6 MCMCglmm
MCMCglmm has the advantage to keep automatically keep the lines with missing data and will try to fit the model use latent variables for missing data. We will remove the missing values from the data before fitting the model.
First load MCMCglmm:
library(MCMCglmm)Loading required package: Matrix
Attaching package: 'Matrix'The following objects are masked from 'package:tidyr':
expand, pack, unpackLoading required package: codaLoading required package: ape
Attaching package: 'ape'The following object is masked from 'package:dplyr':
whereAinv <- inverseA(gryphonped)$Ainv6.0.1 Fitting the model
Fitting a multivariate model in MCMCglmm involves several new consideration above those for fitting univariate models. First, we have to fit multivariate priors; second, we have to specify the ways in which effects on different traits may covary, including the nature of residual (co)variation; and third, we will have to be a little more specific when specifying to MCMCglmm what type of distributions from which we assume our data are drawn. Our most basic model can be specified as:
prior2.1 <- list(
G = list(G1 = list(V = diag(2), nu = 1.002)),
R = list(V = diag(2), nu = 1.002)
)
model2.1 <- MCMCglmm(cbind(bwt, tarsus) ~ trait - 1,
random = ~ us(trait):animal,
rcov = ~ us(trait):units,
family = c("gaussian", "gaussian"),
ginv = list(animal = Ainv),
data = gryphon2, prior = prior2.1, verbose = FALSE
)
summary(model2.1)
Iterations = 3001:12991
Thinning interval = 10
Sample size = 1000
DIC: 7154.208
G-structure: ~us(trait):animal
post.mean l-95% CI u-95% CI eff.samp
traitbwt:traitbwt.animal 3.261 1.9897 4.689 93.45
traittarsus:traitbwt.animal 2.151 -0.1505 4.846 71.29
traitbwt:traittarsus.animal 2.151 -0.1505 4.846 71.29
traittarsus:traittarsus.animal 11.570 5.9963 17.857 86.26
R-structure: ~us(trait):units
post.mean l-95% CI u-95% CI eff.samp
traitbwt:traitbwt.units 3.952 2.830 5.177 130.73
traittarsus:traitbwt.units 3.591 1.781 5.875 75.46
traitbwt:traittarsus.units 3.591 1.781 5.875 75.46
traittarsus:traittarsus.units 18.440 13.139 23.912 102.45
Location effects: cbind(bwt, tarsus) ~ trait - 1
post.mean l-95% CI u-95% CI eff.samp pMCMC
traitbwt 7.478 7.200 7.777 662.6 <0.001 ***
traittarsus 20.431 19.818 20.969 825.3 <0.001 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1plot(model2.1$VCV[, "traittarsus:traittarsus.animal"])
autocorr.diag(model2.1$VCV)[, "traittarsus:traittarsus.animal"][2] Lag 10
0.8428648 We have constructed the prior similarly to the those in the univariate models in tutorial 1, only we are specifying a 2x2 covariance matrix rather than a single variance. In order to provide proper priors, we have set the degree of belief parameter to greater than 1 (1.002). Those priors are not necessarily weak or uninformative in all circumstances. We will consider them adequate nonetheless for this tutorial. Please the vignette of the MCMCglmm packages (Hadfield 2010) for more information on priors. In tutorial 1, we used full autocorrelation tables to evaluate the validity of the posterior distribution. Note that we have not done this here.
For a bivariate model this table can become very complex. Nonetheless, it is worth evaluating, rather it is simply to large to include here. It can be viewed in the console as before. Here we have displayed only the autocorrelation for estimates of additive genetic effects for tarsus length with a lag of one samples (10 iterations given this MCMCglmm run with default values). This lag of 0.8428648 is clearly unacceptable. The posterior distribution of the additive genetic effect on tarsus length is shown in Figure 4, note the autocorrelation evident in the left-hand plot.
We will opt to run the analysis for longer. This longer run could be run using the following code (including a line to save the output):
model2.1 <- MCMCglmm(cbind(bwt, tarsus) ~ trait - 1,
random = ~ us(trait):animal,
rcov = ~ us(trait):units,
family = c("gaussian", "gaussian"),
ginv = list(animal = Ainv),
data = gryphon2,
nitt = 130000, thin = 100, burnin = 30000,
prior = prior2.1, verbose = FALSE
)
save(model2.1, file = "data/MCMCglmm_model2_1_LongRun.rda")However, this run might take as long as an hour. For the purpose of this tutorial we have provided an output for such a run. It can be obtained and manipulated as follows, assuming that the file MCMCglmm_model2_1_LongRun.rda is available at the specified location:
load(file = "data/MCMCglmm_model2_1_LongRun.rda")
autocorr.diag(model2.1$VCV)[, "traittarsus:traittarsus.animal"][2] Lag 100
0.3501744 This level of autocorrelation is more acceptable, at least for the purpose of demonstration in this tutorial. We can recover variance components, heritabilities, and genetic correlations from the posterior distribution of this model:
posterior.mode(model2.1$VCV) traitbwt:traitbwt.animal traittarsus:traitbwt.animal
3.471888 2.949939
traitbwt:traittarsus.animal traittarsus:traittarsus.animal
2.949939 12.012766
traitbwt:traitbwt.units traittarsus:traitbwt.units
3.953930 3.876887
traitbwt:traittarsus.units traittarsus:traittarsus.units
3.876887 19.604460 heritability.bwt2.1 <- model2.1$VCV[, "traitbwt:traitbwt.animal"] / (model2.1$VCV[, "traitbwt:traitbwt.animal"] + model2.1$VCV[, "traitbwt:traitbwt.animal"])
posterior.mode(heritability.bwt2.1) var1
0.4999336 heritability.tarsus2.1 <- model2.1$VCV[, "traittarsus:traittarsus.animal"] / (model2.1$VCV[, "traittarsus:traittarsus.animal"] + model2.1$VCV[, "traittarsus:traittarsus.units"])
