James F. Crow

The origins, patterns and implications of human spontaneous mutation

The germline mutation rate in human males, especially older males, is generally much higher than in females, mainly because in males there are many more germ-cell divisions. However, there are some exceptions and many variations. Base substitutions, insertion–deletions, repeat expansions and chromosomal changes each follow different rules. Evidence from evolutionary sequence data indicates that the overall rate of deleterious mutation may be high enough to have a large effect on human well-being. But there are ways in which the impact of deleterious mutations can be mitigated.Key PointsGermline base substitution mutations occur more frequently in males than in females, especially in older males. The main explanation for the sex and age effect is that a much larger number of germline divisions occurs in the male than in the female, and continues throughout male adulthood. Point mutations at some loci occur almost exclusively in males, whereas others have a smaller excess, roughly ten times more than in females. Which is more typical remains to be determined. For mutations other than point mutations, sex biases in the mutation rate are very variable. However, small deletions are more frequent in females. The total rate of new deleterious mutations for all genes is estimated to be about three per zygote. This value is uncertain, but it is likely that the number is greater than one. It is suggested that quasi-truncation selection is the principal explanation for how the population can rid itself of a large number of mutations with a relatively low fitness cost. Since this form of selection is effective only with sexual reproduction, perhaps the fact that humans reproduce sexually has made it possible to have such a long life cycle.

Evolution in Sexual and Asexual Populations

In an asexual population two favorable mutants can be incorporated into the population only if one occurs in a descendant of the individual in which the other occurred. In a sexual population both mutants can be incorporated through recombination. A mathematical formulation is given of the relative rates of incorporation of the new mutations with and without recombination. Recombination is of the greatest advantage when the double mutant is more advantageous than either single mutant, when the mutant effects are small, when mutations occur with high frequency, and when the population is large. On the other hand, for the incorporation of individually deleterious but collectively beneficial mutations, recombination can be disadvantageous. Close linkage has effects similar to those of asexual reproduction. Experimental data on DDT resistance in Drosophila and chloramphenicol resistance in bacteria are cited showing greater development of coadaptation in an asexual system. The evolution of diploidy from haploidy confers an immediate reduction in the mutation load by concealment of deleterious recessives, but this advantage is lost once a new equilibrium is reached. Thus the development of diploidy may be because of an immediate advantage rather than because of any permanent benefit. On the other hand, there are other possible advantages of diploidy, such as heterosis and protection from somatic mutations.

THE MEASUREMENT OF EFFECTIVE POPULATION NUMBER

Abstract : The effective population number can be defined either in terms of the amount of increase in homozygosity (inbreeding effective number) or the amount of gene frequency drift (variance effective number). Under many circumstances these are the same, but not in general. The effective number is considered in terms of an idealized population in which each individual parent has an equal expectation of progeny. The effective number of an actual population is defined as the size of an idealized population with the same amount of inbreeding or random gene frequency drift as the population under consideration. Formulae are given for determining both kinds of effective numbers when the population is monoecious (including self fertilization) and when there are separate sexes. The formulae are summarized along with special cases of interest. (Author)

Inbreeding and variance effective population numbers

In this paper, a correction and extension of earlier work, we derive expressions for the inbreeding effective number, NeI, and the variance effective number, NeV, with various models. Diploidy, random mating, and discrete generations are assumed and formulas for NeI are given for six situations: isogamous monoecious populations with self‐fertilization permitted or excluded; monoecious populations, male and female gametes distinguished, with self‐fertilization permitted or excluded; and separate sexes with or without male and female progeny distinguished. NeV is given for monoecious and separate‐sexed populations.

MEASUREMENT OF GENE FREQUENCY DRIFT IN SMALL POPULATIONS

The causes of changes in gene frequency from generation to generation in an evolving population may be thought of as being of two kinds (Wright, 1949, 1951): (1) systematic factors (selection, mutation, and migration) which tend to carry the gene frequency to an equilibrium point, and (2) dispersive factors (chance fluctuations in finite populations and variations in the magnitude and direction of the systematic factors) which cause the gene frequency to scatter. The result of these two factors is a stochastic process leading to a succession of changes in gene frequency. The mathematical formulation of this process and the distribution of gene frequency probabilities when a steady state is reached have been the subject of much mathematical inquiry (Fisher, 1922, 1930; Wright, 1931, 1945, 1949, 1952; Kolmogoroff, 1935; Malecot, 1948; Feller, 1951; Kimura, 1954). Wright and others have shown, by various methods, that the process is adequately described by the Fokker-Planck equation

Genetic Loads and the Cost of Natural Selection

The basic ideas of genetic load and the cost of natural selection are both from J. B. S. Haldane. In his early papers on natural selection (1924–1932), Haldane was concerned with both the dynamics and the statics of evolution. He emphasized that, although evolution depends on changes of gene frequency, nevertheless at any one time the population is in approximate equilibrium for most factors.

