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.

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Statistical tests of neutrality of mutations against population growth, hitchhiking and background selection.

When a population experiences a reduction of its effective size, it generally develops a heterozygosity excess at selectively neutral loci, i.e., the heterozygosity computed from a sample of genes is larger than the heterozygosity expected from the number of alleles found in the sample if the population were at mutation drift equilibrium. The heterozygosity excess persists only a certain number of generations until a new equilibrium is established. Two statistical tests for detecting a heterozygosity excess are described. They require measurements of the number of alleles and heterozygosity at each of several loci from a population sample. The first test determines if the proportion of loci with heterozygosity excess is significantly larger than expected at equilibrium. The second test establishes if the average of standardized differences between observed and expected heterozygosities is significantly different from zero. Type I and II errors have been evaluated by computer simulations, varying sample size, number of loci, bottleneck size, time elapsed since the beginning of the bottleneck and level of variability of loci. These analyses show that the most useful markers for bottleneck detection are those evolving under the infinite allele model (IAM) and they provide guidelines for selecting sample sizes of individuals and loci. The usefulness of these tests for conservation biology is discussed.

https://www.genetics.org/content/genetics/144/4/2001.full.pdf

Description and Power Analysis of Two Tests for Detecting Recent Population Bottlenecks from Allele Frequency Data

The genetic effects of pleistocene ice ages are approached by deduction from paleoenvironmental information, by induction from the genetic structure of populations and species, and by their combination to infer likely consequences. (1) Recent palaeoclimatic information indicate rapid global reversals and changes in ranges of species which would involve elimination with spreading from the edge. Leading edge colonization during a rapid expansion would be leptokurtic and lead to homozygosity and spatial assortment of genomes. In Europe and North America, ice age contractions were into southern refugia, which would promote genome reorganization. (2) The present day genetic structure of species shows frequent geographic subdivision, with parapatric genomes, hybrid zones and suture zones. A survey of recent DNA phylogeographic information supports and extends earlier work. (3) The grasshopperChorthippus parallelusis used to illustrate such data and processes. Its range in Europe is divided on DNA sequences into five parapatric races, with southern genomes showing greater haplotype diversity — probably due to southern mountain blocks acting as refugia and northern expansion reducing diversity. (4) Comparison with other recent studies shows a concordance of such phylogeographic data over pleistocene time scales. (5) The role that ice age range changes may have played in changing adaptations is explored, including the limits of range, rapid change in new invasions and refugial differentiation in a variety of organisms. (6) The effects of these events in causing divergence and speciation are explored usingChorthippusas a paradigm. Repeated contraction and expansion would accumulate genome differences and adaptations, protected from mixing by hybrid zones, and such a composite mode of speciation could apply to many organisms.

https://www.fc.up.pt/mestr_biodiv/aulas/hewitt_1996.pdf

Some genetic consequences of ice ages, and their role in divergence and speciation

The origin of organismal complexity is generally thought to be tightly coupled to the evolution of new gene functions arising subsequent to gene duplication. Under the classical model for the evolution of duplicate genes, one member of the duplicated pair usually degenerates within a few million years by accumulating deleterious mutations, while the other duplicate retains the original function. This model further predicts that on rare occasions, one duplicate may acquire a new adaptive function, resulting in the preservation of both members of the pair, one with the new function and the other retaining the old. However, empirical data suggest that a much greater proportion of gene duplicates is preserved than predicted by the classical model. Here we present a new conceptual framework for understanding the evolution of duplicate genes that may help explain this conundrum. Focusing on the regulatory complexity of eukaryotic genes, we show how complementary degenerative mutations in different regulatory elements of duplicated genes can facilitate the preservation of both duplicates, thereby increasing long-term opportunities for the evolution of new gene functions. The duplication-degeneration-complementation (DDC) model predicts that (1) degenerative mutations in regulatory elements can increase rather than reduce the probability of duplicate gene preservation and (2) the usual mechanism of duplicate gene preservation is the partitioning of ancestral functions rather than the evolution of new functions. We present several examples (including analysis of a new engrailed gene in zebrafish) that appear to be consistent with the DDC model, and we suggest several analytical and experimental approaches for determining whether the complementary loss of gene subfunctions or the acquisition of novel functions are likely to be the primary mechanisms for the preservation of gene duplicates. For a newly duplicated paralog, survival depends on the outcome of the race between entropic decay and chance acquisition of an advantageous regulatory mutation. Sidow (1996, p. 717) On one hand, it may fix an advantageous allele giving it a slightly different, and selectable, function from its original copy. This initial fixation provides substantial protection against future fixation of null mutations, allowing additional mutations to accumulate that refine functional differentiation. Alternatively, a duplicate locus can instead first fix a null allele, becoming a pseudogene. Walsh (1995, p. 426) Duplicated genes persist only if mutations create new and essential protein functions, an event that is predicted to occur rarely. Nadeau and Sankoff (1997, p. 1259) Thus overall, with complex metazoans, the major mechanism for retention of ancient gene duplicates would appear to have been the acquisition of novel expression sites for developmental genes, with its accompanying opportunity for new gene roles underlying the progressive extension of development itself. Cooke et al. (1997, p. 362)

