Will male advertisement be a reliable indicator of paternal care, if offspring survival depends on male care?

Existing theory predicts that male signalling can be an unreliable indicator of paternal care, but assumes that males with high levels of mating success can have high current reproductive success, without providing any parental care. As a result, this theory does not hold for the many species where offspring survival depends on male parental care. We modelled male allocation of resources between advertisement and care for species with male care where males vary in quality, and the effect of care and advertisement on male fitness is multiplicative rather than additive. Our model predicts that males will allocate proportionally more of their resources to whichever trait (advertisement or paternal care) is more fitness limiting. In contrast to previous theory, we find that male advertisement is always a reliable indicator of paternal care and male phenotypic quality (e.g. males with higher levels of advertisement never allocate less to care than males with lower levels of advertisement). Our model shows that the predicted pattern of male allocation and the reliability of male signalling depend very strongly on whether paternal care is assumed to be necessary for offspring survival and how male care affects offspring survival and male fitness.