Evol Ecol Res 11: 1141-1168 (2009)     Full PDF if your library subscribes.

A genotype-distinguishing model of senescence

Harry D. Saunders

Decision Processes Incorporated, Danville, California, USA

Correspondence: Harry D. Saunders, Managing Director, Decision Processes Incorporated, 2308 Saddleback Drive, Danville, CA 94506-3118, USA.
e-mail: hsaunders@decisionprocessesinc.com


Questions: How does one include genotypic variation in density-independent matrix models and what are the implications of such variation in the context of standard theories of senescence?

Mathematical methods: An extension of standard matrix methods and the application of dynamic systems theory.

Key assumptions: Populations consist of distinct genotypes that express different trade-offs between intrinsic lifespan and fecundity. Reproduction is asexual; alternatively, accounting considers only females. Genotypes do not always breed true: breeding fidelity and accuracy are both imperfect; each genotype can generate offspring of differing genotype according to a normal probability distribution.

Conclusions: Allowing genotypic variation in lifespan/fecundity trade-offs generates predictions conforming to standard theory, including population fecundity trends with age, population mortality trends with age, Williams’ Hypothesis, the evolution of semelparity and iteroparity, and differential survival for individuals removed from the influence of an extrinsic death rate. The Euler-Lotka equation and expressions deriving from it generalize to the genotype-distinguishing case. In a departure from conventional thinking, the analysis shows that, even in the presence of genotypes expressing an early-age fecundity advantage, populations can evolve that favour genotypes with lower fecundity whose intrinsic lifespan is longer. The analysis also hints that genotype structure is a determinant of equilibrium population size. A new metric that is laboratory-measurable – mean intrinsic lifespan – follows naturally from the methodology. This turns out to be also a metric of semelparity/iteroparity.

Keywords: dynamic systems, Euler-Lotka equation, fecundity trend, genotype variation, intrinsic lifespan, iteroparity, matrix models, mortality trend, semelparity, senescence, survival curve, Williams’ Hypothesis.

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