  The extinction of species is a core process that affects the diversity of
life on Earth. One way of investigating the causes and consequences of
extinctions is to build conceptual ecological models, and to use the dynamical
outcomes of such models to provide quantitative formalization of changes to
Earth's biosphere. In this paper we propose and study a conceptual resource
model that describes a simple and easily understandable mechanism for resource
competition, generalizes the well-known Huisman and Weissing model, and takes
into account species self-regulation, extinctions, and time dependence of
resources. We use analytical investigations and numerical simulations to study
the dynamics of our model under chaotic and periodic climate oscillations, and
show that the stochastic dynamics of our model exhibit strong dependence on
initial parameters. We also demonstrate that extinctions in our model are
inevitable if an ecosystem has the maximal possible biodiversity and uses the
maximal amount of resources. Our conceptual modeling provides theoretical
support for suggestions that non-linear processes were important during major
extinction events in Earth history.
