take a look at a summary of this dataset. We have two options for this. First, we could use R’s summary() function, which would treat our new historically vertically (hfv) formatted dataset as a standard data frame and use the standard summary procedure for data frames. Or, we may use lefko3’s summary_hfv() function, which gives us a little extra information.
summary_hfv(cypraw_v1)
>
> This hfv dataset contains 320 rows, 57 variables, 1 population,
> 3 patches, 74 individuals, and 5 time steps.
> rowid popid patchid individ year2
> Min. : 1.00 Length:320 A: 93 Min. : 164.0 Min. :2004
> 1st Qu.:21.00 Class :character B:154 1st Qu.: 391.0 1st Qu.:2005
> Median :37.50 Mode :character C: 73 Median : 453.0 Median :2006
> Mean :38.45 Mean : 651.5 Mean :2006
> 3rd Qu.:56.00 3rd Qu.: 476.0 3rd Qu.:2007
> Max. :77.00 Max. :1560.0 Max. :2008
> firstseen lastseen obsage obslifespan
> Min. :2004 Min. :2004 Min. :5.000 Min. :0.000
> 1st Qu.:2004 1st Qu.:2009 1st Qu.:6.000 1st Qu.:5.000
> Median :2004 Median :2009 Median :7.000 Median :5.000
> Mean :2004 Mean :2009 Mean :6.853 Mean :4.556
> 3rd Qu.:2004 3rd Qu.:2009 3rd Qu.:8.000 3rd Qu.:5.000
> Max. :2008 Max. :2009 Max. :9.000 Max. :5.000
> sizea1 sizeb1 sizec1 size1added
> Min. :0.000000 Min. : 0.0000 Min. : 0.0 Min. : 0.000
> 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.: 0.0 1st Qu.: 0.000
> Median :0.000000 Median : 0.0000 Median : 1.0 Median : 2.000
> Mean :0.009375 Mean : 0.7469 Mean : 1.9 Mean : 2.656
> 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.: 3.0 3rd Qu.: 4.000
> Max. :1.000000 Max. :18.0000 Max. :13.0 Max. :21.000
> repstra1 repstrb1 repstr1added feca1
> Min. : 0.0000 Min. :0.000000 Min. : 0.0000 Min. :0.0000
> 1st Qu.: 0.0000 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.:0.0000
> Median : 0.0000 Median :0.000000 Median : 0.0000 Median :0.0000
> Mean : 0.7469 Mean :0.009375 Mean : 0.7562 Mean :0.2656
> 3rd Qu.: 1.0000 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.:0.0000
> Max. :18.0000 Max. :1.000000 Max. :18.0000 Max. :7.0000
> fec1added obsstatus1 repstatus1 fecstatus1
> Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
> 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
> Median :0.0000 Median :1.0000 Median :0.0000 Median :0.0000
> Mean :0.2656 Mean :0.7469 Mean :0.2875 Mean :0.1344
> 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
> Max. :7.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
> matstatus1 alive1 stage1 stage1index
> Min. :0.0000 Min. :0.0000 Length:320 Min. : 0.000
> 1st Qu.:1.0000 1st Qu.:1.0000 Class :character 1st Qu.: 6.000
> Median :1.0000 Median :1.0000 Mode :character Median : 8.000
> Mean :0.7688 Mean :0.7688 Mean : 6.144
> 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.: 8.000
> Max. :1.0000 Max. :1.0000 Max. :11.000
> sizea2 sizeb2 sizec2 size2added
> Min. :0.000000 Min. : 0.0000 Min. : 0.000 Min. : 0.000
> 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.: 1.000 1st Qu.: 1.000
> Median :0.000000 Median : 0.0000 Median : 2.000 Median : 2.000
> Mean :0.009375 Mean : 0.8969 Mean : 2.416 Mean : 3.322
> 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.: 3.000 3rd Qu.: 4.000
> Max. :1.000000 Max. :18.0000 Max. :13.000 Max. :24.000
> repstra2 repstrb2 repstr2added feca2
> Min. : 0.0000 Min. :0.000000 Min. : 0.0000 Min. :0.0000
> 1st Qu.: 0.0000 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.:0.0000
> Median : 0.0000 Median :0.000000 Median : 0.0000 Median :0.0000
> Mean : 0.8969 Mean :0.009375 Mean : 0.9062 Mean :0.2906
> 3rd Qu.: 1.0000 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.:0.0000
> Max. :18.0000 Max. :1.000000 Max. :18.0000 Max. :7.0000
> fec2added obsstatus2 repstatus2 fecstatus2
> Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
> 1st Qu.:0.0000 1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.0000
> Median :0.0000 Median :1.0000 Median :0.0000 Median :0.0000
> Mean :0.2906 Mean :0.9531 Mean :0.3688 Mean :0.1562
> 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
> Max. :7.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
> matstatus2 alive2 stage2 stage2index
> Min. :1 Min. :1 Length:320 Min. : 6.000
> 1st Qu.:1 1st Qu.:1 Class :character 1st Qu.: 7.000
> Median :1 Median :1 Mode :character Median : 8.000
> Mean :1 Mean :1 Mean : 7.919
> 3rd Qu.:1 3rd Qu.:1 3rd Qu.: 8.000
> Max. :1 Max. :1 Max. :11.000
> sizea3 sizeb3 sizec3 size3added
> Min. :0.000000 Min. : 0.000 Min. : 0.000 Min. : 0.000
> 1st Qu.:0.000000 1st Qu.: 0.000 1st Qu.: 1.000 1st Qu.: 1.000
> Median :0.000000 Median : 0.000 Median : 1.000 Median : 2.000
> Mean :0.009375 Mean : 1.069 Mean : 2.209 Mean : 3.288
> 3rd Qu.:0.000000 3rd Qu.: 1.000 3rd Qu.: 3.000 3rd Qu.: 4.000
> Max. :1.000000 Max. :18.000 Max. :13.000 Max. :24.000
> repstra3 repstrb3 repstr3added feca3
> Min. : 0.000 Min. :0.000000 Min. : 0.000 Min. :0.0000
> 1st Qu.: 0.000 1st Qu.:0.000000 1st Qu.: 0.000 1st Qu.:0.0000
> Median : 0.000 Median :0.000000 Median : 0.000 Median :0.0000
> Mean : 1.069 Mean :0.009375 Mean : 1.078 Mean :0.4562
> 3rd Qu.: 1.000 3rd Qu.:0.000000 3rd Qu.: 1.000 3rd Qu.:0.0000
> Max. :18.000 Max. :1.000000 Max. :18.000 Max. :8.0000
> fec3added obsstatus3 repstatus3 fecstatus3 matstatus3
> Min. :0.0000 Min. :0.0 Min. :0.0 Min. :0.0000 Min. :1
> 1st Qu.:0.0000 1st Qu.:1.0 1st Qu.:0.0 1st Qu.:0.0000 1st Qu.:1
> Median :0.0000 Median :1.0 Median :0.0 Median :0.0000 Median :1
> Mean :0.4562 Mean :0.9 Mean :0.4 Mean :0.2219 Mean :1
> 3rd Qu.:0.0000 3rd Qu.:1.0 3rd Qu.:1.0 3rd Qu.:0.0000 3rd Qu.:1
> Max. :8.0000 Max. :1.0 Max. :1.0 Max. :1.0000 Max. :1
> alive3 stage3 stage3index
> Min. :0.0000 Length:320 Min. : 0.000
> 1st Qu.:1.0000 Class :character 1st Qu.: 7.000
> Median :1.0000 Mode :character Median : 8.000
> Mean :0.9469 Mean : 7.544
> 3rd Qu.:1.0000 3rd Qu.: 8.000
> Max. :1.0000 Max. :11.000
In the summary of the resulting data frame, we first see that there are 320 rows, 57 variables, one population, three patches, 74 individuals, and 5 time steps. This information gives us a good understanding of the dimensions of the dataset. This is followed by R’s data frame summary, where we see that the first four variables are identifying information - they show the data row (rowid), the population ID (popid), the patch ID (patchid), and the individual ID (individ), in order. These are followed by year at time t (year2), followed by two variables identifying in what monitoring occasion the individual was first seen (firstseen), and in what occasion it was last seen (lastseen). The next variable, obsage, gives the estimated age at time t. The next variable, obslifespan, gives the full length of time that the individual was observed in the dataset. After that, we see a group of 15 variables typically ending with the number 1. These 15 variables correspond to the state of each individual in time t-1 (generally referred to as time1 in the actual code). Similarly, the next 15 variables typically end with the number 2 and represent state in time t, while the last 15 variables typically end in the number 3 and refer to state in time t+1. Most of these variables should be obvious to interpret given the names (definitions are in the help file for this function). Note that the final seven variables in each group are calculated by verticalize3(). These variables represent observation status, reproductive status, fecundity status, maturity status, status as alive or dead, stage name, and stage number (with reference to the stageframe), in order.
The summary_hfv() function can also produce just the initial dimensional output, as below.
summary_hfv(cypraw_v1, full = FALSE)
>
> This hfv dataset contains 320 rows, 57 variables, 1 population,
> 3 patches, 74 individuals, and 5 time steps.
Let’s also create our standardized data frame for the function-based MPM, as below. Remember that some of the settings need to change here because we will use a different life history model. Particularly, we are now going to separate adults not just by size but by reproductive status. So, we will not set NRasRep = TRUE here (the default is NRasRep = FALSE).
cypfb_v1 <- verticalize3(data = cypdata, noyears = 6, firstyear = 2004,
patchidcol = "patch", individcol = "plantid", blocksize = 4,
sizeacol = "Inf2.04", sizebcol = "Inf.04", sizeccol = "Veg.04",
repstracol = "Inf.04", repstrbcol = "Inf2.04", fecacol = "Pod.04",
stageassign = cypframe_fb, stagesize = "sizeadded", NAas0 = TRUE,
age_offset = 4)
summary_hfv(cypfb_v1)
>
> This hfv dataset contains 320 rows, 57 variables, 1 population,
> 3 patches, 74 individuals, and 5 time steps.
> rowid popid patchid individ year2
> Min. : 1.00 Length:320 A: 93 Min. : 164.0 Min. :2004
> 1st Qu.:21.00 Class :character B:154 1st Qu.: 391.0 1st Qu.:2005
> Median :37.50 Mode :character C: 73 Median : 453.0 Median :2006
> Mean :38.45 Mean : 651.5 Mean :2006
> 3rd Qu.:56.00 3rd Qu.: 476.0 3rd Qu.:2007
> Max. :77.00 Max. :1560.0 Max. :2008
> firstseen lastseen obsage obslifespan
> Min. :2004 Min. :2004 Min. :5.000 Min. :0.000
> 1st Qu.:2004 1st Qu.:2009 1st Qu.:6.000 1st Qu.:5.000
> Median :2004 Median :2009 Median :7.000 Median :5.000
> Mean :2004 Mean :2009 Mean :6.853 Mean :4.556
> 3rd Qu.:2004 3rd Qu.:2009 3rd Qu.:8.000 3rd Qu.:5.000
> Max. :2008 Max. :2009 Max. :9.000 Max. :5.000
> sizea1 sizeb1 sizec1 size1added
> Min. :0.000000 Min. : 0.0000 Min. : 0.0 Min. : 0.000
> 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.: 0.0 1st Qu.: 0.000
> Median :0.000000 Median : 0.0000 Median : 1.0 Median : 2.000
> Mean :0.009375 Mean : 0.7469 Mean : 1.9 Mean : 2.656
> 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.: 3.0 3rd Qu.: 4.000
> Max. :1.000000 Max. :18.0000 Max. :13.0 Max. :21.000
> repstra1 repstrb1 repstr1added feca1
> Min. : 0.0000 Min. :0.000000 Min. : 0.0000 Min. :0.0000
> 1st Qu.: 0.0000 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.:0.0000
> Median : 0.0000 Median :0.000000 Median : 0.0000 Median :0.0000
> Mean : 0.7469 Mean :0.009375 Mean : 0.7562 Mean :0.2656
> 3rd Qu.: 1.0000 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.:0.0000
> Max. :18.0000 Max. :1.000000 Max. :18.0000 Max. :7.0000
> fec1added obsstatus1 repstatus1 fecstatus1
> Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
> 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
> Median :0.0000 Median :1.0000 Median :0.0000 Median :0.0000
> Mean :0.2656 Mean :0.7469 Mean :0.2875 Mean :0.1344
> 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
> Max. :7.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
> matstatus1 alive1 stage1 stage1index
> Min. :0.0000 Min. :0.0000 Length:320 Min. : 0.00
> 1st Qu.:1.0000 1st Qu.:1.0000 Class :character 1st Qu.: 6.00
> Median :1.0000 Median :1.0000 Mode :character Median : 8.00
> Mean :0.7688 Mean :0.7688 Mean :14.17
> 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:31.00
> Max. :1.0000 Max. :1.0000 Max. :51.00
> sizea2 sizeb2 sizec2 size2added
> Min. :0.000000 Min. : 0.0000 Min. : 0.000 Min. : 0.000
> 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.: 1.000 1st Qu.: 1.000
> Median :0.000000 Median : 0.0000 Median : 2.000 Median : 2.000
> Mean :0.009375 Mean : 0.8969 Mean : 2.416 Mean : 3.322
> 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.: 3.000 3rd Qu.: 4.000
> Max. :1.000000 Max. :18.0000 Max. :13.000 Max. :24.000
> repstra2 repstrb2 repstr2added feca2
> Min. : 0.0000 Min. :0.000000 Min. : 0.0000 Min. :0.0000
> 1st Qu.: 0.0000 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.:0.0000
> Median : 0.0000 Median :0.000000 Median : 0.0000 Median :0.0000
> Mean : 0.8969 Mean :0.009375 Mean : 0.9062 Mean :0.2906
> 3rd Qu.: 1.0000 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.:0.0000
> Max. :18.0000 Max. :1.000000 Max. :18.0000 Max. :7.0000
> fec2added obsstatus2 repstatus2 fecstatus2
> Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
> 1st Qu.:0.0000 1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.0000
> Median :0.0000 Median :1.0000 Median :0.0000 Median :0.0000
> Mean :0.2906 Mean :0.9531 Mean :0.3688 Mean :0.1562
> 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
> Max. :7.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
> matstatus2 alive2 stage2 stage2index sizea3
> Min. :1 Min. :1 Length:320 Min. : 6.00 Min. :0.000000
> 1st Qu.:1 1st Qu.:1 Class :character 1st Qu.: 7.00 1st Qu.:0.000000
> Median :1 Median :1 Mode :character Median :10.00 Median :0.000000
> Mean :1 Mean :1 Mean :18.17 Mean :0.009375
> 3rd Qu.:1 3rd Qu.:1 3rd Qu.:32.00 3rd Qu.:0.000000
> Max. :1 Max. :1 Max. :54.00 Max. :1.000000
> sizeb3 sizec3 size3added repstra3
> Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. : 0.000
> 1st Qu.: 0.000 1st Qu.: 1.000 1st Qu.: 1.000 1st Qu.: 0.000
> Median : 0.000 Median : 1.000 Median : 2.000 Median : 0.000
> Mean : 1.069 Mean : 2.209 Mean : 3.288 Mean : 1.069
> 3rd Qu.: 1.000 3rd Qu.: 3.000 3rd Qu.: 4.000 3rd Qu.: 1.000
> Max. :18.000 Max. :13.000 Max. :24.000 Max. :18.000
> repstrb3 repstr3added feca3 fec3added
> Min. :0.000000 Min. : 0.000 Min. :0.0000 Min. :0.0000
> 1st Qu.:0.000000 1st Qu.: 0.000 1st Qu.:0.0000 1st Qu.:0.0000
> Median :0.000000 Median : 0.000 Median :0.0000 Median :0.0000
> Mean :0.009375 Mean : 1.078 Mean :0.4562 Mean :0.4562
> 3rd Qu.:0.000000 3rd Qu.: 1.000 3rd Qu.:0.0000 3rd Qu.:0.0000
> Max. :1.000000 Max. :18.000 Max. :8.0000 Max. :8.0000
> obsstatus3 repstatus3 fecstatus3 matstatus3 alive3
> Min. :0.0 Min. :0.0 Min. :0.0000 Min. :1 Min. :0.0000
> 1st Qu.:1.0 1st Qu.:0.0 1st Qu.:0.0000 1st Qu.:1 1st Qu.:1.0000
> Median :1.0 Median :0.0 Median :0.0000 Median :1 Median :1.0000
> Mean :0.9 Mean :0.4 Mean :0.2219 Mean :1 Mean :0.9469
> 3rd Qu.:1.0 3rd Qu.:1.0 3rd Qu.:0.0000 3rd Qu.:1 3rd Qu.:1.0000
> Max. :1.0 Max. :1.0 Max. :1.0000 Max. :1 Max. :1.0000
> stage3 stage3index
> Length:320 Min. : 0.00
> Class :character 1st Qu.: 7.00
> Mode :character Median :10.00
> Mean :18.57
> 3rd Qu.:33.00
> Max. :54.00
The output dataset includes a number of summary variables, but the data is essentially broken down into groups of three consecutive monitoring occasions each (occasions t+1, t, and t-1, corresponding to year3, year2, and year1 in the output, respectively), with individuals spread across multiple rows. The output dataset is further limited to those entries in which the individual is alive in occasion t (year2), meaning that all rows in which an individual is dead or not yet recruited in occasion t are dropped. Since the input data is the same, we should see the same numbers of rows and columns in the raw and function-based cases, regardless of the different stageframes used. Thus, we have 320 rows of data and 57 variables in the raw case, and 320 rows of data and 57 variables in the function-based case.
3.4 Function historicalize3()
What should be done if the dataset is in ahistorical vertical format, in which an individual’s condition across time is recorded across rows in a spreadsheet, with a single row corresponding to either a single observation or to a pair of consecutive observations? In that case, the historicalize3() function can standardize the dataset properly. The inputs to this function are very similar to verticalize3(). However, the historicalize3() function assumes that the input dataset is organized with rows corresponding to individual status in either only one monitoring occasion, or two consecutive occasions. Inputs include a series of variables more or less equivalent to input options in verticalize3(), but some variable names end with 2col, and others end with 3col. The former variables denote status in time t, and are the minimum required for this function to run. If each row includes status in paired consecutive times, then variables ending in 3col can be used to designate status in time t+1. Additionally, this function requires a single variable identifying individuals across rows (individcol), so that each individual’s resighting history can be inferred and each group of three consecutive monitoring times can be put together. All other fields work essentially the same as in verticalize3().
3.4.1 An example of historicalize3()
Package lefko3 also includes dataset cypvert, which is the same dataset as cypdata but set in ahistorical vertical format. Here, we will use the historicalize3() function to standardize this dataset, using the plantid variable as the individual identity term.
data(cypvert)
cypraw_v2 <- historicalize3(data = cypvert, patchidcol = "patch",
individcol = "plantid", year2col = "year2", sizea2col = "Inf2.2",
sizea3col = "Inf2.3", sizeb2col = "Inf.2", sizeb3col = "Inf.3",
sizec2col = "Veg.2", sizec3col = "Veg.3", repstra2col = "Inf2.2",
repstra3col = "Inf2.3", repstrb2col = "Inf.2", repstrb3col = "Inf.3",
feca2col = "Pod.2", feca3col = "Pod.3", repstrrel = 2,
stageassign = cypframe_raw, stagesize = "sizeadded", censorcol = "censor",
censorkeep = 1, censor = FALSE, NAas0 = TRUE, NRasRep = TRUE, age_offset = 4,
reduce = TRUE)
summary_hfv(cypraw_v2)
>
> This hfv dataset contains 320 rows, 57 variables, 1 population,
> 3 patches, 74 individuals, and 5 time steps.
> rowid popid patchid individ year2
> Min. : 0.00 Length:320 A: 93 Min. : 164.0 Min. :2004
> 1st Qu.: 79.75 Class :character B:154 1st Qu.: 391.0 1st Qu.:2005
> Median :159.50 Mode :character C: 73 Median : 453.0 Median :2006
> Mean :159.70 Mean : 651.5 Mean :2006
> 3rd Qu.:239.25 3rd Qu.: 476.0 3rd Qu.:2007
> Max. :321.00 Max. :1560.0 Max. :2008
> firstseen lastseen obsage obslifespan
> Min. :2004 Min. :2004 Min. :5.000 Min. :0.000
> 1st Qu.:2004 1st Qu.:2009 1st Qu.:6.000 1st Qu.:5.000
> Median :2004 Median :2009 Median :7.000 Median :5.000
> Mean :2004 Mean :2009 Mean :6.853 Mean :4.556
> 3rd Qu.:2004 3rd Qu.:2009 3rd Qu.:8.000 3rd Qu.:5.000
> Max. :2008 Max. :2009 Max. :9.000 Max. :5.000
> sizea1 sizeb1 sizec1 size1added
> Min. :0.000000 Min. : 0.0000 Min. : 0.0 Min. : 0.000
> 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.: 0.0 1st Qu.: 0.000
> Median :0.000000 Median : 0.0000 Median : 1.0 Median : 2.000
> Mean :0.009375 Mean : 0.7469 Mean : 1.9 Mean : 2.656
> 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.: 3.0 3rd Qu.: 4.000
> Max. :1.000000 Max. :18.0000 Max. :13.0 Max. :21.000
> repstra1 repstrb1 repstr1added feca1
> Min. :0.000000 Min. : 0.0000 Min. : 0.000 Min. :0.0000
> 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.:0.0000
> Median :0.000000 Median : 0.0000 Median : 0.000 Median :0.0000
> Mean :0.009375 Mean : 0.7469 Mean : 1.503 Mean :0.2656
> 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.: 2.000 3rd Qu.:0.0000
> Max. :1.000000 Max. :18.0000 Max. :36.000 Max. :7.0000
> fec1added obsstatus1 repstatus1 fecstatus1
> Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
> 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
> Median :0.0000 Median :1.0000 Median :0.0000 Median :0.0000
> Mean :0.2656 Mean :0.7469 Mean :0.2875 Mean :0.1344
> 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
> Max. :7.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
> matstatus1 alive1 stage1 stage1index
> Min. :0.0000 Min. :0.0000 Length:320 Min. : 0.000
> 1st Qu.:1.0000 1st Qu.:1.0000 Class :character 1st Qu.: 6.000
> Median :1.0000 Median :1.0000 Mode :character Median : 8.000
> Mean :0.7688 Mean :0.7688 Mean : 6.144
> 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.: 8.000
> Max. :1.0000 Max. :1.0000 Max. :11.000
> sizea2 sizeb2 sizec2 size2added
> Min. :0.000000 Min. : 0.0000 Min. : 0.000 Min. : 0.000
> 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.: 1.000 1st Qu.: 1.000
> Median :0.000000 Median : 0.0000 Median : 2.000 Median : 2.000
> Mean :0.009375 Mean : 0.8969 Mean : 2.416 Mean : 3.322
> 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.: 3.000 3rd Qu.: 4.000
> Max. :1.000000 Max. :18.0000 Max. :13.000 Max. :24.000
> repstra2 repstrb2 repstr2added feca2
> Min. :0.000000 Min. : 0.0000 Min. : 0.000 Min. :0.0000
> 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.:0.0000
> Median :0.000000 Median : 0.0000 Median : 0.000 Median :0.0000
> Mean :0.009375 Mean : 0.8969 Mean : 1.803 Mean :0.2906
> 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.: 2.000 3rd Qu.:0.0000
> Max. :1.000000 Max. :18.0000 Max. :36.000 Max. :7.0000
> fec2added obsstatus2 repstatus2 fecstatus2
> Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
> 1st Qu.:0.0000 1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.0000
> Median :0.0000 Median :1.0000 Median :0.0000 Median :0.0000
> Mean :0.2906 Mean :0.9531 Mean :0.3688 Mean :0.1562
> 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
> Max. :7.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
> matstatus2 alive2 stage2 stage2index
> Min. :1 Min. :1 Length:320 Min. : 6.000
> 1st Qu.:1 1st Qu.:1 Class :character 1st Qu.: 7.000
> Median :1 Median :1 Mode :character Median : 8.000
> Mean :1 Mean :1 Mean : 7.919
> 3rd Qu.:1 3rd Qu.:1 3rd Qu.: 8.000
> Max. :1 Max. :1 Max. :11.000
> sizea3 sizeb3 sizec3 size3added
> Min. :0.000000 Min. : 0.000 Min. : 0.000 Min. : 0.000
> 1st Qu.:0.000000 1st Qu.: 0.000 1st Qu.: 1.000 1st Qu.: 1.000
> Median :0.000000 Median : 0.000 Median : 1.000 Median : 2.000
> Mean :0.009375 Mean : 1.069 Mean : 2.209 Mean : 3.288
> 3rd Qu.:0.000000 3rd Qu.: 1.000 3rd Qu.: 3.000 3rd Qu.: 4.000
> Max. :1.000000 Max. :18.000 Max. :13.000 Max. :24.000
> repstra3 repstrb3 repstr3added feca3
> Min. :0.000000 Min. : 0.000 Min. : 0.000 Min. :0.0000
> 1st Qu.:0.000000 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.:0.0000
> Median :0.000000 Median : 0.000 Median : 0.000 Median :0.0000
> Mean :0.009375 Mean : 1.069 Mean : 2.147 Mean :0.4562
> 3rd Qu.:0.000000 3rd Qu.: 1.000 3rd Qu.: 2.000 3rd Qu.:0.0000
> Max. :1.000000 Max. :18.000 Max. :36.000 Max. :8.0000
> fec3added obsstatus3 repstatus3 fecstatus3 matstatus3
> Min. :0.0000 Min. :0.0 Min. :0.0 Min. :0.0000 Min. :1
> 1st Qu.:0.0000 1st Qu.:1.0 1st Qu.:0.0 1st Qu.:0.0000 1st Qu.:1
> Median :0.0000 Median :1.0 Median :0.0 Median :0.0000 Median :1
> Mean :0.4562 Mean :0.9 Mean :0.4 Mean :0.2219 Mean :1
> 3rd Qu.:0.0000 3rd Qu.:1.0 3rd Qu.:1.0 3rd Qu.:0.0000 3rd Qu.:1
> Max. :8.0000 Max. :1.0 Max. :1.0 Max. :1.0000 Max. :1
> alive3 stage3 stage3index
> Min. :0.0000 Length:320 Min. : 0.000
> 1st Qu.:1.0000 Class :character 1st Qu.: 7.000
> Median :1.0000 Mode :character Median : 8.000
> Mean :0.9469 Mean : 7.544
> 3rd Qu.:1.0000 3rd Qu.: 8.000
> Max. :1.0000 Max. :11.000Let’s also create the function-based MPM version, which differs primarily in the use of the function-based model stageframe.
cypfb_v2 <- historicalize3(data = cypvert, patchidcol = "patch",
individcol = "plantid", year2col = "year2", sizea2col = "Inf2.2",
sizea3col = "Inf2.3", sizeb2col = "Inf.2", sizeb3col = "Inf.3",
sizec2col = "Veg.2", sizec3col = "Veg.3", repstra2col = "Inf2.2",
repstra3col = "Inf2.3", repstrb2col = "Inf.2", repstrb3col = "Inf.3",
feca2col = "Pod.2", feca3col = "Pod.3", repstrrel = 2,
stageassign = cypframe_fb, stagesize = "sizeadded", censorcol = "censor",
censorkeep = 1, censor = FALSE, NAas0 = TRUE, age_offset = 4, reduce = TRUE)
summary_hfv(cypfb_v2)
>
> This hfv dataset contains 320 rows, 57 variables, 1 population,
> 3 patches, 74 individuals, and 5 time steps.
> rowid popid patchid individ year2
> Min. : 0.00 Length:320 A: 93 Min. : 164.0 Min. :2004
> 1st Qu.: 79.75 Class :character B:154 1st Qu.: 391.0 1st Qu.:2005
> Median :159.50 Mode :character C: 73 Median : 453.0 Median :2006
> Mean :159.70 Mean : 651.5 Mean :2006
> 3rd Qu.:239.25 3rd Qu.: 476.0 3rd Qu.:2007
> Max. :321.00 Max. :1560.0 Max. :2008
> firstseen lastseen obsage obslifespan
> Min. :2004 Min. :2004 Min. :5.000 Min. :0.000
> 1st Qu.:2004 1st Qu.:2009 1st Qu.:6.000 1st Qu.:5.000
> Median :2004 Median :2009 Median :7.000 Median :5.000
> Mean :2004 Mean :2009 Mean :6.853 Mean :4.556
> 3rd Qu.:2004 3rd Qu.:2009 3rd Qu.:8.000 3rd Qu.:5.000
> Max. :2008 Max. :2009 Max. :9.000 Max. :5.000
> sizea1 sizeb1 sizec1 size1added
> Min. :0.000000 Min. : 0.0000 Min. : 0.0 Min. : 0.000
> 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.: 0.0 1st Qu.: 0.000
> Median :0.000000 Median : 0.0000 Median : 1.0 Median : 2.000
> Mean :0.009375 Mean : 0.7469 Mean : 1.9 Mean : 2.656
> 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.: 3.0 3rd Qu.: 4.000
> Max. :1.000000 Max. :18.0000 Max. :13.0 Max. :21.000
> repstra1 repstrb1 repstr1added feca1
> Min. :0.000000 Min. : 0.0000 Min. : 0.000 Min. :0.0000
> 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.:0.0000
> Median :0.000000 Median : 0.0000 Median : 0.000 Median :0.0000
> Mean :0.009375 Mean : 0.7469 Mean : 1.503 Mean :0.2656
> 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.: 2.000 3rd Qu.:0.0000
> Max. :1.000000 Max. :18.0000 Max. :36.000 Max. :7.0000
> fec1added obsstatus1 repstatus1 fecstatus1
> Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
> 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
> Median :0.0000 Median :1.0000 Median :0.0000 Median :0.0000
> Mean :0.2656 Mean :0.7469 Mean :0.2875 Mean :0.1344
> 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
> Max. :7.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
> matstatus1 alive1 stage1 stage1index
> Min. :0.0000 Min. :0.0000 Length:320 Min. : 0.00
> 1st Qu.:1.0000 1st Qu.:1.0000 Class :character 1st Qu.: 6.00
> Median :1.0000 Median :1.0000 Mode :character Median : 8.00
> Mean :0.7688 Mean :0.7688 Mean :14.17
> 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:31.00
> Max. :1.0000 Max. :1.0000 Max. :51.00
> sizea2 sizeb2 sizec2 size2added
> Min. :0.000000 Min. : 0.0000 Min. : 0.000 Min. : 0.000
> 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.: 1.000 1st Qu.: 1.000
> Median :0.000000 Median : 0.0000 Median : 2.000 Median : 2.000
> Mean :0.009375 Mean : 0.8969 Mean : 2.416 Mean : 3.322
> 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.: 3.000 3rd Qu.: 4.000
> Max. :1.000000 Max. :18.0000 Max. :13.000 Max. :24.000
> repstra2 repstrb2 repstr2added feca2
> Min. :0.000000 Min. : 0.0000 Min. : 0.000 Min. :0.0000
> 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.:0.0000
> Median :0.000000 Median : 0.0000 Median : 0.000 Median :0.0000
> Mean :0.009375 Mean : 0.8969 Mean : 1.803 Mean :0.2906
> 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.: 2.000 3rd Qu.:0.0000
> Max. :1.000000 Max. :18.0000 Max. :36.000 Max. :7.0000
> fec2added obsstatus2 repstatus2 fecstatus2
> Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
> 1st Qu.:0.0000 1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.0000
> Median :0.0000 Median :1.0000 Median :0.0000 Median :0.0000
> Mean :0.2906 Mean :0.9531 Mean :0.3688 Mean :0.1562
> 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
> Max. :7.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
> matstatus2 alive2 stage2 stage2index sizea3
> Min. :1 Min. :1 Length:320 Min. : 6.00 Min. :0.000000
> 1st Qu.:1 1st Qu.:1 Class :character 1st Qu.: 7.00 1st Qu.:0.000000
> Median :1 Median :1 Mode :character Median :10.00 Median :0.000000
> Mean :1 Mean :1 Mean :18.17 Mean :0.009375
> 3rd Qu.:1 3rd Qu.:1 3rd Qu.:32.00 3rd Qu.:0.000000
> Max. :1 Max. :1 Max. :54.00 Max. :1.000000
> sizeb3 sizec3 size3added repstra3
> Min. : 0.000 Min. : 0.000 Min. : 0.000 Min. :0.000000
> 1st Qu.: 0.000 1st Qu.: 1.000 1st Qu.: 1.000 1st Qu.:0.000000
> Median : 0.000 Median : 1.000 Median : 2.000 Median :0.000000
> Mean : 1.069 Mean : 2.209 Mean : 3.288 Mean :0.009375
> 3rd Qu.: 1.000 3rd Qu.: 3.000 3rd Qu.: 4.000 3rd Qu.:0.000000
> Max. :18.000 Max. :13.000 Max. :24.000 Max. :1.000000
> repstrb3 repstr3added feca3 fec3added
> Min. : 0.000 Min. : 0.000 Min. :0.0000 Min. :0.0000
> 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.:0.0000 1st Qu.:0.0000
> Median : 0.000 Median : 0.000 Median :0.0000 Median :0.0000
> Mean : 1.069 Mean : 2.147 Mean :0.4562 Mean :0.4562
> 3rd Qu.: 1.000 3rd Qu.: 2.000 3rd Qu.:0.0000 3rd Qu.:0.0000
> Max. :18.000 Max. :36.000 Max. :8.0000 Max. :8.0000
> obsstatus3 repstatus3 fecstatus3 matstatus3 alive3
> Min. :0.0 Min. :0.0 Min. :0.0000 Min. :1 Min. :0.0000
> 1st Qu.:1.0 1st Qu.:0.0 1st Qu.:0.0000 1st Qu.:1 1st Qu.:1.0000
> Median :1.0 Median :0.0 Median :0.0000 Median :1 Median :1.0000
> Mean :0.9 Mean :0.4 Mean :0.2219 Mean :1 Mean :0.9469
> 3rd Qu.:1.0 3rd Qu.:1.0 3rd Qu.:0.0000 3rd Qu.:1 3rd Qu.:1.0000
> Max. :1.0 Max. :1.0 Max. :1.0000 Max. :1 Max. :1.0000
> stage3 stage3index
> Length:320 Min. : 0.00
> Class :character 1st Qu.: 7.00
> Mode :character Median :10.00
> Mean :18.57
> 3rd Qu.:33.00
> Max. :54.00
One important consideration is the use of censor variables. Censoring a demographic dataset is typically accomplished by including a binary variable in the dataset denoting whether a datum is to be kept or excluded. The objects cypraw_v2 and cypfb_v2 were both created without censoring. However, because the datasets actually included censor variables (all data were set to be included, with no suspect data), we wished to incorporate those variables in the final datasets. Hence, although censor = FALSE in both the call to verticalize3() and the call to historicalize3(), we noted censorcol = "censor" and censorkeep = 1 in the call to historicalize3(). Failing to add these options to the call to historicalize3() will produce approximately the same dataset, but with some zeros entering variables censor1, censor2, and censor3 in the historicalized dataset that do not exist in the first, verticalized dataset. This occurs because the vertical dataset that we standardized only includes entries for each individual actually observed at each time, while the horizontal dataset includes entries for all individuals at all times, regardless of whether they were observed. Thus, by setting these options, we have produced datasets that are exactly the same except for variable order. We can see hints of that by looking at the dimensions of our datasets, as below.
summary_hfv(cypraw_v1, full = FALSE)
>
> This hfv dataset contains 320 rows, 57 variables, 1 population,
> 3 patches, 74 individuals, and 5 time steps.
summary_hfv(cypraw_v2, full = FALSE)
>
> This hfv dataset contains 320 rows, 57 variables, 1 population,
> 3 patches, 74 individuals, and 5 time steps.
summary_hfv(cypfb_v1, full = FALSE)
>
> This hfv dataset contains 320 rows, 57 variables, 1 population,
> 3 patches, 74 individuals, and 5 time steps.
summary_hfv(cypfb_v2, full = FALSE)
>
> This hfv dataset contains 320 rows, 57 variables, 1 population,
> 3 patches, 74 individuals, and 5 time steps.
One final consideration in historicalize3() regards the use of the 3col sets of options. If users have vertical datasets with pairs of consecutive states, then setting the 3col options to the latter state in each row means that the final year will be included in the historicalized dataset. Failing to enter the 3col set in these cases would mean that the final monitoring occasion may be dropped, since it likely only appears in rows holding data for the second to last monitoring occasion.
