Glossary

Accuracy: The lack of bias in an estimator of a model parameter or model prediction.

Allee effects: A discounting of population growth rates in small populations. It is a form of density dependence (often known as depensatory density dependence) which populations can overcome when they benefit from a critical size. For instance, in small (or low-density) populations, Allee effects may originate from the inability of individuals to encounter suitable breeding mates, or to form efficient hunting packs.

Antagonistic resources: Two resources that, when taken together, offset the benefits of each other.

Autocorrelation: Random variables at proximate points in space or time may tend to be more similar than at points further apart. This idea translates to the statistical notion of (positive) autocorrelation: the correlation of a variable measured here and now, with the same variable measured at a certain distance or time interval in the past.

Available locations or Background locations: Locations in geographic or environmental space that are assumed to be accessible to individuals under study. These are locations that moving animals or dispersing plants can reach but may not eventually be found in.

Camera trap: A stationary, autonomous camera, triggered by movement.

Climate envelope models: A model of the distribution of a species with particular applications to climate change. Model predictions are based on a species’ tolerances to different climate covariates (e.g. temperature or precipitation). Tolerances are represented as deterministic or probabilistic ranges (or, envelopes).

Colonization credit: The opposite of extinction debt. The number of species or members of a species that can reestablish in a region, and will do so given enough time.

Complementary resources: Two resources that, when taken together, have a more beneficial effect (per resource) than when taken individually.

Condition: Environmental variable (such as ambient temperature, humidity, salinity or pressure) that influences an organism’s functioning. Extreme values of conditions (e.g. very high or very low temperatures) are usually detrimental to an organism, so responses to conditions are often modeled with non-linear (unimodal) functions.

Demography: The study of birth, death, immigration and emigration rates at the level of populations.

Demographic sorting: The process of habitat-driven changes in the vital rates (i.e. survival, growth and reproduction) that lead to differences in species density between habitats.

Density, species: The observed or expected number of individuals per unit of area. See also intensity function.

Density estimation method: A statistical method for estimating the number organisms per unit of area in a landscape, often relying on smoothing or spatial interpolation between observations.

Depletion: The reduction of resource density caused by the action of an organism (e.g. through consumption or occupation).

Design matrix: A matrix containing the values of explanatory variables for a set of observations. Each row represents a different observation and the columns contain the specific values of the explanatory variables associated with that observation. The design matrix provides a convenient shorthand for describing and implementing regression models.

Deterministic variable: A variable whose exact value can be predicted from a mathematical model (to a predetermined degree of precision) without the need for it to be measured experimentally.

Dirichlet tessellation: Divides a two-dimensional geographic space into a set of geometric shapes or tiles with no overlap or gaps. In a spatial point pattern, the Dirichlet tile associated with a particular point is the region of space that is closer to that point than to any other point. The Dirichlet tessellation is also known as the Voronoi or Thiessen tessellation.

Dispersal: The movement of members of a species (or their propagules) away from their birth site.

Distance sampling: Methodology for estimating density or population abundance using point or line-transect sampling. The distances of individuals to observers is used parameterize detection functions, which describe how the probability of detection depends on distance from the observer.

Extinction debt: The opposite of colonization credit. The number of species that are doomed to (local) extinction due to environmental change, but have yet to become extinct. In relation to species distributions, it implies that SHA-models predict zero density for a region, but remnants of the species are still present.

Ecosystem engineers: A species that significantly modifies its environment, thereby shaping the distribution and abundance of other species.

Empirical model or Phenomenological model A mathematical model whose behavior emulates the behavior of a physical phenomenon, but whose mathematical structure has not been derived from first principles. All mathematical models are, at some level, empirical, particularly in ecology, because the reductionist approach of specifying every aspect of a model from first principles leads to unnecessarily complicated models. (Contrast with Mechanistic model). Classic examples of empirical models are statistical regression models, but many of the time-honored physical models (e.g. Newton’s law of gravitation) are also empirical.

Environmental Space (E-space): The space whose dimensions are environmental variables (compare with Geographical space).

Environmental variable: A measurable environmental trait that, for a particular focal species, could represent a resource, a condition or risk. In SHA models, the term is synonymous with explanatory variable or covariate.

Equilibrium assumption: The assumption that sufficient time has elapsed for a species to reach a stable spatial distribution. This assumption is vulnerable not just because of transient dynamics, but also due to persistent, long-term instabilities in species-habitat associations.

