Evol Ecol Res 8: 591-604 (2006)     Full PDF if your library subscribes.

Population dynamics of Batesian mimicry under interspecific competition

Fuga Kumazawa,1,2 Takahiro Asami,2* Tarou Hayashi1 and Jin Yoshimura1,3,4

1Department of Systems Engineering, Shizuoka University, Hamamatsu 432-8561, Japan, 2Department of Biology, Shinshu University, Matsumoto 390-8621, Japan, 3Marine Biosystems Research Centre, Chiba University, Kamogawa 299-5502, Japan and  4Department of Environmental and Forest Biology, State University of New York, College of Environmental Science and Forestry, Syracuse, NY 13210, USA

Author to whom all correspondence should be addressed.
e-mail: asami99@shinshu-u.ac.jp

ABSTRACT

Question: What is the basic feature of population dynamics of Batesian mimicry under interspecific competition?

Mathematical method: We built the population dynamics equation of Batesian mimicry under Lotka-Volterra competition. By means of the phase plane analysis, we examine the dynamics and equilibria in comparison with the four unique phase planes of the Lotka-Volterra competition model with no mimicry.

Key assumptions: Both the benefit of mimicry for a palatable species mimicking a distasteful model species and the cost for the model are dependent on their frequencies relative to each other. The mortality of the model by predation increases as the frequency of the mimic increases, while the mortality of the mimic decreases as the frequency of the model increases.

Predictions: The mimetic species in general benefits from mimicry depending on the adult predatory mortality. The assemblage of the model and mimetic species reaches different equilibria depending on whether the benefit of the mimic or the cost of the model increases under interspecific competition. The most complicated phase plane appears between stable co-existence of the assemblage and survival of the mimetic species only, depending on the initial conditions.

Conclusion: The benefit of the mimic and the cost of the model are key factors in determining the evolutionary process of Batesian mimicry.

Keywords: Batesian mimicry, frequency dependence, Lotka-Volterra competition, predation.