Fundamental Ideas
Two fundamental ideas of Adaptive Dynamics are that the resident population can be assumed to be in a dynamical equilibrium when new mutants appear, and that the eventual fate of such mutants can be inferred from their initial growth rate when rare in the environment consisting of the resident. This rate is known as the invasion exponent when measured as the initial exponential growth rate of mutants, and as the basic reproductive number when it measures the expected total number of offspring that a mutant individual will produce in a lifetime. It can be thought of, and is indeed sometimes also referred to, as the invasion fitness of mutants. In order to make use of these ideas we require a mathematical model that explicitly incorporates the traits undergoing evolutionary change. The model should describe both the environment and the population dynamics given the environment, but in many cases the variable part of the environment consists only of the demography of the current population. We then determine the invasion exponent, the initial growth rate of a mutant invading the environment consisting of the resident. Depending on the model, this can be trivial or very difficult, but once determined, the Adaptive Dynamics techniques can be applied independent of the model structure.
Read more about this topic: Evolutionary Invasion Analysis
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