posterior.mode(heritability.tarsus2.1) var1
0.3719549 genetic.correlation2.1 <- model2.1$VCV[, "traitbwt:traittarsus.animal"] / sqrt(model2.1$VCV[, "traitbwt:traitbwt.animal"] * model2.1$VCV[, "traittarsus:traittarsus.animal"])
posterior.mode(genetic.correlation2.1) var1
0.4041642 6.0.2 Adding fixed and random effects
Fixed and random effects can be added just as for the univariate case. Given that our full model of bwt from tutorial 1 had sex as a fixed effect as well as random effects of byear and mother, we could specify a bivariate formulation of this using the following code (including a line to save the output):
prior2.2 <- list(
G = list(
G1 = list(V = diag(2), nu = 1.002),
G2 = list(V = diag(2), nu = 1.002),
G3 = list(V = diag(2), nu = 1.002)
),
R = list(V = diag(2), nu = 1.002)
)
model2.2 <- MCMCglmm(cbind(bwt, tarsus) ~ trait - 1 + trait:sex,
random = ~ us(trait):animal + us(trait):byear + us(trait):mother,
rcov = ~ us(trait):units,
family = c("gaussian", "gaussian"),
ginv = list(animal = Ainv), data = gryphon2,
nitt = 130000, thin = 100, burnin = 30000,
prior = prior2.2, verbose = FALSE
)
save(model2.2, file = "data/MCMCglmm_model2_2_LongRun.rda")Again we have provided the data from one such run. It can be accessed using the code:
Iterations = 30001:129901
Thinning interval = 100
Sample size = 1000
DIC: 5832.952
G-structure: ~us(trait):animal
post.mean l-95% CI u-95% CI eff.samp
traitbwt:traitbwt.animal 1.558 0.5616 2.488 230.8
traittarsus:traitbwt.animal 2.290 0.3241 4.264 274.8
traitbwt:traittarsus.animal 2.290 0.3241 4.264 274.8
traittarsus:traittarsus.animal 8.083 0.9063 13.599 228.1
~us(trait):byear
post.mean l-95% CI u-95% CI eff.samp
traitbwt:traitbwt.byear 0.96775 0.4124 1.5053 1000
traittarsus:traitbwt.byear 0.07332 -0.8100 0.9791 1000
traitbwt:traittarsus.byear 0.07332 -0.8100 0.9791 1000
traittarsus:traittarsus.byear 3.80720 1.6291 6.3986 1000
~us(trait):mother
post.mean l-95% CI u-95% CI eff.samp
traitbwt:traitbwt.mother 1.335 0.8564 1.8090 871.2
traittarsus:traitbwt.mother -1.508 -2.1667 -0.8288 648.6
traitbwt:traittarsus.mother -1.508 -2.1667 -0.8288 648.6
traittarsus:traittarsus.mother 4.292 2.2380 6.6336 796.0
R-structure: ~us(trait):units
post.mean l-95% CI u-95% CI eff.samp
traitbwt:traitbwt.units 2.13 1.304 2.939 469.2
traittarsus:traitbwt.units 4.81 3.111 6.568 414.7
traitbwt:traittarsus.units 4.81 3.111 6.568 414.7
traittarsus:traittarsus.units 14.51 9.419 19.892 261.3
Location effects: cbind(bwt, tarsus) ~ trait - 1 + trait:sex
post.mean l-95% CI u-95% CI eff.samp pMCMC
traitbwt 6.2734 5.8152 6.7272 1205 <0.001 ***
traittarsus 20.3985 19.4021 21.4106 1000 <0.001 ***
traitbwt:sex2 2.0354 1.7347 2.3529 1000 <0.001 ***
traittarsus:sex2 0.0705 -0.6949 0.7686 1000 0.868
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1autocorr(model2.2$VCV)[, , "traittarsus:traittarsus.animal"][3, 4][1] 0.1026744We can evaluate the fixed effect, their Ci evaluate their significance.
posterior.mode(model2.2$Sol) traitbwt traittarsus traitbwt:sex2 traittarsus:sex2
6.26902047 20.35816977 2.06048779 -0.06501522 HPDinterval(model2.2$Sol, 0.95) lower upper
traitbwt 5.8151983 6.7272503
traittarsus 19.4021008 21.4106029
traitbwt:sex2 1.7347121 2.3528879
traittarsus:sex2 -0.6948574 0.7686074
attr(,"Probability")
[1] 0.95plot(model2.2$Sol)
As before we can obtain the raw variance component estimates and genetic correlations for the random effects:
posterior.mode(model2.2$VCV) traitbwt:traitbwt.animal traittarsus:traitbwt.animal
1.3294950 2.0622374
traitbwt:traittarsus.animal traittarsus:traittarsus.animal
2.0622374 8.3900676
traitbwt:traitbwt.byear traittarsus:traitbwt.byear
0.8118565 0.2327381
traitbwt:traittarsus.byear traittarsus:traittarsus.byear
0.2327381 3.7375906
traitbwt:traitbwt.mother traittarsus:traitbwt.mother
1.4089440 -1.4963686
traitbwt:traittarsus.mother traittarsus:traittarsus.mother
-1.4963686 3.9386669
traitbwt:traitbwt.units traittarsus:traitbwt.units
2.2353960 4.3432849
traitbwt:traittarsus.units traittarsus:traittarsus.units
4.3432849 15.0853981 genetic.correlation2.2 <- model2.2$VCV[, "traitbwt:traittarsus.animal"] / sqrt(model2.2$VCV[, "traitbwt:traitbwt.animal"] * model2.2$VCV[, "traittarsus:traittarsus.animal"])
maternal.correlation2.2 <- model2.2$VCV[, "traitbwt:traittarsus.mother"] / sqrt(model2.2$VCV[, "traitbwt:traitbwt.mother"] * model2.2$VCV[, "traittarsus:traittarsus.mother"])
posterior.mode(genetic.correlation2.2) var1
0.6932486 posterior.mode(maternal.correlation2.2) var1
-0.7431221 Evaluation of the statistical support for these genetic and maternal correlations is straightforward. Because we imposed no constraint on their estimation, we can evaluate the extent to which the posterior distributions overlap zero:
HPDinterval(genetic.correlation2.2, 0.95) lower upper
var1 0.3062932 0.9197543
attr(,"Probability")
[1] 0.95HPDinterval(maternal.correlation2.2, 0.95) lower upper
var1 -0.9432297 -0.3210149
attr(,"Probability")
[1] 0.95Neither or these posterior distributions overlaps zero, so we can consider them both statistically supported.
6.0.3 Partitioning (co)variances
As in the tutorial 1, it is possible to partition the variance-covariance matrix between groups (here sex) Note: the model is simplified without sex-specific covariance for the byear and mother random effect.