Fitness, partial: The fitness of a population living in an environment made up entirely of a single habitat (a set of resources, conditions and risks).

Fitness, individual: From a demographic viewpoint, the log of the combined effect of life-long survival and reproductive success of an individual. Equivalently, from an evolutionary perspective, the log of the individual’s contribution to the gene pool of the next generation (note that this omits the effects of inclusive fitness).

Fitness, population: The average fitness of individuals in a population. In low densities, the population fitness afforded by the environment is equal to the population’s intrinsic growth rate (excluding the possibility of Allee effects).

Fitness integration: The process whereby organisms accumulate resources, reduce risk and mitigate environmental conditions in space or time. As a result, viable populations may be observed in landscapes where no single point in space or time is characterized by positive fitness.

Functional response: In SHA models, the idea that the response of an organism to a particular environmental variable depends critically on the values of other environmental variables. This definition is slightly different to the more often encountered use of the terr in trophic ecology, where a functional response describes the intake rate of a food type by a single consumer, in response to the abundance of that (as well as other) food types.

Gaussian blur: The operation of blurring an image (e.g., a map) by applying a Gaussian kernel to each of its pixels.

Gaussian random field: A stochastic process (or collection of random variables in time or space) that have a multivariate Normal (Gaussian) distribution characterized by a mean function and covariance function.

Geographical Space (G-space): The space defined by physical dimensions (e.g. latitude, longitude and altitude/depth).

Habitat: A point in Environmental space (defined by a set of resources, risks and conditions).

Habitat availability: The relative proportion of habitats making up the region of G-space that is accessible to an organism or population.

Habitat context: The habitat composition within a neighborhood of a particular habitat. This is influenced by the autocorrelation within and cross-correlations between the environmental variables in G-space.

Habitat selection: The process whereby an organisms uses a habitat disproportionately more (or less) than that habitat’s availability. Together with Demographic sorting it shapes species distributions.

Habitat usage: The proportion of an individual’s time or the proportion of a population associated with a single unit (e.g. \(m^2\)) of a particular habitat.

Hessian: Matrix of second derivatives of the log-likelihood with respect to model parameters. The inverse of the Hessian provides an estimate of the variance-covariance matrix of parameters when estimated using maximum Likelihood.

Homogeneous Poisson point Process (HPP): A model for locations or events in geographic space. The number of events in a fixed region, \(G\), is assumed to be Poisson-distributed with rate \(\lambda\). In an HPP, the rate is assumed to be constant across space and time.

Ideal-Free Distribution (IFD): A conceptual model of density-dependent resource exploitation in a patchy environment. Individuals are aware of the quality of each and every patch (i.e. individuals are ideal) and free to enter any patch. As a result, they settle in the most profitable patch. In the special case where the quality of a patch decreases linearly with the density of animals in the patch, the equilibrium density of animals will be proportional to the intrinsic habitat quality of all occupied patches.

Indiscriminate: Hypothetical organisms that do not appear to be selecting one habitat over another. Equivalently, organisms that use G-space uniformly randomly.

Inhomogeneous Poisson point Process (IPP): A model for locations or events in geographic space where the expected density of points depends on local spatial predictors through a spatially-varying intensity function. The number of events in a fixed region, \(G\), is assumed to be Poisson distributed with mean given by the average intensity function over the region.

Intake rate: The uptake of food or other resources per unit of time.

Integrated data models: Models fit simultaneously to multiple data sets, often with the goal of increasing spatial coverage, precision, and accuracy of estimators of species distributions by addressing issues related to sampling bias or imperfect detection.

Intensity function: The Intensity surface described as a function of spatially-varying environmental variables.

Intensity surface: The expected spatial density of individuals or observations.

Intrinsic population growth rate: The population growth rate without any density dependence.

Kernel: A probability density function (usually with mean zero), in one, two or more dimensions, used for re-weighting operations. For example, a kernel applied to every pixel of an image (see Gaussian blur) can be used to generate more diffuse versions of that image. Alternatively, a kernel applied to a finite sample of point observations, can be used to smooth these observations in an attempt to reconstruct the underlying intensity surface that generated them.

Landscape of fear: Quantifies an organism’s perception of risk in space and often has an influence on its distribution.

Likelihood: A statistical expression that describes the data generating mechanism in terms of one or more parameters.

