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

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 for some animals to split into subgroups of animals with similar nutritional needs. We model the costs and benefits of splitting in a herd of cows using a cost function 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 examine how the cow dynamics and cost function depends on the parameters in the model and consider two biologically-motivated examples: (1) group switching and group fission in a herd of relatively homogeneous cows, and (2) a herd with an equal number of adult males (larger animals) and adult females (smaller animals).PACS numbers: 05.45.Xt, 82.39.Rt Keywords: Synchronization, complex systems, animal behavior, collective behavior Although animals gain many advantages -such as protection from predatorsfrom living in groups, they also incur considerable costs. For grazing animals, such as cows and antelopes, these costs include having to balance their own nutritional needs to stay in one place to feed with the need to keep up with a group and stop grazing when the rest of the herd moves on. If the nutritional needs of different individuals are sufficiently disparate, this can lead to the splitting of a group so that those with similar needs to graze, lie, and ruminate remain together. If a group of animals becomes too small, however, this can increase the risk of predation, as small groups are less able than large groups to defend themselves against predators. In this paper, we describe a cost function (CF) that balances predation risk (based on group size) with different individual needs for feeding and lying down to infer the sizes at which group splitting a) Electronic mail: kdgajamannage@wpi.edu. 2 occurs. We model variation in hunger and lying desire using the standard deviation of individuals within a group, and we model predation risk as an inverse exponential function of group size. In a series of examples, we optimize the CF for each individual in a group of animals and examine when groups of cows split into smaller groups.

Leveraging Social Network Analysis for Characterizing Cohesion of Human-Managed Animals

“…Therefore, the optimal interaction range (i.e., number of NNs) which does not make any significant contribution to improve the herd entropy should be the optimal interaction range (Figure 5b). Although having a broader interaction range brings some disadvantages such as higher competition for food and space and risk of falling sick [32], there are some benefits as well, especially in graph-based SNA and also for corporate defending against predator attacks.…”