Investigating a Competitive Two Species System that Produces Oscillations

Abstract

The interactions between two species can have great influences on the ecosystem scale. A mathematical model, based on the model by Gilad et al. (2007) for water limited systems, represents a two species system with a tradeoff between the species. One species is an ecosystem engineer and is responsible for the increased infiltration. The other species is dependent on the first for its water but has, according to the tradeoff, a better resource uptake strategy. The tradeoff leads to oscillatory behavior under the right conditions. This oscillatory behavior can be interpreted as cyclic succession, the initial step of the “Biodiversity Cycling Hypothesis” (BCH) (Shachak et al. 2009). According to this hypothesis the ecosystem engineer is termed the Landscape Modulator Species (LMS) and the second species the Modulator Dependent Species (MDS). The model outcome is compared to fieldwork for the purpose of a field example and validation. The fieldwork compares the species A. serratuloides and N. mucronata to the LMS and MDS respectively, in accordance to modulation effect and resource uptake ability. The results are used to conclude the effects of cycling on hysteresis. These influences cannot be drawn from the results due to the occurrence of chaotic behavior. The extent of hysteresis is severely dependent on the initial conditions of the simulation.