Accounting for temperature-dependent sex determination in<br/><br/>crocodilians using delay differential equations

Friday, April 3, 2009 - 2:30pm - 3:00pm
EE/CS 3-180
Angela Gallegos (Occidental College)
The crocodilia have multiple interesting characteristics that
affect their population dynamics. They are among several
reptile species which exhibit temperature-dependent sex
determination (TSD) in which the temperature of egg
incubation determines the sex of the hatchlings. Their life
parameters, specifically birth and death rates, exhibit
strong age-dependence. We develop delay-differential equation
(DDE) models describing the evolution of a crocodilian
population. In using the delay formulation, we are able to
account for both the TSD and the age-dependence of the life
parameters while maintaining some analytical tractability. In
our single-delay model we also find an equilibrium point and
prove its local asymptotic stability. We numerically solve
the different models and investigate the effects of multiple
delays on the age structure of the population as well as the
sex ratio of the population. For all models we obtain very
strong agreement with the age structure of crocodilian
population data as reported in Smith and Webb (Aust. Wild.
Res. 12, 541–554, 1985). We also obtain reasonable values for
the sex ratio of the simulated population. This is joint
work with Tenecia Plummer, David Uminsky, Cinthia Vega, Clare
Wickman and Michael Zawoiski.
MSC Code: