The sampling theory of neutral alleles and an urn model in population genetics

The behaviour of a Pólya-like urn which generates Ewens' sampling formula in population genetics is investigated. Connections are made with work of Watterson and Kingman and to the Poisson-Dirichlet distribution. The order in which novel types occur in the urn is shown to parallel the age distribution of the infinitely many alleles diffusion model and consequences of this property are explored. Finally the urn process is related to Kingman's coalescent with mutation to provide a rigorous basis for this parallel.This research was partially supported by the Sloan Foundation under Grant 85-6-14 and by the National Science Foundation     

Selection acting upon slow-migrating ADH alleles differing in enzyme activity.

Relative egg to adult viability was compared in three stocks of Drosophila melanogaster differing in alcohol dehydrogenase (ADH) activity. Two of these, Grell's standard ADHS and a mutant ADHS strain producing half the normal number of ADH molecules, had the same electrophoretic mobility. The experiment demonstrated a correlation between survival in alcohol-supplemented media and enzyme activity. This supports the hypothesis that enzyme activity per se, rather than some other attribute of allelic differences, may be responsible for the previously observed selective advantage of high activity alleles on alcohol media.     

The population genetics of synthetic lethals.

Synthetic lethals are variants at different loci that have little or no effect on viability singly but cause lethality in combination. The importance of synthetic lethals and, more generally, of synthetic deleterious loci (SDL) has been controversial. Here, we derive the expected frequencies for SDL under a mutation-selection balance for the complete haploid model and selected cases of the diploid model. We have also obtained simple approximations that demonstrate good fit to exact solutions based on numerical iterations. In the haploid case, equilibrium frequencies of carrier haplotypes (individuals with only a single mutation) are comparable to analogous single-locus results, after allowing for the effects of linkage. Frequencies in the diploid case, however, are much higher and more comparable to the square root of the single-locus results. In particular, when selection operates only on the double-mutant homozygote and linkage is not too tight, the expected frequency of the carriers is approximately the quartic root of the ratio between the mutation rate and the selection coefficient of the synthetics. For a reasonably wide set of models, the frequencies of carriers can be on the order of a few percent. The equilibrium frequencies of these deleterious alleles can be relatively high because, with SDL, both dominance and epistasis act to shield carriers from exposure to selection. We also discuss the possible role of SDL in maintaining genetic variation and in hybrid breakdown.     

Yeast alpha-isopropylmalate isomerase. Factors affecting stability and enzyme activity.

Yeast alpha-isopropylmalate isomerase was found to be markedly stabilized by high concentrations of glycerol and (NH4)2SO4. Such conditions of high ionic strength inhibited the enzyme, stabilized the enzyme to heat, and affected kinetic parameters. The isomerase was found to exhibit ionic strength-dependent hysteresis when enzyme, totally but reversibly inhibited by storage under conditions of high ionic strength of (NH4)2SO4, was transferred to a lower concentration of (NH4)2SO4. Alpha-Isopropylmalate isomerase was found to be sensitive to KCN and certain other chelators. The inactivation by KCN was prevented by high concentrations of (NH4)2SO4. These observations implicated a metal involvement but the nature of the metal was not revealed. The metal involvement and some of the other properties of alpha-isopropylmalate isomerase reveal a similarity to aconitase. The similarities in properties between the isomerase and aconitase are summarized. Studies of yeast alpha-isopropylmalate isomerase indicated that it is a single polypeptide of about Mr = 90,000.     

Molecular population genetics.

Molecular population genetics is entering a new era dominated by studies of genomic polymorphism. Some of the theory that will be needed to analyze data generated by such studies is already available, but much more work is needed. Furthermore, population genetics is becoming increasingly relevant to other fields of biology, for example to genetic epidemiology, because of disease gene mapping in general populations.     

Mitochondrial malic enzyme (E.C. 1.1.1.40) in human leukocytes: Formal genetics and population genetics

Summary Mitochondrial malic enzyme ME_M (E.C. 1.1.1.40) is present in human leukocytes; the polymorphism of ME_M thus can be easily demonstrated using routine starch gel electrophoresis. Data on formal genetics are given. The gene frequency of ME ₁ ^M was estimated to be 0.67±0.02.     

Evolution of advantageous alleles affecting population ecological characteristics in partially inbreeding populations

The fate of advantageous alleles affecting intrinsic growth rate, carrying capacity or intra-specific competitive ability was examined in a partially inbreeding population. Generally, inbreeding had an effect on the evolution of advantageous alleles affecting population ecological characteristics. For example, in a specific underdominant case the number of stable internal equilibria decreased from two to one with only a slight degree of inbreeding. Equilibrium frequencies of stable internal equilibria and stability of fixation equilibria were also affected by the degree of inbreeding. For strictly advantageous alleles, inbreeding had the same qualitative effect on the fixation probability and mean fixation time as predicted in simpler selection models.     

The population genetics of anisogamy

This paper analyses the population genetics of anisogamy controlled by a single locus, in both the haploid and diploid cases. The conclusions of Parker et al. (1972), based on computer calculations, are confirmed analytically. The effects of the existence of two mating types on the evolution of anisogamy are examined. Close linkage between a mating type locus and the gamete size locus may produce non-random associations of alleles, leading to disassortative fusion with respect to gamete size. With loose linkage, there is random association of alleles, but selection favours closer linkage.     

