The dynamics of a specific consumer-resource model for Daphnia magna is studied from
a numerical point of view. In this study, Malthusian, chemostatic, and Gompertz growth laws for
the evolution of the resource population are considered, and the resulting global dynamics of the
model are compared as different parameters involved in the model change. In the case of Gompertz
growth law, a new complex dynamic is found as the carrying capacity for the resource population
increases. The numerical study is carried out with a second-order scheme that approximates the
size-dependent density function for individuals in the consumer population. The numerical method
is well adapted to the situation in which the growth rate for the consumer individuals is allowed to
change the sign and, therefore, individuals in the consumer population can shrink in size as time
evolves. The numerical simulations confirm that the shortage of the resource has, as a biological
consequence, the effective shrink in size of individuals of the consumer population. Moreover, the
choice of the growth law for the resource population can be selected by how the dynamics of the
populations match with the qualitative behaviour of the data.
