[R-sig-ME] animal model: calculating heritability and evolvability from sire effects

[Paul Johnson]

You can estimate heritability and evolvability more directly via estimating the additive genetic variance from an animal model as laid out here:
http://www.wildanimalmodels.org/tiki-download_wiki_attachment.php?attId=4
Best wishes,
Paul


-----Original Message-----
From: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of mikhail matz
Sent: 21 December 2011 09:29
To: r-sig-mixed-models at r-project.org
Cc: Elisha Meyer
Subject: [R-sig-ME] animal model: calculating heritability and evolvability from sire effects

Dear colleagues,

How to calculate heritability (additive genetic variation scaled by total variation) and evolvability (additive genetic variation scaled by the mean of the trait) from the results of a mixed model where the genetics is modeled as sire effects?

We are studying genetics in reef-building corals. Traits are measured in batches of larvae representing full-sib families (i.e., each measurement represents an average over many full-sibs). Traits are either direct measures (for example, color, a continuous variable), or as a response to some treatment or time (for example, size).

in the former (simpler) case, we are after scalar sire effects (i.e., sire-specific intercepts).

For MCMCglmm, I came up with the following:

mc = MCMCglmm ( color ~1, random = ~ sire , family = "gaussian", ... )
heritability = 4 * mc$VCV [ , ' sire ' ] / ( mc$VCV [ , ' sire ' ] + mc$VCV [ , ' units ' ] )
posterior.mode ( heritability )
HPDinterval ( heritability )
evolvability = 4 * mc$VCV [ , ' sire ' ] /  mc$Sol [ , ' (Intercept)' ]
posterior.mode ( evolvability )
HPDinterval ( evolvability )

For lmer:

mr = lmer (color ~ ( 1 | sire ), ... )
var.sire = VarCorr ( mr ) $ sire [ 1 ]
var.resid = as.numeric ( attributes ( summary(m2))$REmat [ attributes (summary(m2)) $REmat [,1] == "Residual" , 3 ] )  # this is a really ugly one! I feel there must be a nicer way to extract residual variance... I will be grateful if you suggest something
heritability = 4 * var.sire / (var.sire + var.resid)
evolvability = 4 * var.sire / fixef (mr) [1]

Are these correct? in particular, the factor of 4 in front of the heritability / evolvability formulae (since we are looking only at sire effects in full-sib families)?

If we are OK so far, the second question is about non-gaussian models. How these formulae would be modified if the response variable is binomial, in the form of counts of successes and failures ?

Seems like for MCMCglmm there will be no change except family = "multinomial2", is that correct?

lmer, on the other hand, does not report residual variance with binomial model, apparently because it is fixed. For logit link function it seems to be fixed at 3.29, so the heritability formula will look like this:

heritability = 4 * var.sire / (var.sire + 3.29)

correct?...

I feel this is way more than enough for one post... I guess I will ask about the models with sire-specific slopes later.

cheers

Misha Matz

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