Summary
A population dynamic model of Batesian mimicry, in which populations of both model and mimetic species were considered, was analyzed. The probability of a predator catching prey on each encouter was assumed to depend on the frequency of the mimic. The change in population size of each species was considered to have two components, growth at the intrinsic growth rate and carrying capacity, and reduction by predation. For simplicity in the analyses, three assumptions were made concerning the carrying capacities of each population: (1) with no density effects on the mimic population growth rate; (2) with no density effects on the model species; and (3) with density effects on both species. The first and second cases were solved analytically, whereas the last was, for the most part, investigated numerically. Under assumption (1), two stable equilibria are possible, in which both species either coexist or go to extinction. Under assumption (2), there are also two stable equilibria possible, in which either only the mimic persists or both go to extinction. These results explain the field records of butterflies (Pachliopta aristolochiae and its mimicPapilio polytes) in the Ryukyu Islands, Japan.
Similar content being viewed by others
References
Brower, J. V. Z. (1960) Experimental studies of mimicry. IV. The reactions of starlings to different proportions of models and mimics.Am. Nat. 94: 271–282.
Charlesworth, D. and B. Charlesworth (1975a) Theoretical genetics of Batesian mimicry I. Single-locus models.J. theor. Biol. 55: 283–303.
Charlesworth, D. and B. Charlesworth (1975b) Theoretical genetics of Batesian, mimicry. II. Evolution of supergenes.J. theor. Biol. 55: 305–324.
Charlesworth, D. and B. Charlesworth (1975c) Theoretical genetics of Batesian mimicry. III. Evolution of dominance.J. theor. Biol. 55: 327–377.
Emlen, J. M. (1968) Batesian mimicry: A preliminary theoretical investigation of quantitative aspects.Am. Nat. 102: 235–241.
Holling, C. S. (1965) The functional response of predators to prey density and its role in mimicry and population regulation.Mem. Entomol. Soc. Can. 45: 1–60.
Huheey, J. E. (1964) Studies of warning coloration and mimicry. IV. A mathematical model of model-mimic frequecies.Ecology 45: 185–188.
Huheey, J. E. (1988) Mathematical models of mimicry.Am. Nat. 131: s22-s41.
Oaten, A., C. E. M. Pearce and M. E. B. Smyth (1975) Batesian mimicry and signal detection theory.Bull. Math. biol. 37: 367–387.
Turner, J. R. G. (1983) Mimicry: The palatability spectrum and its consequences. 141–161. In R. I. Vane-Wright and P. R. Ackery (ed.)The biology of butterflies. Academic Press, London.
Turner, J. R. G., E. P. Kearney and L. S. Exton (1984) Mimicry and the Monte Carlo predator: the palatability spectrum and the origins of mimicry.Biol. J. Linn. Soci. 23: 247–268.
Uesugi, K. (1991) Temporal change in records of the mimetic butterflyPapilio polytes with establishment of its modelPachliopta aristochiae in the Ryukyu Island.Jpn. J. Ent. 59: 183–198.
Uesugi, K. (1992) Polymorphism and mimicry inPapilio polytes.Insectarium,27(6): 168–174. (In Japanese)
Wickler, W. (1968)Mimicry in plants and animals. George Weidenfeld and Nicolson Ltd., London.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yamauchi, A. A population dynamic model of Batesian mimicry. Res Popul Ecol 35, 295–315 (1993). https://doi.org/10.1007/BF02513602
Issue Date:
DOI: https://doi.org/10.1007/BF02513602