# Table 1 Sexual selection indexes and formulas used for their calculations

Sexual selection index Abbreviation Formula
Opportunity for selection I $${\mathrm{var}}(T)/{\mathrm{mean}}(T)^2$$
Opportunity for pre-copulatory sexual selection I S $${\mathrm{var}}(M)/{\mathrm{mean}}(M)^2$$
Opportunity for post-copulatory sexual selection I P $${\mathrm{var}}(P)/{\mathrm{mean}}(P)^2$$
Univariate pre-copulatory (M) gradient (i.e. Bateman gradient)a $${\mathrm{\beta }}_{{\mathrm{SS}}}^{{\mathrm{Uni}}}$$ $$T \sim {\beta}_{{\mathrm{SS}}}^{{\mathrm{Uni}}} \times {M} + {\mathrm{covariates}}$$
Univariate post-copulatory (P) gradienta $${\mathrm{\beta }}_{P}^{{\mathrm{Uni}}}$$ $${T} \sim {\mathrm{\beta }}_{P}^{{\mathrm{Uni}}} \times {P} + {\mathrm{covariates}}$$
Multivariate pre-copulatory gradienta $${\mathrm{\beta }}_{{\mathrm{SS}}}^{{\mathrm{Multi}}}$$
Multivariate post-copulatory gradienta $${\mathrm{\beta }}_{P}^{{\mathrm{Multi}}}$$ $${T} \sim {\beta}_{{\mathrm{SS}}}^{{\mathrm{Multi}}} \times {M} + {\beta}_{P}^{{\mathrm{Multi}}} \times {P} + {\beta}_{N}^{{\mathrm{Multi}}} \times {N} + {\mathrm{covariates}}$$
Multivariate mate productivity gradienta $${\mathrm{\beta }}_{N}^{{\mathrm{Multi}}}$$
Mean P on repetitive matings with the same femalea Repetitive matings with the same females P ~ Matings with the same females + covariates
Multivariate maximum pre-copulatory indexb Multivariate s’max (pre) $${\beta}_{{\mathrm{SS}}}^{{\mathrm{Multi}}({\mathrm{var}})}$$
Multivariate maximum post-copulatory indexb Multivariate s’max (post) $${{\beta}}_{P}^{{\mathrm{Multi}}({\mathrm{var}})}$$
Univariate pre-copulatory Jones’ indexb Univariate Jones’ index (pre) $${\beta}_{{\mathrm{SS}}}^{{\mathrm{Uni}}}{\sqrt{I}}_{S}$$ or $${\beta}_{{\mathrm{Ss}}}^{{\mathrm{var}}}$$
Univariate post-copulatory Jones’ indexb Univariate Jones’ index (post) $${\beta}_{P}^{{\mathrm{Uni}}}{\sqrt{I}}_{P}$$ or $${\beta}_{P}^{{\mathrm{var}}}$$
Sperm competition intensity SCI $$\frac{1}{{\frac{1}{{M_{i}}}}\left({{\sum}_{j}^{M} \frac{1}{{{k}_{j}}}}\right)}$$
Sperm competition intensity correlation SCIC SCI ~ SCIC ×M
1. T focal male reproductive success, M focal male mating success, P focal male paternity share, N focal male’s mate productivity. Covariates include vial fecundity (except for the repetitive mating gradient) and replicate. $$\beta _x^{({\mathrm{var}})}$$ = variance-standardised gradient of x, where x is either M (pre-copulatory) or P (post-copulatory). $$\beta _x^{\mathrm{Uni}}$$ or $$\beta _x^{\mathrm{Multi}}$$ univariate and multivariate mean-standardised gradients of x, where x is either M, P or N. For the SCI calculation, M is the mating success of the focal ith male and kj is mating success of the jth female that mated with the focal male
2. a Mean standardisation as $$x/\overline {x}$$
3. b Variance standardisation as $${x} - \overline {x} /{\mathrm{sd}}(x)$$, where x is either M, P or N