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M W Feldman

Publications and source records attributed to M W Feldman.

At least 19 recordsLinked to original sources
PubMed1992

Gene-culture coevolution: toward a general theory of vertical transmission.

A general formulation of cultural and genetic transmission is developed. The cultural transmission is vertical and the genetics may involve multiple loci. Each individual is represented by a phenogenotype, and conditions are given under which the evolutionary dynamics of phenogenotype frequencies are reducible to phenogametic or phenoallelic frequencies. The interaction between genes and culture is specified by an association measure, and results on the order of magnitude of this association at equilibrium are presented.

Biological Evolution↗
PubMed1992

Assortative mating and grandparental transmission facilitate the persistence of a sign language.

Conditions for the persistence (i.e., protection from loss) of a sign language are investigated assuming monogenic recessive inheritance of deafness, assortative mating for deafness or hearing, and cultural transmission of the sign language to deaf individuals from their deaf parents and deaf maternal grandparents. A new method is introduced to deal with the problem of grandparental transmission in which the basic variables are the frequencies of triplets comprising a mother, a father, and their daughter of permissible phenogenotypes. Usual stability analysis is then done on the system of linear recursions in the frequencies of these triplets, derived on the assumption that signers (users of the sign language) are rare. It is shown that assortative mating is the most important factor contributing to persistence, but that grandparental transmission can also have a significant effect when assortment is as strong as observed in England and the United States.

Deafness↗
PubMed1992

On models of quantitative genetic variability: a stabilizing selection-balance model.

A model of stabilizing selection on a multilocus character is proposed that allows the maintenance of stable allelic polymorphism and linkage disequilibrium. The model is a generalization of Lerner's model of homeostasis in which heterozygotes are less susceptible to environmental variation and hence are superior to homozygotes under phenotypic stabilizing selection. The analysis is carried out for weak selection with a quadratic-deviation model for the stabilizing selection. The stationary state is characterized by unequal allele frequencies, unequal proportions of complementary gametes, and a reduction of the genetic (and phenotypic) variance by the linkage disequilibrium. The model is compared with Mather's polygenic balance theory, with models that include mutation-selection balance, and others that have been proposed to study the role of linkage disequilibrium in quantitative inheritance.

Alleles↗
PubMed1991

Recessive hereditary deafness, assortative mating, and persistence of a sign language.

We model the cultural transmission of sign language when there is one-locus genetic variation for deafness and hearing. Our premises are that the deaf are more motivated to learn sign language than the hearing, and that a vertically transmitted sign language, unlike recessive hereditary deafness, cannot "jump a generation." Conditions are obtained for persistence (i.e. protection from loss) of signers. These conditions are more easily satisfied the greater the fraction of the hearing who also learn sign language and as the frequency of the recessive gene for deafness increases. Persistence is also facilitated by assortative mating for deafness, but not by assortment for signing. With vertical transmission only, it is necessary that one signer parent be able to transmit sign language with greater than one-half the efficiency of two. Under the assumption that the hearing do not learn sign language, the following additional results are obtained. Persistence is more likely with dominant as opposed to recessive inheritance. When recessive hereditary and acquired deafness co-occur, increasing the frequency of the latter has opposite effects depending on the degree of assortment. Opportunities for the deaf to learn sign language outside the family seem not to affect the conditions for persistence.

Deafness↗
PubMed1991

Lewontin and Kojima meet Fisher: linkage in a symmetric model of sex determination.

The effect of linkage and epistasis on the evolution of the sex-ratio is studied in a symmetric two-locus model of autosomal sex determination closely related to the symmetric viability model of R. C. Lewontin and K. Kojima. R. A. Fisher's expectation of an even sex ratio for autosomal sex determination by a single gene governs the dynamics when the loci are tightly linked. However, recombination may preclude optimization of the sex ratio just as occurs in viability selection models. Many of the evolutionary phenomena known for the symmetric viability model also occur here. In addition, we exhibit a series of new phenomena related to the presence of surfaces of even sex ratio.

Animals↗
PubMed1990

Spatial subdivision of populations and estimates of genetic variation.

