A challenging aspect of the implementation of these methods is computing Pr x ij selected , which requires simulations under clear demographic assumptions. In contrast, as discussed earlier, many methods designed to detect markers under positive selection allow for approximating Pr x ij neutral from asymptotic theoretical or empirical distributions. Therefore, composite tests considering only the distributions under neutrality are more appropriate for cattle data.
The original CMS score can be modified to take advantage of the assumed distributions under neutrality in order to relax demographic assumptions and avoid expensive simulations. The most essential modification involves reformulating the problem of detecting markers departing from neutrality. Instead of considering the assessment of whether a marker has been selected or not, one can look for support from the data against the null model, i. First, let the new CMS score be the approximate joint posterior probability of a given variant not being neutral:.
Therefore, the new CMS score can be re-written as:.
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It is important to note that this modification does not allow for the same interpretation as the original CMS method: the composite likelihood does not indicate selection, but rather, that a marker does not fit well the neutral model. Following the ideas expanded from the landmark publication of Grossman et al. For any given statistic, p -values are uniformly distributed in the interval between 0 and 1 under the null hypothesis.
This property makes possible to use an inverse CDF, such as the Gaussian density, to produce scores for each test derived from a single theoretical distribution. These Z-transformed p -values can be then averaged and standardized to produce a composite score. As the Stouffer method assumes the tests are uncorrelated under the shared null hypothesis and the use of pair-wise comparisons produce correlated scores, a weighted average was originally proposed to penalize dependent tests:.
In this setting, a uniform penalization can be applied to control for the inflation of correlated tests. Considering all scores are equally weighted, the corrected composite score can be computed as:. Under the hypothesis of neutrality, these composite scores are distributed as N 0, 1 , so the higher is the Z-transformed value, the worse the marker fits the neutral model. Upper tail p -values can then be obtained from the standard normal CDF. Randhawa et al. Briefly, the vector of test statistics for method j is first sorted and then ranked, taking values 1, …, k. This strategy is equivalent to computing probabilities from an empirical CDF using a step function, as discussed earlier, which has an appealing feature: as fractional ranking can be generated for any particular test, signature blending is made feasible even if the theoretical distributions are unknown or if scores have been averaged in chromosome windows.
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However, a caveat is that the magnitude of the actual test statistics may be lost, so one may expect loss of power compared to the use of theoretical or simulated distributions. Simianer et al. The attractive feature of this method is the possibility of using standardized scores instead of approximate probabilities.
However, as each principal component has heterogeneous loadings from each test, deriving a single synthetic score that summarizes all different tests remains a challenge in this framework. In theory, genome-wide genotypes are a vast source of information that can be explored in the search for large effect mutations that underwent selection.
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However, the existing data and methods still suffer from power issues and confounding effects that can give rise to false positive and false negative signals. Although simulations suggest that only marginal gains in power are obtained when the sample size is increased from tens to hundreds of unrelated samples, marker density and allele frequency spectrum seems to impact power dramatically Lappalainen et al. Genotypes derived from commercial SNP arrays have two important limitations in this context: 1 incomplete genome coverage by markers; and 2 ascertainment bias. The search for SS must be preferentially performed using high density SNP panels, although optimal average intermarker distances to detect a sweep may vary depending on the effective population size, extent of linkage disequilibrium and the nature of the signal.
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Regarding ascertainment bias, commercial SNP arrays are suitable for cattle populations that are closely related to the breeds used in the SNP discovery process, but there is no guarantee they will be informative in genetically distant populations. Indeed, with a few exceptions, little congruence has been reported between candidate selected loci identified using whole genome sequence and different commercial genotyping platforms in African humans not included in the HapMap data Lachance and Tishkoff, Altogether, these arguments suggest that re-sequencing data is the optimal choice in SS studies in cattle.
At some extent, the HD assay is appropriate, as it has a high-density coverage of the genome with SNPs that are less biased than competing panels. Another important source of confounding comes from the methods available to detect SS. First, all methods assume that individuals have no recent relationships in their pedigrees, a condition that is hardly true and generally ignored. It is essential to filter the data for cryptic relationships and assure to include only samples that are unrelated for at least two generations.
Second, most of the methods rely on haplotypes and SNP coordinates, so further improvement of phasing strategies and of the bovine reference genome assembly is crucial to assure high quality results. Third, variants can depart from neutrality not only due to positive selection, but also as consequence of demographic events such as bottlenecks, genetic drift and admixture. Distinguishing loci under selection from neutrally evolving loci remains a major challenge in the field, and will require refinement of existing methods and development of new tests.
Nevertheless, combining signals across different methods seems to be a promising approach to mitigate the individual methodological limitations. Also, when available, the concomitant analysis of environmental data e. Well-planned study designs will be crucial to exploit the full potential of SS in the detection of large effect mutations favored by selection.
The identification of common adaptive phenotypes, together with geographical information data, should be an important player in sampling and decisions of population comparisons. Cattle breeds that are not highly productive but that exhibit genetic local adaptation should be considered as priority targets, as their environmental fitness was probably forged by hundreds of years of natural and artificial selection. In the context of artificial selection for complex traits, as large cattle pedigree cohorts for genomic selection become available, it will be soon possible to actually assess rapid changes in allele frequency using historical data, rather than present date data only.
First demonstrations of such ideas were presented by Decker et al. Similarly, results from a SS scan on the human Genomes data reported by Grossman et al. Pybus et al. The research community would highly benefit from the development of a SS database for livestock species, which would not only facilitate cross-referencing, but would also help researchers willing to dig deep into the functional meaning of the signals to select promising candidates emerging from multiple preexisting studies.
Finally, similarly to the recent developments in human SS Kamberov et al. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Mention of trade name proprietary product or specified equipment in this article is solely for the purpose of providing specific information and does not imply recommendation or endorsement by the authors or their respective institutions. Ajmone-Marsan, P. On the origin of cattle: how aurochs became cattle and colonized the world. Issues News Rev.
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Detecting selection in population trees: the lewontin and krakauer test extended. Genetics , — Bradley, D. Mitochondrial diversity and the origins of African and European cattle. Browning, B. A unified approach to genotype imputation and haplotype-phase inference for large data sets of trios and unrelated individuals.
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Chen, H. Population differentiation as a test for selective sweeps. Genome Res 20, — Curik, I. Inbreeding and runs of homozygosity: a possible solution to an old problem. Darwin, C. On the tendency of species to form varieties; and on the perpetuation of varieties and species by natural means of selection. Decker, J. Worldwide patterns of ancestry, divergence, and admixture in domesticated cattle.