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Biomedical subjects

J R Peck

Publications and source records attributed to J R Peck.

At least 19 recordsLinked to original sources
PubMed2006

The frequency of the perfect genotype in a population subject to pleiotropic mutation.

We consider a large population of asexual organisms characterised by a number of quantitative traits that are subject to stabilising selection. Mutation is taken to act pleiotropically, with every mutation generally changing all of the traits under selection. We focus on the equilibrium distribution of the population, where mutation and selection are in balance. It has been previously established that the equilibrium distribution of genotypic effects may be anomalous, as it may contain a singular spike--a Dirac delta function--corresponding to a non-zero proportion of the population having exactly optimal genotypic values. In the present work, we present exact results for the case where three traits are under selection. These results give the equilibrium genetic variance of the population, and the proportion of the population that have the optimal genotype. This is achieved for two different spherically symmetric distributions of mutant effects. Additionally, a simple and robust numerical approach is also presented that allows the treatment of some other mutation distributions, where there are an arbitrary number of selected traits.

Animals↗
PubMed2004

A one locus, biased mutation model and its equivalence to an unbiased model.

Experimental data suggests that for some continuously-varying characters under stabilising selection, mutation may cause a mean change in the value of the character. A one locus, mathematical model of a continuously-varying biological character with this property of biased mutation is investigated. Via a mathematical transformation, the equilibrium equation describing a large population of individuals is reduced to the equilibrium equation describing a mutationally unbiased problem. Knowledge of an unbiased problem is thus sufficient to determine all equilibrium properties of the corresponding biased problem. In the biased mutation problem, the dependence of the mean equilibrium value of the character, as a function of the mutational bias, is non-monotonic and remains small, for all levels of mutational bias. The analysis presented in this work sheds new light on Turelli's House of Cards Approximation.

Models, Genetic↗
PubMed2003

The anomalous effects of biased mutation.

A model is presented in which alleles at a number of loci combine to influence the value of a quantitative trait that is subject to stabilizing selection. Mutations can occur to alleles at the loci under consideration. Some of these mutations will tend to increase the value of the trait, while others will tend to decrease it. In contrast to most previous models, we allow the mean effect of mutations to be nonzero. This means that, on average, mutations can have a bias, such that they tend to either increase or decrease the value of the trait. We find, unsurprisingly, that biased mutation moves the equilibrium mean value of the quantitative trait in the direction of the bias. What is more surprising is the behavior of the deviation of the equilibrium mean value of the trait from its optimal value. This has a nonmonotonic dependence on the degree of bias, so that increasing the degree of bias can actually bring the mean phenotype closer to the optimal phenotype. Furthermore, there is a definite maximum to the extent to which biased mutation can cause a difference between the mean phenotype and the optimum. For plausible parameter values, this maximum-possible difference is small. Typically, quantitative-genetics models assume an unconstrained model of mutation, where the expected difference in effect between a parental allele and a mutant allele is independent of the current state of the parental allele. Our results show that models of this sort can easily lead to biologically implausible consequences when mutations are biased. In particular, unconstrained mutation typically leads to a continual increase or decrease in the mean allelic effects at all trait-controlling loci. Thus at each of these loci, the mean allelic effect eventually becomes extreme. This suggests that some of the models of mutation most commonly used in quantitative genetics should be modified so as to introduce genetic constraints.

Alleles↗
PubMed2000

Mutation and sex in a competitive world.

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.

Animals↗
PubMed1999

Sex and adaptation in a changing environment.

In this study we consider a mathematical model of a sexual population that lives in a changing environment. We find that a low rate of environmental change can produce a very large increase in genetic variability. This may help to explain the high levels of heritability observed in many natural populations. We also study asexuality and find that a modest rate of environmental change can be very damaging to an asexual population, while leaving a sexual population virtually unscathed. Furthermore, in a changing environment, the advantages of sexuality over asexuality can be much greater than suggested by most previous studies. Our analysis applies in the case of very large populations, where stochastic forces may be neglected.

Adaptation, Physiological↗
PubMed1998

Pleiotropy and the preservation of perfection.

