A population dynamic model of Batesian mimicry

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 mimic Papilio polytes) in the Ryukyu Islands, Japan.     

A mathematical model of population dynamics for Batesian mimicry system

We analyse a mathematical model of the population dynamics among a mimic, a corresponding model, and their common predator populations. Predator changes its search-and-attack probability by forming and losing its search image. It cannot distinguish the mimic from the model. Once a predator eats a model individual, it comes to omit both the model and the mimic species from its diet menu. If a predator eats a mimic individual, it comes to increase the search-and-attack probability for both model and mimic. The predator may lose the repulsive/attractive search image with a probability per day. By analysing our model, we can derive the mathematical condition for the persistence of model and mimic populations, and then get the result that the condition for the persistence of model population does not depend on the mimic population size, while the condition for the persistence of mimic population does depend the predator's memory of search image.     

A mathematical model of population dynamics for Batesian mimicry system

We analyse a mathematical model of the population dynamics among a mimic, a corresponding model, and their common predator populations. Predator changes its search-and-attack probability by forming and losing its search image. It cannot distinguish the mimic from the model. Once a predator eats a model individual, it comes to omit both the model and the mimic species from its diet menu. If a predator eats a mimic individual, it comes to increase the search-and-attack probability for both model and mimic. The predator may lose the repulsive/attractive search image with a probability per day. By analysing our model, we can derive the mathematical condition for the persistence of model and mimic populations, and then get the result that the condition for the persistence of model population does not depend on the mimic population size, while the condition for the persistence of mimic population does depend the predator's memory of search image.     

Batesian mimics influence mimicry ring evolution

Mathematical models of mimicry typically involve artificial prey species with fixed colorations or appearances; this enables a comparison of predation rates to demonstrate the level of protection a mimic might be afforded. Fruitful theoretical results have been produced using this method, but it is also useful to examine the possible evolutionary consequences of mimicry. To that end, we present individual-based evolutionary simulation models where prey colorations are free to evolve. We use the models to examine the effect of Batesian mimics on Müllerian mimics and mimicry rings. Results show that Batesian mimics can potentially incite Müllerian mimicry relationships and encourage mimicry ring convergence.     

Plant defence signals and Batesian mimicry

In a game theory context, we investigated conditions for an evolutionarily stable equilibrium of defended, signalling plants, and plants mimicking these signals – that is, conditions for a stable mimicry complex. We modelled this in three steps. First, we analysed conditions for selection for defended, signalling plants, in a population of undefended plants. Second, we analysed conditions for when mimicking plants can invade a population of defended, signalling plants, leading to a stable equilibrium between the two strategies. Third, we analysed how sampling of signalling plants by herbivores affects the equilibrium between the strategies. The predictions show that mimicry of plant defence signals may be common, and even imperfect mimics could invade a population of defended, signalling plants. Whether the latter prediction holds or not depends on how herbivores generalize over signals, and on the length of their avoidance sequence'. The length of the avoidance sequence is the number of signalling plants that a herbivore avoids to attack, after attacking a defended plant. If herbivores always sample signalling plants, then mimicry cannot evolve, whereas if herbivores have a long avoidance sequence, this may allow selection even for imperfect mimics.     

Optimal-foraging predator favors commensalistic Batesian mimicry

Background

Mimicry, in which one prey species (the Mimic) imitates the aposematic signals of another prey (the Model) to deceive their predators, has attracted the general interest of evolutionary biologists. Predator psychology, especially how the predator learns and forgets, has recently been recognized as an important factor in a predator–prey system. This idea is supported by both theoretical and experimental evidence, but is also the source of a good deal of controversy because of its novel prediction that in a Model/Mimic relationship even a moderately unpalatable Mimic increases the risk of the Model (quasi-Batesian mimicry).

Methodology/Principal Findings

We developed a psychology-based Monte Carlo model simulation of mimicry that incorporates a “Pavlovian” predator that practices an optimal foraging strategy, and examined how various ecological and psychological factors affect the relationships between a Model prey species and its Mimic. The behavior of the predator in our model is consistent with that reported by experimental studies, but our simulation''s predictions differed markedly from those of previous models of mimicry because a more abundant Mimic did not increase the predation risk of the Model when alternative prey were abundant. Moreover, a quasi-Batesian relationship emerges only when no or very few alternative prey items were available. Therefore, the availability of alternative prey rather than the precise method of predator learning critically determines the relationship between Model and Mimic. Moreover, the predation risk to the Model and Mimic is determined by the absolute density of the Model rather than by its density relative to that of the Mimic.

Conclusions/Significance

Although these predictions are counterintuitive, they can explain various kinds of data that have been offered in support of competitive theories. Our model results suggest that to understand mimicry in nature it is important to consider the likely presence of alternative prey and the possibility that predation pressure is not constant.     