gryphon2 <- gryphon2[order(gryphon2$sex), ]
prior2.3 <- list(
G = list(
G1 = list(V = diag(2), nu = 1.002),
G2 = list(V = diag(2), nu = 1.002),
G3 = list(V = diag(2), nu = 1.002),
G4 = list(V = diag(2), nu = 1.002)
),
R = list(
V1 = list(V = diag(2), nu = 1.002),
V2 = list(V = diag(2), nu = 1.002)
)
)
model2.4 <- MCMCglmm(cbind(bwt, tarsus) ~ trait - 1 + trait:sex,
random = ~ us(at.level(sex, "1"):trait):animal + us(at.level(sex, "2"):trait):animal + idh(trait):byear + idh(trait):mother,
rcov = ~ us(at.level(sex, "1"):trait):units + us(at.level(sex, "2"):trait):units,
family = c("gaussian", "gaussian"),
ginv = list(animal = Ainv), data = gryphon2,
nitt = 130000, thin = 100, burnin = 30000,
prior = prior2.3, verbose = FALSE, pr = TRUE,
)
save(model2.4, file = "data/MCMCglmm_model2_4_LongRun.rda")Again we have provided the data from one such run. It can be accessed using the code:
Iterations = 30001:129901
Thinning interval = 100
Sample size = 1000
DIC: 5576.328
G-structure: ~us(at.level(sex, "1"):trait):animal
post.mean
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.animal 1.122
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.animal 1.127
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.animal 1.127
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.animal 3.379
l-95% CI
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.animal 0.1602
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.animal -0.6531
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.animal -0.6531
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.animal 0.1844
u-95% CI
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.animal 2.359
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.animal 3.496
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.animal 3.496
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.animal 8.918
eff.samp
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.animal 167.5
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.animal 119.3
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.animal 119.3
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.animal 102.6
~us(at.level(sex, "2"):trait):animal
post.mean
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.animal 1.598
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.animal 3.099
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.animal 3.099
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.animal 10.218
l-95% CI
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.animal 0.1895
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.animal -0.5506
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.animal -0.5506
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.animal 0.2127
u-95% CI
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.animal 3.305
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.animal 7.864
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.animal 7.864
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.animal 24.230
eff.samp
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.animal 57.28
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.animal 42.01
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.animal 42.01
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.animal 37.21
~idh(trait):byear
post.mean l-95% CI u-95% CI eff.samp
traitbwt.byear 0.9309 0.4614 1.463 1000
traittarsus.byear 4.0310 1.9268 6.724 1000
~idh(trait):mother
post.mean l-95% CI u-95% CI eff.samp
traitbwt.mother 1.924 1.406 2.398 667.6
traittarsus.mother 7.093 4.626 9.681 698.5
R-structure: ~us(at.level(sex, "1"):trait):units
post.mean
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.units 2.090
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.units 4.533
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.units 4.533
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.units 14.113
l-95% CI
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.units 0.9958
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.units 2.4185
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.units 2.4185
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.units 8.1848
u-95% CI
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.units 3.128
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.units 6.875
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.units 6.875
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.units 18.935
eff.samp
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.units 207.2
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.units 168.4
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.units 168.4
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.units 185.3
~us(at.level(sex, "2"):trait):units
post.mean
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.units 1.782
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.units 3.697
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.units 3.697
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.units 12.437
l-95% CI
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.units 0.2776
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.units -0.3141
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.units -0.3141
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.units 0.1776
u-95% CI
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.units 3.115
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.units 7.218
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.units 7.218
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.units 21.903
eff.samp
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.units 52.55
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.units 51.90
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.units 51.90
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.units 39.20
Location effects: cbind(bwt, tarsus) ~ trait - 1 + trait:sex
post.mean l-95% CI u-95% CI eff.samp pMCMC
traitbwt 6.30098 5.89218 6.78834 1000.0 <0.001 ***
traittarsus 20.45577 19.53577 21.34719 1129.8 <0.001 ***
traitbwt:sex2 2.01306 1.63662 2.38011 887.4 <0.001 ***
traittarsus:sex2 0.05817 -0.86635 0.89119 1016.6 0.896
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1autocorr(model2.4$VCV), , at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.animal
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.animal
Lag 0 1.00000000
Lag 100 0.64694479
Lag 500 0.18648179
Lag 1000 0.10392219
Lag 5000 -0.04275072
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.animal
Lag 0 0.84704874
Lag 100 0.60161240
Lag 500 0.20180692
Lag 1000 0.10068129
Lag 5000 -0.03878312
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.animal
Lag 0 0.84704874
Lag 100 0.60161240
Lag 500 0.20180692
Lag 1000 0.10068129
Lag 5000 -0.03878312
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.animal
Lag 0 0.53041407
Lag 100 0.39413485
Lag 500 0.16964194
Lag 1000 0.11264314
Lag 5000 -0.01013697
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.animal
Lag 0 -0.07132000
Lag 100 -0.09608251
Lag 500 -0.05360431
Lag 1000 -0.02600414
Lag 5000 -0.02326421
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.animal
Lag 0 -0.07404287
Lag 100 -0.08742103
Lag 500 -0.05376905
Lag 1000 -0.03219125
Lag 5000 0.02771727
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.animal
Lag 0 -0.07404287
Lag 100 -0.08742103
Lag 500 -0.05376905
Lag 1000 -0.03219125
Lag 5000 0.02771727
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.animal
Lag 0 -0.06663301
Lag 100 -0.07398282
Lag 500 -0.03873715
Lag 1000 -0.03346102