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.

Animals↗
PubMed1997

Imperfect genes, Fisherian mutation and the evolution of sex.

In this paper we present a mathematical model of mutation and selection that allows for the coexistence of multiple alleles at a locus with very small selective differences between alleles. The model also allows for the determination of fitness by multiple loci. Models of this sort are biologically plausible. However, some previous attempts to construct similar models have assumed that all mutations produce a decrease in fitness, and this has led to a tendency for the average fitness of population members to decline when population numbers are finite. In our model we incorporate some of the ideas of R. A. FISHER, so that both deleterious and beneficial mutations are possible. As a result, average fitness tends to approach a stationary distribution. We have used computer simulation methods to apply the Fisherian mutation model to the problem of the evolution of sex and recombination. The results suggest that sex and recombination can provide very large benefits in terms of average fitness. The results also suggest that obligately sexual species will win ecological competitions with species that produce a substantial fraction of their offspring asexually, so long as the number of sites under selection within the genomes of the competing species is not too small and the population sizes are not too large. Our model focuses on fertility selection in an hermaphroditic plant. However, the results are likely to generalize to a wide variety of other situations as well.

Biological Evolution↗
PubMed1996

Limited dispersal, deleterious mutations and the evolution of sex.

This study presents a mathematical model that allows for some offspring to be dispersed at random, while others stay close to their mothers. A single genetic locus is assumed to control fertility, and this locus is subject to the occurrence of deleterious mutations. It is shown that, at equilibrium, the frequency of deleterious mutations in the population is inversely related to the rate of dispersal. This is because dispersal of offspring leads to enhanced competition among adults. The results also show that sexual reproduction can lead to a decrease in the equilibrium frequency of deleterious mutations. The reason for this relationship is that sex involves the dispersal of genetic material, and thus, like the dispersal of offspring, sex enhances competition among adults. The model is described using the example of a hermaphroditic plant population. However, the results should apply to animal populations as well.

Biological Evolution↗
PubMed1994

Cognitive distortion, helplessness, and depressed mood in rheumatoid arthritis: a four-year longitudinal analysis.

Cognitive models of depression have been invoked to explain the development of depressive symptoms and disorders in patients with chronic pain. However, few long-term, prospective studies have examined A. T. Beck's (1967, 1987) model in this context. Seventy-two patients with rheumatoid arthritis completed the Beck Depression Inventory, the Cognitive Errors Questionnaire, and the Arthritis Helplessness Index during an initial assessment and again 4 years later. Initial levels of cognitive distortion were significantly related to follow-up levels of depressed mood, controlling for initial depression levels. This was also true for perceptions of helplessness. In contrast, initial depression levels did not predict changes in these cognitive processes. These results suggest that cognitive distortion and helplessness contribute to depressed mood among patients with arthritis.

Adult↗
PubMed1994

A ruby in the rubbish: beneficial mutations, deleterious mutations and the evolution of sex.

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.

Animals↗
PubMed1993

Frequency-dependent selection, beneficial mutations, and the evolution of sex.

This paper presents a mathematical model of a population in which multiple alleles at a particular locus are maintained by frequency-dependent selection. The results suggest that, if the population reproduces sexually, the benefit conferred on the population by beneficial mutations at other loci will typically be much larger than if the population reproduces by asexual means. In part, this is true because, in asexual populations, beneficial mutations can produce suboptimal distributions of the alleles that are subject to frequency-dependent selection. Another factor that produces an advantage for sex is that, in asexual populations, beneficial mutations that have achieved a high copy number may nevertheless be lost from the population. This is highly unlikely in sexual populations.

Animals↗
PubMed1993

Friendship and the evolution of co-operation.

