Statistical properties of new neutrality tests against population growth

A number of statistical tests for detecting population growth are described. We compared the statistical power of these tests with that of others available in the literature. The tests evaluated fall into three categories: those tests based on the distribution of the mutation frequencies, on the haplotype distribution, and on the mismatch distribution. We found that, for an extensive variety of cases, the most powerful tests for detecting population growth are Fu's F(S) test and the newly developed R(2) test. The behavior of the R(2) test is superior for small sample sizes, whereas F(S) is better for large sample sizes. We also show that some popular statistics based on the mismatch distribution are very conservative.     

Statistical power analysis of neutrality tests under demographic expansions, contractions and bottlenecks with recombination

Several tests have been proposed to detect departures of nucleotide variability patterns from neutral expectations. However, very different kinds of evolutionary processes, such as selective events or demographic changes, can produce similar deviations from these tests, thus making interpretation difficult when a significant departure of neutrality is detected. Here we study the effects of demography and recombination upon neutrality tests by analyzing their power under sudden population expansions, sudden contractions, and bottlenecks. We evaluate tests based on the frequency spectrum of mutations and the distribution of haplotypes and explore the consequences of using incorrect estimates of the rates of recombination when testing for neutrality. We show that tests that rely on haplotype frequencies-especially Fs and ZnS, which are based, respectively, on the number of different haplotypes and on the r2 values between all pairs of polymorphic sites-are the most powerful for detecting expansions on nonrecombining genomic regions. Nevertheless, they are strongly affected by misestimations of recombination, so they should not be used when recombination levels are unknown. Instead, class I tests, particularly Tajima's D or R2, are recommended.     

Statistical tests for detecting positive selection by utilizing high-frequency variants

By comparing the low-, intermediate-, and high-frequency parts of the frequency spectrum, we gain information on the evolutionary forces that influence the pattern of polymorphism in population samples. We emphasize the high-frequency variants on which positive selection and negative (background) selection exhibit different effects. We propose a new estimator of θ (the product of effective population size and neutral mutation rate), θ_L, which is sensitive to the changes in high-frequency variants. The new θ_L allows us to revise Fay and Wu's H-test by normalization. To complement the existing statistics (the H-test and Tajima's D-test), we propose a new test, E, which relies on the difference between θ_L and Watterson's θ_W. We show that this test is most powerful in detecting the recovery phase after the loss of genetic diversity, which includes the postselective sweep phase. The sensitivities of these tests to (or robustness against) background selection and demographic changes are also considered. Overall, D and H in combination can be most effective in detecting positive selection while being insensitive to other perturbations. We thus propose a joint test, referred to as the DH test. Simulations indicate that DH is indeed sensitive primarily to directional selection and no other driving forces.     

Effect of misoriented sites on neutrality tests with outgroup

Several neutrality tests use outgroups to infer the ancestral and derived states for polymorphism data. However, homoplasy can result in the incorrect inference of the derived variant. We show that empirically derived rates of misorientation strongly influence Fay and Wu's H-test, especially when the sample size is large.     

Modified Hudson-Kreitman-Aguade test and two-dimensional evaluation of neutrality tests

There are a number of polymorphism-based statistical tests of neutrality, but most of them focus on either the amount or the pattern of polymorphism. In this article, a new test called the two-dimensional (2D) test is developed. This test evaluates a pair of summary statistics in a two-dimensional field. One statistic should summarize the pattern of polymorphism, while the other could be a measure of the level of polymorphism. For the latter summary statistic, the polymorphism-divergence ratio is used following the idea of the Hudson-Kreitman-Aguadé (HKA) test. To incorporate the HKA test in the 2D test, a summary statistic-based version of the HKA test is developed such that the polymorphism-divergence ratio at a particular region of interest is examined if it is consistent with the average of those in other independent regions.     

Power of neutrality tests to detect bottlenecks and hitchhiking

The power of several neutrality tests to reject a simple bottleneck model is examined in a coalescent framework. Several tests are considered including some relying on the frequency spectrum of mutations and some reflecting the linkage disequilibrium structure of the data. We evaluate the effect of the age and of the strength of the bottleneck, and their interaction. We contrast two qualitatively different bottleneck effects depending on their strength. In genealogical terms, during severe bottlenecks, all lineages coalesce leading to a star-like gene genealogy of the sample. Some time after the bottleneck, once new mutations have arisen, they tend to show an excess of rare variants and a slight excess of haplotypes. On the contrary, more moderate bottlenecks allow several lineages to survive the demographic crash, leading to a balanced genealogy with long internal branches. Soon after the event, data tend to show an excess of intermediate frequency variants and a deficit of haplotypes. We show that for moderate sequencing efforts, severe bottlenecks can be detected only after an intermediate time period has allowed for mutations to occur, preferably by frequency spectrum statistics. Moderate bottlenecks can be more easily detected for more recent events, especially using haplotype statistics. Finally, for a single locus, the bottleneck results closely approximate those of a simple hitchhiking model. The main difference concerns the frequency distribution of mutations and haplotypes after moderate perturbations. Hitchhiking increases the number of rare ancestral mutations and leads to a more predominant major haplotype class. Thus, despite a number of common features between the two processes, hitchhiking cannot be strictly modeled by bottlenecks.     