Lag 5000 0.06535632
traitbwt.byear traittarsus.byear traitbwt.mother traittarsus.mother
Lag 0 -0.002044905 0.06061428 -0.13681757 0.063034744
Lag 100 -0.029101625 0.04741082 -0.09232454 0.062553003
Lag 500 -0.025891155 0.04101237 -0.01510511 -0.026837884
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Lag 0 -0.06644309
Lag 100 -0.03252225
Lag 500 -0.03013542
Lag 1000 0.00413424
Lag 5000 0.09523719
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.units
Lag 0 -0.06644309
Lag 100 -0.03252225
Lag 500 -0.03013542
Lag 1000 0.00413424
Lag 5000 0.09523719
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.units
Lag 0 -0.030836644
Lag 100 -0.012261003
Lag 500 -0.009828189
Lag 1000 0.015985541
Lag 5000 0.120961240
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.units
Lag 0 1.0000000
Lag 100 0.7895424
Lag 500 0.4966907
Lag 1000 0.2824837
Lag 5000 -0.1086586
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.units
Lag 0 0.9162648
Lag 100 0.7897342
Lag 500 0.5546655
Lag 1000 0.3340592
Lag 5000 -0.1357395
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.units
Lag 0 0.9162648
Lag 100 0.7897342
Lag 500 0.5546655
Lag 1000 0.3340592
Lag 5000 -0.1357395
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.units
Lag 0 0.7818908
Lag 100 0.7088815
Lag 500 0.5356249
Lag 1000 0.3410568
Lag 5000 -0.1407239
, , at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.units
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.animal
Lag 0 0.066793402
Lag 100 0.050378446
Lag 500 0.077515159
Lag 1000 0.008812794
Lag 5000 -0.121465553
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.animal
Lag 0 0.093083697
Lag 100 0.084384646
Lag 500 0.074812950
Lag 1000 -0.007598499
Lag 5000 -0.145198558
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.animal
Lag 0 0.093083697
Lag 100 0.084384646
Lag 500 0.074812950
Lag 1000 -0.007598499
Lag 5000 -0.145198558
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.animal
Lag 0 0.039633904
Lag 100 0.030631751
Lag 500 0.008216661
Lag 1000 -0.067574178
Lag 5000 -0.158681853
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.animal
Lag 0 -0.8725969
Lag 100 -0.7772224
Lag 500 -0.5293889
Lag 1000 -0.3047292
Lag 5000 0.1032909
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.animal
Lag 0 -0.9629330
Lag 100 -0.8857980
Lag 500 -0.6314814
Lag 1000 -0.3830396
Lag 5000 0.1372333
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.animal
Lag 0 -0.9629330
Lag 100 -0.8857980
Lag 500 -0.6314814
Lag 1000 -0.3830396
Lag 5000 0.1372333
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.animal
Lag 0 -0.9140715
Lag 100 -0.8566927
Lag 500 -0.6364708
Lag 1000 -0.3975119
Lag 5000 0.1452190
traitbwt.byear traittarsus.byear traitbwt.mother traittarsus.mother
Lag 0 0.03515002 -0.04917083 -0.03778492 0.16291072
Lag 100 0.03091121 -0.05304287 -0.03754739 0.16477625
Lag 500 0.02594763 -0.04411058 -0.04091176 0.15960207
Lag 1000 0.03943697 -0.05730659 -0.07505811 0.12634662
Lag 5000 -0.02494957 -0.03580137 -0.02083442 -0.01955372
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.units
Lag 0 -0.04169552
Lag 100 -0.02400995
Lag 500 -0.05483846
Lag 1000 0.01413904
Lag 5000 0.12137475
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.units
Lag 0 -0.05557720
Lag 100 -0.04292481
Lag 500 -0.04373833
Lag 1000 0.01820822
Lag 5000 0.13061028
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.units
Lag 0 -0.05557720
Lag 100 -0.04292481
Lag 500 -0.04373833
Lag 1000 0.01820822
Lag 5000 0.13061028
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.units
Lag 0 -0.03042350
Lag 100 -0.02364770
Lag 500 -0.02090983
Lag 1000 0.03823823
Lag 5000 0.15598999
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.units
Lag 0 0.9162648
Lag 100 0.7742948
Lag 500 0.5235576
Lag 1000 0.3032634
Lag 5000 -0.1115658
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.units
Lag 0 1.0000000
Lag 100 0.8752177
Lag 500 0.6156893
Lag 1000 0.3715418
Lag 5000 -0.1435973
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.units
Lag 0 1.0000000
Lag 100 0.8752177
Lag 500 0.6156893
Lag 1000 0.3715418
Lag 5000 -0.1435973
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.units
Lag 0 0.9475981
Lag 100 0.8522663
Lag 500 0.6217954
Lag 1000 0.3896947
Lag 5000 -0.1540929
, , at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.units
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.animal
Lag 0 0.066793402
Lag 100 0.050378446
Lag 500 0.077515159
Lag 1000 0.008812794
Lag 5000 -0.121465553
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.animal
Lag 0 0.093083697
Lag 100 0.084384646
Lag 500 0.074812950
Lag 1000 -0.007598499
Lag 5000 -0.145198558
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.animal
Lag 0 0.093083697
Lag 100 0.084384646
Lag 500 0.074812950
Lag 1000 -0.007598499
Lag 5000 -0.145198558
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.animal
Lag 0 0.039633904
Lag 100 0.030631751
Lag 500 0.008216661
Lag 1000 -0.067574178
Lag 5000 -0.158681853
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.animal
Lag 0 -0.8725969
Lag 100 -0.7772224
Lag 500 -0.5293889
Lag 1000 -0.3047292
Lag 5000 0.1032909
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.animal
Lag 0 -0.9629330
Lag 100 -0.8857980
Lag 500 -0.6314814
Lag 1000 -0.3830396
Lag 5000 0.1372333
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.animal
Lag 0 -0.9629330
Lag 100 -0.8857980
Lag 500 -0.6314814
Lag 1000 -0.3830396
Lag 5000 0.1372333
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.animal
Lag 0 -0.9140715
Lag 100 -0.8566927
Lag 500 -0.6364708
Lag 1000 -0.3975119
Lag 5000 0.1452190
traitbwt.byear traittarsus.byear traitbwt.mother traittarsus.mother
Lag 0 0.03515002 -0.04917083 -0.03778492 0.16291072
Lag 100 0.03091121 -0.05304287 -0.03754739 0.16477625
Lag 500 0.02594763 -0.04411058 -0.04091176 0.15960207
Lag 1000 0.03943697 -0.05730659 -0.07505811 0.12634662
Lag 5000 -0.02494957 -0.03580137 -0.02083442 -0.01955372
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.units
Lag 0 -0.04169552
Lag 100 -0.02400995
Lag 500 -0.05483846
Lag 1000 0.01413904
Lag 5000 0.12137475
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.units
Lag 0 -0.05557720
Lag 100 -0.04292481
Lag 500 -0.04373833
Lag 1000 0.01820822
Lag 5000 0.13061028
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.units
Lag 0 -0.05557720
Lag 100 -0.04292481
Lag 500 -0.04373833
Lag 1000 0.01820822
Lag 5000 0.13061028
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.units
Lag 0 -0.03042350
Lag 100 -0.02364770
Lag 500 -0.02090983
Lag 1000 0.03823823
Lag 5000 0.15598999
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.units
Lag 0 0.9162648
Lag 100 0.7742948
Lag 500 0.5235576
Lag 1000 0.3032634
Lag 5000 -0.1115658
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.units
Lag 0 1.0000000
Lag 100 0.8752177
Lag 500 0.6156893
Lag 1000 0.3715418
Lag 5000 -0.1435973
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.units
Lag 0 1.0000000
Lag 100 0.8752177
Lag 500 0.6156893
Lag 1000 0.3715418
Lag 5000 -0.1435973
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.units
Lag 0 0.9475981
Lag 100 0.8522663
Lag 500 0.6217954
Lag 1000 0.3896947
Lag 5000 -0.1540929
, , at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.units
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.animal
Lag 0 0.047978981
Lag 100 0.045079451
Lag 500 0.067970538
Lag 1000 -0.006909171
Lag 5000 -0.132371879
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.animal
Lag 0 0.08843633
Lag 100 0.08879180
Lag 500 0.08319912
Lag 1000 -0.00586568
Lag 5000 -0.15675135
