Title: Mathematical and computational modeling and analysis for hermaphrodite population dynamics
Speaker: Amira Kebir, ENIT-LAMSIN, Tunis el Manar University, Tunisia
Date: Monday, September 20, 2010 12:00 - 1:00 pm
Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ
My research works deal with mathematical and computational modeling and analysis of a hermaphrodite populations. The main objective of these works is to study the implication of a density dependent sex allocation on the dynamic of these populations. Indeed, the sex-ratio of the hermaphrodite species depend on the sex-allocation function and it was proven for some species and in presence of sexual competition that this function is density dependent which lead to a complex population dynamics. Two surrounding areas of modelings were developed to study these species and to reflect their characteristics: a density deterministic approach and an Individuals Based Model approach. For the deterministic approach, two structured discreet matrix models and a structured continuous model (the formulated model is a system of non linear partial differential equations) were realized and analyzed. The analysis of these models, meet with mathematical difficulties linked to the nature of non-linearity. However, results of stability on the equilibrium state and the asymptotic behavior of the solutions, were obtained and interpreted. For individual based approach, the model allows us to take an account the variability of phenotypic (e.g. fitness) and behavioral characteristics (sexual allocation) and the interactions between individuals. This approach complements our information on the effect of sex allocation for hermaphrodite populations. By the analysis of these models we have proved the importance of sex allocation function form as well as survival parameters on the dynamics of hermaphroditic species. In fact, by the manipulation of the hermaphrodite life history parameters, we found the causes and the environmental conditions by which we can observe the stability, the explosion, the extinction or even a more complex dynamics like chaos.
Slides: Mathematical and computational modeling and
analysis for hermaphrodite population dynamics