Theoretical Population Genetics Research Articles

THE EVOLUTION OF ESS THEORY

With the rediscovery of Mendel's Laws at the tum of the century (100), the study of evolutionary processes blossomed. Since then, the discipline of population genetics has been the standard framework for studying evolution­ ary mechanisms-the lingua franca of evolutionary thought. In population genetics, the gene is the fundamental unit of evolution. Dawkins (29) says, We are survival machines-robot vehicles blindly programmed to preserve the selfish molecules known as genes. To some, it seems inappropriate to discuss natural selection without recourse to genes or population genetics. It is interesting to note, however, that Darwin proposed the theory of evolution by natural selection without knowledge of theoretical population genetics. His postulated mechanisms of inheritance, blending inheritance, and a form of Lamarckian transmission have been discarded. So, was Darwin lucky and in his ignorance correct for the wrong reasons? Or does his theory of natural selection prosper because it does not require direct recourse to specific mechanisms of inheritance? To avoid cumbersome genetic models in the application of Darwin's theory, researchers are increasingly using phenotypic or strategic models of evolution (e.g. optimal foraging theory and evolutionary game theory). Evo­ lutionary game theory, as it has built up around Maynard Smith's pioneering definition (65, 67, 69) of evolutionarily stable strategies (ESS), has emerged as an alternative approach to genetic models. Like many good ideas, the ESS

Possible worlds: contributions of J. B. S. Haldane to genetics

Although he possessed no academic qualifications in science, Haldane made significant contributions to genetics, biochemistry, physiology and biometry. In genetics, he was especially noted for his work on theoretical population genetics and human genetics. Through his popular writings and biological predictions, he contributed to our outlook on human biology.

The population genetics of haplo-diploids and X-linked genes

SUMMARYFrom the available electrophoretic data, it is clear that haplodiploid insects have a much lower level of genetic variability than diploid insects, a difference that is only partially explained by the social structure of some haplodiploid species. The data comparingX-linked genes and autosomal genes in the same species is much more sparse and little can be inferred from it. This data is compared with theoretical analyses ofX-linked genes and genes in haplodiploids. (The theoretical population genetics ofX-linked genes and genes in haplodiploids are identical.)X-linked genes under directional selection will be lost or fixed more quickly than autosomal genes as selection acts more directly onX-linked genes and the effective population size is smaller. However, deleterious disease genes, maintained by mutation pressure, will give higher disease incidences atX-linked loci and hence rare mutants are easier to detect atX-linked loci. Considering the forces which can maintain balanced polymorphisms, there are much stronger restrictions on the fitness parameters atX-linked loci than at autosomal loci if genetic variability is to be maintained, and thus fewer polymorphic loci are to be expected on theX-chromosome and in haplodiploids. However, the mutation-random drift hypothesis also leads to the expectation of lower heterozygosity due to the decrease in effective population size. Thus the theoretical results fit in with the data but it is still subject to argument whether selection or mutation-random drift are maintaining most of the genetic variability atX-linked genes and genes in haplodiploids.

MOLECULAR EVOLUTION OVER THE MUTATIONAL LANDSCAPE.