3.5 Handling spatial data and density
Both functions verticalize3() and historicalize3() handle the formatting of spatial coordinates and the estimation of density. There are four important settings that need to be used in the former case, and three in the latter. In both functions, the first two settings correspond to the columns coding for the X coordinate (xcol), and the Y coordinate (ycol). In both cases, the name of the variable or the column number can be used. The third setting (spacing), used in both functions, sets the radius from the coordinate of the individual to search for other individuals. The approach used for density estimation is to find and count all individuals in the same occasion within this radius from each individual, with density estimation performed for each individual in each time. The final setting, used only in verticalize3(), is a logical variable telling R whether the X and Y coordinate variables are single variables for the individual, or whether each individual has potentially new X and Y coordinates at each time that it is observed (coordsRepeat).
Here, we will produce a new version of the function-based cypdata hfv dataset with density at time t estimated using a 1m radius. Notice that the result includes xpos and ypos variables for times t+1, t, and t-1, and local density (density) at time t.
cypfb_vdens <- verticalize3(data = cypdata, noyears = 6, firstyear = 2004,
patchidcol = "patch", individcol = "plantid", blocksize = 4,
xcol = "X", ycol = "Y", sizeacol = "Inf2.04", sizebcol = "Inf.04",
sizeccol = "Veg.04", repstracol = "Inf.04", repstrbcol = "Inf2.04",
fecacol = "Pod.04", stageassign = cypframe_fb, stagesize = "sizeadded",
NAas0 = TRUE, age_offset = 4, coordsRepeat = FALSE, spacing = 1)
summary_hfv(cypfb_vdens)
>
> This hfv dataset contains 320 rows, 64 variables, 1 population,
> 3 patches, 74 individuals, and 5 time steps.
> rowid popid patchid individ year2
> Min. : 1.00 Length:320 A: 93 Min. : 164.0 Min. :2004
> 1st Qu.:21.00 Class :character B:154 1st Qu.: 391.0 1st Qu.:2005
> Median :37.50 Mode :character C: 73 Median : 453.0 Median :2006
> Mean :38.45 Mean : 651.5 Mean :2006
> 3rd Qu.:56.00 3rd Qu.: 476.0 3rd Qu.:2007
> Max. :77.00 Max. :1560.0 Max. :2008
> firstseen lastseen obsage obslifespan xpos1
> Min. :2004 Min. :2004 Min. :5.000 Min. :0.000 Min. : 0.00
> 1st Qu.:2004 1st Qu.:2009 1st Qu.:6.000 1st Qu.:5.000 1st Qu.: 54.40
> Median :2004 Median :2009 Median :7.000 Median :5.000 Median : 60.80
> Mean :2004 Mean :2009 Mean :6.853 Mean :4.556 Mean : 72.53
> 3rd Qu.:2004 3rd Qu.:2009 3rd Qu.:8.000 3rd Qu.:5.000 3rd Qu.: 97.40
> Max. :2008 Max. :2009 Max. :9.000 Max. :5.000 Max. :166.30
> ypos1 sizea1 sizeb1 sizec1
> Min. :-28.00 Min. :0.000000 Min. : 0.0000 Min. : 0.0
> 1st Qu.: 0.00 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.: 0.0
> Median : 70.90 Median :0.000000 Median : 0.0000 Median : 1.0
> Mean : 44.93 Mean :0.009375 Mean : 0.7469 Mean : 1.9
> 3rd Qu.: 79.85 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.: 3.0
> Max. :142.40 Max. :1.000000 Max. :18.0000 Max. :13.0
> size1added repstra1 repstrb1 repstr1added
> Min. : 0.000 Min. : 0.0000 Min. :0.000000 Min. : 0.0000
> 1st Qu.: 0.000 1st Qu.: 0.0000 1st Qu.:0.000000 1st Qu.: 0.0000
> Median : 2.000 Median : 0.0000 Median :0.000000 Median : 0.0000
> Mean : 2.656 Mean : 0.7469 Mean :0.009375 Mean : 0.7562
> 3rd Qu.: 4.000 3rd Qu.: 1.0000 3rd Qu.:0.000000 3rd Qu.: 1.0000
> Max. :21.000 Max. :18.0000 Max. :1.000000 Max. :18.0000
> feca1 fec1added obsstatus1 repstatus1
> Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
> 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
> Median :0.0000 Median :0.0000 Median :1.0000 Median :0.0000
> Mean :0.2656 Mean :0.2656 Mean :0.7469 Mean :0.2875
> 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
> Max. :7.0000 Max. :7.0000 Max. :1.0000 Max. :1.0000
> fecstatus1 matstatus1 alive1 stage1
> Min. :0.0000 Min. :0.0000 Min. :0.0000 Length:320
> 1st Qu.:0.0000 1st Qu.:1.0000 1st Qu.:1.0000 Class :character
> Median :0.0000 Median :1.0000 Median :1.0000 Mode :character
> Mean :0.1344 Mean :0.7688 Mean :0.7688
> 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
> Max. :1.0000 Max. :1.0000 Max. :1.0000
> stage1index xpos2 ypos2 sizea2
> Min. : 0.00 Min. : 46.50 Min. :-28.00 Min. :0.000000
> 1st Qu.: 6.00 1st Qu.: 60.10 1st Qu.: 23.30 1st Qu.:0.000000
> Median : 8.00 Median : 90.65 Median : 77.00 Median :0.000000
> Mean :14.17 Mean : 91.19 Mean : 56.98 Mean :0.009375
> 3rd Qu.:31.00 3rd Qu.:141.80 3rd Qu.: 80.40 3rd Qu.:0.000000
> Max. :51.00 Max. :173.00 Max. :142.40 Max. :1.000000
> sizeb2 sizec2 size2added repstra2
> Min. : 0.0000 Min. : 0.000 Min. : 0.000 Min. : 0.0000
> 1st Qu.: 0.0000 1st Qu.: 1.000 1st Qu.: 1.000 1st Qu.: 0.0000
> Median : 0.0000 Median : 2.000 Median : 2.000 Median : 0.0000
> Mean : 0.8969 Mean : 2.416 Mean : 3.322 Mean : 0.8969
> 3rd Qu.: 1.0000 3rd Qu.: 3.000 3rd Qu.: 4.000 3rd Qu.: 1.0000
> Max. :18.0000 Max. :13.000 Max. :24.000 Max. :18.0000
> repstrb2 repstr2added feca2 fec2added
> Min. :0.000000 Min. : 0.0000 Min. :0.0000 Min. :0.0000
> 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.:0.0000 1st Qu.:0.0000
> Median :0.000000 Median : 0.0000 Median :0.0000 Median :0.0000
> Mean :0.009375 Mean : 0.9062 Mean :0.2906 Mean :0.2906
> 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
> Max. :1.000000 Max. :18.0000 Max. :7.0000 Max. :7.0000
> obsstatus2 repstatus2 fecstatus2 matstatus2 alive2
> Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :1 Min. :1
> 1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:1 1st Qu.:1
> Median :1.0000 Median :0.0000 Median :0.0000 Median :1 Median :1
> Mean :0.9531 Mean :0.3688 Mean :0.1562 Mean :1 Mean :1
> 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:1 3rd Qu.:1
> Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1 Max. :1
> stage2 stage2index xpos3 ypos3
> Length:320 Min. : 6.00 Min. : 46.50 Min. :-28.00
> Class :character 1st Qu.: 7.00 1st Qu.: 60.10 1st Qu.: 23.30
> Mode :character Median :10.00 Median : 90.65 Median : 77.00
> Mean :18.17 Mean : 91.19 Mean : 56.98
> 3rd Qu.:32.00 3rd Qu.:141.80 3rd Qu.: 80.40
> Max. :54.00 Max. :173.00 Max. :142.40
> sizea3 sizeb3 sizec3 size3added
> Min. :0.000000 Min. : 0.000 Min. : 0.000 Min. : 0.000
> 1st Qu.:0.000000 1st Qu.: 0.000 1st Qu.: 1.000 1st Qu.: 1.000
> Median :0.000000 Median : 0.000 Median : 1.000 Median : 2.000
> Mean :0.009375 Mean : 1.069 Mean : 2.209 Mean : 3.288
> 3rd Qu.:0.000000 3rd Qu.: 1.000 3rd Qu.: 3.000 3rd Qu.: 4.000
> Max. :1.000000 Max. :18.000 Max. :13.000 Max. :24.000
> repstra3 repstrb3 repstr3added feca3
> Min. : 0.000 Min. :0.000000 Min. : 0.000 Min. :0.0000
> 1st Qu.: 0.000 1st Qu.:0.000000 1st Qu.: 0.000 1st Qu.:0.0000
> Median : 0.000 Median :0.000000 Median : 0.000 Median :0.0000
> Mean : 1.069 Mean :0.009375 Mean : 1.078 Mean :0.4562
> 3rd Qu.: 1.000 3rd Qu.:0.000000 3rd Qu.: 1.000 3rd Qu.:0.0000
> Max. :18.000 Max. :1.000000 Max. :18.000 Max. :8.0000
> fec3added obsstatus3 repstatus3 fecstatus3 matstatus3
> Min. :0.0000 Min. :0.0 Min. :0.0 Min. :0.0000 Min. :1
> 1st Qu.:0.0000 1st Qu.:1.0 1st Qu.:0.0 1st Qu.:0.0000 1st Qu.:1
> Median :0.0000 Median :1.0 Median :0.0 Median :0.0000 Median :1
> Mean :0.4562 Mean :0.9 Mean :0.4 Mean :0.2219 Mean :1
> 3rd Qu.:0.0000 3rd Qu.:1.0 3rd Qu.:1.0 3rd Qu.:0.0000 3rd Qu.:1
> Max. :8.0000 Max. :1.0 Max. :1.0 Max. :1.0000 Max. :1
> alive3 stage3 stage3index density
> Min. :0.0000 Length:320 Min. : 0.00 Min. : 0.000
> 1st Qu.:1.0000 Class :character 1st Qu.: 7.00 1st Qu.: 0.000
> Median :1.0000 Mode :character Median :10.00 Median : 1.000
> Mean :0.9469 Mean :18.57 Mean : 1.931
> 3rd Qu.:1.0000 3rd Qu.:33.00 3rd Qu.: 3.000
> Max. :1.0000 Max. :54.00 Max. :10.000
Next, let’s create the same formatted dataset, but using the historicalize3() function applied on cypvert. The options to add here are the same as in verticalize3(), except for coordsRepeat (the latter is only available for horizontally formatted dataset inputs). Note that the summaries look essentially the same for both standardized versions of the dataset.
cypfb_hdens <- historicalize3(data = cypvert, patchidcol = "patch",
individcol = "plantid", xcol = "X", ycol = "Y", year2col = "year2",
sizea2col = "Inf2.2", sizea3col = "Inf2.3", sizeb2col = "Inf.2",
sizeb3col = "Inf.3", sizec2col = "Veg.2", sizec3col = "Veg.3",
repstra2col = "Inf2.2", repstra3col = "Inf2.3", repstrb2col = "Inf.2",
repstrb3col = "Inf.3", feca2col = "Pod.2", feca3col = "Pod.3", repstrrel = 2,
stageassign = cypframe_fb, stagesize = "sizeadded", censorcol = "censor",
censorkeep = 1, censor = FALSE, NAas0 = TRUE, age_offset = 4, spacing = 1,
reduce = TRUE)
summary_hfv(cypfb_hdens)
>
> This hfv dataset contains 320 rows, 64 variables, 1 population,
> 3 patches, 74 individuals, and 5 time steps.
> rowid popid patchid individ year2
> Min. : 0.00 Length:320 A: 93 Min. : 164.0 Min. :2004
> 1st Qu.: 79.75 Class :character B:154 1st Qu.: 391.0 1st Qu.:2005
> Median :159.50 Mode :character C: 73 Median : 453.0 Median :2006
> Mean :159.70 Mean : 651.5 Mean :2006
> 3rd Qu.:239.25 3rd Qu.: 476.0 3rd Qu.:2007
> Max. :321.00 Max. :1560.0 Max. :2008
> firstseen lastseen obsage obslifespan xpos1
> Min. :2004 Min. :2004 Min. :5.000 Min. :0.000 Min. : 46.50
> 1st Qu.:2004 1st Qu.:2009 1st Qu.:6.000 1st Qu.:5.000 1st Qu.: 60.10
> Median :2004 Median :2009 Median :7.000 Median :5.000 Median : 90.65
> Mean :2004 Mean :2009 Mean :6.853 Mean :4.556 Mean : 91.19
> 3rd Qu.:2004 3rd Qu.:2009 3rd Qu.:8.000 3rd Qu.:5.000 3rd Qu.:141.80
> Max. :2008 Max. :2009 Max. :9.000 Max. :5.000 Max. :173.00
> ypos1 sizea1 sizeb1 sizec1
> Min. :-28.00 Min. :0.000000 Min. : 0.0000 Min. : 0.0
> 1st Qu.: 23.30 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.: 0.0
> Median : 77.00 Median :0.000000 Median : 0.0000 Median : 1.0
> Mean : 56.98 Mean :0.009375 Mean : 0.7469 Mean : 1.9
> 3rd Qu.: 80.40 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.: 3.0
> Max. :142.40 Max. :1.000000 Max. :18.0000 Max. :13.0
> size1added repstra1 repstrb1 repstr1added
> Min. : 0.000 Min. :0.000000 Min. : 0.0000 Min. : 0.000
> 1st Qu.: 0.000 1st Qu.:0.000000 1st Qu.: 0.0000 1st Qu.: 0.000
> Median : 2.000 Median :0.000000 Median : 0.0000 Median : 0.000
> Mean : 2.656 Mean :0.009375 Mean : 0.7469 Mean : 1.503
> 3rd Qu.: 4.000 3rd Qu.:0.000000 3rd Qu.: 1.0000 3rd Qu.: 2.000
> Max. :21.000 Max. :1.000000 Max. :18.0000 Max. :36.000
> feca1 fec1added obsstatus1 repstatus1
> Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
> 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
> Median :0.0000 Median :0.0000 Median :1.0000 Median :0.0000
> Mean :0.2656 Mean :0.2656 Mean :0.7469 Mean :0.2875
> 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
> Max. :7.0000 Max. :7.0000 Max. :1.0000 Max. :1.0000
> fecstatus1 matstatus1 alive1 stage1
> Min. :0.0000 Min. :0.0000 Min. :0.0000 Length:320
> 1st Qu.:0.0000 1st Qu.:1.0000 1st Qu.:1.0000 Class :character
> Median :0.0000 Median :1.0000 Median :1.0000 Mode :character
> Mean :0.1344 Mean :0.7688 Mean :0.7688
> 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
> Max. :1.0000 Max. :1.0000 Max. :1.0000
> stage1index xpos2 ypos2 sizea2
> Min. : 0.00 Min. : 46.50 Min. :-28.00 Min. :0.000000
> 1st Qu.: 6.00 1st Qu.: 60.10 1st Qu.: 23.30 1st Qu.:0.000000
> Median : 8.00 Median : 90.65 Median : 77.00 Median :0.000000
> Mean :14.17 Mean : 91.19 Mean : 56.98 Mean :0.009375
> 3rd Qu.:31.00 3rd Qu.:141.80 3rd Qu.: 80.40 3rd Qu.:0.000000
> Max. :51.00 Max. :173.00 Max. :142.40 Max. :1.000000
> sizeb2 sizec2 size2added repstra2
> Min. : 0.0000 Min. : 0.000 Min. : 0.000 Min. :0.000000
> 1st Qu.: 0.0000 1st Qu.: 1.000 1st Qu.: 1.000 1st Qu.:0.000000
> Median : 0.0000 Median : 2.000 Median : 2.000 Median :0.000000
> Mean : 0.8969 Mean : 2.416 Mean : 3.322 Mean :0.009375
> 3rd Qu.: 1.0000 3rd Qu.: 3.000 3rd Qu.: 4.000 3rd Qu.:0.000000
> Max. :18.0000 Max. :13.000 Max. :24.000 Max. :1.000000
> repstrb2 repstr2added feca2 fec2added
> Min. : 0.0000 Min. : 0.000 Min. :0.0000 Min. :0.0000
> 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.:0.0000 1st Qu.:0.0000
> Median : 0.0000 Median : 0.000 Median :0.0000 Median :0.0000
> Mean : 0.8969 Mean : 1.803 Mean :0.2906 Mean :0.2906
> 3rd Qu.: 1.0000 3rd Qu.: 2.000 3rd Qu.:0.0000 3rd Qu.:0.0000
> Max. :18.0000 Max. :36.000 Max. :7.0000 Max. :7.0000
> obsstatus2 repstatus2 fecstatus2 matstatus2 alive2
> Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :1 Min. :1
> 1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:1 1st Qu.:1
> Median :1.0000 Median :0.0000 Median :0.0000 Median :1 Median :1
> Mean :0.9531 Mean :0.3688 Mean :0.1562 Mean :1 Mean :1
> 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:1 3rd Qu.:1
> Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1 Max. :1
> stage2 stage2index xpos3 ypos3
> Length:320 Min. : 6.00 Min. : 46.50 Min. :-28.00
> Class :character 1st Qu.: 7.00 1st Qu.: 60.10 1st Qu.: 23.30
> Mode :character Median :10.00 Median : 90.65 Median : 77.00
> Mean :18.17 Mean : 91.19 Mean : 56.98
> 3rd Qu.:32.00 3rd Qu.:141.80 3rd Qu.: 80.40
> Max. :54.00 Max. :173.00 Max. :142.40
> sizea3 sizeb3 sizec3 size3added
> Min. :0.000000 Min. : 0.000 Min. : 0.000 Min. : 0.000
> 1st Qu.:0.000000 1st Qu.: 0.000 1st Qu.: 1.000 1st Qu.: 1.000
> Median :0.000000 Median : 0.000 Median : 1.000 Median : 2.000
> Mean :0.009375 Mean : 1.069 Mean : 2.209 Mean : 3.288
> 3rd Qu.:0.000000 3rd Qu.: 1.000 3rd Qu.: 3.000 3rd Qu.: 4.000
> Max. :1.000000 Max. :18.000 Max. :13.000 Max. :24.000
> repstra3 repstrb3 repstr3added feca3
> Min. :0.000000 Min. : 0.000 Min. : 0.000 Min. :0.0000
> 1st Qu.:0.000000 1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.:0.0000
> Median :0.000000 Median : 0.000 Median : 0.000 Median :0.0000
> Mean :0.009375 Mean : 1.069 Mean : 2.147 Mean :0.4562
> 3rd Qu.:0.000000 3rd Qu.: 1.000 3rd Qu.: 2.000 3rd Qu.:0.0000
> Max. :1.000000 Max. :18.000 Max. :36.000 Max. :8.0000
> fec3added obsstatus3 repstatus3 fecstatus3 matstatus3
> Min. :0.0000 Min. :0.0 Min. :0.0 Min. :0.0000 Min. :1
> 1st Qu.:0.0000 1st Qu.:1.0 1st Qu.:0.0 1st Qu.:0.0000 1st Qu.:1
> Median :0.0000 Median :1.0 Median :0.0 Median :0.0000 Median :1
> Mean :0.4562 Mean :0.9 Mean :0.4 Mean :0.2219 Mean :1
> 3rd Qu.:0.0000 3rd Qu.:1.0 3rd Qu.:1.0 3rd Qu.:0.0000 3rd Qu.:1
> Max. :8.0000 Max. :1.0 Max. :1.0 Max. :1.0000 Max. :1
> alive3 stage3 stage3index density
> Min. :0.0000 Length:320 Min. : 0.00 Min. : 0.000
> 1st Qu.:1.0000 Class :character 1st Qu.: 7.00 1st Qu.: 0.000
> Median :1.0000 Mode :character Median :10.00 Median : 1.000
> Mean :0.9469 Mean :18.57 Mean : 1.931
> 3rd Qu.:1.0000 3rd Qu.:33.00 3rd Qu.: 3.000
> Max. :1.0000 Max. :54.00 Max. :10.000
Before moving on to supplying R with the proxy transitions that we need to properly parameterize our models, let’s take a look at how we might explore our standardized dataset.
