When Optimal Strategy Matters to Prey Fish

Predator-prey interactions are commonly studied with an interest in determining the optimal strategy for prey. However, the implications of deviating from optimal strategy are often unclear. The present study considered these consequences by studying how the direction of an escape response affects the strategy of prey fish. We simulated these interactions with numerical and analytical mathematics and compared our predictions with measurements in zebrafish larvae (Danio rerio), which are preyed upon by adults of the same species. Consistent with existing theory, we treated the minimum distance between predator and prey as the strategic payoff that prey aim to maximize. We found that these interactions may be characterized by three strategic domains that are defined by the speed of predator relative to the prey. The "fast predator" domain occurs when the predator is more than an order of magnitude faster than the prey. The escape direction of the prey had only a small effect on the minimum distance under these conditions. For the "slow predator" domain, when the prey is faster than the predator, we found that differences in direction had no effect on the minimum distance for a broad range of escape angles. This was the regime in which zebrafish were found to operate. In contrast, the optimal escape angle offers a large benefit to the minimum distance in the intermediate strategic domain. Therefore, optimal strategy is most meaningful to prey fish when predators are faster than prey by less than a factor of 10. This demonstrates that the strategy of a prey animal does not matter under certain conditions that are created by the behavior of the predator.