A common observation in phylogenetic comparisons of the amino acid sequences of a particular protein is that the rate of evolution of the protein is nearly constant over extended periods of time. This constancy was first noticed by Zuckerkandl and Pauling (1965) and prompted them to call the amino acid substitution process a evolutionary clock. Since 1965 a great deal of additional data has supported the basic idea of the molecular clock although detailed studies have shown the clock to be a rather erratic one. The detailed studies have been of two different sorts: broadly based statistical studies of a number of proteins over relatively few species (e.g., Langley and Fitch, 1974), or very detailed looks at a particular protein over a large number of species (e.g., Baba et al., 1981). In general, these studies support the crucial observation made by Ohta and Kimura (1971) that the variance in the evolutionary rate is higher than would be expected if the substitution process were a Poisson process. A major goal of theoretical population genetics must be to account for this elevated variance. There are formidable statistical problems associated with the estimation of the variance in the rate of substitutions of amino acids. The problem is compounted by the fact that the variance is only interesting when compared to the mean as in the ratio K = Var(N,)/E(N1), where N, is the number of substitutions in a period of time, t. Obtaining accurate estimates of ratios is difficult in the best of statistical settings. For protein evolution data where the number of substitutions on each leg must themselves be inferred by a procedure such as Fitch and Margoliash's (1967) maximum parsimony procedure, the sampling variance of the final estimate must be relatively high (and itself almost impossible to estimate). Nonetheless, a number of studies have all pointed to a value of K of around 2 to 3. Ohta and Kimura (1971) were the first to estimate K and did so using the available data on hemoglobins and cytochrome c. They reported a value in the range 1.5 to 2.5. The studies by Langley and Fitch (1974) improved on this in the sense of using more data although their procedure was not expressly designed to estimate K. They concluded K was around 2.5. Later, Gillespie and Langley (1979) re-examined the statistical procedure used in the earlier studies and through a very crude argument also claimed that K was around 2.5. In studies that examine only a single protein over a large number of species the aim has been not so much to estimate K as to look more directly for periods of relatively fast or slow evolution in the protein. These studies, such as those by Goodman et al. (1982) generally present fairly convincing evidence of variations in the rates of evolution although Kimura (1981) has called into question the ability of these studies to uncover variation in the rates of evolution. These observations are critical for an understanding of the forces responsible for amino acid substitutions. One of the most appealing theories for the evolution of proteins is the neutral allele theory first proposed by Kimura (1968a, 1968b) and King and Jukes (1969). This theory predicts that the rate of substitutions will be constant although it does not imply that K will equal one as has been commonly assumed. Rather it was shown by Gillespie and Langley (1979) that K will always be greater than one under the neutral allele theory and will actually increase with

Frequency spectra of neutral and deleterious alleles in a finite population

One of the major goals of population genetics is to discover the nature and amount of genetic variation in natural populations. Various measures, including the population heterozygosity at any locus and the number of alleles extant at the locus, have been used for this purpose. An important task of theoretical population genetics is thus to provide expressions for the mean values of these two quantities (when calculated from a sample of genes) for various models of selection, mutation and random drift. This aim has been achieved for the selectively neutral case, where all alleles at the locus are assumed to be selectively equivalent. It is, however, generally agreed that classes of (evolutionarily unimportant) selectively deleterious alleles exist, so that the neutral theory calculations should be extended to cover this case. This has previously been done only for extremely weak selection. In this paper we obtain, via the confluent hypergeometric function and three allied functions, concise and simple exact and approximate formulae for the means of the above measures of population variation for arbitrary selective values. These all derive from the allelic “frequency spectrum”, which is of independent interest in assessing likely models of population variation.

The theory of speciation via the founder principle.

The founder principle has been used to explain many instances of rapid speciation. Advances from theoretical population genetics are incorporated into MAYR's original founder-effect genetic-revolution model to yield a newer model called the genetic transilience. The basic theoretical edifice lies upon the fact that founder event can sometimes lead to an accumulation of inbreeding and an induction of gametic disequilibrium. This, in turn, causes alleles to be selected more for their homozygous fitness effects and for their effects on a more stable genetic background. Selection occurring in multi-locus systems controlling integrated developmental, physiological, behavioral, etc, traits is particularly sensitive to these founder effects. If sufficient genetic variability exists in the founder population, such multilocus genetic systems can respond to drift and the altered selective forces by undergoing a rapid shift to a new adaptive peak known as the genetic transilience. A genetic transilience is, therefore, most likely to occur when the founder event causes a rapid accumulation of inbreeding without a severe reduction in genetic variability. The implications of this model are then examined for three aspects of the founder-effect genetic-transilience model: the attributes of the ancestral population, the nature of the sampling process used to generate the founders and the attributes of the founder population. The model is used to explain several features of the evolution of the Hawaiian Drosophila, and experimental designs are outlined to test the major predictions of the theory. Hence, this theory of speciation can be tested in the laboratory, using systems and techniques that already exist--a rare attribute of most models of speciation.

