Collective behaviour is a commonly observed phenomena which
encompasses a wide range of organisms – from swarming microbes to insects
to aggregation of whales. These groups which from through individual level
interactions exhibit interesting features like shifting from one form of
organization (for example a swarm) to the another (highly polarized). These
shifts are analogous to phase transitions in physical systems, and have
implications in ecology.

Phase transitions (shifts from one state to another) have been studied to a
great deal in physics and various fields of ecology, from lakes to corals
to semi-arid ecosystems. Scientists have developed statistical methods to
recognize and anticipate such shifts. Here we employ some of these methods
to check whether these generic statistical indicators of transitions which
sense shifts between ecological states, also capture signals in behavioural
transitions from one type of collective movement to another (e.g. swarm to
polarised group motion).

We discuss some possible biological motivations to investigate indicators
of transitions. Mass migration of animals is a process where some abiotic
factor (decrease in resources, change in climatic conditions, et cetera)
causes sedentary organisms to disperse to other parts of the world. This
process involves the movement of multiple individuals from a certain point
in space to another and also shift in the form of organization of migrating
animal societies (less polarized/random movement direction of individuals
in swarms to highly coordinated individual movement in groups).

Motivated by the above considerations, here, we simulate a simple agent
based model of the collective movement which generates a number of
biologically realistic grouping patterns through very simple local
interaction rules. We generate time series data of the group alignment by
varying the key local interaction parameters. We then generate a phase
diagram which shows how the state of the collective motion changes across
the key parameter value which we changed. Then, we use the time series data
which exhibit collective behaviour movement transitions to check for
distinct changes in the values of the statistical indicators. Based on the
change in the value of the indicator parameters prior to the shift in the
organizational pattern, we claim whether using these tools we can sense
imminent transitions or not in the time series data.

The time series that we had generated and used for the analysis, have shown
mixed results. We find changes in the values of the statistical measures
prior to the shift in states which inform us about the transition before
its onset. There were also scenarios where we obtained peculiar and also,
failed signals. Hence, these tools have some importance in their ability to
capture systemic changes prior to transitions in the states of collective
motion of animals but they are also not predictive of such events. Our
study suggests that it is worthwhile to test if these signals show similar
or some characteristic patterns before transitions in real animal group
movement data.