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.animal
Lag 0 0.08843633
Lag 100 0.08879180
Lag 500 0.08319912
Lag 1000 -0.00586568
Lag 5000 -0.15675135
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.animal
Lag 0 0.04584246
Lag 100 0.04189200
Lag 500 0.02195919
Lag 1000 -0.05747491
Lag 5000 -0.16717974
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.animal
Lag 0 -0.75254810
Lag 100 -0.68626575
Lag 500 -0.50089775
Lag 1000 -0.29031256
Lag 5000 0.09258748
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.animal
Lag 0 -0.9191068
Lag 100 -0.8549977
Lag 500 -0.6281177
Lag 1000 -0.3837276
Lag 5000 0.1299735
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.animal
Lag 0 -0.9191068
Lag 100 -0.8549977
Lag 500 -0.6281177
Lag 1000 -0.3837276
Lag 5000 0.1299735
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.animal
Lag 0 -0.9650519
Lag 100 -0.9020388
Lag 500 -0.6603730
Lag 1000 -0.4085407
Lag 5000 0.1451290
traitbwt.byear traittarsus.byear traitbwt.mother traittarsus.mother
Lag 0 0.03233249 -0.05392947 -0.04048151 0.17073426
Lag 100 0.03971497 -0.04863212 -0.04603016 0.19100707
Lag 500 0.02833531 -0.02831174 -0.04356222 0.17180604
Lag 1000 0.03018475 -0.05344380 -0.07230573 0.12082866
Lag 5000 -0.04000580 -0.02623878 -0.01322038 -0.01980137
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.units
Lag 0 -0.02086631
Lag 100 -0.02091564
Lag 500 -0.04738890
Lag 1000 0.02308918
Lag 5000 0.12589958
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.units
Lag 0 -0.04717349
Lag 100 -0.04819145
Lag 500 -0.05369332
Lag 1000 0.02184183
Lag 5000 0.13760532
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.units
Lag 0 -0.04717349
Lag 100 -0.04819145
Lag 500 -0.05369332
Lag 1000 0.02184183
Lag 5000 0.13760532
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.units
Lag 0 -0.03748483
Lag 100 -0.03257654
Lag 500 -0.03463265
Lag 1000 0.04295442
Lag 5000 0.15951258
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.units
Lag 0 0.7818908
Lag 100 0.6906357
Lag 500 0.4994770
Lag 1000 0.2932880
Lag 5000 -0.1017144
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.units
Lag 0 0.9475981
Lag 100 0.8462154
Lag 500 0.6150082
Lag 1000 0.3748486
Lag 5000 -0.1355925
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.units
Lag 0 0.9475981
Lag 100 0.8462154
Lag 500 0.6150082
Lag 1000 0.3748486
Lag 5000 -0.1355925
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.units
Lag 0 1.0000000
Lag 100 0.8919817
Lag 500 0.6480975
Lag 1000 0.4037684
Lag 5000 -0.1516651As before we can obtain the raw variance component estimates and genetic correlations for the random effects:
posterior.mode(model2.4$VCV) at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.animal
0.9669729
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.animal
0.1859324
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.animal
0.1859324
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.animal
1.9958915
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.animal
0.8390295
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.animal
-0.1015747
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.animal
-0.1015747
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.animal
0.6444978
traitbwt.byear
0.8339224
traittarsus.byear
2.9032045
traitbwt.mother
1.8371233
traittarsus.mother
6.4835733
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traitbwt.units
2.1384066
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traitbwt.units
4.8421570
at.level(sex, "1"):traitbwt:at.level(sex, "1"):traittarsus.units
4.8421570
at.level(sex, "1"):traittarsus:at.level(sex, "1"):traittarsus.units
13.0119702
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traitbwt.units
2.1428481
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traitbwt.units
6.0868703
at.level(sex, "2"):traitbwt:at.level(sex, "2"):traittarsus.units
6.0868703
at.level(sex, "2"):traittarsus:at.level(sex, "2"):traittarsus.units
18.3836767 #
genetic.correlation2.4.F <- model2.4$VCV[, "at.level(sex, \"1\"):traittarsus:at.level(sex, \"1\"):traitbwt.animal"] / sqrt(model2.4$VCV[, "at.level(sex, \"1\"):traitbwt:at.level(sex, \"1\"):traitbwt.animal"] * model2.4$VCV[, "at.level(sex, \"1\"):traittarsus:at.level(sex, \"1\"):traittarsus.animal"])
residual.correlation2.4.F <- model2.4$VCV[, "at.level(sex, \"1\"):traittarsus:at.level(sex, \"1\"):traitbwt.units"] / sqrt(model2.4$VCV[, "at.level(sex, \"1\"):traitbwt:at.level(sex, \"1\"):traitbwt.units"] * model2.4$VCV[, "at.level(sex, \"1\"):traittarsus:at.level(sex, \"1\"):traittarsus.units"])
genetic.correlation2.4.M <- model2.4$VCV[, "at.level(sex, \"2\"):traittarsus:at.level(sex, \"2\"):traitbwt.animal"] / sqrt(model2.4$VCV[, "at.level(sex, \"2\"):traitbwt:at.level(sex, \"2\"):traitbwt.animal"] * model2.4$VCV[, "at.level(sex, \"2\"):traittarsus:at.level(sex, \"2\"):traittarsus.animal"])
residual.correlation2.4.M <- model2.4$VCV[, "at.level(sex, \"2\"):traittarsus:at.level(sex, \"2\"):traitbwt.units"] / sqrt(model2.4$VCV[, "at.level(sex, \"2\"):traitbwt:at.level(sex, \"2\"):traitbwt.units"] * model2.4$VCV[, "at.level(sex, \"2\"):traittarsus:at.level(sex, \"2\"):traittarsus.units"])
#
posterior.mode(genetic.correlation2.4.F) var1
0.7852385 posterior.mode(residual.correlation2.4.F) var1
0.8738073 posterior.mode(genetic.correlation2.4.M) var1
0.9166822 posterior.mode(residual.correlation2.4.M) var1
0.8658358 Evaluation of the statistical support for these sex-specific correlations is straightforward. Because we imposed no constraint on their estimation, we can evaluate the extent to which the posterior distributions overlap zero or overlap each other:
HPDinterval(genetic.correlation2.4.F, 0.95) lower upper
var1 -0.3742433 0.963575
attr(,"Probability")
[1] 0.95HPDinterval(genetic.correlation2.4.M, 0.95) lower upper
var1 -0.3275444 0.9801895
attr(,"Probability")
[1] 0.95HPDinterval(residual.correlation2.4.F, 0.95) lower upper
var1 0.698292 0.962472
attr(,"Probability")
[1] 0.95HPDinterval(residual.correlation2.4.M, 0.95) lower upper
var1 -0.1744922 0.9796736
attr(,"Probability")
[1] 0.95Here a plot to visualize the overlaps of covariances.
cor.est <- rbind(
cbind(posterior.mode(genetic.correlation2.4.F, ), HPDinterval(genetic.correlation2.4.F, , 0.95)),
cbind(posterior.mode(genetic.correlation2.4.M), HPDinterval(genetic.correlation2.4.M, 0.95)),
cbind(posterior.mode(residual.correlation2.4.F, ), HPDinterval(residual.correlation2.4.F, , 0.95)),
cbind(posterior.mode(residual.correlation2.4.M), HPDinterval(residual.correlation2.4.M, 0.95))
)
plot(c(0.95, 1.05, 1.95, 2.05) ~ cor.est[, 1], xlim = c(-1, 1), ylim = c(0.5, 2.5), xlab = "", ylab = "", col = c("red", "blue"), pch = c(16, 17), cex = 2, yaxt = "n")
arrows(y0 = 0.95, x0 = cor.est[1, 2], y1 = 0.95, x1 = cor.est[1, 3], code = 3, angle = 90, length = 0, col = c("red"), lwd = 2)
arrows(y0 = 1.05, x0 = cor.est[2, 2], y1 = 1.05, x1 = cor.est[2, 3], code = 3, angle = 90, length = 0, col = c("blue"), lwd = 2)
arrows(y0 = 1.95, x0 = cor.est[3, 2], y1 = 1.95, x1 = cor.est[3, 3], code = 3, angle = 90, length = 0, col = c("red"), lwd = 2)
arrows(y0 = 2.05, x0 = cor.est[4, 2], y1 = 2.05, x1 = cor.est[4, 3], code = 3, angle = 90, length = 0, col = c("blue"), lwd = 2)
mtext("Correlation (±CI)", side = 1, las = 1, adj = 0.4, line = 3, cex = 1.6)
axis(2, at = 1, labels = c("genetic"), las = 3, cex.axis = 1.6)
axis(2, at = 2, labels = c("residual"), las = 3, cex.axis = 1.6)
These posterior distributions overlap between each other, which suggested the correlation were not significantly different between sexes.