Sociocultural evolutionism: An untried theory

The author argues that sociocultural evolutionism has never been an evolutionary theory in the sense in which that model is employed in the life sciences, but that instead it sought natural sequential laws of history or employed an analogy with a developing organism rather than with phylogenetic change. Biology, on the other hand, in embracing polythetic or cluster as opposed to Aristotelian classification, implicitly abandoned this approach only to recover it in theoretical population genetics. Biology today remains a bifurcated science with lawful change occurring within gene pools and abrupt historically specific transitions occurring between them. It is argued that this example holds many lessons for the social sciences and that a truly evolutionary model contains solutions to the diffusionist, Boasian, functionalist and conflict critiques of classical sociocultural evolutionism. Some of the kinds of evidence which would be relevant for the verification of such a theory are discussed and it is concluded that biology may be important for the social sciences not because of the reductionist hopes of sociobiology proper but because of the example it provides in how to describe and theorize about an historical process.

Thermal selection of allozyme polymorphisms in barnacles.

Is protein polymorphism adaptive or neutral1? Attempts to assess the neutrality theory on the basis of gene frequencies and theoretical population genetics models seem, at least to some authors, to be unsuccessful2. Possible promising approaches involve the search for direct correlation of isozymes with the environment1 and with physiological function3. We have tested the effects of temperature on barnacles, because temperature affects protein structure and function4,5,6, as well as size7, and because adult barnacles, following larval settlement, are stationary and directly exposed to local temperature variation. Our results suggest strong temperature selection on allozymic and size variations in the acorn barnacle, Balanus amphitrite.

Sampling theory for alleles in a random environment.

A MAJOR effort in theoretical population genetics has been aimed at developing statistical tests to distinguish between various explanations of observed patterns of enzyme variation1. Perhaps the most useful result to emerge from this effort is Ewens' sampling theory of neutral alleles2. This theory allows one to use the number and configuration of alleles in a sample to test for departures from neutrality. Watterson3 has derived the analogous sampling distribution for a finite population subject to the joint effects of mutation and symmetric heterotic selection. It differs from the neutral sampling theory, providing a stronger hypothesis-testing situation than has previously been available. In this note I present a third sampling distribution. It applies to an infinite population in which the selective coefficients fluctuate at random through time and space. Quite unexpectedly, the sampling distribution turns out to be identical to that for the neutral model, indicating that agreement of data with Ewens' sampling distribution does not rule out the possibility that natural selection is responsible for the genetic variation in the sample. Furthermore, the properties of random-selection populations at equilibrium are indistinguishable from neutral-allele populations for observations made at a single time point. This result calls into question the claim that agreement of data with predictions of the neutral model argues against natural selection as an important factor for the maintenance of genetic variation.

The theoretical population genetics of variable selection and migration.

Selection varying with time is reviewed with regard to infinite and finite populations. Geographic effects are reviewed with regard to migration versus selection; genetic drift and migration; and selection. Various models of geographic differentiation are described. (HLW)

The Origins of Theoretical Population Genetics

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The Origins of Theoretical Population Genetics. The Chicago History of Science and Medicine.William B. Provine

The Origins of Theoretical Population Genetics. The Chicago History of Science and Medicine.William B. Provine

The Origins of Theoretical Population Genetics. William B. Provine

<i>The Origins of Theoretical Population Genetics</i>. William B. Provine

The Origins of Theoretical Population Genetics William B. Provine

The Origins of Theoretical Population Genetics William B. Provine

Mendelism v Darwinism

The Origins of Theoretical Population Genetics. By William B. Provine. Pp. xi + 201. (University of Chicago: Chicago and London, December 1971.) £2.50.

The Origins of Theoretical Population Genetics By William B. Provine (review)

