Dwarf males, large hermaphrodites and females in marine species: A dynamic optimization model of sex allocation and growth

In this study, we investigate the evolutionarily stable schedule of growth and sex allocation for marine benthic species that contain dwarf males. We consider a population in an ephemeral microhabitat that receives a constant supply of larvae. Small individuals can immediately reproduce as a dwarf male or remain immature and grow. Large individuals allocate reproductive resources between male and female functions. The fraction c of newly settled individuals who remain immature and the sex allocation of large individuals m are quantities to evolve. In the stationary ESS, if the relative reproductive success of dwarf males is greater than the survivorship of immature individuals until they reach a mature size, then the population is a mixture of females and dwarf males. If the opposite inequality holds, the population is dominated by hermaphrodites and lacks dwarf males. There is no case in which a mixture of hermaphrodites and dwarf males to be the ESS in the stationary solution. The ESS can be solved by dynamic programming when the strategies depend on the age of the microhabitat (c(t) and m(t)). Typically, the ESS schedule begins with a population composed only of hermaphrodites, which is replaced by a mixture of dwarf males and hermaphrodites and then by a mixture of dwarf males and pure females. The relative importance of these three phases depends on multiple parameters.