6.0.4 Between groups (co)variances and the B-matrix
Animal models are amazing model. With different group within a population, it is also possible to estimate how much the different groups shared the same genetic via the cross-group genetic covariance. This covariance is essential to understand ontogenic or sexual conflict, which can constraint or enhanced response to evolution. As an example, we estimate the cross-sex genetic correlation r_{fm}
First, we need to dissociate the trait values for females and males into distinct variables. Then, we use a bivariate model (for one trait: tarsus) and a multivariate model (for various traits: tarsus and bwt). With a multivariate model, the cross-sex-cross trait covariance matrix is also named B matrix.
The coding is a bit complain but pretty straightforward. It is important to modify the covariance matrix at the residual level to avoid the calculation of a cross-sex residual covariance (no individual switched sex during the experiment).
gryphon2$bwt.1 <- NA
gryphon2$tarsus.1 <- NA
animal <- gryphon2[gryphon2$sex == "1", ]$animal
for (i in unique(animal)) {
gryphon2$bwt.1[which(gryphon2$animal == i)] <- gryphon2$bwt[which(gryphon2$animal == i)]
gryphon2$tarsus.1[which(gryphon2$animal == i)] <- gryphon2$tarsus[which(gryphon2$animal == i)]
}
#
gryphon2$bwt.2 <- NA
gryphon2$tarsus.2 <- NA
animal <- gryphon2[gryphon2$sex == "2", ]$animal
for (i in unique(animal)) {
gryphon2$bwt.2[which(gryphon2$animal == i)] <- gryphon2$bwt[which(gryphon2$animal == i)]
gryphon2$tarsus.2[which(gryphon2$animal == i)] <- gryphon2$tarsus[which(gryphon2$animal == i)]
}
#
prior2.4 <- list(
G = list(
G1 = list(V = diag(2), nu = 1.002),
G2 = list(V = diag(2), nu = 1.002),
G3 = list(V = diag(2), nu = 1.002)
),
R = list(
V1 = list(V = diag(2), nu = 1.002)
)
)
#
model.BivSex <- MCMCglmm(cbind(tarsus.1, tarsus.2) ~ trait - 1,
random = ~ us(trait):animal + idh(trait):byear + idh(trait):mother,
rcov = ~ us(trait):units,
family = c("gaussian", "gaussian"),
ginv = list(animal = Ainv), data = gryphon2,
nitt = 130000, thin = 100, burnin = 30000,
prior = prior2.4, verbose = FALSE, pr = TRUE
)
save(model.BivSex, file = "data/MCMCglmm_model_BivSex_LongRun.rda")Again we have provided the data from one such run. It can be accessed using the code:
Iterations = 30001:129901
Thinning interval = 100
Sample size = 1000
DIC: 1670.599
G-structure: ~us(trait):animal
post.mean l-95% CI u-95% CI eff.samp
traittarsus.1:traittarsus.1.animal 6.632 2.136 12.69 85.74
traittarsus.2:traittarsus.1.animal 8.043 2.389 13.54 117.04
traittarsus.1:traittarsus.2.animal 8.043 2.389 13.54 117.04
traittarsus.2:traittarsus.2.animal 16.145 3.128 28.93 21.81
~idh(trait):byear
post.mean l-95% CI u-95% CI eff.samp
traittarsus.1.byear 3.184 0.505 6.515 357.4
traittarsus.2.byear 4.576 1.346 8.476 442.5
~idh(trait):mother
post.mean l-95% CI u-95% CI eff.samp
traittarsus.1.mother 1.777 0.07858 4.714 299.68
traittarsus.2.mother 2.980 0.12204 7.328 70.26
R-structure: ~us(trait):units
post.mean l-95% CI u-95% CI eff.samp
traittarsus.1:traittarsus.1.units 15.455 8.998 21.84 104.923
traittarsus.2:traittarsus.1.units -1.497 -15.500 15.53 8.767
traittarsus.1:traittarsus.2.units -1.497 -15.500 15.53 8.767
traittarsus.2:traittarsus.2.units 9.356 0.239 19.10 21.548
Location effects: cbind(tarsus.1, tarsus.2) ~ trait - 1
post.mean l-95% CI u-95% CI eff.samp pMCMC
traittarsus.1 20.48 19.62 21.48 703.9 <0.001 ***
traittarsus.2 20.46 19.42 21.40 846.8 <0.001 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1autocorr(model.BivSex$VCV), , traittarsus.1:traittarsus.1.animal
traittarsus.1:traittarsus.1.animal traittarsus.2:traittarsus.1.animal
Lag 0 1.00000000 0.48422763
Lag 100 0.73797990 0.27701934
Lag 500 0.43151596 0.08460564
Lag 1000 0.27709357 0.03138071
Lag 5000 0.09623473 0.02508175
traittarsus.1:traittarsus.2.animal traittarsus.2:traittarsus.2.animal
Lag 0 0.48422763 -0.20835012
Lag 100 0.27701934 -0.26518087
Lag 500 0.08460564 -0.27929151
Lag 1000 0.03138071 -0.23408954
Lag 5000 0.02508175 -0.02431482
traittarsus.1.byear traittarsus.2.byear traittarsus.1.mother
Lag 0 0.05650214 -0.059474225 -0.038396947
Lag 100 0.03805347 -0.063250151 -0.012779432
Lag 500 0.03353186 -0.031583736 0.059794328
Lag 1000 0.02971111 0.032191172 -0.004310584
Lag 5000 0.04021796 -0.001198619 -0.065221991
traittarsus.2.mother traittarsus.1:traittarsus.1.units
Lag 0 0.1285643 -0.7394524
Lag 100 0.1416089 -0.5874113
Lag 500 0.1227812 -0.3892610
Lag 1000 0.1054744 -0.2272794
Lag 5000 0.1046093 -0.0490914
traittarsus.2:traittarsus.1.units traittarsus.1:traittarsus.2.units
Lag 0 -0.030661923 -0.030661923
Lag 100 -0.009066847 -0.009066847
