model-averaging beta parameters

[andy smith]

I am studying natural selection on body size in dragonflies. I constraint survival estimates using size as a covariate. I use both linear (i.e., survival~size) and quadratic (i.e., survival~size+size^2) models to test for directional and variance selection, respectively, and use the beta parameters as estimates of the effect of body size on survival. I compare models using AIC, but often no single model has unqualified support; therefore, I am interested in model-averaging the beta parameters over the set of candidate models.

The problem is, in the linear model, the size term estimates slope for the entire function while in the quadratic model, the size term estimates the slope of the function at the origin only. Thus, the linear terms from each model are not directly comparable and cannot be model-averaged. Does anyone have any advice on dealing with this issue? For example, can the linear term from the quadratic model be somehow transformed to estimate mean slope over the entire function?

Thanks in advance for any help.