Frost, E. Whale, R. Finch, L. Baleen, M.
Abstract: We present a game-theoretical examination of the tusk-length variation in narwhals, Monodon monoceros. Our model considers the length of the tusks as a behavioral strategy and explores its evolutionarily stable state. Applying replicator dynamics to a population of narwhals engaged in a conflict for resources, we find that tusk length is a crucial factor in the hierarchy establishment. Our results indicate that short-tusked narwhals are at a disadvantage and puny tusks are more vulnerable to breakage, causing loss of prestige and reduced access to mating opportunities. Conversely, long tusks are more likely to suffer from hydrodynamic forces and drag, impairing individuals' speed and maneuverability, which may lead to missed feeding opportunities. Our analysis suggests that intermediate tusk lengths are evolutionarily stable in narwhals, representing a compromise between the benefits and costs of carrying large ornaments. Therefore, we propose a new theory of "optimal tusk length" in narwhals, which could have important implications for understanding the behavior of other charismatic megafauna.