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Distinguishing the hitchhiking and background selection models.

A simple method to distinguish hitchhiking and background selection is proposed. It is based on the observation that these models make different predictions about the average level of nucleotide diversity in regions of low recombination. The method is applied to data from Drosophila melanogaster and two highly selfing tomato species.

Animals↗

Polygenic variation maintained by balancing selection: pleiotropy, sex-dependent allelic effects and G x E interactions.

We investigate three alternative selection-based scenarios proposed to maintain polygenic variation: pleiotropic balancing selection, G x E interactions (with spatial or temporal variation in allelic effects), and sex-dependent allelic effects. Each analysis assumes an additive polygenic trait with n diallelic loci under stabilizing selection. We allow loci to have different effects and consider equilibria at which the population mean departs from the stabilizing-selection optimum. Under weak selection, each model produces essentially identical, approximate allele-frequency dynamics. Variation is maintained under pleiotropic balancing selection only at loci for which the strength of balancing selection exceeds the effective strength of stabilizing selection. In addition, for all models, polymorphism requires that the population mean be close enough to the optimum that directional selection does not overwhelm balancing selection. This balance allows many simultaneously stable equilibria, and we explore their properties numerically. Both spatial and temporal G x E can maintain variation at loci for which the coefficient of variation (across environments) of the effect of a substitution exceeds a critical value greater than one. The critical value depends on the correlation between substitution effects at different loci. For large positive correlations (e.g., rho(ij)2>3/4), even extreme fluctuations in allelic effects cannot maintain variation. Surprisingly, this constraint on correlations implies that sex-dependent allelic effects cannot maintain polygenic variation. We present numerical results that support our analytical approximations and discuss our results in connection to relevant data and alternative variance-maintaining mechanisms.

Data Interpretation, Statistical↗

Modes of reproduction and the accumulation of deleterious mutations with multiplicative fitness effects.

Mutational load depends not only on the number and nature of mutations but also on the reproductive mode. Traditionally, only a few specific reproductive modes are considered in the search of explanations for the maintenance of sex. There are, however, many alternatives. Including these may give radically different conclusions. The theory on deterministic deleterious mutations states that in large populations segregation and recombination may lead to a lower load of deleterious mutations, provided that there are synergistic interactions. Empirical research suggests that effects of deleterious mutations are often multiplicative. Such situations have largely been ignored in the literature, since recombination and segregation have no effect on mutation load in the absence of epistasis. However, this is true only when clonal reproduction and sexual reproduction with equal male and female ploidy are considered. We consider several alternative reproductive modes that are all known to occur in insects: arrhenotoky, paternal genome elimination, apomictic thelytoky, and automictic thelytoky with different cytological mechanisms to restore diploidy. We give a method that is based on probability-generating functions, which provides analytical and numerical results on the distributions of deleterious mutations. Using this, we show that segregation and recombination do make a difference. Furthermore, we prove that a modified form of Haldane's principle holds more generally for thelytokous reproduction. We discuss the implications of our results for evolutionary transitions between different reproductive modes in insects. Since the strength of Muller's ratchet is reduced considerably for several forms of automictic thelytoky, many of our results are expected to be also valid for initially small populations.

Data Interpretation, Statistical↗

The random phenotype concept, with applications.

A random phenotype is defined as a probability distribution over any given set of phenotypes. This includes as special cases the kinds of phenotypes usually considered (qualitative, quantitative, and threshold characters) and all others. Correspondingly general methods are indicated for analyzing data of all forms in terms of the classical Mendelian factor concept (as distinct from the biometrical methods usually applied to measurement and graded data, associated with the effective factor concept). These are applied in a new analysis of the data of E. L. Green (1951, 1954, 1962) on skeletal variation in the mouse. The adequacies of various classical one-factor and several-factor models are considered. Indications of an underlying scale are found from this new standpoint. The results are compared with those obtained by Green using the scaling approach. An illustrative application is also made to some of Bruell's (1962) continuous behavioural data on mice. This work was substantially completed in 1959 but not previously prepared for publication. The same approach was originated and developed independently by R. L. Collins who has treated a wider range of theoretical problems (cf. Collins 1967, 1968a, 1969b, 1970c) and a wider range of applications (cf. Collins and Fuller 1968; Collins 1968b, 1969a, 1970a). A less general independent development is that of Mode and Gasser 1972.

