“The Price equation, gradient dynamics, and continuous trait game theory”

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Jussi Lehtonen

The Price equation can be used to derive foundational results in game theory and gradient dynamics

Unifying methods using George Price’s lasting contribution to evolutionary theory

The variety of mathematical approaches to modeling natural selection can be bewildering. Although Darwin himself did not provide a mathematical framework for his ideas, this has long since changed, with methods from probability theory to calculus finding a home in evolutionary theory. Luckily, an equation derived by George Price in the 1970s has the level of generality required to unify many seemingly different mathematical approaches. In a recent article in The American Naturalist, David Queller showed how the Price equation unifies a number of important mathematical results in evolutionary theory. In a new article, Jussi Lehtonen of the University of New South Wales in Sydney, Australia, extends Queller’s analysis to derive several fundamental results in the analysis of the evolution of continuous traits using calculus. Combining the Price equation with Taylor polynomials illuminates similarities and differences between approaches, and allows a simple, unified view of game-theoretical and dynamic concepts. Doing so also connects the power of calculus to evolutionary modeling. The same basic approach of applying the Price equation to Taylor polynomials can be used to derive dynamic gradient models, the criterion for evolutionary stability, as well as the direct fitness approach to kin selection. Read the Article