Abstract
Galilee St. Peter's fish shows unusual lability in caring patterns; male-only, female-only and biparental care all occur in the same population. We present a game-theoretical model and investigate the evolutionary stability of the care frequencies observed. Using mean values for each of the model's parameters (estimated previously for the Lake Kinneret population of St. Peter's fish) we find that the current care frequencies are unstable and male-only care is the only evolutionarily stable parental care strategy. However, two key model parameters have significant dispersions: the operational sex ratio (OSR) varies both temporally and spatially, and the advantage of biparental care relative to uniparental care depends critically on clutch size, which can vary dramatically. Within the full ranges of observed OSRs and clutch sizes, there are regions in which each of male-only, female-only and biparental care is an evolutionary stable strategy; there is also a region where no evolutionarily stable strategy exists. Thus natural variations in OSR and clutch size may account for the observed care frequencies.
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