Dimensionless invariants for the optimal size (age) of sex change

Optimization models have been widely and successfully used in evolutionary ecology to predict the attributes of organisms; perhaps the greatest quanti tative success is in the area of sex allocation (sex ratio, sperm versus eg gs for hermaphrodites, time as a male [female] for a sex changer), where th e fact of having only one mother and one father makes Darwinian fitness a s imple product of gain-via-male times gain-via-female. Previous work on sex change used the maximization of this male-female product to successfully pr edict the direction and age (size) for sex change, and that age has been sh own to imply a breeding sex ratio biased towards the first sex. This paper unites recent advances in the comparative demography of organisms with inde terminant growth with the theory of optimal sex change to predict some new invariance rules for the relative age (size) of sex change. One of these ru les is strikingly confirmed in a longterm study of the size-at-sex-change i n the northern shrimp, Pandalus borealis, off Iceland.