Evolution of age-dependent sex-reversal under adaptive dynamics.
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.
Calsina
Angel
A
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain. acalsina@mat.uab.es
Ripoll
Jordi
J
D000367:Age Factors; D000818:Animals; D049628:Body Size; D005260:Female; D005838:Genotype; D057850:Hermaphroditic Organisms; D008297:Male; D008954:Models, Biological; D008957:Models, Genetic; D009154:Mutation; D011336:Probability; D019849:Sex Determination Processes / Q000628:therapy*