3.6 Exploring stage-classified standardized datasets
It is often useful to explore our data before using it to build MPMs. One way to explore the data is to look at the frequencies of the stage assignments that R has developed for each monitoring occasion. For this purpose, we can use function actualstage3(). Below, we show the simplest use of this function - to explore single stage assignments, as for ahistorical MPM development.
explore_2 <- actualstage3(cypraw_v1)
explore_2
> rowid stageindex stage stage2 stage1 year2 Freq actual_prop
> 1 2004 D 6 D D 2004 0 0.00000000
> 2 2004 XSm 7 XSm XSm 2004 23 0.35384615
> 3 2004 Sm 8 Sm Sm 2004 24 0.36923077
> 4 2004 Md 9 Md Md 2004 10 0.15384615
> 5 2004 Lg 10 Lg Lg 2004 7 0.10769231
> 6 2004 XLg 11 XLg XLg 2004 1 0.01538462
> 7 2005 D 6 D D 2005 1 0.01470588
> 8 2005 XSm 7 XSm XSm 2005 23 0.33823529
> 9 2005 Sm 8 Sm Sm 2005 27 0.39705882
> 10 2005 Md 9 Md Md 2005 9 0.13235294
> 11 2005 Lg 10 Lg Lg 2005 6 0.08823529
> 12 2005 XLg 11 XLg XLg 2005 2 0.02941176
> 13 2006 D 6 D D 2006 3 0.04687500
> 14 2006 XSm 7 XSm XSm 2006 22 0.34375000
> 15 2006 Sm 8 Sm Sm 2006 27 0.42187500
> 16 2006 Md 9 Md Md 2006 9 0.14062500
> 17 2006 Lg 10 Lg Lg 2006 2 0.03125000
> 18 2006 XLg 11 XLg XLg 2006 1 0.01562500
> 19 2007 D 6 D D 2007 3 0.04838710
> 20 2007 XSm 7 XSm XSm 2007 20 0.32258065
> 21 2007 Sm 8 Sm Sm 2007 25 0.40322581
> 22 2007 Md 9 Md Md 2007 8 0.12903226
> 23 2007 Lg 10 Lg Lg 2007 6 0.09677419
> 24 2007 XLg 11 XLg XLg 2007 0 0.00000000
> 25 2008 D 6 D D 2008 8 0.13114754
> 26 2008 XSm 7 XSm XSm 2008 20 0.32786885
> 27 2008 Sm 8 Sm Sm 2008 17 0.27868852
> 28 2008 Md 9 Md Md 2008 12 0.19672131
> 29 2008 Lg 10 Lg Lg 2008 2 0.03278689
> 30 2008 XLg 11 XLg XLg 2008 2 0.03278689
> 31 2009 D 6 D D 2009 0 0.00000000
> 32 2009 XSm 7 XSm XSm 2009 15 0.26315789
> 33 2009 Sm 8 Sm Sm 2009 23 0.40350877
> 34 2009 Md 9 Md Md 2009 11 0.19298246
> 35 2009 Lg 10 Lg Lg 2009 6 0.10526316
> 36 2009 XLg 11 XLg XLg 2009 2 0.03508772
Each stage is shown in each year for which data is available. The number of individuals in each stage in each year (column frequency), and the associated proportion of individuals comprising that stage in each year (column actual_prop), are both shown. Deaths have been removed, yielding proportions that sum to 1.0.
Function actualstage3() can also be used to explore the frequencies of ages, age-stages, and historical stage pairs. For example, below we show the frequencies of ages.
explore_age <- actualstage3(cypraw_v1, check_stage = FALSE, check_age = TRUE)
explore_age
> rowid age year2 Freq actual_prop
> 1 2004 5 5 2004 65 1.00000000
> 2 2004 6 6 2004 0 0.00000000
> 3 2004 7 7 2004 0 0.00000000
> 4 2004 8 8 2004 0 0.00000000
> 5 2004 9 9 2004 0 0.00000000
> 6 2004 10 10 2004 0 0.00000000
> 7 2005 5 5 2005 4 0.05882353
> 8 2005 6 6 2005 64 0.94117647
> 9 2005 7 7 2005 0 0.00000000
> 10 2005 8 8 2005 0 0.00000000
> 11 2005 9 9 2005 0 0.00000000
> 12 2005 10 10 2005 0 0.00000000
> 13 2006 5 5 2006 0 0.00000000
> 14 2006 6 6 2006 3 0.04687500
> 15 2006 7 7 2006 61 0.95312500
> 16 2006 8 8 2006 0 0.00000000
> 17 2006 9 9 2006 0 0.00000000
> 18 2006 10 10 2006 0 0.00000000
> 19 2007 5 5 2007 1 0.01612903
> 20 2007 6 6 2007 0 0.00000000
> 21 2007 7 7 2007 2 0.03225806
> 22 2007 8 8 2007 59 0.95161290
> 23 2007 9 9 2007 0 0.00000000
> 24 2007 10 10 2007 0 0.00000000
> 25 2008 5 5 2008 4 0.06557377
> 26 2008 6 6 2008 1 0.01639344
> 27 2008 7 7 2008 0 0.00000000
> 28 2008 8 8 2008 2 0.03278689
> 29 2008 9 9 2008 54 0.88524590
> 30 2008 10 10 2008 0 0.00000000
> 31 2009 5 5 2009 0 0.00000000
> 32 2009 6 6 2009 4 0.06557377
> 33 2009 7 7 2009 1 0.01639344
> 34 2009 8 8 2009 0 0.00000000
> 35 2009 9 9 2009 2 0.03278689
> 36 2009 10 10 2009 54 0.88524590R has assigned age 5 to all individuals seen in the first year automatically (this is due to the age_offset and prebreeding fields in functions verticalize3() and historicalize3()).
Other explorations are possible. For example, if we removed the check_stage = FALSE option from the inputs, then we would get the frequencies of age-stage combinations for each year. Finally, if we remove check_stage = FALSE, check_age = TRUE and add historical = TRUE, then we can see the frequencies of historical stage pairs, as below.
explore_3 <- actualstage3(cypraw_v1, historical = TRUE)
explore_3
> Warning in format.data.frame(if (omit) x[seq_len(n0), , drop = FALSE] else x, :
> corrupt data frame: columns will be truncated or padded with NAs
> rowid stageindex stage stage2 stage1 year2 Freq
> 1 2004 D NotAlive 0 D NotAlive D NotAlive 2004 0
> 2 2004 XSm NotAlive 0 XSm NotAlive XSm NotAlive 2004 23
> 3 2004 Sm NotAlive 0 Sm NotAlive Sm NotAlive 2004 24
> 4 2004 Md NotAlive 0 Md NotAlive Md NotAlive 2004 10
> 5 2004 Lg NotAlive 0 Lg NotAlive Lg NotAlive 2004 7
> 6 2004 XLg NotAlive 0 XLg NotAlive XLg NotAlive 2004 1
> 7 2004 D NotAlive 0 D NotAlive D NotAlive 2004 0
> 8 2004 XSm D 0 XSm D XSm D 2004 0
> 9 2004 Sm D 0 Sm D Sm D 2004 0
> 10 2004 Md D 0 Md D Md D 2004 0
> 11 2004 Lg D 0 Lg D Lg D 2004 0
> 12 2004 XLg D 0 XLg D XLg D 2004 0
> 13 2004 D D 0 D D D D 2004 0
> 14 2004 XSm D 0 XSm D XSm D 2004 0
> 15 2004 Sm XSm 0 Sm XSm Sm XSm 2004 0
> 16 2004 Md XSm 0 Md XSm Md XSm 2004 0
> 17 2004 Lg XSm 0 Lg XSm Lg XSm 2004 0
> 18 2004 XLg XSm 0 XLg XSm XLg XSm 2004 0
> 19 2004 D XSm 0 D XSm D XSm 2004 0
> 20 2004 XSm XSm 0 XSm XSm XSm XSm 2004 0
> 21 2004 Sm XSm 0 Sm XSm Sm XSm 2004 0
> 22 2004 Md Sm 0 Md Sm Md Sm 2004 0
> 23 2004 Lg Sm 0 Lg Sm Lg Sm 2004 0
> 24 2004 XLg Sm 0 XLg Sm XLg Sm 2004 0
> 25 2004 D Sm 0 D Sm D Sm 2004 0
> 26 2004 XSm Sm 0 XSm Sm XSm Sm 2004 0
> 27 2004 Sm Sm 0 Sm Sm Sm Sm 2004 0
> 28 2004 Md Sm 0 Md Sm Md Sm 2004 0
> 29 2004 Lg Md 0 Lg Md Lg Md 2004 0
> 30 2004 XLg Md 0 XLg Md XLg Md 2004 0
> 31 2004 D Md 0 D Md D Md 2004 0
> 32 2004 XSm Md 0 XSm Md XSm Md 2004 0
> 33 2004 Sm Md 0 Sm Md Sm Md 2004 0
> 34 2004 Md Md 0 Md Md Md Md 2004 0
> 35 2004 Lg Md 0 Lg Md Lg Md 2004 0
> 36 2004 XLg Lg 0 XLg Lg XLg Lg 2004 0
> 37 2004 D Lg 0 D Lg D Lg 2004 0
> 38 2004 XSm Lg 0 XSm Lg XSm Lg 2004 0
> 39 2004 Sm Lg 0 Sm Lg Sm Lg 2004 0
> 40 2004 Md Lg 0 Md Lg Md Lg 2004 0
> 41 2004 Lg Lg 0 Lg Lg Lg Lg 2004 0
> 42 2004 XLg Lg 0 XLg Lg XLg Lg 2004 0
> 43 2005 D XLg 0 D XLg D XLg 2005 0
> 44 2005 XSm XLg 0 XSm XLg XSm XLg 2005 0
> 45 2005 Sm XLg 0 Sm XLg Sm XLg 2005 0
> 46 2005 Md XLg 0 Md XLg Md XLg 2005 0
> 47 2005 Lg XLg 0 Lg XLg Lg XLg 2005 0
> 48 2005 XLg XLg 0 XLg XLg XLg XLg 2005 1
> 49 2005 D XLg 0 D XLg D XLg 2005 0
> 50 2005 XSm NotAlive 0 XSm NotAlive XSm NotAlive 2005 2
> 51 2005 Sm NotAlive 0 Sm NotAlive Sm NotAlive 2005 2
> 52 2005 Md NotAlive 0 Md NotAlive Md NotAlive 2005 0
> 53 2005 Lg NotAlive 0 Lg NotAlive Lg NotAlive 2005 0
> 54 2005 XLg NotAlive 0 XLg NotAlive XLg NotAlive 2005 0
> 55 2005 D NotAlive 0 D NotAlive D NotAlive 2005 0
> 56 2005 XSm NotAlive 0 XSm NotAlive XSm NotAlive 2005 2
> 57 2005 Sm D 0 Sm D Sm D 2005 0
> 58 2005 Md D 0 Md D Md D 2005 0
> 59 2005 Lg D 0 Lg D Lg D 2005 0
> 60 2005 XLg D 0 XLg D XLg D 2005 0
> 61 2005 D D 0 D D D D 2005 0
> 62 2005 XSm D 0 XSm D XSm D 2005 0
> 63 2005 Sm D 0 Sm D Sm D 2005 0
> 64 2005 Md XSm 0 Md XSm Md XSm 2005 0
> 65 2005 Lg XSm 0 Lg XSm Lg XSm 2005 1
> 66 2005 XLg XSm 0 XLg XSm XLg XSm 2005 0
> 67 2005 D XSm 0 D XSm D XSm 2005 1
> 68 2005 XSm XSm 0 XSm XSm XSm XSm 2005 15
> 69 2005 Sm XSm 0 Sm XSm Sm XSm 2005 5
> 70 2005 Md XSm 0 Md XSm Md XSm 2005 0
> 71 2005 Lg Sm 0 Lg Sm Lg Sm 2005 0
> 72 2005 XLg Sm 0 XLg Sm XLg Sm 2005 0
> 73 2005 D Sm 0 D Sm D Sm 2005 0
> 74 2005 XSm Sm 0 XSm Sm XSm Sm 2005 6
> 75 2005 Sm Sm 0 Sm Sm Sm Sm 2005 14
> 76 2005 Md Sm 0 Md Sm Md Sm 2005 4
> 77 2005 Lg Sm 0 Lg Sm Lg Sm 2005 0
> 78 2005 XLg Md 0 XLg Md XLg Md 2005 0
> 79 2005 D Md 0 D Md D Md 2005 0
> 80 2005 XSm Md 0 XSm Md XSm Md 2005 0
> 81 2005 Sm Md 0 Sm Md Sm Md 2005 5
> 82 2005 Md Md 0 Md Md Md Md 2005 4
> 83 2005 Lg Md 0 Lg Md Lg Md 2005 1
> 84 2005 XLg Md 0 XLg Md XLg Md 2005 0
> 85 2006 D Lg 0 D Lg D Lg 2006 0
> 86 2006 XSm Lg 0 XSm Lg XSm Lg 2006 0
> 87 2006 Sm Lg 0 Sm Lg Sm Lg 2006 2
> 88 2006 Md Lg 0 Md Lg Md Lg 2006 3
> 89 2006 Lg Lg 0 Lg Lg Lg Lg 2006 1
> 90 2006 XLg Lg 0 XLg Lg XLg Lg 2006 0
> 91 2006 D Lg 0 D Lg D Lg 2006 0
> 92 2006 XSm XLg 0 XSm XLg XSm XLg 2006 0
> 93 2006 Sm XLg 0 Sm XLg Sm XLg 2006 0
> 94 2006 Md XLg 0 Md XLg Md XLg 2006 0
> 95 2006 Lg XLg 0 Lg XLg Lg XLg 2006 1
> 96 2006 XLg XLg 0 XLg XLg XLg XLg 2006 1
> 97 2006 D XLg 0 D XLg D XLg 2006 0
> 98 2006 XSm XLg 0 XSm XLg XSm XLg 2006 0
> 99 2006 Sm NotAlive 0 Sm NotAlive Sm NotAlive 2006 0
> 100 2006 Md NotAlive 0 Md NotAlive Md NotAlive 2006 0
> 101 2006 Lg NotAlive 0 Lg NotAlive Lg NotAlive 2006 0
> 102 2006 XLg NotAlive 0 XLg NotAlive XLg NotAlive 2006 0
> 103 2006 D NotAlive 0 D NotAlive D NotAlive 2006 0
> 104 2006 XSm NotAlive 0 XSm NotAlive XSm NotAlive 2006 0
> 105 2006 Sm NotAlive 0 Sm NotAlive Sm NotAlive 2006 0
> 106 2006 Md D 0 Md D Md D 2006 0
> 107 2006 Lg D 0 Lg D Lg D 2006 0
> 108 2006 XLg D 0 XLg D XLg D 2006 0
> 109 2006 D D 0 D D D D 2006 0
> 110 2006 XSm D 0 XSm D XSm D 2006 0
> 111 2006 Sm D 0 Sm D Sm D 2006 1
> 112 2006 Md D 0 Md D Md D 2006 0
> 113 2006 Lg XSm 0 Lg XSm Lg XSm 2006 0
> 114 2006 XLg XSm 0 XLg XSm XLg XSm 2006 0
> 115 2006 D XSm 0 D XSm D XSm 2006 2
> 116 2006 XSm XSm 0 XSm XSm XSm XSm 2006 14
> 117 2006 Sm XSm 0 Sm XSm Sm XSm 2006 4
> 118 2006 Md XSm 0 Md XSm Md XSm 2006 0
> 119 2006 Lg XSm 0 Lg XSm Lg XSm 2006 0
> 120 2006 XLg Sm 0 XLg Sm XLg Sm 2006 0
> 121 2006 D Sm 0 D Sm D Sm 2006 1
> 122 2006 XSm Sm 0 XSm Sm XSm Sm 2006 7
> 123 2006 Sm Sm 0 Sm Sm Sm Sm 2006 16
> 124 2006 Md Sm 0 Md Sm Md Sm 2006 2
> 125 2006 Lg Sm 0 Lg Sm Lg Sm 2006 0
> 126 2006 XLg Sm 0 XLg Sm XLg Sm 2006 0
> 127 2007 D Md 0 D Md D Md 2007 0
> 128 2007 XSm Md 0 XSm Md XSm Md 2007 1
> 129 2007 Sm Md 0 Sm Md Sm Md 2007 3
> 130 2007 Md Md 0 Md Md Md Md 2007 4
> 131 2007 Lg Md 0 Lg Md Lg Md 2007 1
> 132 2007 XLg Md 0 XLg Md XLg Md 2007 0
> 133 2007 D Md 0 D Md D Md 2007 0
> 134 2007 XSm Lg 0 XSm Lg XSm Lg 2007 0
> 135 2007 Sm Lg 0 Sm Lg Sm Lg 2007 0
> 136 2007 Md Lg 0 Md Lg Md Lg 2007 0
> 137 2007 Lg Lg 0 Lg Lg Lg Lg 2007 2
> 138 2007 XLg Lg 0 XLg Lg XLg Lg 2007 0
> 139 2007 D Lg 0 D Lg D Lg 2007 0
> 140 2007 XSm Lg 0 XSm Lg XSm Lg 2007 0
> 141 2007 Sm XLg 0 Sm XLg Sm XLg 2007 0
> 142 2007 Md XLg 0 Md XLg Md XLg 2007 0
> 143 2007 Lg XLg 0 Lg XLg Lg XLg 2007 1
> 144 2007 XLg XLg 0 XLg XLg XLg XLg 2007 0
> 145 2007 D XLg 0 D XLg D XLg 2007 0
> 146 2007 XSm XLg 0 XSm XLg XSm XLg 2007 0
> 147 2007 Sm XLg 0 Sm XLg Sm XLg 2007 0
> 148 2007 Md NotAlive 0 Md NotAlive Md NotAlive 2007 0
> 149 2007 Lg NotAlive 0 Lg NotAlive Lg NotAlive 2007 0
> 150 2007 XLg NotAlive 0 XLg NotAlive XLg NotAlive 2007 0
> 151 2007 D NotAlive 0 D NotAlive D NotAlive 2007 0
> 152 2007 XSm NotAlive 0 XSm NotAlive XSm NotAlive 2007 1
> 153 2007 Sm NotAlive 0 Sm NotAlive Sm NotAlive 2007 0
