On sperm length mean-variance relationships.

Sperm length is highly variable within ejaculates, between males, among populations, and across species. While theory makes strong predictions about expected mean sperm size, there is less clarity on variation in sperm, although studies have reported sperm-length variation consistent with some theoretical expectations. Typically, the coefficient of variation (CV) is used in these investigations to control for mean-variance scaling. However, a key assumption for this metric to be appropriate in controlling for mean sperm size is that the standard deviation in size scales linearly with the mean. Unfortunately, sperm-length mean-variation relationships are rarely reported making it hard to assess the validity of using CV as a way to compare mean-corrected sperm variation. Here, we investigate mean-variation relationships using 19,873 sperm length measures from 54 species and find little evidence of a consistent relationship between mean sperm-length and sperm-length variation among males within species, meaning CV is not appropriate for comparing relative (mean corrected) variation in sperm size at this level. We also find significant scaling of sperm-length variation with mean sperm-length across species, but the scaling exponent is consistently less than one, the exponent required by analyses using CV to control for sperm size. Our assessment shows that sperm mean-variation scaling relationships are rare within species and strong across species, but that neither supports the uncritical use of CV in studies of relative variation in sperm length.