In the first week of July, Tak attended the Joint Annual Meeting of the Korean Society for Mathematical Biology and the Society for Mathematical Biology, held in Seoul. During the conference, he presented some new results on deriving probability distributions of extinction time for a population model with a growth rate that varies stochastically due to environmental fluctuations. This is an important topic for conservation because many species are in danger of extinction and it is unclear how environmental changes over time affect their extinction risk.

Specifically, the environmental fluctuations in the model are assumed to follow a random process that is called 1/f noise, following empirical evidence that many environmental variables in reality follow such a random process. Analyses of the model show that the mean extinction time should increase with the autocorrelation time of environmental fluctuations, because of non-linear averaging of the proportional growth rate over different sets of environmental conditions (technically, this is an application of Jensen’s inequality to the proportional growth rate). Because environmental variables in marine ecosystems tend to have longer autocorrelation times than in terrestrial systems, our model predicts that the mean extinction time would generally be greater for marine versus terrestrial populations, provided that the populations are comparable in other aspects of their biology.

In addition, Tak engaged with numerous other researchers and exchanged thoughts on different areas in mathematical biology, including but not limited to ecology and evolution. In particular, he met up with Nao Takashina from the University of Tokyo, who collaborated with Tak and Ryan on a recent paper, published in the Journal of Ecology, on mechanistic partitioning of species richness in tropical forest tree communities.

The conference was held at the Seoul campus of Konkuk University (photo used under a CC BY-SA 4.0 license, with credit to Konkukeditor).