> 154 2007 Md NotAlive 0 Md NotAlive Md NotAlive 2007 0
> 155 2007 Lg D 0 Lg D Lg D 2007 0
> 156 2007 XLg D 0 XLg D XLg D 2007 0
> 157 2007 D D 0 D D D D 2007 0
> 158 2007 XSm D 0 XSm D XSm D 2007 2
> 159 2007 Sm D 0 Sm D Sm D 2007 1
> 160 2007 Md D 0 Md D Md D 2007 0
> 161 2007 Lg D 0 Lg D Lg D 2007 0
> 162 2007 XLg XSm 0 XLg XSm XLg XSm 2007 0
> 163 2007 D XSm 0 D XSm D XSm 2007 0
> 164 2007 XSm XSm 0 XSm XSm XSm XSm 2007 11
> 165 2007 Sm XSm 0 Sm XSm Sm XSm 2007 7
> 166 2007 Md XSm 0 Md XSm Md XSm 2007 1
> 167 2007 Lg XSm 0 Lg XSm Lg XSm 2007 0
> 168 2007 XLg XSm 0 XLg XSm XLg XSm 2007 0
> 169 2008 D Sm 0 D Sm D Sm 2008 3
> 170 2008 XSm Sm 0 XSm Sm XSm Sm 2008 7
> 171 2008 Sm Sm 0 Sm Sm Sm Sm 2008 7
> 172 2008 Md Sm 0 Md Sm Md Sm 2008 6
> 173 2008 Lg Sm 0 Lg Sm Lg Sm 2008 0
> 174 2008 XLg Sm 0 XLg Sm XLg Sm 2008 0
> 175 2008 D Sm 0 D Sm D Sm 2008 3
> 176 2008 XSm Md 0 XSm Md XSm Md 2008 2
> 177 2008 Sm Md 0 Sm Md Sm Md 2008 3
> 178 2008 Md Md 0 Md Md Md Md 2008 3
> 179 2008 Lg Md 0 Lg Md Lg Md 2008 0
> 180 2008 XLg Md 0 XLg Md XLg Md 2008 0
> 181 2008 D Md 0 D Md D Md 2008 0
> 182 2008 XSm Md 0 XSm Md XSm Md 2008 2
> 183 2008 Sm Lg 0 Sm Lg Sm Lg 2008 1
> 184 2008 Md Lg 0 Md Lg Md Lg 2008 2
> 185 2008 Lg Lg 0 Lg Lg Lg Lg 2008 1
> 186 2008 XLg Lg 0 XLg Lg XLg Lg 2008 2
> 187 2008 D Lg 0 D Lg D Lg 2008 0
> 188 2008 XSm Lg 0 XSm Lg XSm Lg 2008 0
> 189 2008 Sm Lg 0 Sm Lg Sm Lg 2008 1
> 190 2008 Md XLg 0 Md XLg Md XLg 2008 0
> 191 2008 Lg XLg 0 Lg XLg Lg XLg 2008 0
> 192 2008 XLg XLg 0 XLg XLg XLg XLg 2008 0
> 193 2008 D XLg 0 D XLg D XLg 2008 0
> 194 2008 XSm XLg 0 XSm XLg XSm XLg 2008 0
> 195 2008 Sm XLg 0 Sm XLg Sm XLg 2008 0
> 196 2008 Md XLg 0 Md XLg Md XLg 2008 0
> 197 2008 Lg NotAlive 0 Lg NotAlive Lg NotAlive 2008 0
> 198 2008 XLg NotAlive 0 XLg NotAlive XLg NotAlive 2008 0
> 199 2008 D NotAlive 0 D NotAlive D NotAlive 2008 0
> 200 2008 XSm NotAlive 0 XSm NotAlive XSm NotAlive 2008 3
> 201 2008 Sm NotAlive 0 Sm NotAlive Sm NotAlive 2008 1
> 202 2008 Md NotAlive 0 Md NotAlive Md NotAlive 2008 0
> 203 2008 Lg NotAlive 0 Lg NotAlive Lg NotAlive 2008 0
> 204 2008 XLg D 0 XLg D XLg D 2008 0
> 205 2008 D D 0 D D D D 2008 1
> 206 2008 XSm D 0 XSm D XSm D 2008 1
> 207 2008 Sm D 0 Sm D Sm D 2008 0
> 208 2008 Md D 0 Md D Md D 2008 0
> 209 2008 Lg D 0 Lg D Lg D 2008 1
> 210 2008 XLg D 0 XLg D XLg D 2008 0
> 211 2009 D XSm 0 D XSm D XSm 2009 0
> 212 2009 XSm XSm 0 XSm XSm XSm XSm 2009 9
> 213 2009 Sm XSm 0 Sm XSm Sm XSm 2009 9
> 214 2009 Md XSm 0 Md XSm Md XSm 2009 0
> 215 2009 Lg XSm 0 Lg XSm Lg XSm 2009 0
> 216 2009 XLg XSm 0 XLg XSm XLg XSm 2009 0
> 217 2009 D XSm 0 D XSm D XSm 2009 0
> 218 2009 XSm Sm 0 XSm Sm XSm Sm 2009 1
> 219 2009 Sm Sm 0 Sm Sm Sm Sm 2009 11
> 220 2009 Md Sm 0 Md Sm Md Sm 2009 2
> 221 2009 Lg Sm 0 Lg Sm Lg Sm 2009 1
> 222 2009 XLg Sm 0 XLg Sm XLg Sm 2009 0
> 223 2009 D Sm 0 D Sm D Sm 2009 0
> 224 2009 XSm Sm 0 XSm Sm XSm Sm 2009 1
> 225 2009 Sm Md 0 Sm Md Sm Md 2009 0
> 226 2009 Md Md 0 Md Md Md Md 2009 9
> 227 2009 Lg Md 0 Lg Md Lg Md 2009 3
> 228 2009 XLg Md 0 XLg Md XLg Md 2009 0
> 229 2009 D Md 0 D Md D Md 2009 0
> 230 2009 XSm Md 0 XSm Md XSm Md 2009 0
> 231 2009 Sm Md 0 Sm Md Sm Md 2009 0
> 232 2009 Md Lg 0 Md Lg Md Lg 2009 0
> 233 2009 Lg Lg 0 Lg Lg Lg Lg 2009 2
> 234 2009 XLg Lg 0 XLg Lg XLg Lg 2009 0
> 235 2009 D Lg 0 D Lg D Lg 2009 0
> 236 2009 XSm Lg 0 XSm Lg XSm Lg 2009 0
> 237 2009 Sm Lg 0 Sm Lg Sm Lg 2009 0
> 238 2009 Md Lg 0 Md Lg Md Lg 2009 0
> 239 2009 Lg XLg 0 Lg XLg Lg XLg 2009 0
> 240 2009 XLg XLg 0 XLg XLg XLg XLg 2009 2
> 241 2009 D XLg 0 D XLg D XLg 2009 0
> 242 2009 XSm XLg 0 XSm XLg XSm XLg 2009 0
> 243 2009 Sm XLg 0 Sm XLg Sm XLg 2009 0
> 244 2009 Md XLg 0 Md XLg Md XLg 2009 0
> 245 2009 Lg XLg 0 Lg XLg Lg XLg 2009 0
> 246 2009 XLg NotAlive 0 XLg NotAlive XLg NotAlive 2009 0
> 247 2009 D NotAlive 0 D NotAlive D NotAlive 2009 0
> 248 2009 XSm NotAlive 0 XSm NotAlive XSm NotAlive 2009 0
> 249 2009 Sm NotAlive 0 Sm NotAlive Sm NotAlive 2009 0
> 250 2009 Md NotAlive 0 Md NotAlive Md NotAlive 2009 0
> 251 2009 Lg NotAlive 0 Lg NotAlive Lg NotAlive 2009 0
> 252 2009 XLg NotAlive 0 XLg NotAlive XLg NotAlive 2009 0
> actual_prop
> 1 0.00000000
> 2 0.35384615
> 3 0.36923077
> 4 0.15384615
> 5 0.10769231
> 6 0.01538462
> 7 0.00000000
> 8 0.00000000
> 9 0.00000000
> 10 0.00000000
> 11 0.00000000
> 12 0.00000000
> 13 0.00000000
> 14 0.00000000
> 15 0.00000000
> 16 0.00000000
> 17 0.00000000
> 18 0.00000000
> 19 0.00000000
> 20 0.00000000
> 21 0.00000000
> 22 0.00000000
> 23 0.00000000
> 24 0.00000000
> 25 0.00000000
> 26 0.00000000
> 27 0.00000000
> 28 0.00000000
> 29 0.00000000
> 30 0.00000000
> 31 0.00000000
> 32 0.00000000
> 33 0.00000000
> 34 0.00000000
> 35 0.00000000
> 36 0.00000000
> 37 0.00000000
> 38 0.00000000
> 39 0.00000000
> 40 0.00000000
> 41 0.00000000
> 42 0.00000000
> 43 0.00000000
> 44 0.00000000
> 45 0.00000000
> 46 0.00000000
> 47 0.00000000
> 48 0.01587302
> 49 0.00000000
> 50 0.03174603
> 51 0.03174603
> 52 0.00000000
> 53 0.00000000
> 54 0.00000000
> 55 0.00000000
> 56 0.03174603
> 57 0.00000000
> 58 0.00000000
> 59 0.00000000
> 60 0.00000000
> 61 0.00000000
> 62 0.00000000
> 63 0.00000000
> 64 0.00000000
> 65 0.01587302
> 66 0.00000000
> 67 0.01587302
> 68 0.23809524
> 69 0.07936508
> 70 0.00000000
> 71 0.00000000
> 72 0.00000000
> 73 0.00000000
> 74 0.09523810
> 75 0.22222222
> 76 0.06349206
> 77 0.00000000
> 78 0.00000000
> 79 0.00000000
> 80 0.00000000
> 81 0.07936508
> 82 0.06349206
> 83 0.01587302
> 84 0.00000000
> 85 0.00000000
> 86 0.00000000
> 87 0.03636364
> 88 0.05454545
> 89 0.01818182
> 90 0.00000000
> 91 0.00000000
> 92 0.00000000
> 93 0.00000000
> 94 0.00000000
> 95 0.01818182
> 96 0.01818182
> 97 0.00000000
> 98 0.00000000
> 99 0.00000000
> 100 0.00000000
> 101 0.00000000
> 102 0.00000000
> 103 0.00000000
> 104 0.00000000
> 105 0.00000000
> 106 0.00000000
> 107 0.00000000
> 108 0.00000000
> 109 0.00000000
> 110 0.00000000
> 111 0.01818182
> 112 0.00000000
> 113 0.00000000
> 114 0.00000000
> 115 0.03636364
> 116 0.25454545
> 117 0.07272727
> 118 0.00000000
> 119 0.00000000
> 120 0.00000000
> 121 0.01818182
> 122 0.12727273
> 123 0.29090909
> 124 0.03636364
> 125 0.00000000
> 126 0.00000000
> 127 0.00000000
> 128 0.02857143
> 129 0.08571429
> 130 0.11428571
> 131 0.02857143
> 132 0.00000000
> 133 0.00000000
> 134 0.00000000
> 135 0.00000000
> 136 0.00000000
> 137 0.05714286
> 138 0.00000000
> 139 0.00000000
> 140 0.00000000
> 141 0.00000000
> 142 0.00000000
> 143 0.02857143
> 144 0.00000000
> 145 0.00000000
> 146 0.00000000
> 147 0.00000000
> 148 0.00000000
> 149 0.00000000
> 150 0.00000000
> 151 0.00000000
> 152 0.02857143
> 153 0.00000000
> 154 0.00000000
> 155 0.00000000
> 156 0.00000000
> 157 0.00000000
> 158 0.05714286
> 159 0.02857143
> 160 0.00000000
> 161 0.00000000
> 162 0.00000000
> 163 0.00000000
> 164 0.31428571
> 165 0.20000000
> 166 0.02857143
> 167 0.00000000
> 168 0.00000000
> 169 0.06000000
> 170 0.14000000
> 171 0.14000000
> 172 0.12000000
> 173 0.00000000
> 174 0.00000000
> 175 0.06000000
> 176 0.04000000
> 177 0.06000000
> 178 0.06000000
> 179 0.00000000
> 180 0.00000000
> 181 0.00000000
> 182 0.04000000
> 183 0.02000000
> 184 0.04000000
> 185 0.02000000
> 186 0.04000000
> 187 0.00000000
> 188 0.00000000
> 189 0.02000000
> 190 0.00000000
> 191 0.00000000
> 192 0.00000000
> 193 0.00000000
> 194 0.00000000
> 195 0.00000000
> 196 0.00000000
> 197 0.00000000
> 198 0.00000000
> 199 0.00000000
> 200 0.06000000
> 201 0.02000000
> 202 0.00000000
> 203 0.00000000
> 204 0.00000000
> 205 0.02000000
> 206 0.02000000
> 207 0.00000000
> 208 0.00000000
> 209 0.02000000
> 210 0.00000000
> 211 0.00000000
> 212 0.18000000
> 213 0.18000000
> 214 0.00000000
> 215 0.00000000
> 216 0.00000000
> 217 0.00000000
> 218 0.02000000
> 219 0.22000000
> 220 0.04000000
> 221 0.02000000
> 222 0.00000000
> 223 0.00000000
> 224 0.02000000
> 225 0.00000000
> 226 0.18000000
> 227 0.06000000
> 228 0.00000000
> 229 0.00000000
> 230 0.00000000
> 231 0.00000000
> 232 0.00000000
> 233 0.04000000
> 234 0.00000000
> 235 0.00000000
> 236 0.00000000
> 237 0.00000000
> 238 0.00000000
> 239 0.00000000
> 240 0.04000000
> 241 0.00000000
> 242 0.00000000
> 243 0.00000000
> 244 0.00000000
> 245 0.00000000
> 246 0.00000000
> 247 0.00000000
> 248 0.00000000
> 249 0.00000000
> 250 0.00000000
> 251 0.00000000
> 252 0.00000000
Historical stage pairs include stage in time t and stage in time t-1. In the first year of observation, the stage in time t-1 is unknowable, so is shown above as NotAlive (although it is certainly possible that the individual was alive in the previous year). Starting from the second year, we see many knowable stage pairs with individuals, and as before their proportions within each year sum to 1.0.
Let’s now move on to adding supplemental information to our MPMs.
3.7 Formatting supplemental data
MPMs are often estimated only partially from available demographic datasets. Some transitions are parameterized using information gathered from other studies, whether through direct input in the matrix or through the development of kernels contingent on external information. Other transitions might also be estimated via proxy transitions elsewhere in the matrix. In lefko3, this information can be provided in one of two ways. The preferred and most recently developed method is the supplement table, which can be developed using the supplemental() function. This function allows users to create a data frame detailing:
- specific transitions to set as constants,
- specific transitions to estimate via proxy transitions, which can also be multiplied by fixed values, and
- specific multipliers for fecundity in cases in which fecundity estimates resulting from linear modeling must be modified to characterize the full transition (such multipliers can also be used to inform the matrix creation process with the correct fecundity transitions).
Examples might illustrate where this approach is useful. If I lack my own data on subterranean juvenile stages in a plant species, but I have estimates of survival for those stages form another study, then I might use those estimates as constants in the MPM. Further, if I lack demographic data on the development of germinated seeds to the seedling or earliest adult stage, but I have reason to believe that the survival probabilities should be similar to the survival within an observed stage of seedlings or small adults, then I can use the latter survival-transitions as proxies. Finally, if fecundity is a function of seed production, survival to the next year, and germination probability, then germination probability might be estimated via a separate field germination study. I might wish to incorporate this germination probability both as a constant transition, and as a multiplier on estimated fecundity. Supplement tables provide a means to include all of this information.
