Can Pi be constant if p&c vary?

[jctroxler]

I'm using robust design with Huggins full heterogeneity estimator. There is a strong evidence for sex effect on p and c. Is it appropriate to model pi as constant across sexes when p and c vary by sex? Adding the extra parameter (Pi sex) increases AICc by 1.90 so it is nearly a pretending variable anyway. It seems unlikely that proportions would be the same for both sexes (of bears), however, in this case, the AICc slightly supports Pi . and betas are not signficant for sex effect on Pi. In general, if you suspect group membership (e.g., male vs female) partially accounts for capture heterogeneity and want to model remaining heterogeneity using finite mixture, does it ever make sense to constrain either mixture proportion or capture probability as constant across groups while allowing the other vary by group?