Measures of variation in space are strongly affected by correlations between subdivisions used for sampling. Here we consider variation in gene frequencies across populations. Usually the variance of gene frequencies is standardized by dividing it by the mean gene frequency times one minus the mean (FST). Under the model of isolation by distance (usually called the "stepping stone" model), at the stationary state the correlation between the gene frequencies of two populations falls exponentially with the geographic distance between them. Using this model, we derive formulas for variances of blocks of populations of different sizes in one- and two-dimensional space and suggest that the theoretical results may be useful for understanding real observations, some examples of which are presented. We demonstrate how FST increases with the degree of subdivision among populations. We also show the effect of gaps between the sampled populations. Our results are valid, however, for traits other than gene frequencies, as long as their correlation with geographic distance falls exponentially. In the extension to 2-dimensional spaces, we present in closed form the distributions of distances between nodes of a lattice or of two lattices. These distributions might have applications in ecology.

Blood Group Antigens↗
PubMed1990

Mutation modification with multiplicative fertility selection.

Two diallelic loci in an infinite panmictic population of diploid individuals are modelled. The A/a locus is subject to unidirectional mutation and either multiplicative fertility selection or, equivalently, sex-asymmetric viability selection. The M/m locus acts as a selectively neutral modifier of the mutation rate at A/a. The loci recombine at rate R. If the M/m locus is initially monomorphic, and the A/a locus has reached equilibrium, the fate of a new modifier allele is found to depend not just on its relative effect on mutation but also upon the linkage, R. Each initial equilibrium may be characterized by a critical value of the recombination rate, R*. If 0 less than R* less than 0.5, a sufficiently small "down" modifier of the mutation rate will invade the population when R less than R* whereas a sufficiently small "up" modifier will succeed when R greater than R*. If R* less than 0 or R* greater than 0.5, only mutation reduction may occur. Numerical analysis of 56,000 sample equilibria indicates that mutation rates may be increased, but only when the selection regime is such that the A/a locus would remain polymorphic in the absence of mutation.

Female↗
PubMed1990

Two-locus autosomal sex determination: on the evolutionary genetic stability of the even sex ratio.

In two-locus models of sex determination, there are two kinds of interior (polymorphic) equilibria. One class has the even sex ratio, and the other has equal allele frequencies in the two sexes. Equilibria of the second class may exhibit linkage disequilibrium. The condition for external stability of these second-class equilibria to invasion by a new allele is that the appropriately averaged sex ratio near the equilibrium be moved closer to the even sex ratio than the average among the resident genotypes. However, invasion by a new chromosome depends on the recombination fraction in a way that appears to preclude general results about the evolutionary genetic stability of the even sex ratio in this situation.

Alleles↗
PubMed1989

Pleiotropy and preadaptation in the evolution of human language capacity.

The capacity for spoken language in the human is a genetic trait, but the information communicated by this means is to a large extent culturally determined. Using a gene-culture coevolutionary approach, we model the hypothesis that speech evolved as a channel for the communication of adaptive cultural traits from parent to offspring. The motivation for this paper is a condition obtained previously that initial increase of communication would require at least a two-fold advantage for the transmitted trait. Here, we show that under reasonable assumptions the invasion condition becomes less stringent. In Model 1, we assume that two adaptive cultural traits can be transmitted. A gene which permits communication of the second adaptive trait. In Model 2, we assume that a related function such as greater memory capacity is a prerequisite for speech, and that this function confers an advantage independent of its association with speech. In both models we assume haploid sexual genetics and a simple scheme of vertical transmission. The stability properties of all corner and edge equilibria of the models are analyzed. The two models taken together suggest a possible scenario for the initial stages of the evolution of speech.

Adaptation, Biological↗
PubMed1989

More on recombination and selection in the modifier theory of sex-ratio distortion.

G. Maffi and S.D. Jayakar suggested a model for the two-locus control of sex determination in the mosquito Aedes aegypti (1981, Theor. Pop. Biol. 19, 19-36). This model was extended to multiple alleles and analyzed in mathematical detail by S. Lessard (1987, Theor. Pop. Biol. 31, 339-358). The model supposes that males are "Mm" and females "mm" but the transmission from males is controlled by a second gene with alleles Ai. We show that in addition to the equilibrium in which mAi in females, MAi from males and mAi from males all have the same frequencies, a second class of polymorphic equilibria exists and can be stable. The former class was shown by Lessard to be stable for intermediate and/or loose linkage. The new class of equilibria may be stable for tight linkage under the conditions that preclude stability of the former. We also develop the theory of linkage modification from the neighborhood of the new equilibrium. Successful modifiers of recombination may either reduce or increase the recombination fraction with the outcome depending on the linkage of the modifier to the major genes.

Aedes↗
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↗
PubMed1988

A general asymptotic property of two-locus selection models.

