1,720,969 research outputs found
Is the contribution of Mathematical Models to Biology limited to supply correct predictions?
No full textAbstract: Two simple mathematical models of Population Genetics are introduced to master students in Biology. The first model shows that, in asexual populations, frequency independent selection alone cannot explain the maintenance of polymorphisms. In the second we see that, with the introduction
of sexual reproduction, natural selection may allow a stable polymorphism, at least in large populations. A necessary and sufficient condition for it, in the case of two alleles on one locus, is heterozygote advantage. The result is applied to the case of sickle-cell anemia, where a polymorphism is apparently maintained without heterozygote advantage. This example underlines how the contribution of a mathematical model to Biology is not only in supplying correct quantitative
predictions, but also in forcing to reconsider the assumptions, hence the entire view of a situation, when the predictions do not fit reality
Evolutionary stable strategies and short term selection in Mendelian populations re-visited
No full textAbstract
This note concerns a one locus, two allele, random mating diploid population, subject to frequency-dependent viability selection. It is already known that in such a population, any evolutionarily stable strategies (ESS), if only accessible by the genotype-to-phenotype mapping, is the phenotypic image of a stable genetic equilibrium (Eshel, I. 1982. Evolutionarily stable strategies and viability selection in Mendelian populations. Theor. Popul. Biol. 22(2), 204–217; Cressman et al. 1996. Evolutionary stability in strategic models of single locus frequency-dependent viability selection. J. Math. Biol. 34, 707–733). The opposite is not true. We find necessary and sufficient parametric conditions for global convergence to the ESS, but we also demonstrate conditions under which, although a unique, genetically accessible ESS exists, there is another, ‘‘non-phenotypic’’ genetically stable equilibrium
Gregarious behavior of evasive prey
No full textAbstract. Gregarious behavior of potential prey was explained by Hamilton (1971) on the basis of risk-sharing: The probability of being picked up by a predator is small when one makes part of a large aggregate of prey. This argument holds only if the predator chooses its victims at random. It is not the case for herds of evasive prey in the open, where prey’s gregarious behavior, favorable for the fast group members, makes it easier for the predator to home in on the slowest ones. We show conditions under which gregarious behavior of the relatively fast prey individuals leaves slowest prey with no other choice but to join the group. Failing to do so would signal their vulnerability, making them a preferred target for the predator. Analysis of an n+1 player game of a predator and n unequal prey individuals
clarifies conditions for fully gregarious, partially gregarious, or solitary behavior of the prey
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