Lag 500 -0.014021640 -0.014021640
Lag 1000 -0.038727365 -0.038727365
Lag 5000 -0.053406989 -0.053406989
traittarsus.2:traittarsus.2.units
Lag 0 0.24444681
Lag 100 0.28630940
Lag 500 0.28676382
Lag 1000 0.25016902
Lag 5000 -0.01889626
, , traittarsus.2:traittarsus.1.animal
traittarsus.1:traittarsus.1.animal traittarsus.2:traittarsus.1.animal
Lag 0 0.48422763 1.00000000
Lag 100 0.25316393 0.68722653
Lag 500 -0.01525426 0.30994286
Lag 1000 -0.13117432 0.12750201
Lag 5000 -0.03481149 0.01967858
traittarsus.1:traittarsus.2.animal traittarsus.2:traittarsus.2.animal
Lag 0 1.00000000 0.4372811
Lag 100 0.68722653 0.3171927
Lag 500 0.30994286 0.2173200
Lag 1000 0.12750201 0.2034517
Lag 5000 0.01967858 0.1155543
traittarsus.1.byear traittarsus.2.byear traittarsus.1.mother
Lag 0 -0.028123268 -0.10117282 0.068035501
Lag 100 -0.036441213 -0.06326083 0.058376180
Lag 500 -0.017206400 -0.06159010 -0.002869166
Lag 1000 -0.004346341 0.06173108 -0.017320527
Lag 5000 -0.044798021 0.07734401 -0.083350187
traittarsus.2.mother traittarsus.1:traittarsus.1.units
Lag 0 -0.261520775 -0.32691256
Lag 100 -0.219989670 -0.19037150
Lag 500 -0.171008994 0.03568009
Lag 1000 -0.073253782 0.15052971
Lag 5000 -0.002628408 0.06147675
traittarsus.2:traittarsus.1.units traittarsus.1:traittarsus.2.units
Lag 0 -0.15561461 -0.15561461
Lag 100 -0.11940169 -0.11940169
Lag 500 -0.10722180 -0.10722180
Lag 1000 -0.11888700 -0.11888700
Lag 5000 -0.07749379 -0.07749379
traittarsus.2:traittarsus.2.units
Lag 0 -0.3304177
Lag 100 -0.2624116
Lag 500 -0.1893048
Lag 1000 -0.2045441
Lag 5000 -0.1580773
, , traittarsus.1:traittarsus.2.animal
traittarsus.1:traittarsus.1.animal traittarsus.2:traittarsus.1.animal
Lag 0 0.48422763 1.00000000
Lag 100 0.25316393 0.68722653
Lag 500 -0.01525426 0.30994286
Lag 1000 -0.13117432 0.12750201
Lag 5000 -0.03481149 0.01967858
traittarsus.1:traittarsus.2.animal traittarsus.2:traittarsus.2.animal
Lag 0 1.00000000 0.4372811
Lag 100 0.68722653 0.3171927
Lag 500 0.30994286 0.2173200
Lag 1000 0.12750201 0.2034517
Lag 5000 0.01967858 0.1155543
traittarsus.1.byear traittarsus.2.byear traittarsus.1.mother
Lag 0 -0.028123268 -0.10117282 0.068035501
Lag 100 -0.036441213 -0.06326083 0.058376180
Lag 500 -0.017206400 -0.06159010 -0.002869166
Lag 1000 -0.004346341 0.06173108 -0.017320527
Lag 5000 -0.044798021 0.07734401 -0.083350187
traittarsus.2.mother traittarsus.1:traittarsus.1.units
Lag 0 -0.261520775 -0.32691256
Lag 100 -0.219989670 -0.19037150
Lag 500 -0.171008994 0.03568009
Lag 1000 -0.073253782 0.15052971
Lag 5000 -0.002628408 0.06147675
traittarsus.2:traittarsus.1.units traittarsus.1:traittarsus.2.units
Lag 0 -0.15561461 -0.15561461
Lag 100 -0.11940169 -0.11940169
Lag 500 -0.10722180 -0.10722180
Lag 1000 -0.11888700 -0.11888700
Lag 5000 -0.07749379 -0.07749379
traittarsus.2:traittarsus.2.units
Lag 0 -0.3304177
Lag 100 -0.2624116
Lag 500 -0.1893048
Lag 1000 -0.2045441
Lag 5000 -0.1580773
, , traittarsus.2:traittarsus.2.animal
traittarsus.1:traittarsus.1.animal traittarsus.2:traittarsus.1.animal
Lag 0 -0.2083501 0.43728107
Lag 100 -0.2828015 0.29272735
Lag 500 -0.3313152 0.14658444
Lag 1000 -0.3483078 0.06012732
Lag 5000 -0.1542996 -0.06471744
traittarsus.1:traittarsus.2.animal traittarsus.2:traittarsus.2.animal
Lag 0 0.43728107 1.00000000
Lag 100 0.29272735 0.87775419
Lag 500 0.14658444 0.72227084
Lag 1000 0.06012732 0.61062886
Lag 5000 -0.06471744 0.08074184
traittarsus.1.byear traittarsus.2.byear traittarsus.1.mother
Lag 0 -0.020084226 -0.013645105 0.007263224
Lag 100 -0.015303798 0.015235251 0.013922907
Lag 500 -0.009604004 -0.004276257 -0.022794079
Lag 1000 -0.036443873 0.045216146 0.038406389
Lag 5000 -0.046131641 0.012581835 -0.012187074
traittarsus.2.mother traittarsus.1:traittarsus.1.units
Lag 0 -0.50677816 0.23024103
Lag 100 -0.46549011 0.26517948
Lag 500 -0.35999881 0.31894466
Lag 1000 -0.26148886 0.30787546
Lag 5000 -0.09601646 0.09998448
traittarsus.2:traittarsus.1.units traittarsus.1:traittarsus.2.units
Lag 0 0.03215520 0.03215520
Lag 100 0.04234930 0.04234930
Lag 500 0.01485912 0.01485912
Lag 1000 -0.02777646 -0.02777646
Lag 5000 -0.10000281 -0.10000281
traittarsus.2:traittarsus.2.units
Lag 0 -0.90778147
Lag 100 -0.84400702
Lag 500 -0.70957533
Lag 1000 -0.62450980
Lag 5000 -0.06262314
, , traittarsus.1.byear
traittarsus.1:traittarsus.1.animal traittarsus.2:traittarsus.1.animal
Lag 0 0.05650214 -0.02812327
Lag 100 0.06068975 -0.02687949
Lag 500 0.02342116 -0.03285780
Lag 1000 0.03532201 -0.03419221
Lag 5000 0.02786557 -0.01481811
traittarsus.1:traittarsus.2.animal traittarsus.2:traittarsus.2.animal
Lag 0 -0.02812327 -0.02008423
Lag 100 -0.02687949 -0.02175035
Lag 500 -0.03285780 -0.01196604
