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Article overview
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Two-level Fisher-Wright framework with selection and migration: An approach to studying evolution in group structured populations | | Roberto H. Schonmann
; Renato Vicente
; Nestor Caticha
; | | Date: |
23 Jun 2011 | | Abstract: | A framework for the mathematical modeling of evolution in group structured
populations is introduced. The population is divided into a fixed large number
of groups of fixed size. From generation to generation, new groups are formed
that descend from previous groups, through a two-level Fisher-Wright process,
with selection between groups and within groups and with migration between
groups at rate $m$. When $m=1$, the framework reduces to the often used
trait-group framework, so that our setting can be seen as an extension of that
approach. Our framework allows the analysis of previously introduced models in
which altruists and non-altruists compete, and provides new insights into these
models. We focus on the situation in which initially there is a single
altruistic allele in the population, and no further mutations occur. The main
questions are conditions for the viability of that altruistic allele to spread,
and the fashion in which it spreads when it does. Because our results and
methods are rigorous, we see them as shedding light on various controversial
issues in this field, including the role of Hamilton’s rule, and of the Price
equation, the relevance of linearity in fitness functions and the need to only
consider pairwise interactions, or weak selection. In this paper we analyze the
early stages of the evolution, during which the number of altruists is small
compared to the size of the population. We show that during this stage the
evolution is well described by a multitype branching process. The driving
matrix for this process can be obtained, reducing the problem of determining
when the altruistic gene is viable to a comparison between the leading
eigenvalue of that matrix, and the fitness of the non-altruists before the
altruistic gene appeared. This leads to a generalization of Hamilton’s
condition for the viability of a mutant gene. | | Source: | arXiv, 1106.4783 | | Services: | Forum | Review | PDF | Favorites | |
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