Krzysztof Bartoszek Uppsala University: A branching Ornstein-Uhlenbeck with jumps model

Abstract: Contemporary stochastic evolution models commonly assume gradual change for a phenotype. However the fossil record and biological theory suggests that development should be rather treated as undergoing punctuated change. In this setup one assumes that there are very short time intervals during which dramatic change occurs and between these the species are at stasis. Motivated by this I will present a branching Ornstein-Uhlenbeck model with jumps at speciation points. I will in particular discuss a very recent result concerning a central limit theorem for it - for weak convergence to hold dramatic change has to be a rare event.

Tillbaka till huvudsidan.