Optimal Random Avoidance Strategy in Prey-Predator Interactions

Abstract It has recently been reported that individual animals, ranging from insects to birds and mammals, exhibit a special class of random walks, known as Lévy walks, which can lead to higher search efficiency than normal random walks. However, the role of randomness or unpredictability in animal movements is not very well understood. In the present study, we used a theoretical framework to explore the advantage of Lévy walks in terms of avoidance behaviour in prey-predator interactions and analysed the conditions for maximising the prey’s survival rate. We showed that there is a trade-off relationship between the predictability of the prey’s movement and the length of time of exposure to predation risk, suggesting that it is difficult for prey to decrease both parameters in order to survive. Then, we demonstrated that the optimal degree of randomness in avoidance behaviour could change depending on the predator’s ability. In particular, Lévy walks resulted in higher survival rates than normal random walks and straight movements when the physical ability of the predators was high. This indicates that the advantage of Lévy walks may also be present in random avoidance behaviour and provides new insights into why Lévy walks can evolve in terms of randomness.