Evolutionary Invasion Analysis in Structured Populations

Evolutionary invasion analysis seeks to identify those phenotypes that cannot be invaded and replaced by alternative organismal strategies. This is achieved by first constructing a dynamical system that governs a rare mutant's dynamics when introduced into an ecological setting at equilibrium with a resident strategy. From this, a mutant fitness function is derived whose analysis is dependent on the complexity of the ecological milieu. Invasion analyses of age-, stage-, space-, or otherwise-structured populations typically require that a fitness function, termed the invasion fitness, be extracted as an eigenvalue of the linearized dynamics of the focal organism's ecology. This poses little technical difficulty when populations are structured into a small number (usually < 4) of compartments. However, for more complex ecologies, calculating the invasion fitness can be difficult. Here we present an algorithm to perform such analyses in class-structured populations, even when the resulting dimensionality is high enough to prohibit the direct calculation of a dominant eigenvalue. This algorithm also allows for an assessment of the evolutionary stability and convergence stability conditions, thus providing a tool for the complete evolutionary analysis of class-structured populations.

Automated summary

Evolutionary invasion analysis aims to identify phenotypes that cannot be replaced by alternative strategies, with the difficulty of analysis depending on the complexity of the ecological environment. The algorithm can be applied to structured populations, even in high dimensions, providing a tool for complete evolutionary analysis.