Batesian mimicry and signal detection theory

Signal Detection Theory can be used to provide a mathematical model describing the choice of a predator trying to distinguish between a model and a Batesian mimic. The mathematical model yields a number of a deductions, in particular that it may or may not assist the mimic population if mimics more closely resemble their models. The assumptions underlying the analysis are discussed in some detail.     

Evolution of dominance in polymorphic Batesian mimicry

Models of two simple genetic systems of two alleles segregating at two loci are used to study the evolution of dominance of a Batesian mimic maintained in a population by frequency-dependent selection. The alleles at one locus determine the mimetic patterns, and their dominance is modified by the alleles at the other locus. In the model, the modifiers of dominance may themselves be either fully dominant or have additive effects on the dominance of the mimics. When the modifier is fully dominant in its effect on the dominance of a new mimic, the mimic will evolve dominance irrespective of the initial frequency of the modifier. When the modifiers act additively on the dominance of the mimics, a new mimic will evolve either dominance or recessiveness depending on the initial frequency of the modifiers. Unless the modifier is initially at quite a high frequency dominance will not evolve. And dominance will not evolve fully unless the modifiers are more or less selectively neutral in their effects on all other characters except the mimicry. The significance of these results is discussed with reference to the different dominance relations of the mimics in different races of the butterfly Papilio dardanus.     

How spiders practice aggressive and Batesian mimicry

To understand communication,the interests of the sender and the receiver/s of signals should be considered separately.When our goal is to understand the adaptive significance of specific responses to specific signals by the receiver,questions about signal information are useful.However,when our goal is to understand the adaptive significance to the sender of generating a signal,it may be better to envisage the receiver's response to signals as part of the sender's extended phenotype.By making signals,a sender interfaces with the receiver's model of the world and indirectly manipulates its behaviour.This is especially clear in cases of mimicry,where animals use deceptive signals that indirectly manipulate the behaviour of receivers.Many animals adopt Batesian mimicry to deceive their predators,or aggressive mimicry to deceive their prey.We review examples from the literature on spiders to illustrate how these phenomena,traditionally thought of as distinct,can become entangled in a web of lies.     

Newly emerged Batesian mimicry protects only unfamiliar prey

The evolution of Batesian mimicry was tested experimentally using avian predators. We investigated the effect of a search image on the protection effectiveness of a newly emerged Batesian mimic. The two groups of predators (adult great tits, Parus major) differed in prior experience with prey from which the mimic evolved. The Guyana spotted roach (Blaptica dubia) was used as a palatable prey from which the mimic emerged, and red firebug (Pyrrhocoris apterus) was used as a model. Optical signalization of the insect prey was modified by a paper sticker placed on its back. The cockroaches with the firebug pattern sticker were significantly better protected against tits with no prior experience with cockroaches. The protection of the firebug sticker was equally effective on cockroaches as it was on firebugs. The cockroaches with firebug stickers were not protected against attacks of tits, which were familiar with unmodified cockroaches better than cockroaches with a cockroach sticker. We suppose that pre-trained tits acquired the search image of a cockroach, which helped them to reveal the “fake” Batesian mimic. Such a constraint of Batesian mimicry effectiveness could substantially decrease the probability of evolution of pure Batesian mimic systems.     

Aggressive use of Batesian mimicry by an ant-like jumping spider

Batesian and aggressive mimicry are united by deceit: Batesian mimics deceive predators and aggressive mimics deceive prey. This distinction is blurred by Myrmarachne melanotarsa, an ant-like jumping spider (Salticidae). Besides often preying on salticids, ants are well defended against most salticids that might target them as potential prey. Earlier studies have shown that salticids identify ants by their distinctive appearance and avoid them. They also avoid ant-like salticids from the genus Myrmarachne. Myrmarachne melanotarsa is an unusual species from this genus because it typically preys on the eggs and juveniles of ant-averse salticid species. The hypothesis considered here is that, for M. melanotarsa, the distinction between Batesian and aggressive mimicry is blurred. We tested this by placing female Menemerus sp. and their associated hatchling within visual range of M. melanotarsa, its model, and various non-ant-like arthropods. Menemerus is an ant-averse salticid species. When seeing ants or ant mimics, Menemerus females abandoned their broods more frequently than when seeing non-ant-like arthropods or in control tests (no arthropods visible), as predicted by our hypothesis that resembling ants functions as a predatory ploy.     