Recent theoretical research on the repeated Prisoner's Dilemma game (PD) suggests that the evolution of co-operative behaviour depends on the rate at which social groups break apart and new groups form. Long-lasting social groups tend to favour the evolution of co-operation. It is therefore of interest to construct models in which individuals must choose whether to maintain their current social relationships. This is done in the present paper, and the analysis suggests that unco-operative individuals will seek to move quickly from one social relationship to another, while co-operative individuals will seek to maintain relationships with other co-operative individuals. As a result of their differing decisions about changing social relationships, co-operators tend to interact with other co-operators to a greater extent than do unco-operative individuals, and this difference is an important determinant of the results of the model. In contrast to the original analyses of the repeated Prisoner's Dilemma, the model presented here allows for the existence of stable equilibria with both co-operative and unco-operative individuals simultaneously present in the same population. It is proved that the position of these equilibria (and hence the frequency of co-operators) depends on the size of the various payoffs that define the Prisoner's Dilemma game. In addition, it is proved that co-operation can be maintained at a high frequency so long as co-operators are able to maintain their relationships with other co-operators over long periods of time. This is true even if unco-operative individuals are able to move from one relationship to another at a very high rate.

Biological Evolution↗
PubMed1992

Group selection, individual selection, and the evolution of genetic drift.

In a subdivided population, genetic drift affects variation between groups, and thus it can have an important effect on the outcome of evolution (Wright, 1978). The rate of genetic drift is determined, in part, by the behaviour of population members. This paper presents three mathematical models in which behavioural traits that affect the rate of genetic drift are allowed to coevolve with traits that are under selection at the group and individual levels. The results show that if group selection is strong relative to individual selection, then behavioural traits that enhance the rate of genetic drift will tend to increase in frequency. The strength of this effect depends, in part, on the way in which vacant sites are colonized.

Animals↗
PubMed1990

The evolution of outsider exclusion.

The rate of migration between different parts of a population can be important in determining evolutionary outcomes. This paper presents a mathematical model in which some individuals act to exclude immigrants from their group. It is shown that outsider exclusion can be favoured by evolution, even when outsider excluders incur a large cost. In addition, it is shown that the evolutionary mechanism which causes increases in the frequency of outsider excluders is a form of kin selection or group selection. A second model shows that a similar mechanisms can act to favour the evolution of reluctance to mate with immigrants.

Animals↗
PubMed1990

Helplessness and depression in rheumatoid arthritis.

Depression is common in rheumatoid arthritis (RA) populations and has been hypothesized to result from patients' belief that they cannot control their disease or its impact. In a sample of 106 patients with RA, we found that scores on a measure of helplessness mediated the relationship between severe, disabling RA and depression. Further, this association was independent of the previously demonstrated correlation between cognitive distortion and depression in RA patients. Thus, both helplessness and cognitive distortion may be important factors in the development and treatment of depression among RA patients.

Adaptation, Psychological↗
PubMed1989

Disability and depression in rheumatoid arthritis. A multi-trait, multi-method investigation.

In a sample of 107 patients with classic or definite rheumatoid arthritis (RA), we examined the convergent and divergent validity of measures of disability and depression. Scores on the self-report Disability index of the Health Assessment Questionnaire were highly correlated with physical therapist and spouse ratings of disability. Although Health Assessment Questionnaire disability scores were significantly correlated with self-reported and interviewer-assessed ratings of depression, these correlations were significantly smaller. Factor analyses of the Beck Depression Inventory (BDI) and rheumatologist ratings of BDI items indicated that this measure is highly contaminated by the inclusion of items reflecting RA disease severity. A dysphoric mood subcomponent of the BDI may be a more valid measure of depression in RA populations. Although depression and disability are clearly positively correlated in RA patients, depression scales that include somatic items are likely to yield an overestimate of the association. Finally, self-reported pain intensity was more clearly related to disability and reported recent disease activity than to depression.

Adult↗
PubMed1988

Kin selection and the evolution of monogamy.

A two-locus genetic model is studied in which one locus controls the tendency of individuals to act altruistically toward siblings and the other locus controls the mating habits of females. It is demonstrated that genetic variation at the altruism locus is often sufficient to induce an increase in the frequency of genes that cause females to produce all of their offspring with a single mate. This occurs because of nonrandom associations that develop between genes that cause altruism and those that affect female mating behavior. The results provide a new explanation for the evolution of monogamy, and they suggest a previously unexplored mechanism for the evolution of a variety of other behavioral traits as well.

Altruism↗