A guide for the nonmodeler
By Steven L. Peck
You are facing a crucial decision on whether to allow harvesting of 200 hectares of forest. But you are concerned about a small population of Pseudo faux, the rare and beautiful phoenix. So you pull out a copy of the latest article, “The Movement and Population Dynamics of Pseudo faux.” You survey the salad of mathematical symbols and equations.
“ . . . the deterministic analytic model and the stochastic simulation model both agree with the individual-based model in suggesting that the statistical model is adequate in predicting when and where P. faux will rise from its former ashes.”
Ack! You scream. What do all these things mean? How do they influence the decision you need to make? Can you use the results of the model without understanding its details?
Modeling plays a crucial role in conservation biology, thus it behooves managers to be able to understand and evaluate modeling papers. In complex ecological systems, modeling can be used to predict outcomes, clarify questions, and allow virtual experiments to manipulate key variables that would otherwise be impossible to do in real life. Yet to many, models remain the domain of mathematicians, statisticians, and others from more quantitative disciplines.
Becoming familiar and comfortable with any subject is often a matter of getting to know the terminology and basic tools associated with the discipline. In this article, I set out to demystify some of the basic concepts behind common ecological models and to give you some typical straightforward steps to tackle a modeling paper.
Making Predictions
The key distinction between the ways different models make predictions is whether or not the modeler explicitly incorporates biological processes into the analysis.
Process models attempt to describe the pertinent aspects of the biology behind the behavior we see in the real system and to reproduce the data that we might collect in the field. For example, a process model designed to predict the size of next year’s black-tailed prairie dog population might include variables representing their current population size, the number of pups expected per female, as well as factors such as immigration and emigration, that might influence the size of the population.
Statistical models, however, do not try to explicitly represent underlying processes but rather attempt to find a set of parameters that can be used to describe and predict relationships among the data. The same statistical model can be used both for looking at a relationship between labor and costs in an economic model and between population numbers and habitat characteristics in a conservation biology setting.
Making Assumptions
Assumptions make or break a model. Because a model can never capture every aspect of a natural ecological system, some aspects must be omitted or simplified. This is where modeling becomes more art than science. Are actual population numbers important or will tracking relative proportions be adequate? Do the organisms migrate first and then mate, or do they mate and then migrate? How these kind of questions are addressed comprises the assumptions of a model.
Examining assumptions is the most important contribution non-modelers can make in helping modelers decide if they have created an adequate representation of the biological process they are trying to capture. Assumptions often are not stated explicitly and can be difficult to sort out. When reading a modeling paper, if you can’t find the assumptions or they are unclear, find out more before using the results from the model.
Space in Models
The spatial dimensions in which organisms move plays a major role in ecological processes. Individuals, populations, and even entire ecosystems move at scales ranging from millimeters to thousands of kilometers. To understand what effect space has on the dynamics of a population in the field can be challenging. Models, however, allow the addition of spatial manipulation with comparative ease, but how this is done is pivotal to the usefulness of the model.
Space usually is incorporated either implicitly or explicitly. With spatially implicit models, we look at the proportion of sites with a specific attribute but track nothing about actual locations or spatial relationships. So, there is no measure of distance or direction in spatially implicit models. Conversely, spatially explicit models incorporate the idea of distance. For example, if you are modeling several populations, some would be closer to any given population than others.
Metapopulation models (a type of spatial model) have attracted particular attention in conservation biology. They can handle space implicitly or explicitly. Formally, a metapopulation is defined as a set of populations distributed over a number of patches that are connected by dispersal. In metapopulation models, the question is often about exploring the interaction between habitat patches and a viable population and habitat patches in which the population has become extinct. For example, how many metapopulation patches must be occupied with viable populations, and what movement rates among patches are necessary to avoid extinction of the regional population for a given number of years?
Simulations
The popularity and growth of simulation models, or as they are sometimes called, computer models, have followed the advances in modern computer technology. These models are an important method of capturing processes that are too complicated to handle analytically and may be the only way that some problems can even be approached.
Computers allow us to model very complex processes and, often, are limited only by the imagination of the modeler. This can be problematic because the complexity of simulation models can quickly rise to the level of that found in the biological process itself. One of the principal reasons to model a system is to reduce its complexity so that underlying processes can be understood more clearly. When a simulation model becomes too complex, this advantage is lost.
Simulation models are relatively easy to produce largely because they typically are computer programs designed to mimic aspects of a biological system. Nevertheless, their testing and interpretation can be time-consuming. For example, I worked on a complex simulation model of a moth’s (Heliothis) resistance to transgenic cotton; the model took just over a month to build but more than a year to test and refine. This is typical. Just because models are simple to construct, never let that lull you into thinking they are a quick-and-dirty method of exploring complex questions.
Tackling the Modeling Paper
The most likely modeling paper to cross your desk will discuss a deterministic simulation model (see glossary). These papers need to be carefully reviewed by biologists and managers who are familiar with the system being modeled.
1. Determine what questions the authors are trying to address. Why did they write the model? Was it to make predictions to determine the extinction risk of a particular organism? Was it to conduct computer experiments that would be impossible in the real system? Were the authors exploring theoretical questions? How general or specific did they hope to make their results? The answers to these questions will help in assessing the modelers’ goals and how well they met them.
2. Examine the modelers’ assumptions. First, look for the assumptions offered up front. There typically will be statements such as “We assume that the number of eggs laid per female is . . .” Next, list the variables used in the model. This gives you a picture of what aspects of biology are supposed to be included in the model. Determine if important processes appear to be missing. How did the modelers handle space and time? Remember that the model will always be a simplification of the real system. The key question is Were critical processes omitted?
3. Look at the flow of the model (i.e., the order that events take place). For example, determine if reproduction precedes or follows movement; this can have profound repercussions on the results. Does the order of events mirror the way things really happen in the system being modeled? Do you see red flags that indicate the model is not relevant to the system you are managing?
Exploring a modeling paper does not mean you need to understand everything about the workings inside the model. But you should not be intimidated to the point that you ignore the paper because your modeling background is weak (or nonexistent).
Modelers are usually delighted that someone is using their model. Your input will be invaluable for making the model more practical and, ultimately, useful for making informed decisions and solving real world problems.
For more information
This article was adapted from:
Peck, S.L., 2000. A Tutorial for Understanding Modeling Papers for the Nonmodeler. American Entomologist 46(1): 40-49
