animal model: calculating heritability and evolvability from sire effects

Mikhail,

I'm getting in on this late, but it sounds to me as if you have a 
standard full-sib design, with the slight complication that each dam is 
mated to multiple sires. Why can't you simply use the standard formulas 
to convert from within-family (var_w), among-dam (var_d), and among-sire 
(var_s) variance components to estimate Va, Vd, and Ve?

Va = 4(var_s)
Vd = 4(var_d - var_s)
Ve = var_w - 3*var_d + var_s

You can use either lmer() or MCMCglmm to get estimates of var_s, var_d, 
and var_w. The lmer() estimates will be MLEs, so the estimates of Va, 
Vd, and Ve will also be MLEs (by the invariance principle). You'll get 
the full posterior for var_s, var_d, and var_w from MCMCglmm, and by 
calculating Va, Vd, and Ve from each posterior sample, you'll get the 
full posterior for them.

Unless your sires and dams have a known pedigree, there's no reason to 
use the animal model -- just an appropriate nested design. If the sires 
and dams have a known pedigree, then you'd use the animal model on them 
(and I'd have to think a bit about which variance component from that 
would correspond to var_d and var_s).

Kent

Kent E. Holsinger                kent at darwin.eeb.uconn.edu
                                  http://darwin.eeb.uconn.edu
-- Department of Ecology & Evolutionary Biology
-- University of Connecticut, U-3043
-- Storrs, CT   06269-3043