Convict cichlid fish have biparental care for a period of about 6 weeks lasting from egg laying until the young (fry) have grown to about 10 mm. However, the young can sometimes survive with care from only one parent, and desertion of the mate and offspring by males has been observed. I tested a theoretical model modified from Lazarus (1990) which predicted that mate and offspring desertion by male convict cichlids should be promoted by low predation pressure on fry, high remating opportunities for males, increasing age of fry, and decreasing number of fry. Males deserted 7.8% of 334 broods studied during two breeding seasons in Costa Rican streams. As predicted, males deserted their broods most frequently at sites with the highest brood survivorship (lowest brood predation pressure), when fry were close to independence and when brood size was smaller than average. Sex ratios and interspawning intervals did not indicate any relationship between mate desertion and opportunities for remating for males. The reuse of spawning caves may favor fidelity to the mate and brood, and defending the young from predators at the same time as defending the cave from conspecifics may favor biparental care in this species.