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A mathematical model is presented in which a single mutation can affect multiple phenotypic characters, each of which is subject to stabilizing selection. A wide range of mutations is allowed, including ones that produce extremely small phenotypic changes. The analysis shows that, when three or more characters are affected by each mutation, a single optimal genetic sequence may become common. This result provides a hypothesis to explain the low levels of variation and low rates of substitution that are observed at some loci.

We present the results of a computer simulation model in which a sexual population produces an asexual mutant. We estimate the probability that the new asexual lineage will go extinct. We ¢nd that whenever the asexual lineage does not go extinct the sexual population is out-competed, and only asexual individuals remain after a su¤ciently long period of time has elapsed. We call this type of outcome an asexual takeover. Our results suggest that, given repeated mutations to asexuality, asexual takeover is likely in an unstructured environment. However, if the environment is subdivided into demes that are connected by migration, then asexual takeover becomes less likely. The probability of asexual takeover declines towards zero as the number of demes increases and as the rate of migration decreases. The reason for this is that asexuality leads to a greater loss of ¢tness due to mutation and genetic drift, in comparison to what occurs under sexual reproduction. Population subdivision slows the spread of asexual lineages, which allows more time for the genetic degeneration caused by asexuality to take place.

This study presents a mathematical model in which a single beneficial mutation arises in a very large population that is subject to frequent deleterious mutations. The results suggest that, if the population is sexual, then the deleterious mutations will have little effect on the ultimate fate of the beneficial mutation. However, if most offspring are produced asexually, then the probability that the beneficial mutation will be lost from the population may be greatly enhanced by the deleterious mutations. Thus, sexual populations may adapt much more quickly than populations where most reproduction is asexual. Some of the results were produced using computer simulation methods, and a technique was developed that allows treatment of arbitrarily large numbers of individuals in a reasonable amount of computer time. This technique may be of prove useful for the analysis of a wide variety of models, though there are some constraints on its applicability. For example, the technique requires that reproduction can be described by Poisson processes.

How do deleterious mutations interact to affect fitness? The answer to this question has substantial implications for a variety of important problems in population biology, including the evolution of sex, the rate of adaptation and the conservation of small populations. Here we analyse a mathematical model of competition for food in which deleterious mutations affect competitive ability. We show that, if individuals usually compete in small groups, then competition can easily lead to a type of genetic interaction known as synergistic epistasis. This means that a deleterious mutation is most damaging in a genome that already has many other deleterious mutations. We also show that competition in small groups can produce a large advantage for sexual populations, both in mean fitness and in ability to resist invasion by asexual lineages. One implication of our findings is that experimental efforts to demonstrate synergistic epistasis may not succeed unless the experiments are redesigned to make them much more naturalistic.

Models of sexual haploids under kin selection are constructed. The trait of altruism is transmitted vertically from parent to child, but not in a strictly genetic manner. Two systems of altruism are considered: parent-to-offspring and sib-to-sib. In the former case it is shown that even when Hamilton's conditions for the success of genetically determined altruism are met, genes that increase the transmission of altruism may not invade the population. With sib-to-sib altruism, such genes will always increase initially.Hamilton (1) The way in which the fitness effects are combined is known to influence the conditions for evolution of altruism (2, 3). Departures from simple genetic transmission of altruism should also play a role in determining the conditions for its increase.In this paper, we shall study the evolution of altruistic traits that are transmitted both by genetic means and by vertical (i.e., parent to child) cultural transmission. There is no general agreement as to the best way to construct such a model. Indeed, there has been considerable controversy in recent years concerning the appropriate theoretical methodology whereby the evolution of traits under both genetic and cultural control may be studied.