A Statistical Relation behind Population Dynamics in Fluctuating Environment

      Since the pioneering work of Fisher, the statistical relations in population dynamics have been investigated by various researchers such as Price, Iwasa, Frank, and others for different situations. Such relations clarify the underlying implicit constrains in the evolutionary processes, and also can be used to estimate the evolutionary important quantities such as strength of selection. Finding new relations and quantities is, therefore, crucial to fully understand what is evolution and its consequence.
     In this work, we propose a new relation that is satisfied by the growth rate of cells under fluctuating environment that were intensively analyzed by Haccou and Iwasa. Specifically, we relate the average growth rate and its fluctuation by using the techniques of large deviation and statistical thermodynamics. This relation also reveals how the growth rate fluctuation is determined by the interplay of the fluctuations of environment and cells. We also want to discuss its biological implication especially for the invasion of new species to an established and adapted population.
     This work is an collaboration with Dr. Yuki Sughiyama, Graduate School of Arts and Sciences, University of Tokyo.