Collective dynamics and model verification: Connecting kinetic modeling to data

Kinetic modeling of collective behavior: When a good match goes bad

Theodore Pavlic

Arizona State University


In the study of large groups of animals, macroscopic patterns will sometimes emerge that can easily be captured by the equilibrium demographics of kinetic models. Animals are modeled at the individual level with simple static reactive rules that either change their behavioral state or change the state of some aspect of the environment. Master-equation or mean-field analysis of these models will yield distributions in agreement with observation, providing some validation to the assumption of simple static reactive rules. However, there are often other subtle aspects of natural history that would pose significant technical challenges to a proper modeling attempt if only those observations were initially highlighted by biologists. Several cautionary examples are described in this talk. In one example for the case of decentralized comb construction in honeybees, it is shown how a simple kinetic model of honeybee--cell interactions can robustly regulate drone--worker cell ratios to predictable levels that are independent of the number of workers or the size of the comb. At this level of description, the model is a striking match to observed behavior in nature and gives great insight into the role of conflict in coordinating decentralized colony activities. However, the actual observed spatial distribution of worker and drone cells in combs presents major issues for this modeling approach. In another example for the case of decentralized nest-site selection in rock ants, the easily observable patterns of interactions between ants and the consistent colony-level nest-selection dynamics suggest that simple kinetic models could provide much insight into the basic processes driving those coarse-grained dynamics. However, a fine-grained analysis of individual ant behaviors shows a level of individual behavioral complexity that is comparable to human decision makers whose individual cognitive processes are themselves modeled as drift--diffusion processes and not simple reactive automata. Thus, in looking to biology for new application areas for kinetic modeling, much care should be put into choosing the right coarse-grained variables to use for validation.