Author Archives: Joe Pickrell

An alternative to the breeder’s and Lande’s equations

Posted on by
Reply

An alternative to the breeder’s and Lande’s equations
Bahram Houchmandzadeh (LIPhy)
(Submitted on 2 Sep 2013)

The breeder’s equation is a cornerstone of quantitative genetics and is widely used in evolutionary modeling. The equation which reads R=h^{2}S relates response to selection R (the mean phenotype of the progeny) to the selection differential S (mean phenotype of selected parents) through a simple proportionality relation. The validity of this relation however relies strongly on the normal (Gaussian) distribution of parent’s genotype which is an unobservable quantity and cannot be ascertained. In contrast, we show here that if the fitness (or selection) function is Gaussian, an alternative, exact linear equation in the form of R’=j^{2}S’ can be derived, regardless of the parental genotype distribution. Here R’ and S’ stand for the mean phenotypic lag behind the mean of the fitness function in the offspring and selected populations. To demonstrate this relation, we derive the exact functional relation between the mean phenotype in the selected and the offspring population and deduce all cases that lead to a linear relation between these quantities. These computations, which are confirmed by individual based numerical simulations, generalize naturally to the multivariate Lande’s equation \Delta\mathbf{\bar{z}}=GP^{-1}\mathbf{S} .

Most viewed on Haldane’s Sieve: August 2013

Posted on by
Reply

The most viewed preprints on Haldane’s Sieve this month were:

*”The world” is defined for these purposes as Haldane’s Sieve.

Lineage specific reductions in genome size in salamanders are associated with increased rates of mutation

Posted on by
Reply

Lineage specific reductions in genome size in salamanders are associated with increased rates of mutation
John Herrick, Bianca Sclavi
(Submitted on 4 Aug 2013)

Very low levels of genetic diversity have been reported in vertebrates with large genomes, notably salamanders and lungfish [1-3]. Interpreting differences in heterozygosity, which reflects genetic diversity in a population, is complicated because levels of heterozygosity vary widely between conspecific populations, and correlate with many different physiological and demographic variables such as body size and effective population size. Here we return to the question of genetic variability in salamanders, and report on the relationship between evolutionary rates and genome sizes in five different salamander families. We found that rates of evolution are exceptionally low in salamanders as a group. Evolutionary rates are as low as those reported for cartilaginous fish, which have the slowest rates recorded so far in vertebrates [4]. We also found that, independent of life history, salamanders with the smallest genomes (14 pg) are evolving at rates two to three times faster than salamanders with the largest genomes (>50 pg). After accounting for evolutionary duration, we conclude that speciation events in salamanders are associated with contractions in genome size and concomitant increases in mutation and diversification rates.

Effect of linkage on the equilibrium frequency of deleterious mutations

Posted on by
Reply

Effect of linkage on the equilibrium frequency of deleterious mutations
Sona John, Kavita Jain
(Submitted on 5 Aug 2013)

We study the evolution of an asexual population of binary sequences of finite length in which both deleterious and reverse mutations can occur. Such a model has been used to understand the prevalence of preferred codons due to selection, mutation and drift, and proposed as a possible mechanism for halting the irreversible degeneration of asexual population due to Muller’s ratchet. Using an analytical argument and numerical simulations, we study the dependence of the equilibrium fraction of deleterious mutations on various population genetic parameters. In contrast to the one-locus theory, where the fraction of disadvantageous mutations decreases exponentially fast with increasing population size, we find that in the multilocus model, it decreases to zero exponentially for very large populations but approaches a constant for smaller populations logarithmically. The weak dependence on the population size may explain the similar levels of codon bias seen in populations of different sizes.

Most viewed on Haldane’s Sieve: July 2013

Posted on by
Reply

The most viewed preprints in July 2013 were:

The Population Genetic Signature of Polygenic Local Adaptation

Posted on by
16

The Population Genetic Signature of Polygenic Local Adaptation
Jeremy J. Berg, Graham Coop
(Submitted on 29 Jul 2013)

