Population dynamics of Müllerian mimicry under interspecific competition

Abstract

We ask what the effects of mutualism on population dynamics of two competitive species are. We model the population dynamics of mutualistic interactions with positive density and frequency dependences. We specifically assume the dynamics of Müllerian mimicry in butterflies, where the mortality of both species is reduced depending on the relative frequency of the other species. We assume that the two species are under Lotka-Volterra density-dependent competition. The equilibria are compared with the cases of competition alone. Unlike the traditional model of positive density dependence, population explosion does not appear in the current dynamics, but the new equilibrium is simply achieved. It is because the effects of positive density or frequency dependence are restricted to parts of mortality. Both positive density and frequency dependences do promote coexistence of the mimetic species. However, the two models show a distinctive difference for coexistence. The effects of positive density dependence are rather limited. In contrast, positive frequency dependence always promotes coexistence, irrespective of environmental conditions. The results may imply that the evolutionary origin of Müllerian mimicry may depend on frequency dependence (and density dependence), but that its current population dynamics may depend solely on density dependence. The role of frequency and density dependences on evolutionary dynamics is an open question.

Heterogeneity in predator micro-habitat use and the maintenance of Müllerian mimetic diversity

“…Thus, including competition would not necessarily alter the general patterns presented in this paper. Theoretical research has explored the population dynamics of mutualistic interactions, such as those which occur among comimics, and competitive interactions (Gross, 2008;Kumazawa et al, 2009). These theoretical studies show that community-level species diversity and equilibrium population size are increased by mutualistic interactions.…”

Why aren't warning signals everywhere? On the prevalence of aposematism and mimicry in communities

“…It seems logical to postulate that the number of distinct aposematic signals would have an upper limit determined by environmental context, organismal constraints, and the sensory ecology of the relevant predators, and that this would then impose constraints on the diversity of Batesian mimics. Batesian mimics may also at times be limited by exploitative competition with their models (Kumazawa et al, 2006), particularly if environmentally derived metabolites that are limited in supply (such as brightly coloured carotenoids) are required for the production of warning signals used by both models and mimics (Pfennig & Kikuchi, 2012). There is a dearth of information on competitive relationships between model species and their Batesian mimics.…”

“…It would be very useful to explore how much fine-scale overlap in space and time there is between models and Batesian mimics, since this could govern the likelihood of competitive interactions between them. Müllerian mimicry may also be affected by competition (Kumazawa et al, 2009). Aubier & Elias (2020) predict that either microhabitat or resource-use divergence is required for Müllerian mimics to coexist.…”

Predator discrimination of prey promotes the predator-mediated coexistence of prey species

“…However, a theoretical investigation of the effect of predator discrimination on the coexistence of prey species is insufficient. In previous theoretical studies, mathematical models of mimicry considered the potential inability of predator species to identify their prey species by assuming perfect [21,23,24] or imperfect [22,25,26] mimicry. Given that prey species have multiple traits [27] and that predator species recognize prey items by various cues [16][17][18][19], it is possible that in an actual community, there may be diversity in how predators distinguish prey items.…”