Abstract
Adaptive dynamics is a mathematical framework for studying evolution. It extends evolutionary game theory to account for more realistic ecological dynamics and it can incorporate both frequency- and density-dependent selection. This is a practical guide to adaptive dynamics that aims to illustrate how the methodology can be applied to the study of specific systems. The theory is presented in detail for a single, monomorphic, asexually reproducing population. We explain the necessary terminology to understand the basic arguments in models based on adaptive dynamics, including invasion fitness, the selection gradient, pairwise invasibility plots (PIP), evolutionarily singular strategies, and the canonical equation. The presentation is supported with a worked-out example of evolution of arrival times in migratory birds. We show how the adaptive dynamics methodology can be extended to study evolution in polymorphic populations using trait evolution plots (TEPs). We give an overview of literature that generalises adaptive dynamics techniques to other scenarios, such as sexual, diploid populations, and spatially-structured populations. We conclude by discussing how adaptive dynamics relates to evolutionary game theory and how adaptive-dynamics techniques can be used in speciation research.
Highlights
The basic principle of evolution, survival of the fittest1, was outlined by the naturalist Charles Darwin in his 1859 book On the origin of species
An adaptive-dynamics analysis sidesteps this difficulty by assuming that the mutant is initially so rare that it has no impact on the per capita growth rates and that the resident is at its demographic equilibrium, i.e., we assume that n(t) = nr (r) and nr (t) = r/d respectively
Most of what we have wanted to say has already been presented in the previous sections and all that remains is to give our personal views on two selected topics and to offer recommendations for further reading on the rapidly developing field of adaptive dynamics
Summary
The basic principle of evolution, survival of the fittest , was outlined by the naturalist Charles Darwin in his 1859 book On the origin of species. Though controversial at the time, the central ideas remain largely unchanged to this date, even though much more is known about the biological basis of inheritance and the intricacies of natural and sexual selection. Darwin expressed his arguments verbally, but many attempts have since been made to formalize the theory of evolution. The key feature of adaptive dynamics is that it links population dynamics to evolutionary dynamics and thereby incorporates and generalizes the fundamental idea of frequency-dependent selection from game theory. We give recommendations for further reading and highlight selected extensions of adaptive dynamics theory
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