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

Abstract

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.

Figure 1.—

Power of the test depending on the time elapsed since the expansion, without recombination. N = 100, D_e = 10. (A) S = 10. (B) S = 100. (C) S = 400. (D) θ = 1.93. (E) θ = 19.31. (F) θ = 77.26.

Figure 2.—

Power of the test in the expansion model depending on recombination rates. N = 100, D_e = 10. (A) S = 10, T_e = 0.02. (B) S = 100, T_e = 0.02. (C) S = 10, T_e = 0.15. (D) S = 100, T_e = 0.15.

Figure 3.—

(A) distribution of the values of Tajima's D, Fu and Li's F, R₂, and Kelly's Z_nS under the neutral model and the expansion model at T_e = 0.02 without recombination and with r = 10⁻⁷. (B) Power of the tests to detect recombination in the null model for the right and left tails of the distribution. (A and B) S = 100, n = 100.

Figure 4.—

Error made by statistics when testing for expansions when recombination is under- or overestimated in the null model. S = 100, n = 100, D_e = 10, T_e = 0.15. The cartoon shows how this error is calculated: first, we calculated the real power of the statistic, comparing the null hypothesis with the alternative hypothesis with the same recombination values. Afterward, we calculated the probability of rejecting the null hypothesis when recombination has been erroneously estimated, that is, when the recombination rate used to generate the null hypothesis is different from that of the alternative hypothesis. The error made is the latter (apparent power) minus the real power. (A) The apparent power of the null hypothesis was produced without recombination. (B) The apparent power of the null hypothesis has a recombination rate of 10⁻⁷.