Adaptive dynamics of a stage structure model for sacoglossan sea slugs with larval type dimorphism

Larval type dimorphism, a special strategy utilized by some marine invertebrates to reproduce, has been commonly recognized in a clade of herbivorous sea slugs, the Sacoglossa. To make clear the underlying evolution mechanism and inherent laws of reproductive strategy in these marine invertebrates, in this paper, we propose and investigate a stage structure model describing the larval type dimorphism for sacoglossan sea slugs. We first perform a global analysis of the model when sea slugs have a mixed reproductive strategy. It is shown that the model’s dynamics is completely determined by the ecological reproductive index of sea slugs R0: When R0>1, both the two type larvas can coexist with the adults; while when R0≤1, the total sea slug species will go extinct. Then taking the adults’ benthic offspring reproduction rate q as a trait, we proceed to investigate the adaptive evolution of sea slugs’ reproductive strategy. Our theoretical and numerical results indicate that a mixed reproductive strategy could evolve to a simple one under certain circumstances, and vice versa, and the coexistence of two different mixed reproductive strategies is impossible. In addition, we also consider the impacts of environmental fluctuations on the dynamics of sea slug population, finding that environmental noises potentially affect the diversity of sea slug species. Our results partially explain the mystery in marine evolutionary ecology regarding why so few invertebrates exhibit reproductive dimorphisms resulting in alternative larval types.