Should advertising parental care be honest?

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Abstract
Species with paternal care show less exaggerated sexual ornamentation than those in which males do not care, although direct benefits from paternal care can vastly exceed the indirect benefits of mate choice. Whether condition–dependent handicaps can signal parenting ability is controversial. The good–parent process predicts the evolution of honest signals of parental investment, whereas the differential–allocation model suggests a trade–off between the attractiveness of a mate and his care–provisioning. I show that both alternatives can arise from optimal allocations to advertisement, parental investment and future reproductive value of the male, and that the male's marginal fitness gain from multiple matings determines which option should apply. The marginal gain is diminishing if opportunities for polygyny or extra–pair copulations are limited. Advertisement is then expected to be modest and honest, indicating genetic quality and condition–dependent parental investment simultaneously. Increasing marginal gains are likely to be related to cases where genetic quality has a significant influence on offspring fitness. This alternative leads to differential allocation with stronger advertisement, more frequent extra–pair copulations, and diminished male care. Reliability is also reduced if allocation benefits have thresholds, e.g. if there is a minimum body condition required for survival, or if females use a polygyny–threshold strategy of mate choice.