Dear Fellow Researchgater's,

I want to perform a phenotypic selection analysis on some floral traits using the classic method of Lande & Arnold (1983). For this analysis I estimated fitness measures of 60 individuals in the field. However, I have a total of 9 floral traits which I think may be ecologically important. The problem comes when I want to estimate the non-linear selection gradients since the complete model leaves me with only 5 d.f. (that is because my model looks like this [fitness ~ 9 lineal terms + 9 quadratic terms + 36 interaction terms]).

My questions are:

Does any statistical assumption and/or biological interpretation of the non-linear gradients are affected when using any method to select the statistical model that best explains the data? For instance by using the AIC criteria (e.g. stepwise 'stepAIC' on R) or model averaging (e.g. using 'dredge'). Since this methods take out

out linear, quadratic and/or interaction terms.

Further, is there any 'rule of thumb' for appropiate d.f. for a multiple regression analysis?

Thank you!