Combining motility and bioluminescent signalling aids mate finding in deep-sea fish: a simulation study

We present a model to estimate the mean time required for mate finding among deep-sea fish as a function of motility and the extent of bioluminescent signalling. This model differs from those of previous works in 3 important ways by including (1) sex differences in motility, (2) a maximum detection range of bioluminescent signals derived from a recently published mechanistic model based on physical principles and the physiology of vision, and (3) a novel consideration of the likelihood of individuals passing within detection range only in the interval between flashes and hence, failing to detect the signaller. We argue that the flash rates required for effective detection are low, with rates of less than 1 per minute being entirely plausible, and that predation pressure may further encourage low flash rates. Further, even at high flash frequencies, the energetic cost of bioluminescent signalling is argued to be a trivial fraction of resting metabolic rates. Using empirically derived estimates for parameter values, we estimate that a female will be detected and reached by a male within 2 to 4 h of beginning to signal. Hence, we argue that mate finding may not seriously restrict reproductive success in species that can exploit this signalling system. We further argue that where male motility allows bioluminescent signalling, this may have some advantages over chemical-based signalling. Bioluminescent signalling may, therefore, be more important to mate finding in the deep sea (relative to chemical signals) than some previous works have suggested.