Function supplemental() was developed to provide a robust, general solution to the addition of these data to MPMs. To use this function, first identify each transition that needs to be altered, and split each transition into stage in times t+1, t, and, if conducting a historical analysis, t-1. These stages must then be entered in the same order across the stage3, stage2, and stage1 fields. For example, if I wished to alter the historical transitions from stage A to B to C, and from A to A to C, then I would enter these two transitions as
stage3 = c("C", "C"), stage2 = c("B", "A"), stage1 = c("A", "A")
If I were interested in ahistorical transitions, then I would either set all stage1 values to NA, such as stage1 = c(NA, NA), or simply not include stage1 in the input (the default is a vector of NA elements). If I wished to replace my two transitions with proxy transitions that lefko3 will estimate, then I can designate those proxy transitions using the eststage fields. For example:
eststage3 = c("F", "F"), eststage2 = c("E", "D"), eststage1 = c("D", "D")
The above would replace my original transitions (A-B-C and A-A-C) with the values estimated for transitions D-E-F and D-D-F, respectively. Alternatively, if I wished to set these two transitions to fixed constants, then I could designate those with givenrate. For example, givenrate = c(0.15, 0.25) would set these two transitions to 0.15 and 0.25, respectively. Estimated fecundity, as well as proxy values, can be modified by a multiplier using the multiplier field, and it is important to identify the kind of transition to modify as a survival transition or a fecundity rate using the type field (use type12 also to designate the kind of transition occurs between times t-1 and t in the historical case). Fecundity multipliers should be identified separately, since they are not proxy values. The function requires the input of the stageframe used to generate the stages.
We will start off by creating two supplement tables taking all of these sorts of data for the function-based MPMs. The first is the supplement table for the historical analysis, and the second table covers the ahistorical analysis. Each row refers to a specific transition, and in the historical case, there are codes for 23 given transitions (12 for the ahistorical case). The first 9 of the historical transitions are set to specific probabilities (6 in the ahistorical case), and the next 12 are transitions that will be set to other, estimated transitions (4 in the ahistorical case; these are the non-NA transitions in eststage set below) multiplied by specific constants (either 0.7 or 1.0). The final two terms are fecundity multipliers, which will here be used to handle the seed dormancy rate and the germination rate (both including seed survival over the course of the year). Based on the literature, the proxies for entry into the adult classes are transitions from dormancy, as below. However, in the raw dataset, dormancy is not common enough to use as an effective proxy in raw matrix creation. Hence, we can use different proxies for function-based matrix estimation than for raw matrix estimation. Where necessary, we also use rep and mat as shorthand to code for all reproductive stages and all mature stages, respectively.
Here is the historical supplement table. We will also introduce a variable representing the number of seeds expected per fruit. Note that the number of seeds per fruit is actually likely higher than this, but we are using this number to reflect the relatively stable population dynamics that we see in the population.
seeds_per_fruit <- 5000
sl_mult <- 0.7
cypsupp3_fb <- supplemental(stage3 = c("SD", "SD", "P1", "P1", "P2", "P3", "SL",
"SL", "SL", "D", "V1", "V2", "V3", "D", "V1", "V2", "V3", "mat", "mat",
"mat", "mat", "SD", "P1"),
stage2 = c("SD", "SD", "SD", "SD", "P1", "P2", "P3", "SL", "SL", "SL", "SL",
"SL", "SL", "SL", "SL", "SL", "SL", "D", "V1", "V2", "V3", "rep", "rep"),
stage1 = c("SD", "rep", "SD", "rep", "SD", "P1", "P2", "P3", "SL", "P3", "P3",
"P3", "P3", "SL", "SL", "SL", "SL", "SL", "SL", "SL", "SL", "mat", "mat"),
eststage3 = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, "D", "V1", "V2", "V3", "D",
"V1", "V2", "V3", "mat", "mat", "mat", "mat", NA, NA),
eststage2 = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, "D", "D", "D", "D", "D",
"D", "D", "D", "D", "V1", "V2", "V3", NA, NA),
eststage1 = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, "D", "D", "D", "D", "D",
"D", "D", "D", "V1", "V1", "V1", "V1", NA, NA),
givenrate = c(0.08, 0.08, 0.1, 0.1, 0.1, 0.1, 0.1, 0.05, 0.05, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA),
multiplier = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, sl_mult, sl_mult,
sl_mult, sl_mult, sl_mult, sl_mult, sl_mult, sl_mult, 1, 1, 1, 1,
0.5 * seeds_per_fruit, 0.5 * seeds_per_fruit),
type = c("S", "S", "S", "S", "S", "S", "S", "S", "S", "S", "S", "S", "S", "S",
"S", "S", "S", "S", "S", "S", "S", "R", "R"),
type_t12 = c("S", "F", "S", "F", "S", "S", "S", "S", "S", "S", "S", "S", "S",
"S", "S", "S", "S", "S", "S", "S", "S", "S", "S"),
stageframe = cypframe_fb, historical = TRUE)
cypsupp3_fb
> stage3 stage2 stage1 age2 eststage3 eststage2 eststage1 estage2 givenrate
> 1 SD SD SD NA <NA> <NA> <NA> NA 0.08
> 2 SD SD rep NA <NA> <NA> <NA> NA 0.08
> 3 P1 SD SD NA <NA> <NA> <NA> NA 0.10
> 4 P1 SD rep NA <NA> <NA> <NA> NA 0.10
> 5 P2 P1 SD NA <NA> <NA> <NA> NA 0.10
> 6 P3 P2 P1 NA <NA> <NA> <NA> NA 0.10
> 7 SL P3 P2 NA <NA> <NA> <NA> NA 0.10
> 8 SL SL P3 NA <NA> <NA> <NA> NA 0.05
> 9 SL SL SL NA <NA> <NA> <NA> NA 0.05
> 10 D SL P3 NA D D D NA NA
> 11 V1 SL P3 NA V1 D D NA NA
> 12 V2 SL P3 NA V2 D D NA NA
> 13 V3 SL P3 NA V3 D D NA NA
> 14 D SL SL NA D D D NA NA
> 15 V1 SL SL NA V1 D D NA NA
> 16 V2 SL SL NA V2 D D NA NA
> 17 V3 SL SL NA V3 D D NA NA
> 18 mat D SL NA mat D V1 NA NA
> 19 mat V1 SL NA mat V1 V1 NA NA
> 20 mat V2 SL NA mat V2 V1 NA NA
> 21 mat V3 SL NA mat V3 V1 NA NA
> 22 SD rep mat NA <NA> <NA> <NA> NA NA
> 23 P1 rep mat NA <NA> <NA> <NA> NA NA
> multiplier convtype convtype_t12
> 1 NA 1 1
> 2 NA 1 2
> 3 NA 1 1
> 4 NA 1 2
> 5 NA 1 1
> 6 NA 1 1
> 7 NA 1 1
> 8 NA 1 1
> 9 NA 1 1
> 10 0.7 1 1
> 11 0.7 1 1
> 12 0.7 1 1
> 13 0.7 1 1
> 14 0.7 1 1
> 15 0.7 1 1
> 16 0.7 1 1
> 17 0.7 1 1
> 18 1.0 1 1
> 19 1.0 1 1
> 20 1.0 1 1
> 21 1.0 1 1
> 22 2500.0 3 1
> 23 2500.0 3 1Now we can input the ahistorical supplement table.
cypsupp2_fb <- supplemental(stage3 = c("SD", "P1", "P2", "P3", "SL", "SL", "D",
"V1", "V2", "V3", "SD", "P1"),
stage2 = c("SD", "SD", "P1", "P2", "P3", "SL", "SL", "SL", "SL", "SL", "rep",
"rep"),
eststage3 = c(NA, NA, NA, NA, NA, NA, "D", "V1", "V2", "V3", NA, NA),
eststage2 = c(NA, NA, NA, NA, NA, NA, "D", "D", "D", "D", NA, NA),
givenrate = c(0.08, 0.1, 0.1, 0.1, 0.05, 0.05, NA, NA, NA, NA, NA, NA),
multiplier = c(NA, NA, NA, NA, NA, NA, sl_mult, sl_mult, sl_mult, sl_mult,
0.5 * seeds_per_fruit, 0.5 * seeds_per_fruit),
type = c("S", "S", "S", "S", "S", "S", "S", "S", "S", "S", "R", "R"),
stageframe = cypframe_fb, historical = FALSE)
cypsupp2_fb
> stage3 stage2 stage1 age2 eststage3 eststage2 eststage1 estage2 givenrate
> 1 SD SD <NA> NA <NA> <NA> <NA> NA 0.08
> 2 P1 SD <NA> NA <NA> <NA> <NA> NA 0.10
> 3 P2 P1 <NA> NA <NA> <NA> <NA> NA 0.10
> 4 P3 P2 <NA> NA <NA> <NA> <NA> NA 0.10
> 5 SL P3 <NA> NA <NA> <NA> <NA> NA 0.05
> 6 SL SL <NA> NA <NA> <NA> <NA> NA 0.05
> 7 D SL <NA> NA D D <NA> NA NA
> 8 V1 SL <NA> NA V1 D <NA> NA NA
> 9 V2 SL <NA> NA V2 D <NA> NA NA
> 10 V3 SL <NA> NA V3 D <NA> NA NA
> 11 SD rep <NA> NA <NA> <NA> <NA> NA NA
> 12 P1 rep <NA> NA <NA> <NA> <NA> NA NA
> multiplier convtype convtype_t12
> 1 NA 1 1
> 2 NA 1 1
> 3 NA 1 1
> 4 NA 1 1
> 5 NA 1 1
> 6 NA 1 1
> 7 0.7 1 1
> 8 0.7 1 1
> 9 0.7 1 1
> 10 0.7 1 1
> 11 2500.0 3 1
> 12 2500.0 3 1
These supplement tables provide the best means of adding external data to our MPMs because they allow both specific transitions to be isolated. They also allow the use of shorthand to identify large groups of transitions (e.g. using mat, rep, immat, prop, npr, obs, nobs, or all to signify all mature stages, reproductive stages, immature stages, propagule stages, non-propagule stages, observable stages, unobservable stages, or simply all stages, respectively). Let’s now also supply the supplement tables for the raw MPMs.
cypsupp3_raw <- supplemental(stage3 = c("SD", "SD", "P1", "P1", "P2", "P2",
"P3", "SL", "SL", "SL", "D", "XSm", "Sm", "D", "XSm", "Sm", "mat", "mat",
"mat", "SD", "P1"),
stage2 = c("SD", "SD", "SD", "SD", "P1", "P1", "P2", "P3", "SL", "SL", "SL",
"SL", "SL", "SL", "SL", "SL", "D", "XSm", "Sm", "rep", "rep"),
stage1 = c("SD", "rep", "SD", "rep", "SD", "rep", "P1", "P2", "P3", "SL",
"SL", "SL", "SL", "P3", "P3", "P3", "SL", "SL", "SL", "mat", "mat"),
eststage3 = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, "D", "XSm", "Sm", "D",
"XSm", "Sm", "mat", "mat", "mat", NA, NA),
eststage2 = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, "XSm", "XSm", "XSm",
"XSm", "XSm", "XSm", "D", "XSm", "Sm", NA, NA),
eststage1 = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, "XSm", "XSm", "XSm",
"XSm", "XSm", "XSm", "XSm", "XSm", "XSm", NA, NA),
givenrate = c(0.08, 0.10, 0.10, 0.10, 0.10, 0.10, 0.10, 0.05, 0.05, 0.05, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA),
multiplier = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, sl_mult, sl_mult,
sl_mult, sl_mult, sl_mult, sl_mult, 1, 1, 1, 0.5 * seeds_per_fruit,
0.5 * seeds_per_fruit),
type =c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3),
stageframe = cypframe_raw, historical = TRUE)
cypsupp3_raw
> stage3 stage2 stage1 age2 eststage3 eststage2 eststage1 estage2 givenrate
> 1 SD SD SD NA <NA> <NA> <NA> NA 0.08
> 2 SD SD rep NA <NA> <NA> <NA> NA 0.10
> 3 P1 SD SD NA <NA> <NA> <NA> NA 0.10
> 4 P1 SD rep NA <NA> <NA> <NA> NA 0.10
> 5 P2 P1 SD NA <NA> <NA> <NA> NA 0.10
> 6 P2 P1 rep NA <NA> <NA> <NA> NA 0.10
> 7 P3 P2 P1 NA <NA> <NA> <NA> NA 0.10
> 8 SL P3 P2 NA <NA> <NA> <NA> NA 0.05
> 9 SL SL P3 NA <NA> <NA> <NA> NA 0.05
> 10 SL SL SL NA <NA> <NA> <NA> NA 0.05
> 11 D SL SL NA D XSm XSm NA NA
> 12 XSm SL SL NA XSm XSm XSm NA NA
> 13 Sm SL SL NA Sm XSm XSm NA NA
> 14 D SL P3 NA D XSm XSm NA NA
> 15 XSm SL P3 NA XSm XSm XSm NA NA
> 16 Sm SL P3 NA Sm XSm XSm NA NA
> 17 mat D SL NA mat D XSm NA NA
> 18 mat XSm SL NA mat XSm XSm NA NA
> 19 mat Sm SL NA mat Sm XSm NA NA
> 20 SD rep mat NA <NA> <NA> <NA> NA NA
> 21 P1 rep mat NA <NA> <NA> <NA> NA NA
> multiplier convtype convtype_t12
> 1 NA 1 1
> 2 NA 1 1
> 3 NA 1 1
> 4 NA 1 1
> 5 NA 1 1
> 6 NA 1 1
> 7 NA 1 1
> 8 NA 1 1
> 9 NA 1 1
> 10 NA 1 1
> 11 0.7 1 1
> 12 0.7 1 1
> 13 0.7 1 1
> 14 0.7 1 1
> 15 0.7 1 1
> 16 0.7 1 1
> 17 1.0 1 1
> 18 1.0 1 1
> 19 1.0 1 1
> 20 2500.0 3 1
> 21 2500.0 3 1
cypsupp2_raw <- supplemental(stage3 = c("SD", "P1", "P2", "P3", "SL", "SL", "D",
"XSm", "Sm", "SD", "P1"),
stage2 = c("SD", "SD", "P1", "P2", "P3", "SL", "SL", "SL", "SL", "rep","rep"),
eststage3 = c(NA, NA, NA, NA, NA, NA, "D", "XSm", "Sm", NA, NA),
eststage2 = c(NA, NA, NA, NA, NA, NA, "XSm", "XSm", "XSm", NA, NA),
givenrate = c(0.08, 0.10, 0.10, 0.10, 0.05, 0.05, NA, NA, NA, NA, NA),
multiplier = c(NA, NA, NA, NA, NA, NA, sl_mult, sl_mult, sl_mult,
0.5 * seeds_per_fruit, 0.5 * seeds_per_fruit),
type =c(1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3),
stageframe = cypframe_raw, historical = FALSE)
cypsupp2_raw
> stage3 stage2 stage1 age2 eststage3 eststage2 eststage1 estage2 givenrate
> 1 SD SD <NA> NA <NA> <NA> <NA> NA 0.08
> 2 P1 SD <NA> NA <NA> <NA> <NA> NA 0.10
> 3 P2 P1 <NA> NA <NA> <NA> <NA> NA 0.10
> 4 P3 P2 <NA> NA <NA> <NA> <NA> NA 0.10
> 5 SL P3 <NA> NA <NA> <NA> <NA> NA 0.05
> 6 SL SL <NA> NA <NA> <NA> <NA> NA 0.05
> 7 D SL <NA> NA D XSm <NA> NA NA
> 8 XSm SL <NA> NA XSm XSm <NA> NA NA
> 9 Sm SL <NA> NA Sm XSm <NA> NA NA
> 10 SD rep <NA> NA <NA> <NA> <NA> NA NA
> 11 P1 rep <NA> NA <NA> <NA> <NA> NA NA
> multiplier convtype convtype_t12
> 1 NA 1 1
> 2 NA 1 1
> 3 NA 1 1
> 4 NA 1 1
> 5 NA 1 1
> 6 NA 1 1
> 7 0.7 1 1
> 8 0.7 1 1
> 9 0.7 1 1
> 10 2500.0 3 1
> 11 2500.0 3 13.7.1 Historical transitions and supplemental data
The supplement tables above have different dimensions depending both on the life history model used, and on whether the MPM is to be historical or not. A full introduction to historical MPMs is provided in the next chapter, but here we will illustrate why there is such a difference in dimension and why users should be careful in creating these tables.
A standard MPM includes information on the rates and probabilities associated with transitions from the different life history stages at one time to the next. We generally say that such an MPM shows the probability of transition from one stage at the current time to the next, or the expected rate of offspring production from the current time to the next. Because conceptually such a matrix shows the expected rates and probabilities moving forward from the current time, the standard MPM is not considered to have any individual history. As such, we may refer to these MPMs as ahistorical.
A historical MPM includes information on the rates and probabilities associated with the transition from the current time and one time step back, to the next time forward. Such MPMs include one extra time step of information from the individual’s history. For example, in a historical model, the probability of transition from an extra small adult to a small adult will differ depending on what stage the individual was in immediately before being extra small. So, the probability of transition from extra small at time t to small in time t+1 will differ between those individuals that were extra small in time t-1 and those individuals that were small in time t-1. In an ahistorical model, these transition probabilities would all have the same value.
Supplement tables for historical MPMs and IPMs need to be written to include all three-time transitions that cannot be estimated from the dataset. Because a single ahistorical transition represents a transition that does not depend on stage in time t-1, this means that a single ahistorical transition is broken down into potentially many historical transitions. The result is that supplement tables for historical MPMs are bigger than those for ahistorical MPMs. Failing to account for any relevant historical transition that is not represented in a dataset forces its value to zero, meaning that failing to account for all relevant transitions in a supplement table will cause a break in the life history that will yield a set of matrices leading to low population growth and often complete insensitivity to alterations in fecundity and other vital rates.
For example, in the raw historical supplement table above, the final two transitions noted are the fecundity transitions. The last of these is mat -> rep -> P1, and is shorthand showing that we are setting the transition from all mature stages in time t-1 and all reproductive stages in time t to the 1st year protocorm stage in time t+1. Since we do not have actual individual demographic data for juvenile stages in our dataset, we also need to specify the next transition, which is the survival transition set rep -> P1 -> P2. Note that here, the transition between times t-1 and t is actually a fecundity step, and so refers to the production of offspring by the mother, while the transition from time t to time t+1 is a survival probability for the offspring itself. In deVries format, we would instead use AlmostBorn -> P1 -> P2, since deVries format does not allow mixing fecundity and survival transitions together in historical transitions unless they refer to the same individual (more on this issue in the next chapter). We need still more transitions here, including at least the following to connect offspring stages to the adult portions of the life history.