https://www.genetics.org/content/genetics/151/4/1531.full.pdf

Preservation of Duplicate Genes by Complementary, Degenerative Mutations

Plant populations are not randomly arranged assemblages of genotypes but are structured in space and time (2, 29, 49, 58, 84, 112). This structure may be manifested among geographically distinct populations, within a local group of plants, or even in the progeny of individuals. Genetic structure results from the joint action of mutation, migration, selection, and drift, which in tum must operate within the historical and biological context of each plant species. Ecological factors affecting reproduction and dispersal are likely to be particularly important in determining genetic structure (2, 31, 58). Reproduction is the process that translates the current genotypic array into that of subsequent generations, while the dispersal of pollen and seeds determines the postreproductive pattems of gene dispersion within and among populations. Although the concept of genetic structure has been used in various ways (58, 130, 154), we limit our definition to the nonrandom distribution of alleles or genotypes in space or time and disregard genome organization and meiotic processes that can also affect allele and genotype frequencies. Because of the limited mobility of plants, their genetic structure implies spatial structure, or the actual physical distribution of individuals. While spatial pattems often have genetic implications, nonrandom genetic pattems can exist without a nonrandom distribution of individuals. Conversely, a population may have a nonrandom spatial distribution without any accompanying genetic structure. Spatial and genetic patterns are often assumed to result from environmental heterogeneity and differential selection pressures (22, 53, 131, 132). Selection is a ubiquitous feature of natural populations; it alters gene and

Ecological determinants of genetic structure in plant populations

In a population of constant size the expected heterozygosity for a neutral locus when mutation and genetic drift are balanced is given by 4 Nv/(4Nv + 1) under the assumption that new mutations are always different from the pre-existing alleles in the population, where N is the effective population size and v the mutation rate per locus per generation (Kimura, 1968). The size of a natural population, however, often changes drastically in the evolutionary process. In an extreme case a single inseminated female from a large population may migrate to an unoccupied geographical or ecological territory and establish a new colony, followed by rapid population growth to form a new species. This process seems to have occurred repeatedly in the evolution of Hawaiian Drosophila species (Carson, 1970; 1971) and also in the establishment of the Bogota, Colombia, population of Drosophila pseudoobscura (Prakash, 1972). When population size is suddenly reduced, the average heterozygosity per locus is expected to decline, the rate of decline depending on the effective population size, while if population size increases the aver-

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1558-5646.1975.tb00807.x

The bottleneck effect and genetic variability in populations

https://www.genetics.org/content/genetics/54/6/1337.full.pdf

The mutational load with epistatic gene interactions in fitness.

/pdf/the-mutation-load-in-small-populations-3ig4vqwvox.pdf

The mutation load in small populations.

https://www.genetics.org/content/genetics/80/2/395.full.pdf

Lewontin-Krakauer test for neutral genes

Mathematical properties of the overdominance model with mutation and random genetic drift are studied by using the method of stochastic differential equations (Ito and McKean 1974). It is shown that overdominant selection is very powerful in increasing the mean heterozygosity as compared with neutral mutations, and if 2 Ns ( N = effective population size; s = selective disadvantage for homozygotes) is larger than 10, a very low mutation rate is sufficient to explain the observed level of allozyme polymorphism. The distribution of heterozygosity for overdominant genes is considerably different from that of neutral mutations, and if the ratio of selection coefficient ( s ) to mutation rate (ν) is large and the mean heterozygosity ( h ) is lower than 0.2, single-locus heterozygosity is either approximately 0 or 0.5. If h increases further, however, heterozygosity shows a multiple-peak distribution. Reflecting this type of distribution, the relationship between the mean and variance of heterozygosity is considerably different from that for neutral genes. When s/v is large, the proportion of polymorphic loci increases approximately linearly with mean heterozygosity. The distribution of allele frequencies is also drastically different from that of neutral genes, and generally shows a peak at the intermediate gene frequency. Implications of these results on the maintenance of allozyme polymorphism are discussed.

https://www.genetics.org/content/genetics/98/2/441.full.pdf

Takeo Maruyama

Papers

The bottleneck effect and genetic variability in populations

The mutational load with epistatic gene interactions in fitness.

The mutation load in small populations.

Lewontin-Krakauer test for neutral genes

Genetic variability maintained by mutation and overdominant selection in finite populations.