Abstract
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.
Highlights
Accepted: 26 October 2021Population dynamics is a very active field with different disciplines in which a variety of theoretical studies and different numerical approaches arise
The purpose of this work is to analyse, from a numerical point of view, some aspects of the dynamics of a problem that describes the evolution of a Daphnia magna population, as an example of a consumer-resource model
Through the study of a specific consumerresource model for the dynamics of the Daphnia magna, we cope with the numerical difficulties due to an undefined sign growth law for the individual consumers
Summary
Population dynamics is a very active field with different disciplines (epidemiology, ecology, etc.) in which a variety of theoretical studies and different numerical approaches arise. He described the population as a distributional solution of a classical partial differential equation formulation and explained heuristically why the well-posedness was a problem and to what extent it could be solved He included a dynamical environment in which individuals fed and that evolved with a general growth law in absence of a consumer. Suitable numerical methods were proposed to approximate the solution of the problem and were used to study its dynamics by means of a long-time integration These studies concerned different cases that included an unbounded consumer population [1,2,3,19]. The numerical experimentation is developed with an efficient numerical scheme, which is completely described in Appendix A to make the paper self-contained
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