Table 1 Sexual selection indexes and formulas used for their calculations

From: Sex peptide receptor-regulated polyandry modulates the balance of pre- and post-copulatory sexual selection in Drosophila

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