Hierarchical Competition Model Research Articles

Hierarchical competition models with Allee effects

We consider a two-species hierarchical competition model with a strong Allee effect. The Allee effect is assumed to be caused by predator saturation. Moreover, we assume that there is a ‘silverback’ species x that gets first choice of the resources and where growth is limited by its own intraspecific competition, while the second ‘inferior’ species y gets whatever is left. Both species x and y are assumed to have the property of strong Allee effect. In this paper we determine the impact of the presence of the Allee effect on the global dynamics of both species.

Habitat destruction and the extinction debt revisited: The Allee effect

Habitat destruction, often caused by anthropogenic disturbance, can lead to the extinction of species at an unprecedented rate. It is important, therefore, to consider habitat destruction when assessing population viability. Another factor often ignored in population viability analysis, is the Allee effect that adds to the risk of populations already on the verge of extinction. Understanding the Allee effect on species dynamics and response to habitat destruction has intrinsic value in conservation prioritization. Here, the Allee effect was considered in a multi-species hierarchical competition model. Results showed that species persistence declines dramatically due to the Allee effect, and certain species become more susceptible to habitat destruction than others. Two extinction orders emerged under habitat destruction: either the best competitor becomes extinct first or the best colonizer first. The extinction debt and order, as well as the time lag between habitat destruction and species extinction, were found to be determined by species abundance and the intensity of the Allee effect.

RETRACTED ARTICLE: Interspecific competition among ants in the boreal forest: Testing predictions from a linear hierarchical competition model

Competitive interactions often play an important role in local community structure, and particularly so in ant communities. We test predictions derived from a competition model proposed for Scandinavian ant communities by comparing ant nest densities inside and outside fifty randomly-selected territories of competitively dominant wood ants within 30 km of Umea, northern Sweden. As predicted by the model, competitively-intermediate encounter species, as well as other territorial species, showed complementary occurrences with both studied wood ants, Formica aquilonia Yarrow and F. lugubris Zett.. In contrast, complementary abundances, i.e. lower density of competitively-inferior submissive species in the presence of wood ants, as predicted by the model, was not supported for all submissive species. Of the two studied wood ant species, the nest density of submissive species was negatively correlated only with F. aquilonia. Submissives as a group, as well as Myrmica-species, showed complementary abundances with F. aquilonia, but one Leptothorax and two Serviformica species had higher nest densities in the presence of this competitively-dominant species. We propose that, for Leptothorax, these deviations from the model predictions may be because of limited niche overlap with dominant wood ants, a small worker force and a timid behaviour which does not elicit aggression in wood ants. For the two Serviformica species, we propose a combination of protection against social parasites, inter-specific social control performed by F. aquilonia, and dominance relationships between competitively-inferior submissive species as reasons for the higher nest density inside F. aquilonia territories. Monogyny, and thereby smaller nests, lower worker force, smaller territory (as shown by this study) in F. lugubris, as compared to the polygyny in F. aquilonia, may also help explain the differences in their effects on subordinate species. Our analyses indicate that the linear competition hierarchy model proposed for Scandinavian ants accurately predicts the outcome of interaction between and community composition for dominant territorial and encounter species, but that it needs refinement with respect to the relationship between territorial and submissive species and the resulting community composition. Further studies are needed, especially addressing the complex relationships between these latter groups, and the effects of different competitively-dominant wood ants, to determine the mechanisms determining the outcome of these relationships and to more accurately predict community composition.

Metapopulations, community assembly, and scale invariance in aspect space

The hierarchical competition model has been a useful tool in investigating the mechanisms of coexistence between competing species, and thus for understanding the foundations of biodiversity. Here we show that the geometric picture of community assemblage found by Nowak and May for the constant-fecundity version of this model can be extended to a whole family of tradeoffs between fecundity and mortality. In this picture, the proportion of the remaining space used by a species can be related to the amount of free space (in aspect space) behind the “competitive shadow” of the adjacent superior competitor, and in turn to the size of the competitive shadow cast by the species itself. We show that this geometric model is scale invariant in the rescaled aspect space and use this fact to investigate the limits to diversity and explore how communities assemble under this model.

Complete convergence theorem for a competition model

In this paper we consider a hierarchical competition model. Durrett and Swindle have given sufficient conditions for the existence of a nontrivial stationary distribution. Here we show that under a slightly stronger condition, the complete convergence theorem holds and hence there is a unique nontrivial stationary distribution.