On the maximum avoidance of inbreeding

Mating systems in which the least related individuals are mated have been designated by Wright as having maximum avoidance of inbreeding. For such systems the initial rate of decrease in heterozygosity is minimum. However, some other systems have a lower rate of decrease in later generations. Circular mating, in which each individual is mated with the one to his right and to his left, leads to an asymptotic rate of decrease in heterozygosity of 1– λ ˜ π 2 /(2 N + 4) 2 compared with 1/4 N for maximum avoidance systems. Circular pair mating, in which for example each male progeny is moved one cage to the right, leads to 1– λ ~ π 2 /( N + 12) 2 . Other similar systems are discussed. For minimum gene frequency drift, a mating system should have a constant number of progeny per parent and the population should be broken up as rapidly as possible into the maximum number of lines. The gene frequency variance at generation T within a line is where N is the number in the line and H t is the proportion of heterozygotes in generation t . Although the three mating systems, circular, circular pair, and maximum avoidance (and many others) have the same amount of random drift ultimately, at any generation circular mating has the smallest drift variance, V T , and circular pair next smallest.

Evidence for the Partial Dominance of Recessive Lethal Genes in Natural Populations of Drosophila

An earlier study by Hiraizumi and Crow showed that recessive lethals extracted from nature decreased the viability of heterozygotes by about two to three per cent when tested in the laboratory. In the present article we have used published data on mutation rates, frequency of lethal chromosomes, and proportion of allelism among lethal chromosomes from wild Drosophila populations in order to make an indirect estimate of what the effective dominance of lethals must be in nature. For D. melanogaster the mean value of h̄ + F is .015 and for the other species is .018, where h̄ is the average deleterious effect of a heterozygous lethal gene and F is a measure of non-random mating within a locality. Since F, we believe, is probably small, this analysis is regarded as further evidence for the conclusion that recessive lethals extracted from natural populations (and newly occurring lethal mutants, a fortiori) have a deleterious effect as heterozygotes.

The Rate of Change of a Character Correlated with Fitness.

An extended form of Fishers Fundamental Theorem of Natural Selection gives the rate of change of the mean value, \( \bar{C} \) , of a measured character. For a character determined by multiple alleles at two loci, this is \( \dot{\bar{C}} = {\mathrm{cov}_{g}} (m, \gamma) + \overline{\dot{C}} + \sum\limits^{2}_{n=1} \overline{\Delta^{(n)}\mathring{\theta}^{(n)}}+\overline{\varepsilon\mathring{\theta}} \) where the Newtonian superior dot means the time derivative and the circle is the time derivative of the logarithm. Covg (m, γ) is the genic (additive genetic) covariance of the character and fitness. Specifically, it is the covariance of the average excess of an allele for fitness and its average effect on the character. \( \overline{\dot{C}} \) is the average rate of change of the value of the character for individual genotypes, weighted by their frequencies. The value could be nonzero because of changing environments or change in the age distribution of the population. The third term on the right is the average over all pairs of alleles at both loci of the product of the dominance deviation and the rate of change of ln θ(n), where θ(n) is a measure of departure from random proportions. The last term is a similar expression for epistatic interactions. If selection is much weaker than recombination, after several generations, the last two terms are much smaller than the first. When the measured character is fitness, our result reduces to Kimuras generalization of Fishers Fundamental Theorem of Natural Selection.

On epistasis: why it is unimportant in polygenic directional selection.

There is a difference in viewpoint of developmental and evo-devo geneticists versus breeders and students of quantitative evolution. The former are interested in understanding the developmental process; the emphasis is on identifying genes and studying their action and interaction. Typically, the genes have individually large effects and usually show substantial dominance and epistasis. The latter group are interested in quantitative phenotypes rather than individual genes. Quantitative traits are typically determined by many genes, usually with little dominance or epistasis. Furthermore, epistatic variance has minimum effect, since the selected population soon arrives at a state in which the rate of change is given by the additive variance or covariance. Thus, the breeders custom of ignoring epistasis usually gives a more accurate prediction than if epistatic variance were included in the formulae.