"We then fitted a linear regression including all three life-history traits to estimate the vector of linear selection gradients, β, for each sex (Lande and Arnold 1983). A quadratic regression model incorporating all linear, quadratic, and cross-product terms was then used to estimate the matrix of nonlinear selection gradients, γ, for each sex. "
This is from the paper Evidence for strong intralocus sexual conflict in the Indian meal moth, Ploida interpunctella. I am not sure why they estimate these gradients separetly rather than taking them just from the one full model - any suggestions? Is this normal or have they done it for a reason?
For some similar work see these two papers:
Gosden et al which seems to use only the linear gradients from one model with sex as an effect.
Stearns et al which uses linear, quadratic and correlational estimated from one multiple regressions model per sex (similar to the main paper I cite first but not using a linear terms only model for the linear coefficient).
I have mailed the corresponding author on the quoted paper to ask why, I will let you know what he says if he replies