It is shown that any two-locus, two-allele model of selection with constant fitnesses has at least one polymorphic equilibrium for which the linkage association measure, D, is arbitrarily close to zero for large enough recombination, R. As R----+/- infinity, D----0 in such a way that the product l = RD----a non-zero finite constant. There may be 1, 3, or 5 distinct asymptotic equilibria, depending upon fitness parameters.

Alleles↗
PubMed1987

Behavior-dependent contexts for repeated plays of the Prisoner's Dilemma: II. Dynamical aspects of the evolution of cooperation.

Iterated Prisoner's Dilemma models are proposed in which, at any trial, the probability of staying in the game depends on the outcome of the previous trial. If a player's choice depends on its own play (cooperate or defect) at the previous trial, it becomes possible for cooperative strategies to increase when rare in a population of egoists. A dynamic analysis is used to demonstrate that stable polymorphisms may result, and may involve more strategies than just Tit-for-Tat and all-Defect. The tendency for clustering among like strategists to enhance their initial increase when rare is also explored dynamically.

Behavior↗
PubMed1987

Toward a theory for the evolution of cultural communication: coevolution of signal transmission and reception.

A haploid sexual two-locus model of gene-culture coevolution is examined, in which a dichotomous phenotype subject to natural selection is transmitted vertically with probabilities dependent on the chosen parent's genotype and phenotype and the offspring's genotype. Stability conditions for the genetically monomorphic corner equilibria are obtained. In a specialization of this general model, one locus controls the transmission and the other controls the reception of adaptive information. The corner and edge equilibria of this doubly coevolutionary model are fully analyzed, and conditions for transmission and reception to coevolve are derived in terms of the efficiency of vertical transmission, the selective advantage gained from possessing the information, the costs of transmission and reception, and the recombination fraction between the two loci. Possible applications of the model are to the evolution of semantic alarm calls in vervet monkeys and the phonetic aspects of human language. In a third model with diploid genetics, we consider the initial increase of cultural transmission from a mutation-selection balance in which the adaptive phenotype is the consequence of a dominant gene at one locus. A second gene controls the transmission of the phenotype in such a way that a new mutant at this second locus permits learning of the adaptive phenotype from a parent who has it. This new mutant cannot increase when rare.

Animal Communication↗
PubMed1987

Selection, generalized transmission and the evolution of modifier genes. I. The reduction principle.

Modifier gene models are used to explore the evolution of features of organisms, such as the genetic system, that are not directly involved in the determination of fitness. Recent work has shown that a general "reduction principle" holds in models of selectively neutral modifiers of recombination, mutation, and migration. Here we present a framework for models of modifier genes that shows these reduction results to be part of a more general theory, for which recombination and mutation are special cases. The deterministic forces that affect the genetic composition of a population can be partitioned into two categories: selection and transmission. Selection includes differential viabilities, fertilities, and mating success. Imperfect transmission occurs as a result of such phenomena as recombination, mutation and migration, meiosis, gene conversion, and meiotic drive. Selectively neutral modifier genes affect transmission, and a neutral modifier gene can evolve only by generating association with selected genes whose transmission it affects. We show that, in randomly mating populations at equilibrium, imperfect transmission of selected genes allows a variance in their marginal fitnesses to be maintained. This variance in the marginal fitnesses of selected genes is what drives the evolution of neutral modifier genes. Populations with a variance in marginal fitnesses at equilibrium are always subject to invasion by modifier genes that bring about perfect transmission of the selected genes. It is also found, within certain constraints, that for modifier genes producing what we call "linear variation" in the transmission processes, a new modifier allele can invade a population at equilibrium if it reduces the level of imperfect transmission acting on the selected genes, and will be expelled if it increases the level of imperfect transmission. Moreover, the strength of the induced selection on the modifier gene is shown to range up to the order of the departure of the genetic system from perfect transmission.

Biological Evolution↗
PubMed1986

Modifiers of mutation rate: a general reduction principle.

A deterministic two-locus population genetic model with random mating is studied. The first locus, with two alleles, is subject to mutation and arbitrary viability selection. The second locus, with an arbitrary number of alleles, controls the mutation at the first locus. A class of viability-analogous Hardy-Weinberg equilibria is analyzed in which the selected gene and the modifier locus are in linkage equilibrium. It is shown that at these equilibria a reduction principle for the success of new mutation-modifying alleles is valid. A new allele at the modifier locus succeeds if its marginal average mutation rate is less than the mean mutation rate of the resident modifier allele evaluated at the equilibrium. Internal stability properties of these equilibria are also described.

Alleles↗