Time required for sex change in teleost fishes: Hormonal dynamics shaped by selection

Bidirectional sex change is observed in many teleost fish. When social conditions change, the sex transition may take place over a period of several days to a few months. To understand temporal differences for sex change in either direction, I propose a simple mathematical model for the hormone-enzyme dynamics. Aromatase (P450arom) catalyses the synthesis of estradiol from testosterone. I assume that a change in social conditions for individuals affects the rates of production and degradation of P450arom. I then consider the evolution of parameters in the dynamics. Optimal parameter values are those that minimize total fitness cost, defined as the sum of fitness losses due to delay in being a functional male or female, and the cost of accelerated degradation of P450arom in changing from female to male sex. The model predicts that, in haremic species, sex change promotes a faster degradation of P450arom, resulting in a faster female-to-male transition than male-to-female transition. In contrast, in monogamous species, or with a small number of females, there is no benefit in a faster degradation of P450arom when changing to male, resulting in approximately equal timespans for sex change in either direction.