Phylogenetic trees are central to many areas of biology, ranging from population genetics and epidemiology to microbiology, ecology, and macroevolution. The ability to summarize properties of trees, compare different trees, and identify distinct modes of division within trees is essential to all these research areas. But despite wide-ranging applications, there currently exists no common, comprehensive framework for such analyses. Here we present a graph-theoretical approach that provides such a framework. We show how to construct the spectral density profiles of phylogenetic trees from their Laplacian graphs. Using ultrametric simulated trees as well as non-ultrametric empirical trees, we demonstrate that the spectral density successfully identifies various properties of the trees and clusters them into meaningful groups. Finally, we illustrate how the eigengap can identify modes of division within a given tree. As phylogenetic data continue to accumulate and to be integrated into various areas of the life sciences, we expect that this spectral graph-theoretical framework to phylogenetics will have powerful and long-lasting applications.

The realisation that heterozygosity can be heritable has recently generated some elegant research. However, none of this work has discussed the fact that when heterozygote advantage occurs, heterozygosity can be heritable, yet allele frequencies remain at equilibrium and do not evolve with time. From a quantitative genetic perspective this means the character is heritable, is under selection, yet no response to selection is observed. We explain why this is the case, and discuss potential implications for the study of evolution in the wild.

We present an open source package for performing evolutionary quantitative genetics analyses in the R environment for statistical computing. Evolutionary theory shows that evolution depends critically on the available variation in a given population. When dealing with many quantitative traits this variation is expressed in the form of a covariance matrix, particularly the additive genetic covariance matrix or sometimes the phenotypic matrix, when the genetic matrix is unavailable. Given this mathematical representation of available variation, the EvolQG package provides functions for calculation of relevant evolutionary statistics, estimation of sampling error, corrections for this error, matrix comparison via correlations and distances, and functions for testing evolutionary hypotheses on taxa diversification.

A central aim of evolutionary genomics is to identify the relative roles that various evolutionary forces have played in generating and shaping genetic variation within and among species. Here we used whole-genome re-sequencing data from three related Populus species to characterize and compare genome-wide patterns of nucleotide polymorphism, site frequency spectrum, population-scaled recombination rate and linkage disequilibrium. Our analyses revealed that P. tremuloides has the highest level of genome-wide variation, skewed allele frequencies and population-scaled recombination rates, whereas P. trichocarpa harbors the lowest. Consistent with this, linkage disequilibrium decay was fastest in P. tremuloides and slowest in P. trichocarpa. Pervasive natural selection has been proven to be the primary force creating significant positive correlations between neutral polymorphism and recombination rate in all three species. Disparate effective population sizes and recombination rates among species, on the other hand, drive the distinct magnitudes and signatures of linked selection and consequent heterogeneous patterns of genomic variation among them. We find that purifying selection against slightly deleterious non-synonymous mutations is more effective in regions experiencing high recombination, which may provide one explanation for a partially positive association between recombination rate and gene density in these species. Moreover, distinct signatures of linked selection dependent on gene density are found between genic and intergenic regions within each species. To our knowledge, the present work is the first comparative population genomic study among forest tree species and represents an important step toward dissecting how the interactions of various evolutionary forces have shaped genomic variation within and among these ecologically and economically important tree species.

In this work two complementary methods for detection of divergent selection between pairs of populations connected by migration are introduced. The new statistics do not require knowledge on the ancestral or derived allelic state and are robust to false positives. Additionally, it is not necessary to perform neutral simulations to obtain critical cut-off values for the identification of candidates. The utility of the methods is demonstrated in simulations. First method, called nvdFST, combines information from the haplotype patterns with inter-population differences in allelic frequency. Remarkably, this is not a FST outlier test because highest FSTs are not a priori selected to identify loci. On the contrary, candidate loci are chosen based upon haplotype allelic class metric and then the FST for these loci are estimated and compared to the overall FST. Evidence of divergent selection is concluded only when both the haplotype pattern and the FST value indicate that outcome. It is shown that powers ranging from 70-90% are achieved in many of the scenarios assayed while the false positive rate is controlled below the desired nominal level (γ = 0.05). Additionally, the method is also robust to demographic scenarios involving population bottleneck and expansion. The second method is developed for cases with independently segregating markers, where the information contained in the haplotypes vanishes. In this case, the power to detect selection is attained by developing a new FST extreme-outlier test based on a k-means clustering algorithm. Both kinds of strategies have been implemented in the program HacDivSel

Methods for inference and interpretation of evolutionary quantitative genetic parameters, and for prediction of evolution in response to natural selection, are best developed for traits with normal distributions, yet many traits of evolutionary interest, such as most life history and behavioural traits, have inherently non-normal distributions. It is therefore becoming increasingly common to estimate quantitative genetic parameters, such as additive genetic variances, for non-normal traits using generalised linear mixed model (GLMM) analyses. These statistical methods provide inferences on a statistically-convenient latent scale, but not on the scale upon which traits are expressed. We provide a general approach for calculating quantitative genetic parameters on the observed scale for arbitrary GLMMs. Our approach requires no additional assumptions beyond those that made when adopting GLMM-based quantitative genetic analysis. We show that existing formulae for Binomial and Poisson distributions, in particular the threshold models for binary traits, are special cases in our framework. We use simulations to demonstrate the accuracy of our method for predicting the evolutionary response to selection and further illustrate our approach by applying it to data from a natural study population with pedigree information. Our framework is implemented in an R package, \textsc{QGglmm} (\url{https://github.com/devillemereuil/qgglmm}).

Human migration and human isolation serve as the driving forces of modern human civilization. Recent migrations of long isolated populations has resulted in genetically admixed populations. The history of population admixture is generally complex; however, understanding the admixture process is critical to both evolutionary and medical studies. Here, we utilized admixture induced linkage disequilibrium (LD) to infer occurrence of continuous admixture events, which is common for most existing admixed populations. Unlike previous studies, we expanded the typical continuous admixture model to a more general admixture scenario with isolation after a certain duration of continuous gene flow, and we demonstrated that such treatment significantly improved the accuracy of inference under complex admixture scenarios. Based on the extended models, we developed a method based on weighted LD to infer the admixture history considering continuous and complex demographic process of gene flow between populations. We evaluated the performance of the method by computer simulation and applied our method to real data analysis of a few well-known admixed populations.

Our method for “Time to most recent common ancestor” TMRCA of genetic trees for the first time deals with natural selection by apriori mathematics and not as a random factor. Bioprocesses such as “kin selection” generate a few overrepresented “singular lineages” while almost all other lineages terminate. This non-uniform branching gives greatly exaggerated TMRCA with current methods. Thus we introduce an inhomogenous stochastic process which will detect singular lineages by asymmetries, whose “reduction” then gives true TMRCA. This gives a new phylogenetic method for computing mutation rates, with results similar to “pedigree” (meiosis) data. Despite these low rates, reduction implies younger TMRCA, with smaller errors. We establish accuracy by a comparison across a wide range of time, indeed this is only y-clock giving consistent results for 500-15,000 ybp. In particular we show that the dominant European Y-haplotypes R1a1a & R1b1a2, expand from c4000BC, not reaching Anatolia before c3800BC. This contradicts previous clocks dating R1b1a2 to either the Neolithic Near East or Paleo-Europe. However our dates match R1a1a & R1b1a2 found in Yamnaya cemetaries of c3300BC by Nielsen et al (2015), Pääbo et al(2015), together proving R1a1a & R1b1a2 originates in the Russian Steppes.