BOOK REVIEWS The Origins of Theoretical Population Genetics. By William B. Provine. The Chicago History of Science and Medicine, edited by Allen G. Debus. Chicago: University of Chicago Press, 1971- Pp. xi + 201. $7.75. A former colleague of mine recommended that space should be made in the departmental library by relegating books and periodicals several years old to dead storage. "I read nothing published more than two or three years ago," he said pridefully. This is, to be sure, an extreme case. However, lack of interest in the history of their science is a rule rather than an exception among "modern" biologists . The book under review may stimulate such interest. Its author is a historian of science who knows enough biology to become a professional biologist if he would wish to do so. The felicity of his style makes the book equally readable to biologists with at least a trace of interest in history, and to historians with at least a trace of interest in biology. He forgoes technicalities without sacrificing accuracy; his characterizations of the scientists whose work he describes are brief but sufficient to make them real persons rather than merely names, but not so chatty as to become mere gossip. My major criticism is that the title of the book is not descriptive of its contents. Theoretical population genetics is mainly mathematical exercise; pencil and paper (and nowadays computers, rather than experimental animals and plants, are the chief sources of information. To be sure, the fifth (and last) chapter of the book treats mathematical studies of R. A. Fisher, Sewall Wright, and J. B. S. Haldane, who laid the theoretical foundations of the modern biological theory of evolution. However, the book as a whole is concerned with the growth of understanding of the causes of evolutionary changes. This understanding is traced from Darwin, through Galton, Mendel, and the early twentiethcentury Mendelians; the acrimonious controversy of Bateson with Pearson and the school of biometricians, Johannsen, Jennings, Castle, Morgan, and his school; and on to the Fisher-Wright-Haldane trio. Some readers may accuse the author of Anglo-American chauvinism, since he largely ignores the contributions of nonEnglish -writing authors. The bibliography has only six titles in German, the remainder being in English. The author knows that Chetverikov published "in 1927 a very important paper" (the real date is 1926, not 1927), but blandly disregards it because "by the time this paper was known in England and the United States, the theoretical constructs erected by Fisher, Haldane and Wright had progressed beyond it." Many other European authors do not rate even this much attention. Otherwise, the author is judicious and fair throughout. Looked at from the vantage point of our present understanding, some of the early conceptions and controversies seem wildly unwarranted and confused. How, for example, could Mendelism and the discovery of mutations be construed as disproving Darwin ? It is the business of a historian to understand such things by temporarily Perspectives in Biology and Medicine · Summer 1972 | 645 denying to himself the benefits of hindsight. Our misguided predecessors are dren seen to have been no less smart than we are; this is a lesson in humility which is grossly deficient in many of us. The history of the studies of the causes of evolution contains many zigzags and blind alleys, and this makes it particularly interesting and instructive. Provine's book is a good guide. Theodosius Dobzhansky Department of Genetics University of California, Davis A History of Medicine. Edited by Lester S. King. History of Science Readings. Baltimore: Penguin Books, 1971. Pp. 316. $5.75. This is a well-selected collection of readings. Part 1, "The Classical Heritage," includes "Airs, Waters, Places" and "The Sacred Disease" by Hippocrates and "On the Natural Faculties" by Galen. Part 2, "Revolt," includes "De Corporis Fabrica (1543)" by Vesalius, "Volumen Medicinae Paramirum (?1529)" by Paracelsus, and "Movement of the Heart and Blood in Animals" by William Harvey. Part 3, "Development," is made up of eleven classical papers from 1676 to 1849. Part 4, "Fruition," consists of papers by Virchow, Claude Bernard, Robert Koch, Walter Reed, Banting and Best, and Simon and Harley. The scholarly introduction and sketches by the editor...

Application of method of small parameters to multi-niche population genetic models

In theoretical population genetics it has been customary to analyze models in which most or all of the parameters are assigned specific values. For example, one of the earliest models discussed by Haldane was concerned with the rate of elimination of a recessive lethal, and in this model the viabilities assigned to genotypes AA, Au, au are 1, 1, 0, respectively. Implicit in the study of such models is the assumption that the conclusions derived, in their general qualitative aspects, and to some extent in their quantitative features, will be applicable to more “realistic” models in which the parameter values are only approximately the same as those assigned in the model. In the above example an assignment of b, , b, , 15, as the respective viabilities, with b, and b, nearly 1 and b, nearly zero, should not alter the qualitative features of the model and should result in only small changes of the important quantitative aspects. A gene perfectly dominant in all its pleiotropic effects coupled with a recessive allele perfectly lethal when homozygous, even in the complex natural environment, comprise a structure of little interest, except to the extent that it may serve as an idealized approximation for cases in which the dominance and the lethality are not quite perfect. This paper is one of several companion papers in which a theory of perturbation of parameters in deterministic genetic systems is developed. The most naive application of this perturbation theory would be to show that the qualitative and quantitative conclusions derived from models, such as the aforementioned model of Haldane, do indeed persist under small perturbations of the parameters in the model. However, the theory has more valuable and less obvious applications in the analysis of complex genetic population systems composed of a number of interacting subpopulations, or generally subsystems. A number of examples are presented below which illustrate this kind of application.

The Origins of Theoretical Population Genetics.

The Origins of Theoretical Population Genetics.