Replicator Equations, Response Functions
And Entropy Measures In Science:
Mathematical Background
Author(s)
Y. A. Pykh & I. G. Malkina-Pykh
Abstract
Replicator dynamics is an evolutionary strategy well established in different
disciplines of biological sciences. It describes the evolution of self-reproducing
entities called replicators in various independent models of, e.g., genetics,
ecology, prebiotic evolution, and sociobiology. Besides this, replicator selection
has been applied to problem solving in combinatorial optimization and to
learning in neural networks and also in fluid mechanics, game and laser theory.
So, the replicator systems arise in an extraordinary variety of modeling
situations. In this report we’ll consider the new class of generalized replicator
equations with nonlinear response functions and construct the Energy Lyapunov
function and entropy measures for this system.
Keywords: replicator equations, Lyapunov functions, entropy, distance measure.
1 An overview and introduction
A replicator is a fundamental unit in evolutionary processes, representing a
population type, and characterized by two attributes: ()i p t, its proportion in the
population at time t , and its non-negative fitness at time t . A replicator's fitness
is a measure of its significance to the future evolution of the population. The
proportions of replicators in a population change as a result of their mutual
interactions, and their relative fitnesses.
The founding fathers of evolutionary genetics, Fisher, Haldane and Wright
used mathematical models to generate a synthesis between Mendelian genetics
and Darwinian evolution. Kimura’s theory of neutral evolution, Hamilton’s kin
Keywords
replicator equations, Lyapunov functions, entropy, distance measure.
Related Book
Other papers in this volume
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