The physiology of weak selection

Reaction rates in metabolic pathways typically exhibit a kind of diminishing returns in which small variations in the activities of the individual enzymes have very little effect on overall flux. These effects are measured by the control coefficients of the enzymes, and most systems are governed by the summation theorem stating that all control coefficients must sum to unity. One implication is that complex systems will not usually contain single rate limiting steps, but rather be controlled to a greater or lesser extent by many enzymes, each exerting relatively small control. Wright understood this principle in 1934 and used it for his physiological theory of dominance. With respect to small variations in enzyme activity, the principle implies that many small variations should have only mild effects on fitness. Analysis of nucleotide polymorphisms in the genes for glucose-6-phosphate dehydrogenase and alkaline phosphatase in Escherichia coli implies that most amino acid replacements are harmful, and that the average selection coefficient against amino acid replacements that are polymorphic in natural populations is 1 x 10(-7) to 5 x 10(-7). In experiments to determine the a priori distribution of selection coefficients among random amino acid replacements, 25 replacements in beta-galactosidase were created by genetic means, and 22 of these produced selective effects too small to be detected in chemostat competition experiments (s less than 0.004 per generation).     

SCANMS: adjusting for multiple comparisons in sliding window neutrality tests

SUMMARY: A Perl utility called SCANMS was written that operates on parametric bootstrap data generated by Hudson's simulator MS. SCANMS simulates sliding window analysis of Tajima's D or Fu and Li's D(*) or F(*) over the replicates and generates the empirical joint distribution of window minima and maxima. This distribution may then be used to calculate achieved significance values or significance cutoffs that account for multiple comparisons in sliding window analysis of real data. AVAILABILITY: SCANMS is available free of charge under the terms of the Academic Free License 2.0 and may be downloaded from http://www.lcb.uu.se/~dave/SCANMS     

Convergence of multilocus systems under weak epistasis or weak selection

 The convergence of multilocus systems under viability selection with constant fitnesses is investigated. Generations are discrete and nonoverlapping; the monoecious population mates at random. The number of multiallelic loci, the linkage map, dominance, and epistasis are arbitrary. It is proved that if epistasis or selection is sufficiently weak (and satisfies a certain nondegeneracy assumption whose genericity we establish), then there is always convergence to some equilibrium point. In particular, cycling cannot occur. The behavior of the mean fitness and some other aspects of the dynamics are also analyzed. Received: 15 November 1997 / Revised version: 25 May 1998     

DNA evolution under weak selection

Some DNA data show patterns of variation not expected under the neutral theory. Here, the independent multicodon (IMC) model, a nearly neutral mutation model assuming no interaction among codons, was studied when population size changes using computer simulation. Patterns of variation expected under the model were investigated using statistics for the neutrality tests. The average dispersion index is more than one when population size changes slowly but it never becomes large. The diversity at linked silent site decreases when the strength of selection is intermediate and the reduction is larger when population size changes slowly. Tajima's (1989. Genetics 123, 585-595) D is generally negative. Rejections by the Tajima's test occur more frequently if population size changes quickly but the effect of selection is confounded with the size change itself in this case. If we apply the test of McDonald and Kreitman (1991. Nature 351, 652-654), the rejection is always in the direction of excess replacement polymorphisms. The rejection probability decreases as the rate of population size changes decreases. These results show that the predictions of the IMC model are consistent with the pattern observed in mitochondrial DNA data but not consistent with some data of nuclear DNA. Interaction among codons or variable selection would be necessary to explain such cases.     

Genealogies and weak purifying selection

The assumption that selection alters the genealogical tree of a sample of alleles from a population relative to the neutral expectation underlies several "tests of neutrality." Two recent papers have studied the effect of purifying selection; their suggestive but incomplete results indicate that, in the single site case, the shape of a gene genealogy for a locus may differ only from the neutral expectation. We verify this finding for weak selection using the "ancestral selection graph." We consider a wider range of models, including both a four-allele single-site model and an infinite-sites model. Our results confirm the previous claim for the symmetric-mutation single site model. We emphasize, however, that a neutral-seeming genealogy is consistent with detectable effects of selection on the distribution of allele frequences within the sample. With selection operating, the information about a sample cannot be reduced to the genealogy. As a result, a distinction needs to be made between the selected sites themselves, for which the genealogy offers insufficient information, and linked neutral variation. This distinction seems to have been overlooked in previous papers, yet it has significant implications for the interpretation of data on DNA sequence variation. In particular, it predicts that under purifying selection, the frequency spectrum of neutral mutations will not reflect the skew toward rare polymorphisms at replacement sites even if there is no recombination between them. We caution, however, that the effect of weak selection on the genealogy is specific to the model; a (more realistic) model of multiple linked sites could lead to a more distorted genealogy than is observed for a single site.     

