The chapter presents history of modeling in ecology briefly. Starting from
initial efforts of A. J. Lotka and Vito Volterra, it discusses all the models of well–mixed
type which are represented by difference or differential equations. Merits and demerits
of every model is presented. Well–mixed mathematical models (WMMs) described by
coupled ordinary differential equation represent ecosystems which are realized in
“micro-cosm” experiments. A mathematical theory of ecological chaos is presented
which makes testable predictions. Theory is based on mathematical models of
ecological communities described by ordinary differential equations. It is shown that
deterministic chaos exists in narrow parameter ranges. Non-linear dynamics
(oscillations and chaos) favor species coexistence. It was demonstrated that population
dynamics of species competing for abiotic resources could display oscillations and
chaos. The model, that these investigators used, belong to a new class of models called
resource competition models which link the population dynamics of competing species
with the dynamics of the resources that these species are competing for. An attractive
feature of these models is that they use biological traits of species to predict the
dynamics of competition.
Keywords: Ecosystems, Dynamical systems theory, Discrete–time dynamical
systems, Nicholson–bailey model, Continuous–time dynamical systems,
Stochastic dynamical systems, Ecological chaos, Multi–species competition,
Resource competition models, Maintenance of biodiversity, Paradox of the
plankton, Janzen–connell hypothesis, Food chain, Food web, Upadhyay–rai
model, Upadhyay–rai class of models, Simulation experiments, Edge of chaos,
Weak trophic interactions, Oscillatory dynamics.
