Evolution of age-dependent sex-reversal under adaptive dynamics

Àngel Calsina, Jordi Ripoll

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5 Citations (Scopus)

Abstract

We investigate the evolution of the age (or size) at sex-reversal in a model of sequential hermaphroditism, by means of the function-valued adaptive dynamics. The trait is the probability law of the age at sex-reversal considered as a random variable. Our analysis starts with the ecological model which was first introduced and analyzed by Calsina and Ripoll (Math Biosci 208(2), 393-418, 2007). The structure of the population is extended to a genotype class and a new model for an invading/mutant population is introduced. The invasion fitness functional is derived from the ecological setting, and it turns out to be controlled by a formula of Shaw-Mohler type. The problem of finding evolutionarily stable strategies is solved by means of infinite-dimensional linear optimization. We have found that these strategies correspond to sex-reversal at a single particular age (or size) even if the set of feasible strategies is considerably broader and allows for a probabilistic sex-reversal. Several examples, including in addition the population-dynamical stability, are illustrated. For a special case, we can show that an unbeatable size at sex-reversal must be larger than 69.3% of the expected size at death. © Springer-Verlag 2009.
Original languageEnglish
Pages (from-to)161-188
JournalJournal of Mathematical Biology
Volume60
DOIs
Publication statusPublished - 1 Sep 2010

Keywords

  • Evolutionarily stable strategies (ESS)
  • Function-valued traits
  • Gender-structured population models
  • Sequential hermaphroditism
  • Sex-ratio

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