Mass action in two-sex population models

encounters, mating encounters and the associated numerical correction

  • Katherine Snyder Utah State University
  • Brynja Kohler Utah State University
  • Luis F. Gordillo Utah State University
Keywords: Mass action, dimensional analysis, environmental stochasticity

Abstract

Ideal gas models are a paradigm used in Biology for the phenomenological modelling of encounters between individuals of different types. These models have been used to approximate encounter rates given densities, velocities and distance within which an encounter certainly occurs. When using mass action in two-sex populations, however, it is necessary to recognize the difference between <italic>encounters</italic> and <italic>mating encounters</italic>. While the former refers in general to the (possibly simultaneous) collisions between particles, the latter represents pair formation that will produce offspring. The classical formulation of the law of mass action does not account this difference. In this short paper, we present an alternative derivation of the law of mass action that uses dimensional reduction together with simulated data. This straightforward approach allows to correct the expression for the rate of mating encounters between individuals in a two-sex population with relative ease. In addition, variability in mating encounter rates (due to environmental stochasticity) is numerically explored through random fluctuations on the new mass action proportionality constant. The simulations show how the conditioned time to extinction in a population subject to a reproductive Allee effect is affected.

Published
2017-01-01
How to Cite
Snyder, Katherine, Brynja Kohler, and Luis F. Gordillo. 2017. “Mass Action in Two-Sex Population Models”. Letters in Biomathematics 4 (1), 101-11. https://doi.org/10.1080/23737867.2017.1302827.
Section
Research