Modeling the lowest-cost splitting of a herd of cows by optimizing a cost function

TL;DR

This paper develops a model to determine the optimal splitting of a herd of cows into subgroups by minimizing a cost function that accounts for hunger, lying desire, and predation risk, providing insights into herd dynamics.

Contribution

It introduces a novel cost function-based model for herd splitting that incorporates individual variation and predation risk, advancing understanding of animal grouping behavior.

Findings

Optimal herd splitting depends on individual hunger and lying desire variations.

Predation risk decreases exponentially with increasing group size.

Model demonstrates different splitting behaviors in homogeneous and mixed-size herds.

Abstract

Animals live in groups to defend against predation and to obtain food. However, for some animals --- especially ones that spend long periods of time feeding --- there are costs if a group chooses to move on before their nutritional needs are satisfied. If the conflict between feeding and keeping up with a group becomes too large, it may be advantageous to some animals to split into subgroups of animals with similar nutritional needs. We model the costs and benefits of splitting by a herd of cows using a cost function (CF) that quantifies individual variation in hunger, desire to lie down, and predation risk. We model the costs associated with hunger and lying desire as the standard deviations of individuals within a group, and we model predation risk as an inverse exponential function of group size. We minimize the cost function over all plausible groups that can arise from a given herd and study the dynamics of group splitting. We explore our model using two examples: (1) we consider group switching and group fission in a herd of relatively homogeneous cows; and (2) we examine a herd with an equal number of adult males (larger animals) and adult females (smaller animals).