Logistic population model: A population model that formulates the rate of population growth as a decreasing function of population density. It therefore incorporates conspecific crowding effects acting through biological processes such as competition or cannibalism.

Marginal Value Theorem: Theorem that states an animal should leave its current habitat patch when that patch’s quality (measured in terms of energy gain per unit time) falls below the average quality of other habitat patches available to the animal.

MaxEnt or Maximum entropy: A use-availability method (or software) for modeling species distributions. It uses entropy as a model fitting criterion, as opposed to likelihood.

Maximum Likelihood: A method for estimating parameters in a statistical model. Parameter values are chosen to make the likelihood of the data as large as possible.

Mechanistic model: A model whose mathematical form is derived, to some extent, from physical or biological first principles. For example, in dispersal studies, deriving a diffusion kernel from a model of Brownian motion adds mechanistic content to the process of dispersal. In mechanistic models, the participating parameters often have a clear physical interpretation (contrast with Empirical model).

Monte-Carlo integration: A simulation-based method for approximating an integral when a closed-form analytical solution may not exist.

Niche, fundamental: The set of points in E-space (habitats) that allow the intrinsic growth rate of a population to be positive.

Niche, realized: The collection of all habitats where a species has been found.

Niche, Grinnellian: See fundamental niche, but with the inclusion of other influential species (e.g. prey, predators) as resource or risk dimensions of the environmental space.

Niche, Eltonian: See fundamental niche, but with the inclusion of bi-directional relationship between the focal species and other environmental variables and non-focal species, and thereby acknowledging that a species also influences the availability and behavior of properties of its environment.

Nugget, semivariogram: The intercept of the semivariogram curve at zero distance. The physical interpretation of a zero nugget is that there is some measurement uncertainty or process stochasticity that generates variability in repeated measurements, even if these are made at exactly the same location.

Null model, general: A mathematical construct, derived from a set of baseline assumptions. Often it is a simplification of a physical process that forms the basis for further model development, as the baseline assumptions become increasingly relaxed.

Null model, SHA: The equilibrium density of a species at habitat x being proportional to the intrinsic growth rate at low density in habitat x (also see Pseudo-equilibrium assumption and Ideal-free distribution).

Numerical integration: A formal set of rules applied to an integral that allows us to approximate its value when a closed-form analytical solution is not available.

Occupancy: The presence of (at least one member of) a species within a predefined spatial region and time window.

Occurrence distribution: Statistical distribution describing the position of an animal during a specific observation time window.

Offset: A predictor variable with regression coefficient fixed at the value 1, often used to account for varying (but known) levels of observation effort in time or space.

Opportunistic sampling: Data collected without a formal sampling design. An example is a web site that allows citizen scientists to report any observed locations of a species of interest.

Parameter: A numerical quantity that participates in a model and (together with the model’s mathematical structure and any initial conditions), shapes the model’s behavior. Parameters are not observed directly and are usually assumed not to change. Instead, they are estimated via statistical inference methods. So, parameters should not be confused with variables, or covariates.

Phenotype: The composite observable characteristics or traits of an organism.

Probabilistic survey: A survey that samples a fixed region and uses a randomized design for allocating survey effort.

Precision: The level of uncertainty in a parameter estimate or model prediction.

Point Process Events: (or points, locations): observations of animals in space.

Population closure: An assumption often made when estimating abundance or occupancy that the sampled population is not changing during the observation period (i.e., there are no births, deaths, or immigration or emigration).

Predictor function: A function on the log scale, describing the effect of environmental variables on habitat selection. It is equivalent to the link-scale predictor in GLMs and GAMs.

Principal component analysis (PCA): An axis-rotation technique for multivariate data that results in a new set of variable definitions. These new variables are orthogonal and each accounts for a decreasing amount of variation in the original data (from maximum to minimum). PCA is used to eliminate collinearity between candidate covariates and is sometimes used to achieve dimension-reduction, by only retaining those variables that account for most of the variation in the original data.

Profile method, SDM: In the species distribution literature, this is a name occasionally used to describe a model that predicts habitat usage while ignoring variations in habitat availability.

Process component: The process component of a SHA model deals with the biological phenomena of interest. Its parameters should be interpretable in terms of organism responses to their environment, their density or their conspecifics.

Pseudo-equilibrium assumption: The assumption that the density of species at any point in a landscape responds to the measured habitat covariates with no delay, and that this is a reflection of the species fitness at that point.

