The evolution of sexual size dimorphism in fish *

Life history strategy models in which female size depends on fecundity and male size on male‐male competition, are used to predict male and female size. Sperm competition alone—without any form of contest competition—cannot readily generate size ratios (male weight/female weight) greater than 1·0, and if sperm competition is very weak, small or even dwarf males are predicted. Increasing sperm competition increases male size, but only with high numbers of competing males can male size approach that of females. Size dimorphism is also affected by the ratio: growth rate/mortality rate in each sex. If this is higher in one sex, its size increases. Two trade‐offs in fish could affect this ratio but neither appears likely to yield size ratios above unity under sperm competition. Male‐male combat is capable of pushing male size beyond that of females, but male size seems never to exceed female size by more than one order of ten, whilst the reverse can proceed to many orders of ten (dwarf males), a pattern which applies generally in animals. Reasons for this asymmetry in size ratio include buffering effects of reducing growth rate (‘von Bertalanffy buffering’), and an asymmetry in the homeostatic effect of operational sex ratio (‘OSR buffering’). High adult male mortality and weak male‐male competition can generate dwarf males. A fundamental problem concerns why the sexes are often so similar in size: this may relate to sperm competition, size buffering effects, and many other features not considered in the present models.