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Identifying and quantifying fitness effects across loci
The following guest post by Ethan Jewett is cross-posted from the is cross-posted from the CEHG blog at Stanford. Enjoy!
The degree to which similarities and differences among species are the result of natural selection, rather than genetic drift, is a major question in population genetics. Related questions include: what fraction of sites in the genome of a species are affected by selection? What is the distribution of the strength of selection across genomic sites, and how have selective pressures changed over time? To address these questions, we must be able to accurately identify sites in a genome that are under selection and quantify the selective pressures that act on them.
Difficulties with existing approaches for quantifying fitness effects
A recent paper in Trends in Genetics by David Lawrie and Dmitri Petrov (Lawrie and Petrov, 2014) provides intuition about the power of existing methods for identifying genomic regions affected by purifying selection and for quantifying the selective pressures at different sites. The paper proposes a new framework for quantifying the distribution of fitness effects across a genome. This new framework is a synthesis of two existing forms of analysis – comparative genomic analyses to identify genomic regions in which the level of divergence among two or more species is smaller than expected, and analyses of the distribution of the frequencies of polymorphisms (the site frequency spectrum, or SFS) within a single species (Figure 1). Using simulations and heuristic arguments, Lawrie and Petrov demonstrate that these two forms of analysis can be combined into a framework for quantifying selective pressures that has greater power to identify selected regions and to quantify selective strengths than either approach has on its own.
Lawrie and Petrov begin by discussing the strengths and weaknesses of the two existing approaches. Comparative analyses of genomic divergence are beneficial for identifying genomic regions under purifying selection, which will exhibit lower-than-expected levels of divergence among species. However, as Lawrie and Petrov note, it can be difficult to use comparative analyses to quantify the strength of selection in a region because even mild purifying selection can result in complete conservation among species within the region (Figure 2). For example, whether the population-scaled selective strength, 4Nes, in a region is 20 or 200, the same genomic signal will be observed, complete conservation.
In contrast to comparative approaches, analyses of within-species polymorphisms based on the site frequency spectrum (SFS) within a region can be used to more precisely quantify the strength of selection. For example, Figure 1 shows that different selective strengths can produce very different site frequency spectra. Moreover, if the SFS can be estimated precisely enough, it can allow us to distinguish between two different selective strengths (e.g., 4Nes1 = 20 and 4Nes2 = 200) that would both lead to total conservation in a comparative study, and would therefore be indistinguishable. The problem is that it takes a lot of polymorphisms to obtain an accurate estimate of the SFS, and a genomic region of interest may contain too few polymorphisms, especially if the region is under purifying selection, which decreases the apparent mutation rate. Sampling additional individuals from the same species may provide little additional information about the SFS because few novel polymorphisms may be observed in the additional sample. For example, recall that for a sample of n individuals from a wildly idealized panmictic species, the expected number of novel polymorphisms observed in the n+1st sampled individual is proportional to 1/n (Watterson, 1975).
The need for sampling depth and breadth
Lawrie and Petrov demonstrate that studying polymorphisms by sampling many individuals across several related species (rather than sampling more individuals within a single species) could increase the observed number of polymorphisms in a region, and therefore, could increase the power to quantify the strength of selection (Figure 3) – as long as the selective forces in the genomic region are sufficiently similar across the different species.
Without getting bogged down in the details, it’s the rare variants that are often the most important for quantifying the effects of purifying selection, so one still has to sample deeply within each species; however, overall, sampling from additional species is a more efficient way of increasing the absolute number of variants that can be used to estimate the SFS in a region, compared with sampling more deeply within the same species.
The simulations and heuristic arguments presented by Lawrie and Petrov consider idealized cases for simplicity; however, the usefulness of approaches that consider polymorphisms across multiple species has been demonstrated in methods such as the McDonald-Kreitman test (McDonald and Kreitman, 1991), which have long been important tools for studying selection. More recent empirical applications of approaches that consider information about polymorphisms across multiple species appear to do a good job of quantifying selective pressures across genomes (Wilson et al., 2011; Gronau et al., 2013), even when species are closely related (De Maio et al., 2013). Overall, the simulations and arguments presented in Lawrie and Petrov’s paper provide useful guidelines for researchers interested in identifying and quantifying selective forces, and their recommendation to sample deeply within species and broadly across many species comes at a time when such analyses are becoming increasingly practical, given the recent availability of sequencing data from many species.
De Maio, N., Schlötterer, C., and Kosiol, C. 2013. Linking great apes genome evolution across time scales using polymorphism-aware phylogenetic models. Molecular Biology and Evolution. 30:2249-2262. doi: 10.1093/molbev/mst131.
Gronau, I., Arbiza, L., Mohammed, J., and Siepel, A. 2013. Inference of natural selection from interspersed genomic elements based on polymorphism and divergence. Molecular Biology and Evolution. 30:1159-1171. doi: 10.1093/molbev/mst019.
Lawrie, D.S. and Petrov, D.A. 2014. Comparative population genomics: power and principles for the inference of functionality. Trends in Genetics. 30:133-139. doi: 10.1016/j.tig.2014.02.002.
Watterson, G.A. 1975. On the number of segregating sites in genetical models without recombination. Theoretical Population Biology. 7:256-276. doi: 10.1016/0040-5809(75)90020-9.
Wilson, D.J., Hernandez, R.D., Andolfatto, P., and Przeworski, M. 2011. A population genetics-phylogenetics approach to inferring natural selection in coding sequences. PLOS Genetics. 7:e1002395. doi: 10.1371/journal.pgen.1002395.
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