One Day Workshop “Recent Topics in Mathematical Biology”

Predicting a new emerging strain of flu is a challenging subject of public health. Here I examine how the probability of successful emergence of a new flu strain depends on the epidemic size of its parental strain, and on the time of its introduction, by analyze a time-dependent birth-death process for the number of a new-strain infected hosts. The analysis reveals that extreme care should be taken for the newescape mutants that emerge in an early stage of an epidemic, rather than those emerging in the middle of epidemics, as they are most likely to be the strains causing the next major outbreak.

Adaptive dynamics method is a common tool for analyzing the evolutionary dynamics of quantitative traits. The method is based on an important assumption, that is, a mutant’s trait is not so far away from the parent’s. However, some recent theoretical studies pointed out that varying the variance in mutants’ traits brings different evolutionary results. We studied global- and local-mutation models in generalized asymmetric 2×2 games and compared the evolutionary results in both models. In this talk we show how different the evolutionary results are between when mutations are only local and when they can be global in asymmetric 2×2 games.

The aim of this lecture is to introduce the delay equation formulation of a quite general class of size-structured consumer-resource models and next to show how one can derive biological insights by studying how the roots of a characteristic equation depend on parameters.

The lecture is based on joint work with Mats Gyllenberg, Hans Metz, Andre de Roos and Shinji Nakaoka.

In speciation research, it is of paramount importance to predict to what extent introgression is suppressed by a particular kind of reproductive isolation. As long as “parapatric” scenarios (scenarios with weak mixture) are concerned, there is a well established population-genetic methodology for this purpose. In this presentation, I will talk about a more powerful and general method we have recently developed. This is applicable to “sympatric” scenarios (scenarios with strong mixture) as well as parapatric ones, allowing extensive comparison between speciation models with diverse isolating mechanisms.

Indirect reciprocity refers to a mechanism in which cooperators are rewarded by a third party via reputation. Reputation can be either good or bad, but how to judge people, namely moral judgement, is not trivial. In this talk I will present a theoretical framework to study social norms that allow cooperation by indirect reciprocity. I start from a basic model. The effect of costly punishment on indirect reciprocity is also studied.

Organizers:

• Takenori Takada (GSEES, Hokkaido University)
• Yasumasa Nishiura (RIES, Hokkaido University)

Supported by

Post-Silicon Materials and Devices Research Alliance (Post-Silicon Alliance)
(特別教育研究経費「附置研究所間連携事業」ポストシリコン物質・デバイス創製基盤技術アライアンス)