The probability of joint monophyly of all species in an arbitrary species tree.

Monophyly is a feature of a set of genetic lineages in which every lineage in the set is more closely related to all other members of the set than it is to any lineage outside the set. Multiple sets of lineages that are separately monophyletic are said to be reciprocally monophyletic, or jointly monophyletic. The prevalence of reciprocal monophyly, or joint monophyly, has been used to evaluate phylogenetic and phylogeographic hypotheses, as well as to delimit species. These applications often make use of a probability of joint monophyly under models of gene lineage evolution. Studies in coalescent theory have computed this joint monophyly probability for small numbers of separate groups in arbitrary species trees, and for arbitrary numbers of separate groups in trivial species trees. Here, generalizing existing results on monophyly probabilities under the multispecies coalescent, we derive the probability of joint monophyly for arbitrary numbers of separate groups in arbitrary species trees. We illustrate how our result collapses to previously examined cases. We also study the effect of tree height, sample size, and number of species on the probability of joint monophyly. The result also enables computation of relatively simple lower and upper bounds on the joint monophyly probability. Our results expand the scope of joint monophyly calculations beyond small numbers of species, subsuming past formulas that have been used in simpler cases.

How Our Cells Become Our Selves: The Cellular Phylodynamic Biology of Growth and Development

Our lives begin with 1 cell, then 2, then 4, then the trillion cell adult, comprised of cell lineages, tissues, organs. How does this occur? Examination in numbers of cells, N, Cellular Phylodynamics, revealed two previously unappreciated processes: UNI-GROWTH, the slowing of growth that occurs as we become larger, caused by fewer cells dividing, captured by the Universal Mitotic Fraction and Universal Growth Equations, with accuracy confirmed for 13 species, including nematodes, mollusks, and vertebrates; and ALLO-GROWTH, the creation of body parts from Founder Cells, captured by the Cellular Allometric Growth Equation, which describes mitotic expansion by Cell-Heritable change in the Cell Cycle Time. These equations can generate cell lineage approximations, bringing the power of coalescent theory to developmental biology.

Pointing the Way to Additional Topics

This concluding chapter highlights many of the concepts that are important to understanding modern-day population genetics research and explains that while they may not have been covered in this book, they are built on the foundations laid out in the preceding chapters. A series of small sections are provided which briefly introduce important concepts for continued learning. These focus especially on the coalescent theory but also touch on tests of neutrality, linkage disequilibrium, deleterious alleles, fixation probability, selfish genetic elements, future directions, and R packages.

Coalescent Theory of Migration Network Motifs

Natural populations display a variety of spatial arrangements, each potentially with a distinctive impact on genetic diversity and genetic differentiation among subpopulations. Although the spatial arrangement of populations can lead to intricate migration networks, theoretical developments have focused mainly on a small subset of such networks, emphasizing the island-migration and stepping-stone models. In this study, we investigate all small network motifs: the set of all possible migration networks among populations subdivided into at most four subpopulations. For each motif, we use coalescent theory to derive expectations for three quantities that describe genetic variation: nucleotide diversity, FST, and half-time to equilibrium diversity. We describe the impact of network properties on these quantities, finding that motifs with a high mean node degree have the largest nucleotide diversity and the longest time to equilibrium, whereas motifs with low density have the largest FST. In addition, we show that the motifs whose pattern of variation is most strongly influenced by loss of a connection or a subpopulation are those that can be split easily into disconnected components. We illustrate our results using two example data sets—sky island birds of genus Sholicola and Indian tigers—identifying disturbance scenarios that produce the greatest reduction in genetic diversity; for tigers, we also compare the benefits of two assisted gene flow scenarios. Our results have consequences for understanding the effect of geography on genetic diversity, and they can assist in designing strategies to alter population migration networks toward maximizing genetic variation in the context of conservation of endangered species.

Neutral Evolution in One- and Two-Locus Systems

This chapter reviews the population-genetic theory of neutral alleles in finite populations, examining the probabilities and times to loss or fixation, summary statistics for molecular variation, coalescent theory (the distribution of times back to common ancestry for a sample of alleles), and both mutation-drift and mutation-drift-migration equilibrium models.

Reconstructing the history of polygenic scores using coalescent trees

1AbstractGenome-wide association studies (GWAS) have revealed that many traits are highly polygenic, in that their within-population variance is governed in part by small-effect variants at many genetic loci. Standard population-genetic methods for inferring evolutionary history are ill-suited for polygenic traits—when there are many variants of small effect, signatures of natural selection are spread across the genome and subtle at any one locus. In the last several years, several methods have emerged for detecting the action of natural selection on polygenic scores, sums of genotypes weighted by GWAS effect sizes. However, most existing methods do not reveal the timing or strength of selection. Here, we present a set of methods for estimating the historical time course of a population-mean polygenic score using local coalescent trees at GWAS loci. These time courses are estimated by using coalescent theory to relate the branch lengths of trees to allele-frequency change. The resulting time course can be tested for evidence of natural selection. We present theory and simulations supporting our procedures, as well as estimated time courses of polygenic scores for human height. Because of its grounding in coalescent theory, the framework presented here can be extended to a variety of demographic scenarios, and its usefulness will increase as both GWAS and ancestral recombination graph (ARG) inference continue to progress.

Coalescent theory of migration network motifs

ABSTRACTNatural populations display a variety of spatial arrangements, each potentially with a distinctive impact on genetic diversity and genetic differentiation among subpopulations. Although the spatial arrangement of populations can lead to intricate migration networks, theoretical developments have focused mainly on a small subset of such networks, emphasizing the island-migration and stepping-stone models. In this study, we investigate all small network motifs: the set of all possible migration networks among populations subdivided into at most four subpopulations. For each motif, we use coalescent theory to derive expectations for three quantities that describe genetic variation: nucleotide diversity, FST, and half-time to equilibrium diversity. We describe the impact of network properties on these quantities, finding that motifs with a large mean node degree have the largest nucleotide diversity and the longest time to equilibrium, whereas motifs with small density have the largest FST. In addition, we show that the motifs whose pattern of variation is most strongly influenced by loss of a connection or a subpopulation are those that can be split easily into several disconnected components. We illustrate our results using two example datasets—sky island birds of genus Brachypteryx and Indian tigers—identifying disturbance scenarios that produce the greatest reduction in genetic diversity; for tigers, we also compare the benefits of two assisted gene flow scenarios. Our results have consequences for understanding the effect of geography on genetic diversity and for designing strategies to alter population migration networks to maximize genetic variation in the context of conservation of endangered species.