Deciphering speciation processes: a mathematical modelling approach to biodiversity patterns

The grandeur and complexity of Earth’s biodiversity present a challenge to comprehend the intricate mechanisms underlying speciation. Once dubbed by Darwin as the “mystery of mysteries,” speciation remains a frontier in biology, with much still cloaked in obscurity. Applying mathematical models inspired by population genetics and individual-based simulations, I aim to shed light on the complex mechanisms underlying speciation. In this talk, I focus on the concept of a “speciation cycle,” a recurring pattern integral to the formation of biodiversity. In contrast to traditional views that focus solely on a single speciation event, our approach argues for the necessity of multiple intertwined processes. These include the coexistence of closely related species, ongoing diversification, and the accumulation of new species, all while avoiding extinction. By overviewing mathematical models of each evolutionary and ecological process, I will introduce their basic ideas, and examine under what conditions the formation and coexistence of new species are promoted. Then we further explore the temporal and spatial dimensions of speciation, looking closely at the intervals between speciation events and the steady buildup of biodiversity over geological timescales. By bridging the gap between microevolutionary processes and macroevolutionary patterns, I hope to enable the prediction of biodiversity patterns based on a deeper understanding of speciation mechanisms.