Collective behavior is a phenomena present ubiquitously in biological systems. Collectively moving animals show complex patterns and dynamics. The behavior leading to such patterns could confer evolutionary advantage to animals. Therefore, it is important to study how such patterns are formed and what function they provide to an animal. This has been a subject of many theoretical and empirical studies. Theoretical models have shown that a mobile group self-organizes by virtue of simple local interactions among near-neighbors. These models are constructed based on theoretical insights (sometimes intuitive) of mechanistic processes underlying these patterns. However, many of the model assumptions may not hold true in reality. Moreover, the nature of these findings has largely remained qualitative. Therefore, in our work, we wish to derive a mathematical model using empirical data that can provide a quantitative framework for understanding the scales of interaction in a mobile group.
Broadly, this thesis aims to provide a quantitative framework of the mechanistic drivers of collective motion and ecological conditions under which such behavior evolves.
In the first objective, we model a group level property (average orientation) that describes the state of the system. We derive a stochastic ordinary differential equation model by applying a coarse grained approach to real data from fish schools. The model predicts a change in the group level property as a function of group size. Future work involves making a general model applicable over a range of group sizes.
In the second objective, we aim to understand dynamics over smaller spatial scale within the group. Therefore, we will monitor a local level property of the group that varies both across space and time. Using this data we will derive a stochastic partial differential equation that can describe the spatio-temporal evolution of the locally varying property within the group.
In the third objective, we aim to decipher interaction rules between individuals using an evolutionary approach. Our premise is that those set of rules that result in the system showing an expected state, might also be the rules operational in real world systems. Therefore, we will explore different situations leading to the evolution of the system to an expected state. This thesis thus uses multiple approaches to investigate the mechanisms driving collective motion in animals.