Models of the population genetics of transposable elements

Although transposable elements (TEs) have been found in all organisms in which they have been looked for, the ways in which they invade genomes and populations are still a matter of debate. By extending the classical models of population genetics, several approaches have been developed to account for the dynamics of TEs, especially in Drosophila melanogaster . While the formalism of these models is based on simplifications, they enable us to understand better how TEs invade genomes, as a result of multiple evolutionary forces including duplication, deletion, self-regulation, natural selection and genetic drift. The aim of this paper is to review the assumptions and the predictions of these different models by highlighting the importance of the specific characteristics of both the TEs and the hosts, and the host/TE relationships. Then, perspectives in this domain will be discussed.     

Comparative population genetics of a mimicry locus among hybridizing Heliconius butterfly species

The comimetic Heliconius butterfly species pair, H. erato and H. melpomene, appear to use a conserved Mendelian switch locus to generate their matching red wing patterns. Here we investigate whether H. cydno and H. pachinus, species closely related to H. melpomene, use this same switch locus to generate their highly divergent red and brown color pattern elements. Using an F2 intercross between H. cydno and H. pachinus, we first map the genomic positions of two novel red/brown wing pattern elements; the G locus, which controls the presence of red vs brown at the base of the ventral wings, and the Br locus, which controls the presence vs absence of a brown oval pattern on the ventral hind wing. The results reveal that the G locus is tightly linked to markers in the genomic interval that controls red wing pattern elements of H. erato and H. melpomene. Br is on the same linkage group but approximately 26 cM away. Next, we analyze fine-scale patterns of genetic differentiation and linkage disequilibrium throughout the G locus candidate interval in H. cydno, H. pachinus and H. melpomene, and find evidence for elevated differentiation between H. cydno and H. pachinus, but no localized signature of association. Overall, these results indicate that the G locus maps to the same interval as the locus controlling red patterning in H. melpomene and H. erato. This, in turn, suggests that the genes controlling red pattern elements may be homologous across Heliconius, supporting the hypothesis that Heliconius butterflies use a limited suite of conserved genetic switch loci to generate both convergent and divergent wing patterns.     

Behavioural mimicry in flight path of Batesian intraspecific polymorphic butterfly Papilio polytes

Batesian mimics that show similar coloration to unpalatable models gain a fitness advantage of reduced predation. Beyond physical similarity, mimics often exhibit behaviour similar to their models, further enhancing their protection against predation by mimicking not only the model''s physical appearance but also activity. In butterflies, there is a strong correlation between palatability and flight velocity, but there is only weak correlation between palatability and flight path. Little is known about how Batesian mimics fly. Here, we explored the flight behaviour of four butterfly species/morphs: unpalatable model Pachliopta aristolochiae, mimetic and non-mimetic females of female-limited mimic Papilio polytes, and palatable control Papilio xuthus. We demonstrated that the directional change (DC) generated by wingbeats and the standard deviation of directional change (SDDC) of mimetic females and their models were smaller than those of non-mimetic females and palatable controls. Furthermore, we found no significant difference in flight velocity among all species/morphs. By showing that DC and SDDC of mimetic females resemble those of models, we provide the first evidence for the existence of behavioural mimicry in flight path by a Batesian mimic butterfly.     

Reproduction and the energy cost of defense in a Batesian mimicry complex

Summary The amount of energy invested in reproduction and in defense was examined in a Batesian mimicry complex consisting of the modelEleodes obscura and the mimicStenomorpha marginata (both Coleoptera: Tenebrionidae). Models live up to 4 y as adults while mimic adults live only 3 mo. The energy content of the eggs of the model and mimic was determined by microbomb calorimetry. The energy content of the defensive secretions produced by the model was determined by computational chemistry and MNDO computer programming. Contrary to the predictions of some life-history theory, the long-lived model annually produces many small eggs each of low energetic content, while the short-lived mimic annually produces fewer, larger eggs each of high energetic content. However, in terms of total energy, the long-lived model has an annual investment in reproduction equal to that of the short-lived mimic. During the 3 mo of co-ocurrence of models and mimics within a year, an average individual model's cost in using defensive secretions against potential predators is 12% of the amount of energy tied up in the eggs that it produces within the year. The annual cost of defense for the model is 18% of the energy contained in the mean number of eggs produced. When the energy allocated to eggs is added to that allocated to defense, the model has an annual investiment that is greater than the annual investment in reproduction by the mimic. Although the energy invested in defense by the model is small relative to the energy invested in egg production, it buys the model considerable protection from predation. Nevertheless, the cost of defense does not explain the deviations from the predictions of life-history theory.     

Stability and bifurcation analysis of a ratio-dependent community dynamics model on Batesian mimicry

Journal of Mathematical Biology - Batesian mimicry is the similarity of coloration and patterns in an unpalatable species (the “model-species”) and a palatable species (the...