I am really pleased that a new publication – a first book chapter from lab and first paper of 2019 – is now out! Its led by Jitesh Jhawar, a final year PhD student in our lab and in collaboration with Richard Morris – a former postdoc at NCBS.
Jitesh Jhawar, Richard Morris, and Vishwesha Guttal, 2019, Deriving mesoscopic models of collective behaviour for finite populations, In Handbook of Statistics Vol 40: Integrated Population Biology and Modeling (edited by Arni Srini Rao and C R Rao), Part B, 551-594. DOI: https://doi.org/10.1016/bs.host.2018.10.002; Pre-print from Arxiv; Codes and data on github. Download PDF
Collective behaviours of animal groups are often modelled via agent-based simulations. They are relatively difficult to tract analytically. The main highlight here is that we present two analytical methods that are used in the literature (statistical physics and physical chemistry); we compare which method offers ease of model construction.
A second point worth highlighting is that most analytical methods often assume that group/population sizes are infinitely large. The methods we present accounts for the fact that real animal groups are finite in size and individuals interact with each other in inherently probabilistic ways! The resulting scale of description is also referred to as mesoscopic — a term that appears in the title of the book chapter.
The mesoscopic descriptions yield very counter-intuitive results,; for example, noise can actually facilitate collective order!!! Read the chapter for more details.
The writing style we have adopted is pedagogical so that even undergraduate students from physics and mathematics can understand the methods presented here.
Finally, I also want to highlight that the first author of the paper – Jitesh Jhawar – did his bachelor and masters degrees in Biotechnology – but in this chapter, he uses mathematical techniques like Fokker-Planck equations, Langevin equations, Ito Calculus, etc! So even biology background students can learn hard-core mathematical/theoretical biology if you really love doing theory!