Phylogenetics

Bridge Phylogenetic generalised least squares (PGLS) corrects for the non- independence of closely related species by modelling trait covariance as proportional to shared branch length on the phylogenetic tree, bridging evolutionary biology to multivariate statistics through the variance- covariance structure of trait evolution under Brownian motion.

Fields: Evolutionary Biology, Statistics, Phylogenetics, Comparative Biology, Ecology

PROBLEM: Closely related species share evolutionary history — a regression of body mass on metabolic rate across 100 mammal species treats data as 100 independent observations, but phylogenetic correl...

Bridge Phylogeography uses the coalescent theory from population genetics as a backward- time statistical model to date past population splits and migrations from present-day DNA sequences, with the molecular clock assumption providing the rate calibration that transforms branch lengths in mutations per site into years — making evolutionary biology a direct application of stochastic process theory.

Fields: Evolutionary Biology, Statistics, Genetics, Phylogenetics

The coalescent (Kingman 1982) describes how a sample of gene copies traces back to a common ancestor, with coalescence events occurring at rate C(k,2)/N_e for k gene copies in a population of effectiv...

Bridge Phylogenetic trees are rooted Cayley trees — graph-theoretic objects — and maximum likelihood phylogenetics maximizes P(sequences|tree, model) over a combinatorially vast tree topology space of (2n-3)!! topologies, making exact search NP-hard and requiring heuristic graph algorithms from combinatorics.

Fields: Mathematics, Graph Theory, Combinatorics, Biology, Phylogenetics, Evolutionary Biology

A rooted bifurcating phylogenetic tree for n taxa is a Cayley tree — a graph with n leaves, n-1 internal nodes, and 2n-2 edges, with the property that each internal node has exactly 3 incident edges (...