A Mathematical Technique for Estimating Blastodisc:Yolk Volume Ratios instead of Egg Sizes

Abstract

Egg size alone is a poor and misleading variable in life-history studies. A mathematical technique for estimating yolk and blastodisc volume ratios in fishes, a much more meaningful character, is generated from first principles. The technique is demonstrated with an example of early ontogeny in fishes of the genus Lucania (Pisces: Cyprinodontidae). Wild, adult rainwater killifish, Lucania parva, and bluefin killifish, L. goodei, were collected in Florida and transported to the laboratory, where offspring were reared under controlled conditions. Offspring were sampled at the onset of cleavage, for simple measurements of yolk and blastodisc morphology. Application of mathematical equations allowed estimates of yolk and blastodisc volumes in the two species. No significant differences were found in clutch size, blastodisc volume, or egg density; however, significant differences existed in the absolute yolk investments, and blastodisc:yolk volume ratios. These differences in reproductive investment within the genus Lucania are interpreted by the altricial-precocial life-history model as a possible causal mechanism in the evolution of species within this genus. The mathematical equations presented in this study enabled us to partition reproductive investment into components that are more biologically meaningful than simple ‘egg size’.