1 Introduction
Survey a group of fishery biologists and many would say that they entered the field because of a love of the outdoors. They might also admit that, despite a preference for being outside, much of their work is done at a computer. There are mundane tasks like email correspondence, but of greater importance (and relevance for this book) are the steps in getting the information needed for effective management. Those steps include planning and conducting field studies, carrying out correct analyses, and presenting results in reports and presentations. A strong statistical foundation is essential for accomplishing these tasks. Otherwise, management ends up being a trial-and-error process that is inefficient and often ineffective. The purpose of this book is to provide an introduction to these quantitative methods.
The models that we will investigate have a statistical foundation but our interest is primarily in parameter estimation rather than hypothesis testing. This is the opposite of most university statistics courses, but it reflects the reality of fishery management. For example, we might conduct a tagging study in order to estimate the exploitation rate, or the fraction of the legal-sized fish that are harvested in a year. We are not interested in a trivial hypothesis test (“Is the exploitation rate 0?”) but just in getting a reliable estimate. If a substantial fraction of the population is being harvested, then the fishery manager might consider harvest restrictions such as a closed season or size limit. The tagging study could be done using red tags that have a reward of $100 and yellow tags that have a reward of $5. Anglers typically return high-reward tags at a higher rate than low-reward tags, so one part of the planning process would be to decide how many tags of each type to use. Once the study is complete, the model used for planning can often be modified for analysis of the tag-return data. One step in the process would be to determine whether the model needs separate parameters for the return rates of high- and low-reward tags. That could be viewed as a hypothesis-testing situation, but can also be thought of as model selection (simpler model with one rate versus a more complex model with two). Ultimately, we simply want to produce the best possible information about the effect of fishing on the population. This would include not only a point estimate but also measures of uncertainty that aid in decision making.
Examples in the chapters that follow use Bayesian statistical methods to illustrate the steps in planning and analysis of field studies. Fisheries analyses (and university statistics courses) have traditionally been based on so-called frequentist statistical methods, that are based on the expected frequency of observing the data in hand, if the study were repeated many times (McCarthy 2007). Until recently, an important advantage of frequentist methods was that parameter estimation, hypothesis testing, etc. could be implemented with commonly available computing resources (Dorazio 2016). In contrast, Bayesian methods of statistical inference were not practical until fairly recently, when generic algorithms known as Markov Chain Monte Carlo (see Section 4.3) became available (Dorazio 2016). Another important factor in the increased adoption of Bayesian methods is the availability of public-domain software to fit the models (Kéry and Schaub 2011). The earliest version was known as BUGS (Bayesian inference Using Gibbs Sampling; Lunn et al. (2009)), followed by a Windows version WinBUGS (Lunn et al. 2000), then an open version OpenBUGS (Lunn et al. 2009), as well as JAGS (Plummer 2003) which was developed independently but uses essentially identical code. The BUGS language is an important development in that it “frees the modeler in you” (Kéry 2010). Rather than trying to force the data into a rigid black box for analysis, study-specific code can be produced that is readable and biologically meaningful. Another advantage of BUGS software is that it forces you to think about the biological and field-sampling processes that generated your data. Thus it is a great tool both for learning and for getting work done. We will use JAGS in this book, but the code should work without modification in other versions of the BUGS family. The JAGS code will be run from R (R Core Team 2019), a general software environment that is briefly described below.
Bayesian methods differ from frequentist approaches in that they take into account not only the new data but also prior information. This can be viewed as either an advantage or disadvantage, depending on the availability of prior data and one’s statistical philosophy (Ellison 2004; McCarthy 2007; Kéry 2010; Kéry and Schaub 2011; Dorazio 2016). The prior information takes the form of a statistical distribution that defines the range of possible values and the likelihood (prior to collecting the new data). For example, a prior distribution for growth rate could be a uniform distribution specifying that all values between lower and upper bounds were equally likely. Those bounds could be informative, based on a pilot study, but in general, the approach for this book will be to use uninformative prior distributions. An example of an uninformative prior distribution would be to use a uniform 0-1 distribution for a probability (because probabilities are by definition constrained to be between 0 and 1). Bayesian analyses done in this way usually give the same results as a frequentist analysis (McCarthy 2007; Kéry 2010; Kéry and Schaub 2011). This will allow us to avoid some of the controversy, and focus simply on uses and advantages of the BUGS language for fisheries analysis.