We consider a two-competitor/one-prey model in which both competitors exhibit a general functional response and one of the competitors exhibits a density-dependent mortality rate. It is shown that the two competitors can coexist upon the single prey.As an example, we consider a two-competitor/one-prey model with a Holling II functional response. Our results demonstrate that density-dependent mortality in one of the competitors can prevent competitive exclusion. Moreover, by constructing a Liapunov function, the system has a globally stable positive equilibrium.
Two questions central to the population ecology of mutualism include:(1) what mechanisms prevent the inherent positive feedback of mutualism from leading to unbounded population growth; and (2) what mechanisms prevent instability from arising due to overexploitation. Theory and empiricism suggest that preventing such instability requires density-dependent processes. A recent theory proposes that if benefits and costs to a mutualist vary with the density of its partner, then instability can be prevented if the former species can control demographic rates and regulate (or limit) the population density of its partner. The ecological and evolutionary feasibility of this theory of interspecific population regulation has been demonstrated using quantitative models of mutualism between plants and pollinating seed-consuming insects. In these models, resource-limited fruit set and ensuing fruit abortion are mechanisms that can lead to density-dependent recruitment and population regulation of the insects. Yet, there has been little interplay between these theoretical results and empirical research. A recent study empirically examined the density-dependent effects of resourcelimited fruit set and fruit abortion in the Yucca /moth mutualism. An analysis of the study led to the conclusion that, even though fruit abortion can account for !/95% of moth mortality, it is largely a density-independent source of mortality that cannot regulate moth population density. Here, we re-analyze those empirical data and conduct further theoretical analyses to examine the nature of fruit abortion on moth recruitment. We conclude that resource-limited fruit set and fruit abortion can effectively regulate and limit moth populations, due to its densitydependent feedback on moth recruitment. Nonetheless, in any given interaction, multiple sources of mortality may contribute to the regulation and limitation of populations, and hence the stability of mutualism, including, larval competition and mortality due to locule damage in the Yucca /moth mutualism.Understanding how interspecific interactions affect the abundance and dynamics of populations is a central focus of ecology. While there is still much to learn about FORUM is intended for new ideas or new ways of interpreting existing information. It provides a chance for suggesting hypotheses and for challenging current thinking on ecological issues. A lighter prose, designed to attract readers, will be permitted. Formal research reports, albeit short, will not be accepted, and all contributions should be concise with a relatively short list of references. A summary is not required.
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