A simple fitness proxy for structured populations with continuous traits, with case studies on the evolution of haplo-diploids and genetic dimorphisms

Metz JAJ & Leimar O (2011). A simple fitness proxy for structured populations with continuous traits, with case studies on the evolution of haplo-diploids and genetic dimorphisms. Biological Dynamics 5 (2): 163-190. DOI:10.1080/17513758.2010.502256.

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Abstract

For structured populations in equilibrium with everybody born equal, ln(R0) is a useful fitness proxy for evolutionarily steady strategy (ESS) and most adaptive dynamics calculations, with R0 the average lifetime number of offspring in the clonal and haploid cases, and half the average lifetime number of offspring fathered or mothered for Mendelian diploids. When individuals have variable birth states, as is, for example, the case in spatial models, R0 is itself an eigenvalue, which usually cannot be expressed explicitly in the trait vectors under consideration. In that case, Q(Y| X):=-det (I-L(Y| X)) can often be used as fitness proxy, with L the next-generation matrix for a potential mutant characterized by the trait vector Y in the (constant) environment engendered by a resident characterized by X. If the trait space is connected, global uninvadability can be determined from it. Moreover, it can be used in all the usual local calculations like the determination of evolutionarily singular trait vectors and their local invadability and attractivity. We conclude with three extended case studies demonstrating the usefulness of Q: the calculation of ESSs under haplo-diploid genetics (I), of evolutionarily steady genetic dimorphisms (ESDs) with a priori proportionality of macro- and micro-gaetic outputs (an assumption that is generally made but the fulfillment of which is a priori highly exceptional) (II), and of ESDs without such proportionality (III). These case studies should also have some interest in their own right for the spelled out calculation recipes and their underlying modelling methodology.

Item Type: Article
Uncontrolled Keywords: Fitness; Fitness proxy; Haplo-diploid ESS; Evolutionarily steady genetic dimorphism; Evolutionarily stable genetic dimorphism; Ideal-free genetic dimorphism; Evolutionarily steady polymorphism; Evolutionarily stable polymorphism; Ideal-free polymorphism
Research Programs: Evolution and Ecology (EEP)
Bibliographic Reference: Biological Dynamics; 5(2):163-190 (2 March 2011)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 08:45
Last Modified: 25 Feb 2016 11:06
URI: http://pure.iiasa.ac.at/9626

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