[R-sig-ME] binary trait correlation across environments (experimental trials) using MCMCglmm?

[Plough, Louis]

Dear list,
I am trying to estimate the genetic correlation between binary traits
(survival) across trial (experimental) exposures of oysters to low
salinity.  I have a 50 family half-sib design (with replicates) that have
been deployed in a randomized design. Estimates of heritability with
MCMCglmm were reasonable in each of the two trials (same families used but
different individuals) but I am interested in estimating the genetic
correlation for survival between the two trials.

Code and suggestions I have read on this and other online forums seem to
apply to genetic correlations (rG) estimated for two traits measured on the
SAME individuals at the same time (environment) e.g. tarsus length and
color of birds.  For example, code like this from a a  2017 R-Sig-ME post
<https://stat.ethz.ch/pipermail/r-sig-mixed-models/2017q1/025532.html>:

*Bin.Bin.corr <- MCMCglmm(cbind(bin1, bin2) ~ trait - 1, random =
**~us(trait):animal, **rcov = ~corg(trait):units, family =
c("threshold",
**"threshold"), pedigree = Ped, prior = Prior1rG, **data = Data, nitt
= 4050000, burnin = 50000, thin = 2000, **verbose =**FALSE)*


Note that  Jerrod suggested different priors and modeling the
interaction of sex and animal with: *us(sex):animal *but Im not sure
this approach would applies to a cross-environment correlation
estimate?


So, my question is, what is the best way to proceed to estimate a
cross environment genetic correlation of a binary trait (survival)? My
data look like this (head and tail of file) where "Trial" is the
relevant 'environment' variable (with conditions A and B):






  animal
  Family
  rep
  sire
  dam
  Surv
  Trial


  20160010411501
  1
  A
  20135319911008
  20142889911003
  1
    A


  20160010411502
  1
  A
  20135319911008
  20142889911003
  1
    A


  20160010411503
  1
  A
  20135319911008
  20142889911003
  1
    A


  20160010411504
  1
  A
  20135319911008
  20142889911003
  1
    A


  20160010411505
  1
  A
  20135319911008
  20142889911003
  1
    A


  20160010411506
  1
  A
  20135319911008
  20142889911003
  1
    A


  .....








  animal
  Family
  rep
  sire
  dam
  Surv
  Trial


  20160880411657
  88
  C
  20140019911002
  20135319911007
  0
    B


  20160880411658
  88
  C
  20140019911002
  20135319911007
  0
    B


  20160880411659
  88
  C
  20140019911002
  20135319911007
  0
    B


  20160880411660
  88
  C
  20140019911002
  20135319911007
  0
    B


  20160880411661
  88
  C
  20140019911002
  20135319911007
  0
    B


  20160880411662
  88
  C
  20140019911002
  20135319911007
  0
    B



Here are two possible approaches I have come up with, though I am
unsure of their validity.


1) With my binary phenotype (Surv) indexed by Trial (A or B), I could
estimate the interaction of animal:Trial (e.g. ~us(Trial):animal) as
suggested by Jerrod for that previous R-Sig-Me post, however, its not
clear to me

what to do next with the outcome of that term?  Running a model like this:


bi_model_trial <- MCMCglmm(Surv ~ 1, random = ~us(Trial):animal,
family = "threshold",prior = prior, pedigree = pedigree.t, data =
trials, nitt = 5e+04, burnin = 15000, thin = 10)


the following output is achieved (I know the eff. sample sizes are WAY
too low, but just trying to understand what to do with the output)


> summary(bi_model_trial)

 Iterations = 15001:49991
 Thinning interval  = 10
 Sample size  = 3500

 DIC: 5868.55

 G-structure:  ~us(Trial):animal

                     post.mean l-95% CI u-95% CI eff.samp
TrialA:TrialA.animal    0.3803   0.1330   0.6587    27.94
TrialB:TrialA.animal    0.1074  -0.1775   0.3795    77.64
TrialA:TrialB.animal    0.1074  -0.1775   0.3795    77.64
TrialB:TrialB.animal    1.6707   0.6172   2.9186    17.74

 R-structure:  ~units

      post.mean l-95% CI u-95% CI eff.samp
units    0.4744   0.2055   0.8418    15.82

 Location effects: phen ~ 1

            post.mean l-95% CI u-95% CI eff.samp  pMCMC
(Intercept)     3.625    2.657    4.557    3.169 <3e-04 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

 Cutpoints:
                     post.mean l-95% CI u-95% CI eff.samp
cutpoint.traitphen.1     4.186    3.046    5.221    2.318


Im not sure how to interpret these interaction terms or how a genetic
correlation would be calculated from them? Is this even the right way
to setup the model for estimating genetic correlation between trials?


2) A Second approach would be to simply estimate the correlation of
family means (survival) between trials using a set of equations from
this   paper <https://onlinelibrary.wiley.com/doi/full/10.1111/j.1420-9101.2005.00997.x>.

It would seem most appropriate to use equation (5) and substitute Sire
variance in place of Family variance (half sib design), and thus
genetic correlation Rg = Variance.sire / (  Variance.sire +
Variance.Sire*Variance.Env).


The question is, how to get the appropriate interaction variance
components (Var. Sire*Env)   from the MCMCglmm output or how to code
the model appropriately? Perhaps another package is better suited for
this?


Any advice on my understanding of the problem (i.e. cross
environmental genetic correlation is different from simple bivariate
genetic correlation of traits within an environment/trial) and how to
accomplish the cross environmental genetic co

correlation ( approach 1 or 2 or something completely different),
would be most appreciated.


Thanks!


LVP




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