Animals↗

Genetic drift in clines which are maintained by migration and natural selection.

Genetic drift will cause a migration-selection cline to wobble about its expected position. A rough linear approximation is developed, valid when local populations are large. This is used to calculate effects of genetic drift on clines in a stepping-stone model with abrupt and with gradual changes of selection coefficients at a single haploid locus. Among the quantities calculated are measures of slope, standardized variation of gene frequencies around their expected values, and correlation among neighboring populations with respect to deviations from the expected gene frequencies. These quantities appear to be primarily functions of Ns and Nm for a given pattern of selection. Computer simulation gives rough confirmation of these results. Standardized variances of gene frequencies and correlation of neighbors differ along the cline in the case of smooth changes in selection. In no case is pathological behavior of gene frequency deviations found near the boundaries of selective regions. Local behavior of gene frequences of nearby colonies is approximately predicted by a simple adaptation of the stepping-stone theory of Kimura and Weiss. Approximate measures of the lateral variation of the midpoint of a cline and the probability of non-monotonicity are also calculated and discussed.

Gene Frequency↗

Selection for rate and efficiency of lean gain in the rat.

Full-sib family selection for rate (WP) or efficiency (WP/F) of protein gain in rats from 3 to 9 weeks of age was applied for five generations. Three rats per litter were killed to estimate carcass protein. Standardized response/cumulative selection for WP was .19+/-.10 for WP, .28+/-.10 for 3- to 9-week gain .28+/-.08 for 9-week weight, .16+/-.08 for litter size, .22+/-.12 for skinning loss and -.07+/-.09 for fraction of protein in the live weight. Response from selection for WP/F was .18+/-.16 for WP/F, .20+/-.11 for WP, .21+/-.11 for weight gain, .16+/-.11 for 3-week weight, .21+/-.10 for 9-week weight, but negligible for skinning loss or body protein. Response to WP/F selection was extremely variable among generations, associated with generation differences in weight and composition at 9 weeks. Estimates of heritability from offspring-midparent regression were .20+/-.12 for WP and .24+/-.08 for WP/F. Estimates of genotype-generation environment interaction were large for growth, feed intake and skinning loss. Maternal effects were large for weaning weight, fraction of body protein and WP. Sire component genetic correlations were 1.08+/-.13 for WP with total gain, .92+/-.08 for WP/F with gross efficiency and .29+/-.25 for WP with WP/F. A partitional calorimeter was used to evaluate heat production of rats. Lines differed in average heat loss but not in heat loss per unit actual or metabolic weight. Response to selection has been steady for WP but probably could be improved by selecting for WP/F at a constant weight rather than a constant age.

Animals↗

Genetic variance and correlation after selection for two traits by index, independent culling levels and extreme selection.

Three two-trait selection methods were analyzed for their effects on genetic variance and correlation by multivariate methods, two-locus methods and computer simulation. The two-trait selection methods studied were independent culling levels (ICL), index (IND) and extreme (EXT) selection. The effects of the selection methods on genetic variance and correlation were partitioned into permanent effects due to changes in gene frequencies and temporary effects due to nonrandom association of alleles at different loci. Multivariate methods were used to predict temporary effects from a single generation of selection by each method and from several generations of index selection. Two-locus theory was used to determine the stability and rank of temporary effects on genetic correlation for all three methods. Predictions were compared to computer simulation results. When selection increased the means of both traits, EXT had the lowest (closest to -1.0) genetic correlation and highest variances, while ICL tended to have the highest (closest to 1.0) genetic correlation. When selection increased the mean of one trait and decreased th mean of the other, EXT had the highest genetic variances and correlation, while ICL had the lowest genetic variance and correlation.

Alleles↗

Doubled haploids for estimating mean and variance of recombination values.

In a diallel cross analysis using doubled haploids, both additive and additive x additive genetic variances can be estimated. In addition, mean and variance of recombination values can also be estimated. Linkage affects the covariance between half-sibs the most, the covariance between grandparents and grand offspring to an intermediate degree and the covariance between full sibs the least. The covariance of parent and offspring is not affected by linkage.

Epistaxis↗