This lecture is part of the IICD & Probability and Society Initiative Joint Seminar Series, mini-series on Evolutionary processes and patterns of biodiversity.
The evolutionary history of species can be represented by a tree called phylogeny. We explain how birth-death processes are standardly used to model the diversification of species (speciation, extinction) and how their parameters can be inferred from the phylogeny, notably via the so-called coalescent point process. We then expose the species paradox and explain how to model the formation of new species from first principles. We apply these models to an empirical question (why are species phylogenies imbalanced?) and to a theoretical question (how does the graph describing the ability to interbreed look like?).