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 encounters and mating encounters. 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 encount...
Highlights
In chemistry, the law of mass action states that the rate of a reaction is proportional to the product of the concentrations of the reactants
We present an alternative derivation of the law of mass action that uses dimensional reduction together with simulated data
This paper addresses the modelling of encounters that lead to reproduction, which requires ruling out simultaneous encounters that occur in the ideal gas model, i.e. encounters where a single female mates two or more males simultaneously, otherwise the rate at which new offspring appear would be overestimated
Summary
The law of mass action states that the rate of a reaction is proportional to the product of the concentrations of the reactants. Our aim here is to present a correction for the constant used in the mass action term corresponding to the ideal gas model that accounts for the pair formation To achieve this goal, we first build a functional relation among the variables using dimensional reduction and simulated data of individuals’ movement. We use the new constant in the mass action law to explore the effects of environmental stochasticity on the conditioned time to extinction for a population model via the variability on encounter rates. The simulations reveal the effects that simultaneous random fluctuations around the new constant (and the mating encounter rate) and demographic stochasticity have on the extinction time This elementary example justifies having reasonable approximations for the non-linear term that models encounters: it demonstrates how variability in the environment could play an essential role in regulating the time to extinction distribution
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
