ABSTRACT
In this work we present a mathematical model describing the dynamics of a population where sex allocation remains flexible throughout adult life and so can be adjusted to current environmental conditions. We consider that the fractions of immature individuals acquiring male and female sexual roles are density dependent through nonlinear functions of a weighted total population size. The main goal of this work is to understand the role of life-history parameters on the stabilization or destabilization of the population dynamics. The model turns out to be a nonlinear discrete model which is analysed by studying the existence of fixed points as well as their stability conditions in terms of model parameters. The existence of more complex asymptotic behaviours of system solutions is shown by means of numerical simulations. Females have larger fertility rate than males. On the other hand, increasing population density favours immature individuals adopting the male role. A positive equilibrium of the system exists whenever fertility and survival rates of one of the sexual roles, if shared by all adults, allow population growing while the opposite happens with the other sexual role. In terms of the female inherent net reproductive number, eta(F), it is shown that the positive equilibria are stable when eta(F) is larger and closed to 1 while for larger values of eta(F) a certain asymptotic assumption on the investment rate in the female function implies that the population density is permanent. Depending on the other parameters values, the asymptotic behaviour of solutions becomes more complex, even chaotic. In this setting the stabilization/destabilization effects of the abruptness rate in density dependence, of the survival rates and of the competition coefficients are analysed.
Subject(s)
Population Dynamics , Sex Factors , Animals , Behavior, Animal , Birth Rate , Disorders of Sex Development , Environment , Female , Male , Models, Biological , Models, Theoretical , Population Density , Sexual Behavior, AnimalABSTRACT
Larvae susceptibility to chlorpyrifos is studied on four Tunisian Anopheles larvas samples: Anopheles labranchiae from Rades (South of Tunis) and Menchar (region of Beja), in the North of Tunisia, A. sergentii from Meknassy and A. multicolor from Sidi Bouzid, both in the Centre of Tunisia. The test results of larvae susceplibility indicate that the LC50 and the LC95 values are less than 0.002 and 0.02 mg l-1 respectively and their 95% confidence limits overlap. We also notice that the studied samples show the same susceptibility to chlorpyrifos. The results can be used as a base data further studies on the susceptibility of Anopheles to chemical insecticides.
