Models are everywhere. We all use them to try and understand the world around us. Science consists of developing a model of a system, making predictions from that model, testing them, and then revising our model from the results. All models start out as a verbal explanation of a process. For example, we might hypothesize that a major rainfall will result in large populations of host-seeking mosquitoes. We can test this, by collecting mosquitoes in conjunction with rainfall. After examining the data, we modify this model based on the results. If we found large populations 10 days after heavy rain, our model now might be that rainfall provides oviposition sites, and larval development takes 10 days. However, something weird happens when a "modeler" converts a verbal model into a mathematical one. All of a sudden it's something esoteric, slightly scary, and to be avoided at all costs! But mathematical models are an increasingly important part of science and management and are being used in many ways, from populations of mosquitoes to aerial spray drifting. It is important to be able to assess models and decide if the results are meaningful. You can do this without going through the detailed mathematics! The first thing to consider is the basic type of model. Models can be characterized in many different ways, but one of the most important is whether they are statistical, describing relationships between observed patterns; or process based, describing underlying biological processes.

Statistical models are methods for finding and describing the relationships between observed variables in a data set without determining the mechanism. They range from simple, such as a single variable linear regression, to complex models such as multiple and nonlinear regression, principal components analyses, or GIS-based analyses. In our example, we might use linear regression to look for a relationship between rainfall and mosquito populations. Past rainfall might be included to consider delayed effects. Or, if we had data on different locations, we could use GIS analyses to look for a spatial pattern. A more complex model might include other weather variables or spatial variables such as the type of habitat. Significant associations in the analyses tell us there is a relationship between variables. Statistical models describe these relationships without making any assumptions about how they work.

Process based models incorporate a biological description of the processes in the system. These, also, can range from simple to complex, and are used to study biological processes from the molecular level to entire ecosystems. In our example, we hypothesized that rainfall affects mosquito populations by providing oviposition sites. To study this, we could start with a simple model looking at larval development. With estimates for larval development rates from experiments or the literature, we could build a model predicting when we expect to see adults emerge. This model could be developed further by considering other biological factors such as mortality, searching ability, or fecundity, which might give us more information on about the number of adults we expect as well. One of the most powerful aspects of this type of model is the ability to consider how changes in the input parameters (e.g. larval development time) affect our outcome variable (when adults emerge). We can compare the outcome of the model with data on the number of adults emerging over time, and ask whether our hypotheses about larval development seem valid. Simple models may consider basic factors common to many systems, and provide insights about broad questions, but not about the specifics of one particular species. More complex models can incorporate biological details about one system, and answer questions about that the biology of that system, but we may not be able to generalize the results.

The purpose. Surprisingly enough, people often misunderstand the purpose of a model. First, it is important to understand "prediction". We are always trying to predict things, whether it's when we expect to see mosquito populations increase or the effect of a control treatment. However, predictions can be general (e.g. mosquito populations increase after rain) or very detailed (e.g. "a 10-fold increase 10 days after rainfall greater than 1"). Frequently, the purpose of a model is not detailed prediction, but we learn a great deal from models at all levels of prediction. With statistical models, the goal often is to determine the relationships between variables for future research and for general rather than detailed predictions. In some cases, this seems obvious, but until we do the statistics we may not realize there are more complex relationships. With process based models, we are testing a hypothesis of the underlying processes, considering alternative hypotheses or investigating variation in parameters. Our predictions can be general, such as the factors important in mosquito populations, or detailed, with expectations of precise patterns of abundance. When a process based model is compared with data, we are testing our hypothesis of the mechanism. We often learn more from a model that doesn't 'fit' the data than one that does, since we can then ask what was left out or what assumptions were incorrect.

All models leave things out, just as all experiments control some variables to focus on others. A model must be designed with particular questions and hypotheses in mind, just as an experiment is designed. In any modeling study, you should be able to identify the purpose of the model, the type of model and the basic assumptions (which we will discuss in a future article). Based on those features, you can decide if the results are meaningful, and how applicable they are to your interests.

Cynthia C. Lord, Ph.D.
Associate Professor
UF/IFAS/Florida Medical Entomology Laboratory

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