Pattern formation in a predator-prey model with nutrient enrichment

Program Code: 
1881
Contact: 

Dr Isaac Towers (i.towers@adfa.edu.au)

Description of Work: 

Project Description and Objective:

Ecological systems are characterised by the interaction between species and their natural environment. Such interaction may occur over a wide range of spatial and temporal scales.

Predator-prey dynamics change when the environment is no longer constant but changes with the presence of a biotic or an abiotic resource. The effect of the resource is accounted for by including an addition rate equation to the predator-prey model. In this project the carrying capacity of both the predator and prey are assumed to depend on the resource density. In this way we can model the effect of environmental enrichment on the stability of the predator and prey populations. This leads to the so called ratio-depend models. The ratio-dependent predator-prey models are known to exhibit very rich temporal dynamics.

On the other hand, we live in a spatial world, and spatial patterns are ubiquitous in nature, these patterns modify the temporal dynamics and stability properties of population densities at a range of spatial scales, their effects must be incorporated in temporal ecological models that do not represent space explicitly.

Pattern formation in nonlinear complex systems is one of the central problems of the natural, social, and technological sciences. Spatial patterns and aggregated population distributions are common in nature and in a variety of spatiotemporal models with local ecological interactions.

We investigate the emergence of a ratio-dependent predator-prey system with resource enrichment and reaction-diffusion. We seek to understand the effect of nutrient enrichment on the process of pattern formation. Specifically,:

  • understand the combined effects of enrichment and of diffusion on pattern formation,
  • investigate how enrichment changes the symmetry-breaking bifurcations that lead to spatiotemporal patterns and their stability.
  • determine if stationary patterns are sensitive to the initial conditions,
  • establish the role enrichment plays on spatially chaotic patterns.

Although this project is theoretical in nature, it may however be applicable to an aquatic community in a real marine environment.