Adaptation in response to selection on polygenic phenotypes occurs via subtle allele frequencies shifts at many loci. Current population genomic techniques are not well posed to identify such signals. In the past decade, detailed knowledge about the specific loci underlying polygenic traits has begun to emerge from genome-wide association studies (GWAS). Here we combine this knowledge from GWAS with robust population genetic modeling to identify traits that have undergone local adaptation. Using GWAS data, we estimate the mean additive genetic value for a give phenotype across many populations as simple weighted sums of allele frequencies. We model the expected differentiation of GWAS loci among populations under neutrality to develop simple tests of selection across an arbitrary number of populations with arbitrary population structure. To find support for the role of specific environmental variables in local adaptation we test for correlations with the estimated genetic values. We also develop a general test of local adaptation to identify overdispersion of the estimated genetic values values among populations. This test is a natural generalization of QST /FST comparisons based on GWAS predictions. Finally we lay out a framework to identify the individual populations or groups of populations that contribute to the signal of overdispersion. These tests have considerably greater power than their single locus equivalents due to the fact that they look for positive covariance between like effect alleles. We apply our tests to the human genome diversity panel dataset using GWAS data for six different traits. This analysis uncovers a number of putative signals of local adaptation, and we discuss the biological interpretation and caveats of these results.

The missing heritability revealed in Arabidopsis thaliana

Posted on by
Reply

The missing heritability revealed in Arabidopsis thaliana
Xia Shen
(Submitted on 30 Jul 2013)

Although high-throughput genomic data are widely available, a large proportion of the narrow sense heritability of many complex traits have not been successfully uncovered. In this study, focusing on phenotype prediction, I show that by properly selecting a small number of loci, a significant amount of missing heritability can be revealed. The results provide new insights into the missing heritability problem and the underlying genetic architecture of complex traits.

A path integral formulation of the Wright-Fisher process with genic selection

Posted on by
1

A path integral formulation of the Wright-Fisher process with genic selection
Joshua G. Schraiber
(Submitted on 29 Jul 2013)

The Wright-Fisher process with selection is an important tool in population genetics theory. Traditional analysis of this process relies on the diffusion approximation. The diffusion approximation is usually studied in a partial differential equations framework. In this paper, I introduce a path integral formalism to study the Wright-Fisher process with selection and use that formalism to obtain a simple perturbation series to approximate the transition density. The perturbation series can be understood in terms of Feynman diagrams, which have a simple probabilistic interpretation in terms of selective events. The perturbation series proves to be an accurate approximation of the transition density for weak selection and is shown to be arbitrarily accurate for any selection coefficient.

Ancient west Eurasian ancestry in southern and eastern Africa

Posted on by
7

Ancient west Eurasian ancestry in southern and eastern Africa
Joseph K. Pickrell, Nick Patterson, Po-Ru Loh, Mark Lipson, Bonnie Berger, Mark Stoneking, Brigitte Pakendorf, David Reich
(Submitted on 30 Jul 2013)

The history of southern Africa involved interactions between indigenous hunter-gatherers and a range of populations that moved into the region. Here we use genome-wide genetic data to show that there are at least two admixture events in the history of Khoisan populations (southern African hunter-gatherers and pastoralists who speak non-Bantu languages with click consonants). One involved populations related to Niger-Congo-speaking African populations, and the other introduced ancestry most closely related to west Eurasian (European or Middle Eastern) populations. We date this latter admixture event to approximately 900-1,800 years ago, and show that it had the largest demographic impact in Khoisan populations that speak Khoe-Kwadi languages. A similar signal of west Eurasian ancestry is present throughout eastern Africa. In particular, we also find evidence for two admixture events in the history of Kenyan, Tanzanian, and Ethiopian populations, the earlier of which involved populations related to west Eurasians and which we date to approximately 2,700 – 3,300 years ago. We reconstruct the allele frequencies of the putative west Eurasian population in eastern Africa, and show that this population is a good proxy for the west Eurasian ancestry in southern Africa. The most parsimonious explanation for these findings is that west Eurasian ancestry entered southern Africa indirectly through eastern Africa.

Characterizing Compatibility and Agreement of Unrooted Trees via Cuts in Graphs

Posted on by
Reply

Characterizing Compatibility and Agreement of Unrooted Trees via Cuts in Graphs
Sudheer Vakati, David Fernández-Baca
(Submitted on 30 Jul 2013)

Deciding whether there is a single tree -a supertree- that summarizes the evolutionary information in a collection of unrooted trees is a fundamental problem in phylogenetics. We consider two versions of this question: agreement and compatibility. In the first, the supertree is required to reflect precisely the relationships among the species exhibited by the input trees. In the second, the supertree can be more refined than the input trees.
Tree compatibility can be characterized in terms of the existence of a specific kind of triangulation in a structure known as the display graph. Alternatively, it can be characterized as a chordal graph sandwich problem in a structure known as the edge label intersection graph. Here, we show that the latter characterization yields a natural characterization of compatibility in terms of minimal cuts in the display graph, which is closely related to compatibility of splits. We then derive a characterization for agreement.