Across a species range, islands of stressful habitats impose similar selection pressures on isolated populations. It is as yet unclear, when populations respond to these selective pressures, the extent to which this results in convergent genetic evolution and whether convergence is due to independent mutations or shared ancestral variation. We address these questions investigating a classic example of adaptation by natural selection – the colonization of plant species to heavy metal contaminated soils. We use field-based reciprocal transplant experiments to demonstrate that mine alleles at a major copper tolerance QTL, Tol1, are strongly selected in the mine environment, but are neutral, or nearly so, in the off-mine environment. To identify scaffolds in genetic linkage with this locus, we assemble the genome of a mine adapted M. guttatus genotype and sequence near isogenic lines (NILs) homozygous for tolerant or non-tolerant alleles at Tol1. We identify genes with differential expression between NILs and differences in allele frequency between independent pairs of mine and off-mine populations to identify Tol1 candidate genes. We identify a single gene, a multicopper oxidase, with large differences in expression between NILs and allele frequency between populations. Furthermore, we find patterns of genetic variation at Tol1, and four additional candidate adaptation loci, are consistent with selection acting upon beneficial haplotypes that predates the existence of the copper mine habitat. We estimate the age of selected Tol1 haplotype to be at least 1700 years old and was at a frequency of 0.4-0.6% in the ancestral population when mining was initiated 150 years ago. These results suggest that adaptation to the mine habitat routinely occurs via selection on ancestral variation, rather than independent de-novo mutations or migration between populations.
Decomposing the site frequency spectrum: the impact of tree topology on neutrality tests
Alice Ledda, Guillaume Achaz, Thomas Wiehe, Luca Ferretti
We investigate the dependence of the site frequency spectrum (SFS) on the topological structure of coalescent trees. We show that basic population genetic statistics – for instance estimators of theta or neutrality tests such as Tajima’s D – can be decomposed into components of waiting times between coalescent events and of tree topology. Our results clarify the relative impact of the two components on these statistics. We provide a rigorous interpretation of positive or negative values of neutrality tests in terms of the underlying tree shape. In particular, we show that values of Tajima’s D and Fay and Wu’s H depend in a direct way on a measure of tree balance which is mostly determined by the root balance of the tree. We also compute the maximum and minimum values for neutrality tests as a function of sample size.
Focusing on the standard coalescent model of neutral evolution, we discuss how waiting times between coalescent events are related to derived allele frequencies and thereby to the frequency spectrum. Finally, we show how tree balance affects the frequency spectrum. In particular, we derive the complete SFS conditioned on the root imbalance. We show that the conditional spectrum is peaked at frequencies corresponding to the root imbalance and strongly biased towards rare alleles.
On the Balance of Unrooted Trees
Mareike Fischer, Volkmar Liebscher
We solve a class of optimization problems for (phylogenetic) X-trees or their shapes. These problems have recently appeared in different contexts, e.g. in the context of the impact of tree shapes on the size of TBR neighborhoods, but so far these problems have not been characterized and solved in a systematic way. In this work we generalize the concept and also present several applications. Moreover, our results give rise to a nice notion of balance for trees. Unsurprisingly, so-called caterpillars are the most unbalanced tree shapes, but it turns out that balanced tree shapes cannot be described so easily as they need not even be unique.
Estimation of the True Evolutionary Distance under the Fragile Breakage Model
Nikita Alexeev, Max A. Alekseyev
The ability to estimate the evolutionary distance between extant genomes plays a crucial role in many phylogenomic studies. Often such estimation is based on the parsimony assumption, implying that the distance between two genomes can be estimated as the minimal number of genome rearrangements required to transform one genome into the other. However, in reality the parsimony assumption may not always hold, emphasizing the need for estimation that does not rely on the minimal number of genome rearrangements. While there exists a method for such estimation, it however assumes that genomes can be broken by rearrangements equally likely at any position in the course of evolution. This assumption, known as the random breakage model, has recently been refuted in favor of the more rigorous fragile breakage model postulating that only certain “fragile” genomic regions are prone to rearrangements. We propose a new method for estimating the evolutionary distance between two genomes with high accuracy under the fragile breakage model.
A general approximation for the dynamics of quantitative traits
Katarína Boďová, Gašper Tkačik, Nicholas H. Barton
Selection, mutation and random drift affect the dynamics of allele frequencies and consequently of quantitative traits. While the macroscopic dynamics of quantitative traits can be measured, the underlying allele frequencies are typically unobserved. Can we understand how the macroscopic observables evolve without following these microscopic processes? The problem has previously been studied by analogy with statistical mechanics: the allele frequency distribution at each time is approximated by the stationary form, which maximises entropy. We explore the limitations of this method when mutation is small (4Nμ<1) so that populations are typically close to fixation and we extend the theory in this regime to account for changes in mutation strength. We consider a single diallelic locus under either directional selection, or with over-dominance, and then generalise to multiple unlinked biallelic loci with unequal effects. We find that the maximum entropy approximation is remarkably accurate, even when mutation and selection change rapidly.