Biological Conditions for Oscillations and Chaos Generated by Multispecies Competition

Abstract

Abstract. We investigate biological mechanisms that generate oscillations and chaos in multispecies competition models. For this purpose, we use a competition model concerned with competition for abiotic essential resources. Because phytoplankton and plants consume quite a number of abiotic essential resources, the model is particularly relevant for phytoplankton communities and terrestrial vegetation. We show that the predicted dynamics depend crucially on the relationship between the resource requirements and the resource consumption characteristics of the species. More specifically, the model predicts that competition generates (1) stable coexistence if species consume most of the resources for which they have high requirements, (2) oscillations and chaos if species consume most of the resources for which they have intermediate requirements, and (3) competitive exclusion with a winner that depends on the initial conditions if species consume most of the resources for which they have low requirements. The theoretical predictions are compared with available data on resource utilization patterns of phytoplankton species.

Patterns of succession between bloom-forming cyanobacteria Aphanizomenon flos-aquae and Microcystis and related environmental factors in large, shallow Dianchi Lake, China

“…The lowest remaining biovolume of Microcystis in the water column exceeded 1.01 9 10 7 and 4.21 9 10 7 cells/l in 2011 and 2012, respectively, even though water temperature was around 9-10°C. It has also been reported that Microcystis biomass persisted in the water column during winter (5-8°C) in the shallow Czech reservoir of NovéMlýnyat, at densities of 120-200,000 cells/ml, and also in several Dutch shallow lakes (Š ejnohová & Maršálek, 2012).This scenario may provide opportunities for Microcystis to quickly recruit and dominate, and become more competitive than A. flos-aquae, which has no competitive advantages compared with Microcystis (Huisman & Weissing, 2001).…”

Leading indicators of phytoplankton transitions caused by resource competition

“…In the usual model of resourcebased competition among two groups of phytoplankton, it is not clear whether this will happen (Huisman and Weissing 2001). For example, in some cases, the dominant eigenvalue remains negative as the transition occurs (Huisman and Weissing 2001), suggesting that the behavior of the statistical indicators will be different from what has been seen in fold bifurcations. Yet species shifts due to resource competition are thought to be common in ecosystems and are arguably the simplest case of alternate stable states.…”

“…As this eigenvalue approaches 0, variance and skewness increase and the lag-1 autocorrelation and autoregression coefficients approach 1 (Carpenter and Brock 2006;Guttal and Jayaprakash 2008;van Nes and Scheffer 2007). In the usual model of resourcebased competition among two groups of phytoplankton, it is not clear whether this will happen (Huisman and Weissing 2001). For example, in some cases, the dominant eigenvalue remains negative as the transition occurs (Huisman and Weissing 2001), suggesting that the behavior of the statistical indicators will be different from what has been seen in fold bifurcations.…”

A Dynamic Model of an Estuarine Invasion by a Non-Native Seagrass

“…Interspecific competition in model populations and communities has been found to result in cycling of the competing species (Li and Smith 2003;Huisman and Weissing 2001). Some models suggest that while cycling allows coexistence between competitors (Durrett and Levin 1998;Silvertown et al 1992), the competitive relationship itself does not necessarily generate the cycling, and when it does, more than two species are required (Durrett and Levin Li and Smith 2003;Gilpin 1975).…”