How can statistical mechanics help population ecology?

XLIII Congresso Paulo Leal Ferreira de Física
Prof. Ricardo Martinez-Garcia
October 30, 2020
Statistical mechanics is the branch of physics that explains how macroscopic properties of matter emerge from the behavior of its microscopic constituents. Population ecology studies how and why populations change over time and space, mostly due to the interaction among individuals and between individuals and the environment. Although seemingly very different, both disciplines aim to explain large-scale phenomena based on a detailed description of their underlying drivers, and tools from statistical mechanics have been largely used to formalize population ecology.
For over 100 years, however, mathematical models in population ecology have relied on very strong and unrealistic assumptions about the way individuals move and get to interact with each other and with the environment. Specifically, they assume that individuals behave like the molecules of an ideal gas: following completely random trajectories through the entire area occupied by the population and only interacting with each other when their trajectories intersect. In this presentation, I will first discuss how traditional models of population dynamics emerge from ideal gas assumptions. Then, I will present our recent work showing how we can refine those models using more elaborated tools from statistical physics and stochastic calculus.
References:
- Martinez-Garcia, R., Fleming, C. H., Seppelt, R., Fagan, W. F., & Calabrese, J. M. (2020). How range residency and long-range perception change encounter rates. Journal of Theoretical Biology, 110267.
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