Related papers: Mathematical Framework for Phylogenetic Birth-And-…
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…
Phylogenetic comparative methods are well established tools for using inter-species variation to analyse phenotypic evolution and adaptation. They are generally hampered, however, by predominantly univariate approaches and failure to…
We compare three basic kinds of discrete mathematical models used to portray phylogenetic relationships among species and higher taxa: phylogenetic trees, Hennig trees and Nelson cladograms. All three models are trees, as that term is…
Phylogenetic networks are becoming increasingly popular in phylogenetics since they have the ability to describe a wider range of evolutionary events than their tree counterparts. In this paper, we study Markov models on phylogenetic…
Plasticity-led evolution is a form of evolution where a change in the environment induces novel traits via phenotypic plasticity, after which the novel traits are genetically accommodated over generations under the novel environment. This…
Models of random phylogenetic networks have been used since the inception of the field, but the introduction and rigorous study of mathematically tractable models is a much more recent topic that has gained momentum in the last 5 years.…
Distance-based approaches in phylogenetics such as Neighbor-Joining are a fast and popular approach for building trees. These methods take pairs of sequences from them construct a value that, in expectation, is additive under a stochastic…
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…
Stochastic modeling of phylogenies raises five questions that have received varying levels of attention from quantitatively inclined biologists. 1) How large do we expect (from the model) the ration of maximum historical diversity to…
Inference of the marginal likelihood of sample allele configurations using backward algorithms yields identical results with the Kingman coalescent, the Moran model, and the diffusion model (up to a scaling of time). For inference of…
Stem cell heterogeneity is essential for the homeostasis in tissue development. This paper established a general formulation for understanding the dynamics of stem cell regeneration with cell heterogeneity and random transitions of…
Phylogenetic profiles - presence-absence patterns of genes across taxa - are rich information sources for inferring the evolutionary history of genes and gene families. When aggregated across many genes, these profiles can reveal…
Phylogenetic comparative methods explore the relationships between quantitative traits adjusting for shared evolutionary history. This adjustment often occurs through a Brownian diffusion process along the branches of the phylogeny that…
A geophylogeny is a phylogenetic tree (or dendrogram) where each leaf (e.g. biological taxon) has an associated geographic location (site). To clearly visualize a geophylogeny, the tree is typically represented as a crossing-free drawing…
We define phylogenetic projective toric model of a trivalent graph as a generalization of a binary symmetric model of a trivalent phylogenetic tree. Generators of the pro- jective coordinate ring of the models of graphs with one cycle are…
Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…
Null models of binary phylogenetic trees are useful for testing hypotheses on real world phylogenies. In this paper we consider phylogenies as binary trees without edge lengths together with a sampling measure and encode them as algebraic…
We study the evolution of sexual and asexual populations in general fitness landscapes. We find deep relations between the mathematics of biological evolution and the formalism of quantum mechanics. We give the general structure of the…
Time-calibrated species phylogenies are critical for addressing a wide range of questions in evolutionary biology, such as those that elucidate historical biogeography or uncover patterns of coevolution and diversification. Because…
Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…