Introduction to Population ModelingThe focus is on the formulation and solution of mathematical models with the idea of a population employed mainly as a pedogogical tool. If the biological setting is stripped away, the material can be interpreted as topics or the qualitative behavior of differential and difference equations. The first group of models investigate the dynamics of a single species, with particular interest in the consequences of treating time and population size in discrete and continuous terms. The second group study is the interaction of two or more species. A final section on complexity and stability attempts to summarize one of the basic questions in ecology using many of the developed ideas. At the conclusion of each topic, problems are provided to provide practice with mathematical concepts and techniques and an annotated list of references is also given at these points in the material. The document concludes with solutions to problems. (MP) |
Contents
Simple Single Species Population Models | 1 |
Stochastic Birth and Death Processes | 13 |
Time Delayed Logistic Equations | 35 |
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animals Assume becomes behavior biological Birth called Carrying Capacity Characteristic Equation Clearly competition complex consider constant continuous cycles death Define depends determine developed differential discussed disturbance dy dt effect environment equations equilibrium point example expected exponential extinction fact figure fixed points follows function given graphical grows growth happens illustrated initial integrate interaction interesting interpret leads limit linearized Logistic look mathematical means method mode monograph mutualism nature Note Notice observations occurs origin oscillation oscillatory period plane Population Models population size possible predator prey probability problem proceed Process Pure quadratic rabbits Recall References roots shown simple single situation solution solve space species species present Stability Analysis tend tion tuning parameter unstable variable