Competition among eggs shifts to cooperation along a sperm supply gradient in an external fertilizer

Competition among gametes for fertilization imposes strong selection. For external fertilizers, this selective pressure extends to eggs for which spawning conditions can range from sperm limitation (competition among eggs) to sexual conflict (overabundance of competing sperm toxic to eggs). Yet existing fertilization models ignore dynamics that can alter the functional nature of gamete interactions. These factors include attraction of sperm to eggs, egg crowding effects or other nonlinearities in per capita rates of sperm-egg interaction. Such processes potentially allow egg concentrations to drastically affect viable fertilization probabilities. I experimentally tested whether such egg effects occur using the urchin $\textit{Strongylocentrotus purpuratus}$ and parameterized a newly derived model of fertilization dynamics and existing models modified to include such interactions. The experiments revealed that at low sperm concentrations, eggs compete for sperm while at high sperm concentrations eggs cooperatively reduce abnormal fertilization (a proxy for polyspermy). I show that these observations are consistent with declines in the per capita rate at which sperm and eggs interact as eggs increase in density. The results suggest a fitness trade-off of egg release during spawning: as sperm range from scarce to superabundant, interactions among eggs transition from highly competitive to cooperative in terms of viable fertilization probabilities.