Allele excess at neutrally evolving microsatellites and the implications for tests of neutrality

Skews in the observed allele-frequency spectrum are frequently viewed as an indication of non-neutral evolution. Recent surveys of microsatellite variability have used an excess of alleles as a statistical approach to infer positive selection. Using neutral coalescent simulations we demonstrate that the mean numbers of alleles expected under the stepwise-mutation model and infinite-allele model deviate from the observed numbers of alleles. The magnitude of this difference is dependent on the sample size, mutation rates (theta-values) and observed gene diversities. Moreover, we show that the number of observed alleles differs among loci with the same observed gene diversity but different mutation rates (theta-values). We propose that a reliable test statistic based on allele excess must determine the confidence interval by computer simulations conditional on the observed gene diversity and theta-values. As the latter are notoriously difficult to obtain for experimental data, we suggest that other statistics, such as lnRV, may be better suited to the identification of microsatellite loci subject to selection.     

Statistical tests for natural selection on regulatory regions based on the strength of transcription factor binding sites

Background  

Although cis -regulatory changes play an important role in evolution, it remains difficult to establish the contribution of natural selection to regulatory differences between species. For protein coding regions, powerful tests of natural selection have been developed based on comparisons of synonymous and non-synonymous substitutions, and analogous tests for regulatory regions would be of great utility.     

Effective population size and tests of neutrality at cytoplasmic genes in Arabidopsis.

Cytoplasmic genomes typically lack recombination, implying that genetic hitch-hiking could be a predominant force structuring nucleotide polymorphism in the chloroplast and mitochondria. We test this hypothesis by analysing nucleotide polymorphism data at 28 loci across the chloroplast and mitochondria of the outcrossing plant Arabidopsis lyrata, and compare patterns with multiple nuclear loci, and the highly selfing Arabidopsis thaliana. The maximum likelihood estimate of the ratio of effective population size at cytoplasmic relative to nuclear genes in A. lyrata does not depart from the neutral expectation of 0.5. Similarly, the ratio of effective size in A. thaliana is close to unity, the neutral expectation for a highly selfing species. The results are thus consistent with neutral organelle polymorphism in these species or with comparable effects of hitch-hiking in both cytoplasmic and nuclear genes, in contrast to the results of recent studies on gynodioecious taxa. The four-gamete test and composite likelihood estimation provide evidence for very low levels of recombination in the organelles of A. lyrata, although permutation tests do not suggest that adjacent polymorphic sites are more closely linked than more distant sites across the two genomes, suggesting that mutation hotspots or very low rates of gene conversion could explain the data.     

Postglacial history of a widespread conifer produces inverse clines in selective neutrality tests

Deviations of the site frequency spectrum of mutations (SFS) from neutral expectations may be caused by natural selection or by demographic processes such as population subdivision or temporal changes in population size. As most widespread temperate and boreal tree species have expanded from glacial refugia in the past 13 000 years, colonization bottlenecks associated with this migration may have left variable demographic signatures among geographic populations corresponding to distance from the refugia. To determine whether the signature of postglacial re‐colonization has skewed the SFS in the widely distributed conifer Sitka spruce (Picea sitchensis (Bong.) Carr.), we re‐sequenced 153 nuclear genes in six populations from across the species range. We found that while the SFS for the pooled sample produced negative values for Tajima’s D and Fay and Wu’s H, these statistics exhibited strong clinal variation when populations were analysed separately (R² = 0.84, P = 0.007 for Tajima’s D and R² = 0.65, P = 0.033 for Fay and Wu’s H). When historical bottlenecks of varying age were simulated using approximate Bayesian computation, distance of populations from the southern range limit explained most of the variation in bottleneck timing among populations (R² = 0.89, P = 0.003). These data suggest that sequential population bottlenecks during postglacial re‐colonization have resulted in diverse among‐population signatures within the contemporary SFS in Sitka spruce, with rare variants more common in the south, and medium‐frequency variants more common in the north. Our results also emphasize the need to consider sampling strategy and to explore population‐specific null demographic models in surveys of nucleotide variation in widely distributed species.