Quadrature points: Points within the domain of integration at which a function is evaluated when approximating an integral numerically. See numerical integration.

Quadrature weights: Weights given to different points when evaluating an integral numerically. See numerical integration.

Random variable or Variate: A measurable quantity whose value is unknown before a measurement is taken (contrast with Deterministic variable).

Range, Semivariogram: The distance (in time or space) over which observations are correlated.

Range distribution: The asymptotic (or equilibrium) distribution that results from assuming animals move consistently in a range-restricted manner.

Raster: A rectangular grid containing data, with an associated spatial extent and resolution or cell size.

Regression methods: Statistical models that relate the mean value of one (response or dependent) variable to the values of several other (explanatory or independent) variables.

Resource: A substance, object or place required by an organism for growth, maintenance and reproduction, and whose quantities may be reduced by the organism. In contrast to conditions and risks, resources are assumed to always have a positive effect on fitness in the context of a SHA model.

Resource (standing stock) density: The density of a resource at a specific point in space and time. This value is most influential on the intrinsic growth rate or population fitness.

Resource productivity: The change in resource density per unit of area and time. This variable is most influential on the equilibrium density of a species.

Resource selection function: A weighting function that describes the relative likelihood of selecting a location as a function of its environmental characteristics; equivalent to the intensity function of a Inhomogeneous Poisson point-process model with the intercept removed.

Ricker model: A particular version of the logistic population model which has the density-dependent part inside an exponential function.

Risk: Environmental variable that has a negative relationship with fitness by lowering the actual or perceived chances of individual survival or reproduction.

Robustness, model: The desirable combination of accurate and precise predictions from a model even when its assumptions are violated to some extent.

Scaling: An operation that enlarges or shrinks a quantity, or a vector. The factor by which the scale is enlarged or diminished is determined by a non-negative number (a scalar). In mapping operations, upscaling implies an increase in resolution (and downscaling is a resolution decrease).

Semivariogram: A function that measures the degree of statistical dependence between observations as a function of their distance (in space or time). It displays expected variability between two points as a function of their distance, so it increases from low values to a high asymptote (the sill, representing baseline variability between distant, independent points).

Sill, Semivariogram: The asymptote of a semivariogram; describes the spatial or temporal variance for locations that are far enough to be statistically independent.

Spatial point-process model: A model for the data-generating process associated with locations or events in geographic space.

Substitutable resources: Two resources that contribute similarly to an individual’s fitness, such that an organism can replace one lost unit of one resource by a fixed number of units of the other resource.

Species distribution model (SDM): A model that captures variations in species density as a function of spatial coordinates or environmental covariates.

Species-habitat association (SHA): A model that connects aspects of habitat (resources, conditions, risks) to particular observations about a species (recorded at the individual, group or population levels). Most often, the observations relate to species densities (see Species distribution model), but can also relate to population fitness or changes in species density. The main difference between a SHA and SDM is that in SHA model we acknowledge and account for species distributions not being at equilibrium.

Stationary coefficients: The assumption that the coefficients of a regression model do not vary in time and space.

Step-selection function: A weighting function that describes the relative likelihood of selecting a location as a function of its environmental characteristics; used in models that characterize time-specific habitat availability using a model of animal movement.

Synoptic SHA model: A model of space use that incorporates both home range and resource-selection processes.

Telemetry: A collection of measurements (animal locations and other physiological readings) obtained remotely.

Thinned point-process model: A point-process model that assumes only a subset of locations or events in space are observed. The “thinning” process provides a way to model observation biases. Specifically, the full set of locations are “thinned” based on model mechanisms, resulting in the data set that is available for analysis.

Transferability of model predictions: The ability to use a model to make accurate and precise predictions in new time and place.

Use-availability scheme: A SHA model that combines information on habitat usage together with habitat availability in order to quantify habitat selection and predict usage in a transferable way.

Utilization distribution: Or usage. A spatial probability distribution describing the expected time of an individual or the expected density of a population at a particular place.

Weighted distribution theory: A framework for modeling distributions of observed random variables that are influenced by various forms of selection biases.

Zero-niche paradox: The ability of animals to survive in environments where no single point affords positive fitness, via complementary use of resources from different locations (also see Fitness integration). An equivalent idea can be considered for plants, whereby integration of fitness happens across instants in time (e.g. across seasons).