The population genetics of reinforcing selection

A common outcome of disruptive selection experiments between two differentiated populations which produce disadvantageous hybrids is an increase in homogamy. Experiments reported here result in another outcome when ‘classical’ selection experiments are redesigned. In these modified experiments, frequencies of genotypes in the mating population were not artificially maintained at parity but were instead determined from progeny proportions in the previous generation. In these selection lines another outcome, apart from an increase in homogamy, was demonstrated. Under a high selection coefficient against heterozygotes, elimination of a homozygote and the corresponding fixation of the other was observed. No selection line demonstrated the maintenance of two differentiated populations concurrently with the selection process of heterozygote disadvantage. A high number of generations of selection under this population genetical process is necessary to increase differences between two populations. However, the instability of gene frequencies which results in fixation or elimination of a homozygote is shown to be extremely rapid by comparison. Classical experiments were repeated and after 21 generations of selection there was no increase in divergence. For lower selection coefficients, high levels of introgression are apparent, and hence the genetical distinctness of the two populations decreases over time. This is in addition to the problem of an unstable equilibrium under selection against heterozygotes. Both aspects are important but not previously considered in experimental evidence for speciation models for which their implications are discussed.     

The population genetics of nodule bacteria

The data are reviewed on the population structure and evolutionary dynamics of the nodule bacteria (rhizobia) which are among the most intensively studied microorganisms. High level of the population polymorphism was demonstrated for the rhizobia populations using the enzyme electrophoresis (MLEE profiles). The average value of Nei's coefficient of heterogeneity (H = 1 - sigma pi2 [n/(n - 1)]) were: 0.590 for rhizobia (Rhizobium, Bradyrhizobium), 0.368 for enterobacteria (Escherichia, Salmonella, Shigella) and 0.452 for pathogenic bacteria (Bordetella, Borrelia, Erysipelothrix, Haemophilus, Helicobacter, Listeria, Mycobacterium, Neisseria, Staphylococcus) populations. In spite of being devoid of the effective systems for the gene conjugative transfer, many rhizobia populations possess an essentially panmictic structure. However, the enterobacteria populations in which the gene transfer may be facilitated due to the conjugative F- and R-factors, usually display the clonal population structure. The legume host plant is proved to be a key factor that determines the high levels of polymorphism and of panmixis as well as high evolutionary rates of the symbiotic bacteria populations. The host may ensure: a) an increase in mutation and gene transfer frequencies; b) stimulation of the competitive (selective) processes in both symbiotic and free-living rhizobia populations. A "cyclic" model of the rhizobia microevolution is presented which allows to assess the inputs the interstrain competition for the saprophytic growth and for the host nodulation into evolution of a plant-associated rhizobia population. The nodulation competitiveness in the rhizobia populations is responsible for the frequency-dependent selection of the rare genotypes which may arise in the soil bacterial communities as a result of the transfer of symbiotic (sym) genes from virulent rhizobia strains to either avirulent rhizobia or to the other (saprophytic, phytopathogenic) bacteria. Therefore, the nodulation competitiveness may ensure: a) panmictic structure of the natural rhizobia populations; b) high taxonomic diversity of rhizobia which was apparently caused by a broad sym gene expansion in the soil bacterial communities. The kin selection models are presented which explain evolution of the "altruistic" (essential for the host plant, but not for the bacteria themselves) symbiotic traits (e.g., the ability for symbiotic nitrogen fixation and for differentiation into non-viable bacteroids) in the rhizobia populations. These models are based on preferential multiplication of the nitrogen-fixing clones either in planta (due to an elevated supply of the nitrogen-fixing nodules with photosynthates) or ex planta (due to a release of the rhizopines from the nitrogen-fixing nodules). Speaking generally, interactions with the host plants provide a range of mechanisms increasing a genetic heterogeneity and an evolutionary potential in the associated rhizobia populations.     

The population genetics of multistage carcinogenesis

Despite the many successes of cancer research, we lack the framework necessary to predict the ratio of familial (inherited) to sporadic (non-inherited) cancers. An evolutionary model of multistage carcinogenesis provides this framework by demonstrating that the number of tumour suppressor loci (TSLs) preventing cancer in a given tissue is expected to depend upon the tissue's vulnerability to pre-reproductive somatic mutation. Since this vulnerability increases with tissue size, single gene control of human cancer may be restricted to retinoblastoma, a cancer of the tiny embryonic retina. The model is used to estimate the frequency of mutant alleles causing inherited cancers, based on the population genetics of the mutation-selection balance between new mutations arising and selection that eliminates them. For each specific cancer, this balance is determined by the effectiveness with which pre-reproductive cancer is suppressed in the non-mutant genotype characteristic of that population. Effectiveness depends on an interaction between the number of TSLs suppressing the cancer and factors determining the tissue-wide somatic mutation rate, such as tissue size and number of pre-reproductive cell divisions. The model predicts that the commonest pre-reproductive cancers will have the lowest proportion of familial cases, and that cancers associated with the most TSLs will have the highest post-reproductive incidence but no elevated pre-reproductive risk (a pattern seen in human epithelial cancers).     

Spontaneous mutations affecting glycerol-3-phosphate dehydrogenase enzyme activity in Drosophila melanogaster.

Significant genetic variance in glycerol-3-phosphate dehydrogenase (GPDH) activity was observed between chromosome lines of Drosophila melanogaster that had each accumulated spontaneous mutations for approximately 300 generations. No restriction map variation was found in a 26-kb region surrounding the entire Gpdh gene. The restriction analysis used is capable of detecting insertions/deletions larger than 0.05 kb. The survey would also detect chromosomal recombinations that include the entire Gpdh coding region. Therefore, if the spontaneous mutations that affected the enzyme activity are located inside the Gpdh gene region, then they are base pair substitutions or structural changes that are smaller than the limit in resolution described above.