"99 years after: modernity and revival of Yule's mathematical theory of evolution"Lambert, AmauryIn 1925, the famous British statistician G.U. Yule published a paper entitled "A mathematical theory of evolution" that introduced the pure-birth process and is commonly cited as the first paper to deal with random tree models of phylogenies. We will discuss some historical aspects of this paper and of its legacy, including some overlooked aspects and common misattributions. We will then show how to generalize Yule's results on the frequency of genera of a given age and size (number of species) when species diversification within genera follows any integer-valued process, including species extinctions. Studying such macroevolutionary patterns in this broader context allows us to identify cases where genus size has a power-law tail distribution, with new applications to urn schemes, in the vein of Simon (1955). |
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