\(P1 \rightarrow P2 \rightarrow P3\)
\(P2 \rightarrow P3 \rightarrow SL\)
\(P3 \rightarrow SL \rightarrow D\)
\(P3 \rightarrow SL \rightarrow XSm\)
\(P3 \rightarrow SL \rightarrow Sm\)
\(SL \rightarrow D \rightarrow mat\)
\(SL \rightarrow XSm \rightarrow mat\)
\(SL \rightarrow Sm \rightarrow mat\)
Let’s consider another example. In figure 3.3 below, we show the portion of the life history most closely tied to fecundity. The "rep" argument refers to reproductive stages, and the "mat" argument refers to mature stages. The "rep" to "DS" ahistorical transition, then, refers to 24 different transitions in the function-based stageframe, because there are 24 reproductive (i.e. flowering) stages. Counting up the ahistorical transitions, then, we find that we have 24 + 24 + 1 + 1 + 1 = 51 ahistorical transitions shown. In the historical case, the "mat" to "rep" to "DS" transition set refers to \(24 \times 49 = 1176\) transitions. So, counting everything up, we actually see 1176 + 1176 + 24 + 24 + 1 + 1 = 2402 transitions here. Missing even a single one of these impacts projected population dynamics.
The most important thing to consider in building a supplement table, then, is that all stages must be connected to all other stages as diagrammed in the original life history model. If a single transition noted in the above paragraph is missed, then at least one stage is not properly connected to the other stages in the model, and there is likely a 0 value associated with a particular transition that should have a non-zero value. In that circumstance, users will find that their MPM or IPM likely predicts a lower growth rate, and nothing that they do will be able to change it (typically, the asymptotic growth rate will not just decline, but be completely insensitive to changes in survival or fecundity transitions).
3.7.2 An older alternative to the supplement table
Supplement tables provide all of the supplemental information that we need. However, there is an alternative means of supplying this information, and that is through the creation of a reproductive matrix and an overwrite table. The reproductive matrix is an ahistorical matrix detailing where fecundity rates are set, and at what level. Cypripedium candidum produces seeds that germinate by the following growing season (stage P1, or a first year protocorm), or that remain dormant for the next year (stage SD). In the following matrix, we detail that the fecundity of each reproductive stage needs to be split into two between each of these output stages. The actual split places 50% of the fecundity of a reproductive stage into each category of recruit, where the full fecundity is estimated by linear models that we will create. This reproductive matrix can be used in historical MPM construction, and it is assumed that stage at occasion t-1 is set to all.
rep.assumptions_fb <- matrix(0, 54, 54)
rep.assumptions_fb[1:2,31:54] <- 0.5 * seeds_per_fruit
rep.assumptions_fb
> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
> [1,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [2,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [3,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [4,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [5,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [6,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [7,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [8,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [9,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [10,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [11,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [12,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [13,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [14,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [15,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [16,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [17,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [18,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [19,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [20,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [21,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [22,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [23,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [24,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [25,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [26,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [27,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [28,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [29,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [30,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [31,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [32,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [33,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [34,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [35,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [36,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [37,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [38,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [39,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [40,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [41,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [42,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [43,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [44,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [45,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [46,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [47,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [48,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [49,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [50,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [51,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [52,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [53,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [54,] 0 0 0 0 0 0 0 0 0 0 0 0 0
> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
> [1,] 0 0 0 0 0 0 0 0 0 0 0 0
> [2,] 0 0 0 0 0 0 0 0 0 0 0 0
> [3,] 0 0 0 0 0 0 0 0 0 0 0 0
> [4,] 0 0 0 0 0 0 0 0 0 0 0 0
> [5,] 0 0 0 0 0 0 0 0 0 0 0 0
> [6,] 0 0 0 0 0 0 0 0 0 0 0 0
> [7,] 0 0 0 0 0 0 0 0 0 0 0 0
> [8,] 0 0 0 0 0 0 0 0 0 0 0 0
> [9,] 0 0 0 0 0 0 0 0 0 0 0 0
> [10,] 0 0 0 0 0 0 0 0 0 0 0 0
> [11,] 0 0 0 0 0 0 0 0 0 0 0 0
> [12,] 0 0 0 0 0 0 0 0 0 0 0 0
> [13,] 0 0 0 0 0 0 0 0 0 0 0 0
> [14,] 0 0 0 0 0 0 0 0 0 0 0 0
> [15,] 0 0 0 0 0 0 0 0 0 0 0 0
> [16,] 0 0 0 0 0 0 0 0 0 0 0 0
> [17,] 0 0 0 0 0 0 0 0 0 0 0 0
> [18,] 0 0 0 0 0 0 0 0 0 0 0 0
> [19,] 0 0 0 0 0 0 0 0 0 0 0 0
> [20,] 0 0 0 0 0 0 0 0 0 0 0 0
> [21,] 0 0 0 0 0 0 0 0 0 0 0 0
> [22,] 0 0 0 0 0 0 0 0 0 0 0 0
> [23,] 0 0 0 0 0 0 0 0 0 0 0 0
> [24,] 0 0 0 0 0 0 0 0 0 0 0 0
> [25,] 0 0 0 0 0 0 0 0 0 0 0 0
> [26,] 0 0 0 0 0 0 0 0 0 0 0 0
> [27,] 0 0 0 0 0 0 0 0 0 0 0 0
> [28,] 0 0 0 0 0 0 0 0 0 0 0 0
> [29,] 0 0 0 0 0 0 0 0 0 0 0 0
> [30,] 0 0 0 0 0 0 0 0 0 0 0 0
> [31,] 0 0 0 0 0 0 0 0 0 0 0 0
> [32,] 0 0 0 0 0 0 0 0 0 0 0 0
> [33,] 0 0 0 0 0 0 0 0 0 0 0 0
> [34,] 0 0 0 0 0 0 0 0 0 0 0 0
> [35,] 0 0 0 0 0 0 0 0 0 0 0 0
> [36,] 0 0 0 0 0 0 0 0 0 0 0 0
> [37,] 0 0 0 0 0 0 0 0 0 0 0 0
> [38,] 0 0 0 0 0 0 0 0 0 0 0 0
> [39,] 0 0 0 0 0 0 0 0 0 0 0 0
> [40,] 0 0 0 0 0 0 0 0 0 0 0 0
> [41,] 0 0 0 0 0 0 0 0 0 0 0 0
> [42,] 0 0 0 0 0 0 0 0 0 0 0 0
> [43,] 0 0 0 0 0 0 0 0 0 0 0 0
> [44,] 0 0 0 0 0 0 0 0 0 0 0 0
> [45,] 0 0 0 0 0 0 0 0 0 0 0 0
> [46,] 0 0 0 0 0 0 0 0 0 0 0 0
> [47,] 0 0 0 0 0 0 0 0 0 0 0 0
> [48,] 0 0 0 0 0 0 0 0 0 0 0 0
> [49,] 0 0 0 0 0 0 0 0 0 0 0 0
> [50,] 0 0 0 0 0 0 0 0 0 0 0 0
> [51,] 0 0 0 0 0 0 0 0 0 0 0 0
> [52,] 0 0 0 0 0 0 0 0 0 0 0 0
> [53,] 0 0 0 0 0 0 0 0 0 0 0 0
> [54,] 0 0 0 0 0 0 0 0 0 0 0 0
> [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
> [1,] 0 0 0 0 0 2500 2500 2500 2500 2500 2500 2500
> [2,] 0 0 0 0 0 2500 2500 2500 2500 2500 2500 2500
> [3,] 0 0 0 0 0 0 0 0 0 0 0 0
> [4,] 0 0 0 0 0 0 0 0 0 0 0 0
> [5,] 0 0 0 0 0 0 0 0 0 0 0 0
> [6,] 0 0 0 0 0 0 0 0 0 0 0 0
> [7,] 0 0 0 0 0 0 0 0 0 0 0 0
> [8,] 0 0 0 0 0 0 0 0 0 0 0 0
> [9,] 0 0 0 0 0 0 0 0 0 0 0 0
> [10,] 0 0 0 0 0 0 0 0 0 0 0 0
> [11,] 0 0 0 0 0 0 0 0 0 0 0 0
> [12,] 0 0 0 0 0 0 0 0 0 0 0 0
> [13,] 0 0 0 0 0 0 0 0 0 0 0 0
> [14,] 0 0 0 0 0 0 0 0 0 0 0 0
> [15,] 0 0 0 0 0 0 0 0 0 0 0 0
> [16,] 0 0 0 0 0 0 0 0 0 0 0 0
> [17,] 0 0 0 0 0 0 0 0 0 0 0 0
> [18,] 0 0 0 0 0 0 0 0 0 0 0 0
> [19,] 0 0 0 0 0 0 0 0 0 0 0 0
> [20,] 0 0 0 0 0 0 0 0 0 0 0 0
> [21,] 0 0 0 0 0 0 0 0 0 0 0 0
> [22,] 0 0 0 0 0 0 0 0 0 0 0 0
> [23,] 0 0 0 0 0 0 0 0 0 0 0 0
> [24,] 0 0 0 0 0 0 0 0 0 0 0 0
> [25,] 0 0 0 0 0 0 0 0 0 0 0 0
> [26,] 0 0 0 0 0 0 0 0 0 0 0 0
> [27,] 0 0 0 0 0 0 0 0 0 0 0 0
> [28,] 0 0 0 0 0 0 0 0 0 0 0 0
> [29,] 0 0 0 0 0 0 0 0 0 0 0 0
> [30,] 0 0 0 0 0 0 0 0 0 0 0 0
> [31,] 0 0 0 0 0 0 0 0 0 0 0 0
> [32,] 0 0 0 0 0 0 0 0 0 0 0 0
> [33,] 0 0 0 0 0 0 0 0 0 0 0 0
> [34,] 0 0 0 0 0 0 0 0 0 0 0 0
> [35,] 0 0 0 0 0 0 0 0 0 0 0 0
> [36,] 0 0 0 0 0 0 0 0 0 0 0 0
> [37,] 0 0 0 0 0 0 0 0 0 0 0 0
> [38,] 0 0 0 0 0 0 0 0 0 0 0 0
> [39,] 0 0 0 0 0 0 0 0 0 0 0 0
> [40,] 0 0 0 0 0 0 0 0 0 0 0 0
> [41,] 0 0 0 0 0 0 0 0 0 0 0 0
> [42,] 0 0 0 0 0 0 0 0 0 0 0 0
> [43,] 0 0 0 0 0 0 0 0 0 0 0 0
> [44,] 0 0 0 0 0 0 0 0 0 0 0 0
> [45,] 0 0 0 0 0 0 0 0 0 0 0 0
> [46,] 0 0 0 0 0 0 0 0 0 0 0 0
> [47,] 0 0 0 0 0 0 0 0 0 0 0 0
> [48,] 0 0 0 0 0 0 0 0 0 0 0 0
> [49,] 0 0 0 0 0 0 0 0 0 0 0 0
> [50,] 0 0 0 0 0 0 0 0 0 0 0 0
> [51,] 0 0 0 0 0 0 0 0 0 0 0 0
> [52,] 0 0 0 0 0 0 0 0 0 0 0 0
> [53,] 0 0 0 0 0 0 0 0 0 0 0 0
> [54,] 0 0 0 0 0 0 0 0 0 0 0 0
> [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49]
> [1,] 2500 2500 2500 2500 2500 2500 2500 2500 2500 2500 2500 2500
> [2,] 2500 2500 2500 2500 2500 2500 2500 2500 2500 2500 2500 2500
> [3,] 0 0 0 0 0 0 0 0 0 0 0 0
> [4,] 0 0 0 0 0 0 0 0 0 0 0 0
> [5,] 0 0 0 0 0 0 0 0 0 0 0 0
> [6,] 0 0 0 0 0 0 0 0 0 0 0 0
> [7,] 0 0 0 0 0 0 0 0 0 0 0 0
> [8,] 0 0 0 0 0 0 0 0 0 0 0 0
> [9,] 0 0 0 0 0 0 0 0 0 0 0 0
> [10,] 0 0 0 0 0 0 0 0 0 0 0 0
> [11,] 0 0 0 0 0 0 0 0 0 0 0 0
> [12,] 0 0 0 0 0 0 0 0 0 0 0 0
> [13,] 0 0 0 0 0 0 0 0 0 0 0 0
> [14,] 0 0 0 0 0 0 0 0 0 0 0 0
> [15,] 0 0 0 0 0 0 0 0 0 0 0 0
> [16,] 0 0 0 0 0 0 0 0 0 0 0 0
> [17,] 0 0 0 0 0 0 0 0 0 0 0 0
> [18,] 0 0 0 0 0 0 0 0 0 0 0 0
> [19,] 0 0 0 0 0 0 0 0 0 0 0 0
> [20,] 0 0 0 0 0 0 0 0 0 0 0 0
> [21,] 0 0 0 0 0 0 0 0 0 0 0 0
> [22,] 0 0 0 0 0 0 0 0 0 0 0 0
> [23,] 0 0 0 0 0 0 0 0 0 0 0 0
> [24,] 0 0 0 0 0 0 0 0 0 0 0 0
> [25,] 0 0 0 0 0 0 0 0 0 0 0 0
> [26,] 0 0 0 0 0 0 0 0 0 0 0 0
> [27,] 0 0 0 0 0 0 0 0 0 0 0 0
> [28,] 0 0 0 0 0 0 0 0 0 0 0 0
> [29,] 0 0 0 0 0 0 0 0 0 0 0 0
> [30,] 0 0 0 0 0 0 0 0 0 0 0 0
> [31,] 0 0 0 0 0 0 0 0 0 0 0 0
> [32,] 0 0 0 0 0 0 0 0 0 0 0 0
> [33,] 0 0 0 0 0 0 0 0 0 0 0 0
> [34,] 0 0 0 0 0 0 0 0 0 0 0 0
> [35,] 0 0 0 0 0 0 0 0 0 0 0 0
> [36,] 0 0 0 0 0 0 0 0 0 0 0 0
> [37,] 0 0 0 0 0 0 0 0 0 0 0 0
> [38,] 0 0 0 0 0 0 0 0 0 0 0 0
> [39,] 0 0 0 0 0 0 0 0 0 0 0 0
> [40,] 0 0 0 0 0 0 0 0 0 0 0 0
> [41,] 0 0 0 0 0 0 0 0 0 0 0 0
> [42,] 0 0 0 0 0 0 0 0 0 0 0 0
> [43,] 0 0 0 0 0 0 0 0 0 0 0 0
> [44,] 0 0 0 0 0 0 0 0 0 0 0 0
> [45,] 0 0 0 0 0 0 0 0 0 0 0 0
> [46,] 0 0 0 0 0 0 0 0 0 0 0 0
> [47,] 0 0 0 0 0 0 0 0 0 0 0 0
> [48,] 0 0 0 0 0 0 0 0 0 0 0 0
> [49,] 0 0 0 0 0 0 0 0 0 0 0 0
> [50,] 0 0 0 0 0 0 0 0 0 0 0 0
> [51,] 0 0 0 0 0 0 0 0 0 0 0 0
> [52,] 0 0 0 0 0 0 0 0 0 0 0 0
> [53,] 0 0 0 0 0 0 0 0 0 0 0 0
> [54,] 0 0 0 0 0 0 0 0 0 0 0 0
> [,50] [,51] [,52] [,53] [,54]
> [1,] 2500 2500 2500 2500 2500
> [2,] 2500 2500 2500 2500 2500
> [3,] 0 0 0 0 0
> [4,] 0 0 0 0 0
> [5,] 0 0 0 0 0
> [6,] 0 0 0 0 0
> [7,] 0 0 0 0 0
> [8,] 0 0 0 0 0
> [9,] 0 0 0 0 0
> [10,] 0 0 0 0 0
> [11,] 0 0 0 0 0
> [12,] 0 0 0 0 0
> [13,] 0 0 0 0 0
> [14,] 0 0 0 0 0
> [15,] 0 0 0 0 0
> [16,] 0 0 0 0 0
> [17,] 0 0 0 0 0
> [18,] 0 0 0 0 0
> [19,] 0 0 0 0 0
> [20,] 0 0 0 0 0
> [21,] 0 0 0 0 0
> [22,] 0 0 0 0 0
> [23,] 0 0 0 0 0
> [24,] 0 0 0 0 0
> [25,] 0 0 0 0 0
> [26,] 0 0 0 0 0
> [27,] 0 0 0 0 0
> [28,] 0 0 0 0 0
> [29,] 0 0 0 0 0
> [30,] 0 0 0 0 0
> [31,] 0 0 0 0 0
> [32,] 0 0 0 0 0
> [33,] 0 0 0 0 0
> [34,] 0 0 0 0 0
> [35,] 0 0 0 0 0
> [36,] 0 0 0 0 0
> [37,] 0 0 0 0 0
> [38,] 0 0 0 0 0
> [39,] 0 0 0 0 0
> [40,] 0 0 0 0 0
> [41,] 0 0 0 0 0
> [42,] 0 0 0 0 0
> [43,] 0 0 0 0 0
> [44,] 0 0 0 0 0
> [45,] 0 0 0 0 0
> [46,] 0 0 0 0 0
> [47,] 0 0 0 0 0
> [48,] 0 0 0 0 0
> [49,] 0 0 0 0 0
> [50,] 0 0 0 0 0
> [51,] 0 0 0 0 0
> [52,] 0 0 0 0 0
> [53,] 0 0 0 0 0
> [54,] 0 0 0 0 0Next we will create the overwrite tables, which outline transitions that cannot be estimated from the data set and need to be set by other means. Here is an example of two overwrite tables for the Cypripedium candidum analysis. Note that they are fundamentally similar to supplement tables, but do not allow the addition of multipliers and transition types from occasion t-1 to t, nor do they involve a check of entered stages against the stageframe.
