Modeling the effect of growth rate and survivability trade-offs on species coexistence and spatial topology at a traveling invasive wave-front

Abstract

The introduction and spread of non-native species is now recognized as one of the most significant threats to natural ecosystems world-wide. Land degradation due to such invasion has been responsible for the displacement of native species and for the destruction of the quality of wildlife habitats. The success or failure of such invasion depends upon a number of factors, perhaps two of the most important being the relative growth rates of the invasive and native species and their different ability to survive the competition for limited resources. For an invasive species with greater fecundity and rate-of-growth than the native species, all other things being equal, the invasive species will ultimately prevail driving the native species to extinction. If, on the other hand, the native species is characterized by greater survivability within habitats with limited resources, all other things being equal, the invasive species will not be able to penetrate the native habitat and will be driven to extinction where there may have been initial coexistence. The intermediate situation is therefore of interest where the difference or trade-off between growth and survival is not that extreme and the details of which may lead to either extinction or coexistence. To investigate the effect of such trade-off at an invasive wave-front, a cellular "ceiling model" of population growth below a fixed carrying capacity has examined the diffusive invasion of a native habitat. This is accomplished by modifying the "ceiling model" of population growth and limitation, to mirror differences in species survivability by a simple zero-sum partitioning of the demographic fixed carrying capacity. Calculations are performed for a single deme and for a 200 × 200 cellular grid of demes. For the cellular grid, the relative values of such trade-off are shown to yield either regions of species coexistence or extinction and this effect on the topological features of the wave-front is illustrated. This new model, motivated by paradigmatic considerations and consequently idealistic, addresses formal issues and may be considered a template for future investigations motivated by more pragmatic considerations. © 2006 Elsevier B.V. All rights reserved.