Title of Oral/Poster Presentation

A heuristic approach to model mating encounter rates

Presenter Information

Katherine SnyderFollow

Class

Article

Department

Mathematics and Statistics

Faculty Mentor

Luis Gordillo

Presentation Type

Oral Presentation

Abstract

In chemistry the Law of Mass Action states that the rate of a reaction is proportional to the product of the masses of the reacting substances. This law has been applied to numerous fields of study starting with its use by Alfred Lotka in a predator-prey system of differential equations. Lotka argued the use of mass action in ecological encounters because of its use in the kinetic theory of gases (ideal gas models) and since then it has been applied to describe a variety of interactions between groups within mathematical ecology. Specifically, the ideal gas model has been the standard approach for studying mating encounters between individuals of different sex. However, the ideal gas model was deduced directly from geometrical abstractions for molecular collision frequency among particles and it is rare to find instances where the predicted encounter rates are compared with observations. It seems that the limitations of the model can be reduced by improving the way the proportionality constant in the expression for the law is computed. Our objective is to substantiate the use of the mass action for predicting mating encounters through a derivation of the ideal gas model using dimensional analysis together with simulated data. In our approach we follow the stringent assumptions used in the traditional modeling to derive the model and a proportionality constant using dimensional analysis and simulated data. As our interest is primarily in the application of the law of mass action to mating encounters, we also look into the variability that may occur in encounter rate of many animal species due to environmental stochasticity by exploring numerically how random fluctuation on our model affect the conditioned time to extinction of a two-sex population subject to a reproductive Allee effect.

Start Date

4-9-2015 3:00 PM

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Apr 9th, 3:00 PM

A heuristic approach to model mating encounter rates

In chemistry the Law of Mass Action states that the rate of a reaction is proportional to the product of the masses of the reacting substances. This law has been applied to numerous fields of study starting with its use by Alfred Lotka in a predator-prey system of differential equations. Lotka argued the use of mass action in ecological encounters because of its use in the kinetic theory of gases (ideal gas models) and since then it has been applied to describe a variety of interactions between groups within mathematical ecology. Specifically, the ideal gas model has been the standard approach for studying mating encounters between individuals of different sex. However, the ideal gas model was deduced directly from geometrical abstractions for molecular collision frequency among particles and it is rare to find instances where the predicted encounter rates are compared with observations. It seems that the limitations of the model can be reduced by improving the way the proportionality constant in the expression for the law is computed. Our objective is to substantiate the use of the mass action for predicting mating encounters through a derivation of the ideal gas model using dimensional analysis together with simulated data. In our approach we follow the stringent assumptions used in the traditional modeling to derive the model and a proportionality constant using dimensional analysis and simulated data. As our interest is primarily in the application of the law of mass action to mating encounters, we also look into the variability that may occur in encounter rate of many animal species due to environmental stochasticity by exploring numerically how random fluctuation on our model affect the conditioned time to extinction of a two-sex population subject to a reproductive Allee effect.