A foraging ocean sunfish and the 'nearest neighbor' problem

A predator that preys on randomly-distributed stationary energetically-equivalent small prey will probably choose its next prey to be the nearest one. But what if no prey is found within the detection range of the predator? It is hypothesized that in this case the predator will move along an arbitrary chosen direction until a prey is detected, and turn towards it. In a stochastic environment this strategy leads to a certain distribution function of distances that the predator moves between consequent prey catches. It is shown that when the detection range of the predator exceeds the average distance between prey, this distribution function becomes the nearest neighbor distribution function, whereas; wherew when the detection range is small as compared with the average distance between prey, it becomes the exponential distribution, as the distribution of distances between neighbors on a line. In the first case, the average distance between catches becomes roughly half the average distance between prey; in the second case, it becomes inversely proportional to the square of the detection range. Ocean sunfish preys on practically stationary jellyfish at depth of more than a hundred meters, in dim light. Plausibly, it can detect jellyfish only at close quarters, and hence its detection range is probably small as compared with the average distance between prey. Analysis of the tracking data from seven animals over a few days yielded many thousands of swimming segments separating consequent prey catches. Indeed, lengths of these segments were shown to have the exponential distribution. This finding not only supports the initial hypothesis of this study, but also reveals the fragility of the energetic balance of this animal. A two-fold decrease in the detection range (e.g. due to a decreased visibility) is expected to increase the average distance it moves between catches four-fold, and hence decrease its specific energy intake (the number of jellyfishes per distance moved) by the same rate.