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Many species of reef fishes form large spawning aggregations that are highly predictable in space and time. Prior research has suggested that aggregating fish derive fitness benefits not just from mating at high density but, also, from oceanographic features of the spatial locations where aggregations occur. Using a probabilistic biophysical model of larval dispersal coupled to a fine resolution hydrodynamic model of the Florida Straits, we develop a stochastic landscape of larval fitness. Tracking virtual larvae from release to settlement and incorporating changes in larval behavior through ontogeny, we found that larval success was sensitive to the timing of spawning. Indeed, propagules released during the observed spawning period had higher larval success rates than those released outside the observed spawning period. In contrast, larval success rates were relatively insensitive to the spatial position of the release site. In addition, minimum (rather than mean) larval survival was maximized during the observed spawning period, indicating a reproductive strategy that minimizes the probability of recruitment failure. Given this landscape of larval fitness, we take an inverse optimization approach to define a biological objective function that reflects a tradeoff between the mean and variance of larval success in a temporally variable environment. Using this objective function, we suggest that the length of the spawning period can provide insight into the tradeoff between reproductive risk and reward.

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This paper characterizes the component structure of the space of composition operators acting on H ∞ (BN ), both in the operator norm topology and in the topology induced by the essential norm. Mathematics Subject Classification (2000). Primary 47B33, Secondary 32A99.

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