cypover3_fb <- overwrite(stage3 = c("SD", "SD", "P1", "P1", "P2", "P3", "SL",
"SL", "SL", "D", "V1", "V2", "V3", "D", "V1", "V2", "V3", "mat", "mat",
"mat", "mat"),
stage2 = c("SD", "SD", "SD", "SD", "P1", "P2", "P3", "SL", "SL", "SL", "SL",
"SL", "SL", "SL", "SL", "SL", "SL", "D", "V1", "V2", "V3"),
stage1 = c("SD", "rep", "SD", "rep", "SD", "P1", "P2", "P3", "SL", "P3", "P3",
"P3", "P3", "SL", "SL", "SL", "SL", "SL", "SL", "SL", "SL"),
eststage3 = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, "D", "V1", "V2", "V3", "D",
"V1", "V2", "V3", "mat", "mat", "mat", "mat"),
eststage2 = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, "D", "D", "D", "D", "D",
"D", "D", "D", "D", "V1", "V2", "V3"),
eststage1 = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, "D", "D", "D", "D", "D",
"D", "D", "D", "V1", "V1", "V1", "V1"),
givenrate = c(0.08, 0.08, 0.1, 0.1, 0.1, 0.1, 0.1, 0.05, 0.05, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA))
> This function is deprecated. Please use supplemental() instead
cypover3_fb
> stage3 stage2 stage1 eststage3 eststage2 eststage1 givenrate convtype
> 1 SD SD SD <NA> <NA> <NA> 0.08 1
> 2 SD SD rep <NA> <NA> <NA> 0.08 1
> 3 P1 SD SD <NA> <NA> <NA> 0.10 1
> 4 P1 SD rep <NA> <NA> <NA> 0.10 1
> 5 P2 P1 SD <NA> <NA> <NA> 0.10 1
> 6 P3 P2 P1 <NA> <NA> <NA> 0.10 1
> 7 SL P3 P2 <NA> <NA> <NA> 0.10 1
> 8 SL SL P3 <NA> <NA> <NA> 0.05 1
> 9 SL SL SL <NA> <NA> <NA> 0.05 1
> 10 D SL P3 D D D NA 1
> 11 V1 SL P3 V1 D D NA 1
> 12 V2 SL P3 V2 D D NA 1
> 13 V3 SL P3 V3 D D NA 1
> 14 D SL SL D D D NA 1
> 15 V1 SL SL V1 D D NA 1
> 16 V2 SL SL V2 D D NA 1
> 17 V3 SL SL V3 D D NA 1
> 18 mat D SL mat D V1 NA 1
> 19 mat V1 SL mat V1 V1 NA 1
> 20 mat V2 SL mat V2 V1 NA 1
> 21 mat V3 SL mat V3 V1 NA 1
> convtype_t12
> 1 1
> 2 1
> 3 1
> 4 1
> 5 1
> 6 1
> 7 1
> 8 1
> 9 1
> 10 1
> 11 1
> 12 1
> 13 1
> 14 1
> 15 1
> 16 1
> 17 1
> 18 1
> 19 1
> 20 1
> 21 1
cypover2_fb <- overwrite(stage3 = c("SD", "P1", "P2", "P3", "SL", "SL", "D",
"V1", "V2", "V3"),
stage2 = c("SD", "SD", "P1", "P2", "P3", "SL", "SL", "SL", "SL", "SL"),
eststage3 = c(NA, NA, NA, NA, NA, NA, "D", "V1", "V2", "V3"),
eststage2 = c(NA, NA, NA, NA, NA, NA, "D", "D", "D", "D"),
givenrate = c(0.08, 0.1, 0.1, 0.1, 0.05, 0.05, NA, NA, NA, NA),
type = c("S", "S", "S", "S", "S", "S", "S", "S", "S"))
> This function is deprecated. Please use supplemental() instead
cypover2_fb
> stage3 stage2 stage1 eststage3 eststage2 eststage1 givenrate convtype
> 1 SD SD <NA> <NA> <NA> <NA> 0.08 1
> 2 P1 SD <NA> <NA> <NA> <NA> 0.10 1
> 3 P2 P1 <NA> <NA> <NA> <NA> 0.10 1
> 4 P3 P2 <NA> <NA> <NA> <NA> 0.10 1
> 5 SL P3 <NA> <NA> <NA> <NA> 0.05 1
> 6 SL SL <NA> <NA> <NA> <NA> 0.05 1
> 7 D SL <NA> D D <NA> NA 1
> 8 V1 SL <NA> V1 D <NA> NA 1
> 9 V2 SL <NA> V2 D <NA> NA 1
> 10 V3 SL <NA> V3 D <NA> NA 1
> convtype_t12
> 1 1
> 2 1
> 3 1
> 4 1
> 5 1
> 6 1
> 7 1
> 8 1
> 9 1
> 10 1Let’s now also supply the overwrite tables and reproductive matrix for the raw MPMs.
rep_cyp_raw <- matrix(0, 11, 11)
rep_cyp_raw[1:2,7:11] <- 0.5 * seeds_per_fruit
rep_cyp_raw
> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
> [1,] 0 0 0 0 0 0 2500 2500 2500 2500 2500
> [2,] 0 0 0 0 0 0 2500 2500 2500 2500 2500
> [3,] 0 0 0 0 0 0 0 0 0 0 0
> [4,] 0 0 0 0 0 0 0 0 0 0 0
> [5,] 0 0 0 0 0 0 0 0 0 0 0
> [6,] 0 0 0 0 0 0 0 0 0 0 0
> [7,] 0 0 0 0 0 0 0 0 0 0 0
> [8,] 0 0 0 0 0 0 0 0 0 0 0
> [9,] 0 0 0 0 0 0 0 0 0 0 0
> [10,] 0 0 0 0 0 0 0 0 0 0 0
> [11,] 0 0 0 0 0 0 0 0 0 0 0
cypover2_raw <- overwrite(stage3 = c("SD", "P1", "P2", "P3", "SL", "SL", "D",
"XSm", "Sm"),
stage2 = c("SD", "SD", "P1", "P2", "P3", "SL", "SL", "SL", "SL"),
eststage3 = c(NA, NA, NA, NA, NA, NA, "D", "XSm", "Sm"),
eststage2 = c(NA, NA, NA, NA, NA, NA, "XSm", "XSm", "XSm"),
givenrate = c(0.08, 0.10, 0.10, 0.10, 0.05, 0.05, NA, NA, NA),
type = c("S", "S", "S", "S", "S", "S", "S", "S", "S"))
> This function is deprecated. Please use supplemental() instead
cypover2_raw
> stage3 stage2 stage1 eststage3 eststage2 eststage1 givenrate convtype
> 1 SD SD <NA> <NA> <NA> <NA> 0.08 1
> 2 P1 SD <NA> <NA> <NA> <NA> 0.10 1
> 3 P2 P1 <NA> <NA> <NA> <NA> 0.10 1
> 4 P3 P2 <NA> <NA> <NA> <NA> 0.10 1
> 5 SL P3 <NA> <NA> <NA> <NA> 0.05 1
> 6 SL SL <NA> <NA> <NA> <NA> 0.05 1
> 7 D SL <NA> D XSm <NA> NA 1
> 8 XSm SL <NA> XSm XSm <NA> NA 1
> 9 Sm SL <NA> Sm XSm <NA> NA 1
> convtype_t12
> 1 1
> 2 1
> 3 1
> 4 1
> 5 1
> 6 1
> 7 1
> 8 1
> 9 1
cypover3_raw <- overwrite(stage3 = c("SD", "SD", "P1", "P1", "P2", "P2",
"P3", "SL", "SL", "SL", "D", "XSm", "Sm", "D", "XSm", "Sm", "mat", "mat",
"mat"),
stage2 = c("SD", "SD", "SD", "SD", "P1", "P1", "P2", "P3", "SL", "SL", "SL",
"SL", "SL", "SL", "SL", "SL", "D", "XSm", "Sm"),
stage1 = c("SD", "rep", "SD", "rep", "SD", "rep", "P1", "P2", "P3", "SL",
"SL", "SL", "SL", "P3", "P3", "P3", "SL", "SL", "SL"),
eststage3 = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, "D", "XSm", "Sm", "D",
"XSm", "Sm", "mat", "mat", "mat"),
eststage2 = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, "XSm", "XSm", "XSm",
"XSm", "XSm", "XSm", "D", "XSm", "Sm"),
eststage1 = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, "XSm", "XSm", "XSm",
"XSm", "XSm", "XSm", "XSm", "XSm", "XSm"),
givenrate = c(0.08, 0.10, 0.10, 0.10, 0.10, 0.10, 0.10, 0.05, 0.05, 0.05, NA,
NA, NA, NA, NA, NA, NA, NA, NA),
type = c("S", "S", "S", "S", "S", "S", "S", "S", "S", "S", "S", "S"))
> This function is deprecated. Please use supplemental() instead
cypover3_raw
> stage3 stage2 stage1 eststage3 eststage2 eststage1 givenrate convtype
> 1 SD SD SD <NA> <NA> <NA> 0.08 1
> 2 SD SD rep <NA> <NA> <NA> 0.10 1
> 3 P1 SD SD <NA> <NA> <NA> 0.10 1
> 4 P1 SD rep <NA> <NA> <NA> 0.10 1
> 5 P2 P1 SD <NA> <NA> <NA> 0.10 1
> 6 P2 P1 rep <NA> <NA> <NA> 0.10 1
> 7 P3 P2 P1 <NA> <NA> <NA> 0.10 1
> 8 SL P3 P2 <NA> <NA> <NA> 0.05 1
> 9 SL SL P3 <NA> <NA> <NA> 0.05 1
> 10 SL SL SL <NA> <NA> <NA> 0.05 1
> 11 D SL SL D XSm XSm NA 1
> 12 XSm SL SL XSm XSm XSm NA 1
> 13 Sm SL SL Sm XSm XSm NA 1
> 14 D SL P3 D XSm XSm NA 1
> 15 XSm SL P3 XSm XSm XSm NA 1
> 16 Sm SL P3 Sm XSm XSm NA 1
> 17 mat D SL mat D XSm NA 1
> 18 mat XSm SL mat XSm XSm NA 1
> 19 mat Sm SL mat Sm XSm NA 1
> convtype_t12
> 1 1
> 2 1
> 3 1
> 4 1
> 5 1
> 6 1
> 7 1
> 8 1
> 9 1
> 10 1
> 11 1
> 12 1
> 13 1
> 14 1
> 15 1
> 16 1
> 17 1
> 18 1
> 19 1
The overwrite() approach is much less powerful than the supplement table approach, particularly because it lacks the ability to handle multipliers, it lacks some shorthand stage abbreviations, and it lacks inconsistency checks. The supplemental() approach can also provide supplement tables for all kinds of MPs / IPMs developed in lefko3, including age-by-stage and even Leslie MPMs, and is actively maintained while overwrite() is essentially deprecated. So, we encourage the use of supplemental() rather than overwrite().
3.8 Handling complex life histories
Situations may occur in which the life history of the organism includes two sets of stages with transitions only occurring in one direction between them. For example, let’s consider the following life history model (figure 3.4).
Raw MPMs have no problem with this situation, provided that each stage has its own, unique set of characteristics. However, function-based MPMs (including IPMs) will have a default tendency to estimate survival transitions from the adult reproductive stages (in blue box) back to the pre-adult non-reproductive stages (in red box). We can deal with this problem using stage grouping.
First, we will create a new stageframe that encapsulates all of the stages above. Note that the primary addition that we will make to the sf_create() input is the group option.
sizevector <- c(0, 0, 0, 0, 0, 0, 1, 3, 1, 3, 6, 11, 20, 31)
stagevector <- c("SD", "P1", "P2", "P3", "SL", "pD", "pXSm", "pSm", "XSm", "Sm",
"Md", "Lg", "XLg", "XXLg")
repvector <- c(0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1)
obsvector <- c(0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1)
matvector <- c(0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1)
immvector <- c(0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0)
propvector <- c(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
indataset <- c(0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1)
binvec <- c(0, 0, 0, 0, 0, 0.5, 0.5, 1.5, 0.5, 1.5, 1.5, 3.5, 5.5, 5.5)
group <- c(0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2)
comments <- c("Dormant seed", "1st yr protocorm", "2nd yr protocorm",
"3rd yr protocorm", "Seedling", "Dormant pre-adult",
"Extra small pre-adult (1 shoot)", "Small pre-adult (2-4 shoots)",
"Extra small adult (1 shoot)", "Small adult (2-4 shoots)",
"Medium adult (5-7 shoots)", "Large adult (8-14 shoots)",
"Extra large adult (20 shoots)", "Extra extra large adult (>24.5 shoots")
cypframe_alt <- sf_create(sizes = sizevector, stagenames = stagevector,
repstatus = repvector, obsstatus = obsvector, matstatus = matvector,
propstatus = propvector, immstatus = immvector, indataset = indataset,
binhalfwidth = binvec, group = group, comments = comments)
cypframe_alt
> stage size size_b size_c min_age max_age repstatus obsstatus propstatus
> 1 SD 0 NA NA NA NA 0 0 1
> 2 P1 0 NA NA NA NA 0 0 0
> 3 P2 0 NA NA NA NA 0 0 0
> 4 P3 0 NA NA NA NA 0 0 0
> 5 SL 0 NA NA NA NA 0 0 0
> 6 pD 0 NA NA NA NA 0 0 0
> 7 pXSm 1 NA NA NA NA 0 1 0
> 8 pSm 3 NA NA NA NA 0 1 0
> 9 XSm 1 NA NA NA NA 1 1 0
> 10 Sm 3 NA NA NA NA 1 1 0
> 11 Md 6 NA NA NA NA 1 1 0
> 12 Lg 11 NA NA NA NA 1 1 0
> 13 XLg 20 NA NA NA NA 1 1 0
> 14 XXLg 31 NA NA NA NA 1 1 0
> immstatus matstatus indataset binhalfwidth_raw sizebin_min sizebin_max
> 1 0 0 0 0.0 0.0 0.0
> 2 1 0 0 0.0 0.0 0.0
> 3 1 0 0 0.0 0.0 0.0
> 4 1 0 0 0.0 0.0 0.0
> 5 1 0 0 0.0 0.0 0.0
> 6 1 0 1 0.5 -0.5 0.5
> 7 1 0 1 0.5 0.5 1.5
> 8 1 0 1 1.5 1.5 4.5
> 9 0 1 1 0.5 0.5 1.5
> 10 0 1 1 1.5 1.5 4.5
> 11 0 1 1 1.5 4.5 7.5
> 12 0 1 1 3.5 7.5 14.5
> 13 0 1 1 5.5 14.5 25.5
> 14 0 1 1 5.5 25.5 36.5
> sizebin_center sizebin_width binhalfwidthb_raw sizebinb_min sizebinb_max
> 1 0 0 NA NA NA
> 2 0 0 NA NA NA
> 3 0 0 NA NA NA
> 4 0 0 NA NA NA
> 5 0 0 NA NA NA
> 6 0 1 NA NA NA
> 7 1 1 NA NA NA
> 8 3 3 NA NA NA
> 9 1 1 NA NA NA
> 10 3 3 NA NA NA
> 11 6 3 NA NA NA
> 12 11 7 NA NA NA
> 13 20 11 NA NA NA
> 14 31 11 NA NA NA
> sizebinb_center sizebinb_width binhalfwidthc_raw sizebinc_min sizebinc_max
> 1 NA NA NA NA NA
> 2 NA NA NA NA NA
> 3 NA NA NA NA NA
> 4 NA NA NA NA NA
> 5 NA NA NA NA NA
> 6 NA NA NA NA NA
> 7 NA NA NA NA NA
> 8 NA NA NA NA NA
> 9 NA NA NA NA NA
> 10 NA NA NA NA NA
> 11 NA NA NA NA NA
> 12 NA NA NA NA NA
> 13 NA NA NA NA NA
> 14 NA NA NA NA NA
> sizebinc_center sizebinc_width group comments
> 1 NA NA 0 Dormant seed
> 2 NA NA 0 1st yr protocorm
> 3 NA NA 0 2nd yr protocorm
> 4 NA NA 0 3rd yr protocorm
> 5 NA NA 0 Seedling
> 6 NA NA 1 Dormant pre-adult
> 7 NA NA 1 Extra small pre-adult (1 shoot)
> 8 NA NA 1 Small pre-adult (2-4 shoots)
> 9 NA NA 2 Extra small adult (1 shoot)
> 10 NA NA 2 Small adult (2-4 shoots)
> 11 NA NA 2 Medium adult (5-7 shoots)
> 12 NA NA 2 Large adult (8-14 shoots)
> 13 NA NA 2 Extra large adult (20 shoots)
> 14 NA NA 2 Extra extra large adult (>24.5 shoots
Now that we have our stageframe, the only thing we need to do is to specify that survival-transitions from group 2 stages to group 1 stages are equal to 0. We can do this with the supplemental() function. Here, we will set these transitions, and also set the fecundity multipliers as before.
cypsupp2_alt <- supplemental(stage3 = c("group1", "SD", "P1"),
stage2 = c("group2", "rep", "rep"), eststage3 = c(NA, NA, NA),
eststage2 = c(NA, NA, NA), givenrate = c(0, NA, NA),
multiplier = c(NA, (0.5 * seeds_per_fruit), (0.5 * seeds_per_fruit)),
type =c(1, 3, 3), stageframe = cypframe_alt, historical = FALSE)
cypsupp2_alt
> stage3 stage2 stage1 age2 eststage3 eststage2 eststage1 estage2 givenrate
> 1 group1 group2 <NA> NA <NA> <NA> <NA> NA 0
> 2 SD rep <NA> NA <NA> <NA> <NA> NA NA
> 3 P1 rep <NA> NA <NA> <NA> <NA> NA NA
> multiplier convtype convtype_t12
> 1 NA 1 1
> 2 2500 3 1
> 3 2500 3 1
This supplement table can now be input into a matrix estimator function to tell that function that these transitions must be 0. We will see how to do this with different styles of MPM in the next four chapters.
We can now proceed in the next chapter to create raw matrices.
3.9 Points to remember
- Functions
verticalize3()andhistoricalize3()can be used to take horizontally or vertically arranged demographic datasets and standardize them into the appropriate format for MPM creation and analysis. - Function
summary_hfv()provides summaries of hfv datasets, including the overall dimensions, the numbers of individuals, and other important characteristics. - Function
actualstage3()provides a means of exploring standardized datasets, showing the actual frequencies and proportions of each stage, age, age-stage, or historical stage-pair alive in each year. - Function
supplemental()provides the means to incorporate given transition values obtained from external studies, set transitions to proxy values to be estimated bylefko3, and incorporate multipiers on survival transitions, fecundity estimates, and proxy survival transitions. - Great care must be taken to include every missing transition within the supplement table. Otherwise, models will predict dying populations, and asymptotic analyses will be invariant to changes in survival and fecundity terms.
- Stage groups can be used to add directionality and other complex relationships between groups of life history stages.