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## Collective motion models

The methods for analysing the data are founded on old, and in some cases ancient, mathematics, including trigonometry, which has been studied for over two thousand years, and is first introduced to most modern students during early high school.

Dr Timothy Schaerf, Mathematics, School of Science and Technology

Animals are capable of remarkable feats of coordinated, collective group motion. Collective animal motion arises in many forms, from the spectacular patterns of shoaling fish, starling murmurations, the flight of honeybee swarms, to the immense swarming movements of Antarctic krill, which can be comprised of millions of individuals. How do animals coordinate such large scale group movement?

The prevailing theory is that coordinated collective motion is the result of the repeated application of simple, instinctive, rules of interaction by individuals within a group. These rules dictate how individuals adjust their velocity (speed and direction of movement) in response to the relative positions and behaviours of their groupmates. This theory has been interrogated repeatedly since the 1970s using computational and mathematical models. These models apply at least one of the following simple rules of interaction: (1) individuals will adjust their velocity to avoid collisions with other groupmates who are very close, (2) individuals will align their direction of motion with nearby groupmates, and (3) individuals will adjust their velocity to move towards groupmates who are farther away, so as to avoid separation from the group. With such rules in action, simulated groups are capable of generating group level patterns of movement that are convincing visual matches for flocking birds, large shoals of fish, insect swarms, and even the movements of human crowds. You may have even seen the end result of such simulations in use as part of the computer-generated imagery (CGI) of large moving groups in film.

In spite of the success of models in replicating the group level patterns of collective movement, this does not necessarily mean that real animals use exactly the same sorts of rules of interaction as those prescribed in models. Nevertheless, model based theory dominated understanding of collective movement for decades because the technology did not exist to infer or resolve interaction rules directly from observations of animal movement. This all changed in the latter part of the 2000s with advances in both tracking technology (both GPS, and computer based automated visual tracking methods) and the methods used to analyse movement behaviour. These advances facilitated a sequence of studies that first found evidence through group structure that starlings in flight and surf scoters swimming on the surface of the ocean did indeed coordinate their movement through rules of interaction like those used in theoretical models, and then that pigeons in flight applied explicit alignment rules. A subsequent pair of studies in 2011, including one that UNE’s Dr  Timothy Schaerf was involved in,[1] revealed that small shoaling fish adjusted their movements consistent with collision avoidance, alignment, and separation avoidance rules, in agreement with the broad principles of theoretical models, but the details of how the fish applied these rules differed to those usually used within models. The team involved in the study that Dr Schaerf worked on included biologists (James Herbert-Read, Andrea Perna, and Ashley Ward), a statistician (Richard Mann), and two applied mathematicians (David Sumpter and Dr Schaerf); a truly multidisciplinary team.

The methods for obtaining reliable and affordable individual tracking data for animals rely on modern advances in computer technology from the 21st century. However,cthe methods for analysing the data are founded on old, and in some cases ancient, mathematics, including trigonometry, which has been studied for over two thousand years, and is first introduced to most modern students during early high school.

Since 2011 Dr Schaerf has worked with Ashley Ward and many of his former PhD students (James Herbert-Read, Matthew Hansen, Alicia Burns, and Mia Kent) on multiple studies of the individual and collective movement of fish, continually refining and expanding the methods first used in the 2011 study. In recent work[2] this team has examined how the rules of interaction of x-ray tetras (small, beautiful fish with translucent bodies) change according to ecological context, specifically the presence of cues in the water indicating the presence of food, or the aftermath of a predator strike, and how the rules of interaction of eastern mosquitofish (a very resilient invasive species in Australia) change under active threat. Beyond this work, the team are now applying their tracking and analysis methods to species other than fish, including crabs, fruit bats, and humans, in an effort to identify similarities and differences in interaction rules across taxa and species. The goal of their work is to understand if there are universal rules of interaction used to coordinate group movement in all, or many species.

Dr Schaerf’s research work in this area has been focused on understanding how real animals coordinate collective motion, but, he says, other researchers, scientists and engineers have taken inspiration from the theory of collective motion to help develop new technology. One such example is the guidance system for a prototype driverless car, the EPORO, which is based around similar principles to that of collective motion models: collision avoidance at close range, alignment at intermediate range, and separation avoidance at long range.

What will the future hold? Technological change will affect how people live and travel, interact with the environment, and will shape the jobs of the future.

1 J E Herbert-Read, A Perna, R P Mann, T M Schaerf, D J T Supmter and A J W Ward, Inferring the rules of interaction of shoaling fish, PNAS, 108:18726-18731, 2011.
2 T M Schaerf, P W Dillingham, and A J W Ward, The effects of external cues on individual and collective behavior of shoaling fish, Science Advances 3: e1603201, 2017.
[Banner photo courtesy of ABC RN: Teresa Tan.]