Table 1 List of symbols

I _{i, j}

regulation of allele i by j, which can take values -1, 0, +1

Z _i

allele i is capable of regulation if Z _i = 1, or not if Z _i = 0

T _i

constitutive expression of allele i is low (T _i = -1) or high (T _i = +1)

k

positive constant affecting constitutive expression level

σ(x)

sigmoid function varying between 0 and 1

h

steepness of sigmoid function σ(x)

D locus

expression level at D locus controls sex determination and fitness

m, f

ancestral alleles at D locus

m⁺, f⁺, m^-, f^-

mutant alleles of m and f allowing positive (⁺) or negative (^-) regulation

R locus

regulator of D locus

a

ancestral allele at R locus

A

mutant allele at R locus, capable of regulating D locus alleles

${\widehat{S}}_{\text{D}}$

steady state expression of both alleles at D locus

$\Delta {\widehat{S}}_{\text{D}}$

D locus expression difference (evolved minus ancestral)

θ

sex determination threshold; if ${\widehat{S}}_{\text{D}}>\theta$ then female, otherwise male.

w_M, w_F

selection on males and females respectively

W_M, W_F

fitness of male and female respectively