Mathematical modeling in ecology: On the hawk vs. Dove game

Abstract

Mathematical modeling is a synthetic combination of variables with dominant effects on a natural system. Thus it provides a tool to understand the meaning and the new reformulation of hypothesis in the wide range of biological systems: from the cell to the complex ecosystems. Unfortunately, because of the difficult understanding between biologist and mathematicians, this is far from appreciated to most students and professionals. But mathematical models also have some limitations. Even if they were a feasible approximation to the biological problem, then only work when they solve doubts and/or transcend the knowledge with respect to an observational or experimental approach. The goal of the present study is to describe some steps in the construction of models fitted to a biological problem. I used a known behavioral example: the hawk vs. dove behavioral dilemma firstly formulated by Maynard Smith. First, I fitted four different models to reproduce the behavior of mixed proportions of hawks and doves that confront between them by the property of a valuable resource. Second, I analyze the dynamic and the evolutionarily stable strategy in dimorphic populations. And third, I discuss the range of valuable predictions and the limitations of these models when confronted to natural populations.