Encounter models and Deep-Sea fishes: numerical simulations and the mate location problem in Sternoptyx diaphana (Pisces, Sternoptychidae)

Encounter models were used to simulate the mate location problem in the deep-sea hatchetfish Sternoptyx diaphana and other sparsely distributed meso- and bathypelagic fishes. For S. diaphana the local density of adult males varies considerably with time, depth and geographic location. It is the local density of males and their relative movement that are critical to female reproductive success. Over the range of male densities and mean swimming speeds expected in nature, encounter probabilities between adult males and females are exponentially related to the distance at which a mate is recognized (the perception distance). At the slow swim speeds and sparse population densities considered here, there are strong non-linearities in the relationship of male-female encounter probability to perception distance. In these threshold regions, small changes in perception distance result in relatively larger changes in encounter frequencies. At perception distances of less than 2 m, mean mate location times for females of S. diaphana are predicted by the model to be on the order of days and weeks and considerably longer for more sparsely distributed populations. Perception distances of from 4 to over 10 m are indicated in order to ensure mate location in S. diaphana within a day. Much longer perception distances are required for similar performance for the other populations considered. For sparsely distributed species like S. diaphana, low encounter frequencies can place limitations on net reproduction independent of the per capita resource base. Mechanisms that increase perception distances (e.g., olfaction) in deep sea fishes should be particularly effective in enhancing mate location. Bioluminescence may serve that purpose in S. diaphana. Irrespective of sensory modalities, at least one sex must maintain significant mean swim speed for considerable lengths of time to effect reproduction. The simulations also reveal the importance of scale and non-linearities in determining encounter frequencies among marine organisms. Encounter dynamics are in turn critical to various transfer functions and rates in oceanic ecosystems such as reproduction and predation.