Developing realistic models for stressed ecosystems
Project Description and Objective:
Many ecosystems are “stressed” when external perturbations such as pollution, land clearing and sudden shocks to the environment arise. However, most current models that are used by ecologists do not take the changing environment into consideration. Recent models developed by our group directly couple the dynamics of one or two species with their environments. This is achieved by treating the carrying capacity, a proxy for the state of the environment, as a state variable in the governing equations of the model. Thereby, any changes to the environment can be naturally reflected in the survival, movement and competition of the species within the ecosystem.
In the case of two competing species (such as the classical predator-prey models) with variable carrying capacity, we have shown from our earlier work that the dynamics can be different. Here, the ultimate state for the ecosystem depends on the developmental rate of the environment (for instance rehabilitation of the environment). For a range of values below some threshold, persistence of both species which are in equilibrium with its environment can occur. However, beyond this threshold, the prey always dies out. This has immediate consequences relating to conservation that may need to be addressed. In other words, it may be necessary.
Our current models, however, do not adequately represent realistic ecosystems. The species have a single age-structure and both the species and environment change instantaneously to external perturbations and stressors.
In reality, the feedback about the state of the environment (available resources) reaches with a delay due to various factors such as generation and maturation periods, differential resource consumption with respect to age-structure, hunger threshold levels, migration and diffusion of populations, markedly differing birth rates in interaction species and delays in behavioural responses to a changing environment.
Realistic models must account for these disparate sources of feedback by incorporating (multiple) time delays. In other contexts, it is known that delays can cause instability in the system giving rise to oscillatory or even chaotic dynamics.
We will employ a combination of analytic and numerical methods to investigate the dynamics of an ecosystem with time delays. Of particular importance is to establish critical values for the onset of instabilities which often signals changes in the dynamics of the ecosystem. This can lead to a better understand of the long term survivability of a particular species whose environment is stressed.