Theoretical study of collective dynamics of a prey swarm: exploring the influence of inertia, heterogeneity, and local interactions on its survival under predator attack

Chakraborty, Dipanjan (2022) Theoretical study of collective dynamics of a prey swarm: exploring the influence of inertia, heterogeneity, and local interactions on its survival under predator attack. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Dipanjan Chakraborty (15RS040)) 15RS040.pdf - Submitted Version Restricted to Repository staff only Download (3MB)

Abstract

The collective motion of living organisms has gained prime importance over the last two to three decades, and thus it has emerged as a new active area of research. Understanding the complex collective dynamics of these active systems is quite challenging, both experimentally and theoretically. Fascinating patterns are observed due to the collective coherent motion of the self-propelled biological organisms, such as flocking of birds, lane formation by ants, swarming of insects, schooling of fishes, and even in the human crowd. Various animal species manifest collective behaviour that sometimes becomes disadvantageous in their living, such as sharing constant resources within the group, higher predation rates, and more intense competition for mates. Despite this, many animals move and stay in a group because the group formation provides various compensating benefits. Among them, the crucial reason for cohesive group formation is to avoid the predator attack and survive. The simple reason is the dilution effect on the predator as it becomes more difficult for the predator to focus on an individual prey in a large prey group. On the other hand, staying within a group could also become unfavourable as the predator can easily track and attack the group. Thus, there is often a trade-off between staying together versus individual needs. Hence, efficient strategies have been taken by the prey groups to counter the predator attack and survive. A swarm of prey, when attacked by a predator, is known to rely on their cooperative interactions to escape. Understanding such interactions of collectively moving prey and the emerging patterns of their escape trajectories is still not well studied. In this thesis, we have developed a theoretical model to investigate how the range of cooperative interactions within a prey group affects the survival chances of the group while chased by a predator. As observed in nature, the interaction range of prey may vary due to their vision, age, or even physical structure. Based on a simple theoretical prey-predator model, we show that an optimality criterion for survival can be established on the interaction range of prey. Very short-range or long-range interactions are shown to be inefficient for the escape mechanism. Interestingly, for an intermediate range of interaction, the survival probability of the prey group is found to be maximum. Our analysis also shows that the nature of the escape trajectories strongly depends on the range of interactions between prey and corroborates with the naturally observed escape patterns. Moreover, we find that the optimal survival interaction regime varies depending on the prey group size and also on the strength of the predator and the prey interactions. Further, we have explored the effect of inertial forces on the survival chances of a prey swarm under predator attacks. We consider the same framework of a particle-based model where all prey interacts via pairwise attractive and repulsive forces, and a predator chases the group from a nearby place. Including the inertial forces, we have solved the equation of motion numerically and found the escape patterns change with varying prey and predator mass and match well with the naturally observed patterns. Also, as we incorporate the inertial force terms, a transition from stable ring formation to unstable ring formation is noticed in a certain prey mass and predator mass regime. Stability analysis calculation validates this transition from stable to unstable ring formation. Moreover, in the higher strength of the predator, our study reveals the transition from non-survival to survival of the prey group as we increase the mass of the predator, keeping the mass of prey fixed. The number of survived prey has been calculated as a function of predator mass which demonstrates the existence of three regimes as we vary the predator mass: (i) transient regime where frequent chase and capture leads to non-survival of the prey group, (ii) a competitive regime where pursuit and capture occur with lower frequency, and (iii) the survival regime with no capture. Thus, our study shows the existence of an optimal value of the predator-prey mass ratio for efficient capture, as we vary the masses, which has also been observed in field studies. The variation of predator strength significantly affects the optimal value of the predator-prey mass ratio, whereas the varying prey group size has little influence. Moreover, in a prey swarm, there exists individual-level heterogeneity due to variations in sensitivity, vision, and other phenotypic characters. So, we introduce the individual-level heterogeneity or phenotypic heterogeneity in the prey swarm by choosing the attractive strength of each prey and prey-predator repulsive strength from a uniform distribution of a certain width instead of fixed values which signifies that the strength of each prey to attract all other prey is not the same, even with in the same group. Solving the dynamical equation of motion, strikingly, we find that increasing phenotypic heterogeneity enhances the survival chances of the prey swarm under a predator attack. On the contrary, as we introduce an external perturbation in the form of instantaneous noise in the prey-predator system, representing the disturbances in the surrounding, the prey group could not survive the predator attack. Up to now, we have considered the case where a single predator attacks the whole prey group. However, there are several instances where predators form groups and attack the prey swarm. Thus we have further studied the dynamics of group hunting and also compared the outcome with the case of a single predator chasing the prey group. We have developed a theoretical model incorporating predator-predator interactions, prey-prey interactions, and predator-prey interactions. In this case, predator-predator interaction is included, and the form of prey-prey interaction has been modified. Now, keeping the predator-predator interaction same, as we vary the number of predators, various escape patterns emerge, such as ring formation by the prey group around the predator, chasing dynamics, prey swarm escape by forming different subgroups, prey swarm escaping collectively as a flock, etc. Further, our study shows that increasing the number of predators in the group enhances hunting success. To quantify the survival chances of the prey swarm, the total catch time to capture all the prey in the group has been calculated, which exhibits a power law as a function of the number of predators. Further, we investigate the effect of predator-predator attractive interaction on the prey swarm dynamics, keeping the number of predators fixed. Our study yields that the increasing cohesive interaction among the predator group lowers the predation success, which enhances the survival chances of the prey swarm. Thus, no cohesion or little cohesion within the predator group is beneficial for predation success. In summary, our study shows that the theoretical models are immensely helpful in getting insights into the governing dynamics of prey swarms under predator attacks. Theoretical modelling and empirical data analysis can work hand in hand for qualitative understanding of many such conceptual questions in natural scenarios.

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