Related papers: The Shape of Phylogenies Under Phase-Type Distribu…
Forward-time models of diversification (i.e., speciation and extinction) produce phylogenetic trees that grow "vertically" as time goes by. Pruning the extinct lineages out of such trees leads to natural models for reconstructed trees…
A popular line of research in evolutionary biology is the use of time-calibrated phylogenies for the inference of diversification processes. This requires computing the likelihood of a given ultrametric tree as the reconstructed tree…
Simple stochastic models for phylogenetic trees on species have been well studied. But much paleontology data concerns time series or trees on higher-order taxa, and any broad picture of relationships between extant groups requires use of…
A wide variety of stochastic models of cladogenesis (based on speciation and extinction) lead to an identical distribution on phylogenetic tree shapes once the edge lengths are ignored. By contrast, the distribution of the tree's edge…
Phylogenetic trees describe the relationships between species in the evolutionary process, and provide information about the rates of diversification. To understand the mechanisms behind macroevolution, we consider a class of multitype…
Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
The selection of the most suitable evolutionary model to analyze the given molecular data is usually left to biologist's choice. In his famous book, J Felsenstein suggested that certain linear equations satisfied by the expected…
We use a combination of analytic models and computer simulations to gain insight into the dynamics of evolution. Our results suggest that certain interesting phenomena should eventually emerge from the fossil record. For example, there…
In this paper we present a new way to understand the timing of branching events in phylogenetic trees. Our method explicitly considers the relative timing of diversification events between sister clades; as such it is complimentary to…
Phylogenetic trees represent the evolutionary relationships between extant lineages, where extinct or non-sampled lineages are omitted. Extending the work of Stadler and collaborators, this paper focuses on the branch lengths in…
Phylogenetic tree shapes capture fundamental signatures of evolution. We consider ``ranked'' tree shapes, which are equipped with a total order on the internal nodes compatible with the tree graph. Recent work has established an elegant…
Phylogenetic diversity is a measure for describing how much of an evolutionary tree is spanned by a subset of species. If one applies this to the (unknown) subset of current species that will still be present at some future time, then this…
For a model of molecular evolution to be useful for phylogenetic inference, the topology of evolutionary trees must be identifiable. That is, from a joint distribution the model predicts, it must be possible to recover the tree parameter.…
We introduce a model for the evolution of species triggered by generation of novel features and exhaustive combination with other available traits. Under the assumption that innovations are rare, we obtain a bursty branching process of…
The reliability of a phylogenetic inference method from genomic sequence data is ensured by its statistical consistency. Bayesian inference methods produce a sample of phylogenetic trees from the posterior distribution given sequence data.…
As researchers collect increasingly large molecular data sets to reconstruct the Tree of Life, the heterogeneity of signals in the genomes of diverse organisms poses challenges for traditional phylogenetic analysis. A class of phylogenetic…
Covarion models of character evolution describe inhomogeneities in substitution processes through time. In phylogenetics, such models are used to describe changing functional constraints or selection regimes during the evolution of…
Interpretation of empirical results based on a taxa's lifetime distribution shows apparently conflicting results. Species' lifetime is reported to be exponentially distributed, whereas higher order taxa, such as families or genera, follow a…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…