Background selection

Abstract: The main purpose of this article is to present several new statistical tests of neutrality of mutations against a class of alternative models, under which DNA polymorphisms tend to exhibit excesses of rare alleles or young mutations. Another purpose is to study the powers of existing and newly developed tests and to examine the detailed pattern of polymorphisms under population growth, genetic hitchhiking and background selection. It is found that the polymorphic patterns in a DNA sample under logistic population growth and genetic hitchhiking are very similar and that one of the newly developed tests, Fs, is considerably more powerful than existing tests for rejecting the hypothesis of neutrality of mutations. Background selection gives rise to quite different polymorphic patterns than does logistic population growth or genetic hitchhiking, although all of them show excesses of rare alleles or young mutations. We show that Fu and Li's tests are among the most powerful tests against background selection. Implications of these results are discussed.

Abstract: SUMMARY When a selectively favourable gene substitution occurs in a population, changes in gene frequencies will occur at closely linked loci. In the case of a neutral polymorphism, average heterozygosity will be reduced to an extent which varies with distance from the substituted locus. The aggregate eifect of substitution on neutral polymorphism is estimated; in populations of total size 10 6 or more (and perhaps of 10 4 or more), this eifect will be more important than that of random fixation. This may explain why the extent of polymorphism in natural populations does not vary as much as one would expect from a consideration of the equilibrium between mutation and random fixation in populations of different sizes. For a selectively maintained polymorphism at a linked locus, this process will only be important in the long run if it leads to complete fixation. If the selective coefficients at the linked locus are small compared to those at the substituted locus, it is shown that the probability of complete fixation at the linked locus is approximately exp (— Nc), where c is the recombinant fraction and N the population size. It follows that in a large population a selective substitution can occur in a cistron without eliminating a selectively maintained polymorphism in the same cistron.

Abstract: Selection against deleterious alleles maintained by mutation may cause a reduction in the amount of genetic variability at linked neutral sites. This is because a new neutral variant can only remain in a large population for a long period of time if it is maintained in gametes that are free of deleterious alleles, and hence are not destined for rapid elimination from the population by selection. Approximate formulas are derived for the reduction below classical neutral values resulting from such background selection against deleterious mutations, for the mean times to fixation and loss of new mutations, nucleotide site diversity, and number of segregating sites. These formulas apply to random-mating populations with no genetic recombination, and to populations reproducing exclusively asexually or by self-fertilization. For a given selection regime and mating system, the reduction is an exponential function of the total mutation rate to deleterious mutations for the section of the genome involved. Simulations show that the effect decreases rapidly with increasing recombination frequency or rate of outcrossing. The mean time to loss of new neutral mutations and the total number of segregating neutral sites are less sensitive to background selection than the other statistics, unless the population size is of the order of a hundred thousand or more. The stationary distribution of allele frequencies at the neutral sites is correspondingly skewed in favor of rare alleles, compared with the classical neutral result. Observed reductions in molecular variation in low recombination genomic regions of sufficiently large size, for instance in the centromere-proximal regions of Drosophila autosomes or in highly selfing plant populations, may be partly due to background selection against deleterious mutations.

Abstract: (i) A computer simulation study has been made of selection on two linked loci in small populations, where both loci were assumed to have additive effects on the character under selection with no interaction between loci. If N is the effective population size, i the intensity of selection in standard units, α and β measure the effects of the two loci on the character under selection as a proportion of the pheno-typic standard deviation and c is the crossover distance between them, it was shown that the selection process can be completely specified by Ni α, Ni βand Nc and the initial gene frequencies and linkage disequilibrium coefficient. It is then easily possible to generalize from computer runs at only one population size. All computer runs assumed an initial population at linkage equilibrium between the two loci. Analysis of the results was greatly simplified by considering the influence of segregation at the second locus on the chance of fixation at the first (defined as the proportion of replicate lines in which the favoured allele was eventually fixed). (ii) The effects of linkage are sufficiently described by Nc. The relationship between chance of fixation at the limit and linkage distance (expressed as 2Nc /( 2Nc + 1)) was linear in the majority of computer runs. (iii) When gene frequency changes under independent segregation were small, linkage had no effect on the advance under selection. In general, segregation at the second locus had no detectable influence on the chance of fixation at the first if the gene effects at the second were less than one-half those at the first. With larger gene effects at the second locus, the chance of fixation passed through a minimum and then rose again. For two loci to have a mutual influence on one another, their effects on the character under selection should not differ by a factor of more than two. (iv) Under conditions of suitable relative gene effects, the influence of segregation at the second locus was very dependent on the initial frequency of the desirable allele. The chance of fixation at the first, plotted against initial frequency of the desirable allele at the second, passed through a minimum when the chance of fixation at the second locus was about 0·8. (v) A transformation was found which made the influence of segregation at the second locus on the chance of fixation at the first almost independent of initial gene frequency at the first and of gene effects at the first locus when these are small. (vi) In the population of gametes at final fixation, linkage was not at equilibrium and there was an excess of repulsion gametes. (vii) The results were extended to a consideration of the effect of linkage on the limits under artificial selection. Linkage proved only to be of importance when the two loci had roughly equal effects on the character under selection. The maximum effect on the advance under selection occurred when the chance of fixation at both of the loci was between 0·7 and 0·8. When the advance under selection is most sensitive to changes in recombination value, a doubling of the latter in no case increased the advance under selection by more than about 6%. The proportion selected to give maximum advance under individual selection (0·5 under independent segregation) was increased, but only very slightly, when linkage is important. (viii) These phenomena could be satisfactorily accounted for in terms of the time scale of the selection process and the effective size of the population within which changes of gene frequency at the locus with smaller effect must take place.