Antlers honestly advertise sperm production and quality

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Abstract
Evolutionary theory proposes that exaggerated male traits have evolved via sexual selection, either through female mate choice or male–male competition. While female preferences for ornamented males have been amply demonstrated in other taxa, among mammals sexual characters are commonly regarded as weapons whose main function is to enhance male competitiveness in agonistic encounters. One particularly controversial hypothesis to explain the function of male sexual characters proposes that they advertise male fertility. We test this hypothesis in red deer (Cervus elaphus), a species where sexual characters (antlers) reach an extreme degree of elaboration. We find that a global measure of relative antler size and complexity is associated with relative testes size and sperm velocity. Our results exclude the possibility that condition dependence, age or time of culling, drive these associations. Red deer antlers could signal male fertility to females, the ability to avoid sperm depletion throughout the reproductive season and/or the competitive ability of ejaculates. By contrast, male antlers could also signal to other males not only their competitive ability at the behavioural level (fighting ability) but also at the physiological level (sperm competition).