Lag 1000 -0.03419221 -0.03085934
Lag 5000 -0.01481811 0.01496886
traittarsus.1.byear traittarsus.2.byear traittarsus.1.mother
Lag 0 1.00000000 -0.008840935 -0.034026465
Lag 100 0.23201455 -0.040849216 0.006952432
Lag 500 0.10173419 0.018677216 0.021915445
Lag 1000 0.05656314 0.045347703 -0.069023041
Lag 5000 -0.02674433 0.003879773 -0.031727649
traittarsus.2.mother traittarsus.1:traittarsus.1.units
Lag 0 0.041524616 -0.131561587
Lag 100 0.022654125 -0.091920671
Lag 500 -0.003137523 -0.023174815
Lag 1000 0.093233105 0.017723781
Lag 5000 -0.001576843 0.003971118
traittarsus.2:traittarsus.1.units traittarsus.1:traittarsus.2.units
Lag 0 0.06264243 0.06264243
Lag 100 0.06240060 0.06240060
Lag 500 0.03789653 0.03789653
Lag 1000 0.03352306 0.03352306
Lag 5000 0.05768588 0.05768588
traittarsus.2:traittarsus.2.units
Lag 0 0.013826338
Lag 100 0.015690413
Lag 500 0.020546446
Lag 1000 -0.006052117
Lag 5000 -0.020241900
, , traittarsus.2.byear
traittarsus.1:traittarsus.1.animal traittarsus.2:traittarsus.1.animal
Lag 0 -0.059474225 -0.10117282
Lag 100 -0.029542673 -0.06571088
Lag 500 0.019127206 0.02553144
Lag 1000 -0.006675716 0.03933732
Lag 5000 -0.020363086 -0.01801919
traittarsus.1:traittarsus.2.animal traittarsus.2:traittarsus.2.animal
Lag 0 -0.10117282 -0.013645105
Lag 100 -0.06571088 -0.001743299
Lag 500 0.02553144 0.024080673
Lag 1000 0.03933732 0.020998801
Lag 5000 -0.01801919 -0.036422613
traittarsus.1.byear traittarsus.2.byear traittarsus.1.mother
Lag 0 -0.008840935 1.00000000 0.019871390
Lag 100 0.003895756 0.15813110 0.000200299
Lag 500 -0.028206511 0.02861588 0.028238837
Lag 1000 -0.022327614 0.02577769 0.069995240
Lag 5000 0.054519302 -0.01863939 0.021348106
traittarsus.2.mother traittarsus.1:traittarsus.1.units
Lag 0 0.02790731 0.04582166
Lag 100 -0.02533496 0.01584625
Lag 500 -0.04228406 -0.01965332
Lag 1000 -0.03776489 -0.05592538
Lag 5000 0.04026220 0.02293994
traittarsus.2:traittarsus.1.units traittarsus.1:traittarsus.2.units
Lag 0 -0.01692229 -0.01692229
Lag 100 -0.03014201 -0.03014201
Lag 500 -0.05685394 -0.05685394
Lag 1000 -0.05775898 -0.05775898
Lag 5000 -0.04474406 -0.04474406
traittarsus.2:traittarsus.2.units
Lag 0 -0.05647151
Lag 100 -0.01120227
Lag 500 -0.02826105
Lag 1000 -0.01902149
Lag 5000 0.04653422
, , traittarsus.1.mother
traittarsus.1:traittarsus.1.animal traittarsus.2:traittarsus.1.animal
Lag 0 -0.03839695 0.068035501
Lag 100 -0.01125448 0.090872487
Lag 500 -0.01822303 0.074904451
Lag 1000 -0.06684368 -0.009049799
Lag 5000 0.01882807 -0.038704215
traittarsus.1:traittarsus.2.animal traittarsus.2:traittarsus.2.animal
Lag 0 0.068035501 0.007263224
Lag 100 0.090872487 0.009427782
Lag 500 0.074904451 -0.008966636
Lag 1000 -0.009049799 -0.062208885
Lag 5000 -0.038704215 -0.090802212
traittarsus.1.byear traittarsus.2.byear traittarsus.1.mother
Lag 0 -0.034026465 0.019871390 1.00000000
Lag 100 -0.044009625 -0.022642909 0.53848292
Lag 500 0.033149894 -0.058758981 0.05060514
Lag 1000 -0.034811076 -0.041691079 -0.01263351
Lag 5000 0.003520887 -0.007417182 -0.01561154
traittarsus.2.mother traittarsus.1:traittarsus.1.units
Lag 0 -0.053312892 -0.274551627
Lag 100 -0.021399368 -0.183188795
Lag 500 0.001127949 -0.004741630
Lag 1000 0.017008055 0.049168722
Lag 5000 -0.013865361 -0.003898312
traittarsus.2:traittarsus.1.units traittarsus.1:traittarsus.2.units
Lag 0 0.021389916 0.021389916
Lag 100 0.010504830 0.010504830
Lag 500 0.005067944 0.005067944
Lag 1000 0.024425517 0.024425517
Lag 5000 -0.004626176 -0.004626176
traittarsus.2:traittarsus.2.units
Lag 0 0.02429791
Lag 100 0.01285473
Lag 500 0.02017728
Lag 1000 0.06093906
Lag 5000 0.10720949
, , traittarsus.2.mother
traittarsus.1:traittarsus.1.animal traittarsus.2:traittarsus.1.animal
Lag 0 0.12856434 -0.2615208
Lag 100 0.14693139 -0.2325836
Lag 500 0.21342005 -0.1621874
Lag 1000 0.23353394 -0.1119149
Lag 5000 0.02771044 0.0396288
traittarsus.1:traittarsus.2.animal traittarsus.2:traittarsus.2.animal
Lag 0 -0.2615208 -0.50677816
Lag 100 -0.2325836 -0.48725853
Lag 500 -0.1621874 -0.40888208
Lag 1000 -0.1119149 -0.34699264
Lag 5000 0.0396288 0.02549716
traittarsus.1.byear traittarsus.2.byear traittarsus.1.mother
Lag 0 0.04152462 0.027907314 -0.05331289
Lag 100 0.02194445 0.054336046 -0.04284508
Lag 500 -0.03327513 -0.020857444 -0.02968159
Lag 1000 0.02573536 -0.040238713 -0.03336616
Lag 5000 0.01374507 0.005808512 0.07687084
traittarsus.2.mother traittarsus.1:traittarsus.1.units
Lag 0 1.00000000 -0.13910701
Lag 100 0.70222369 -0.13691118
Lag 500 0.35625516 -0.18735521
Lag 1000 0.19638031 -0.21082439
Lag 5000 -0.04114072 -0.04387536
traittarsus.2:traittarsus.1.units traittarsus.1:traittarsus.2.units
Lag 0 0.04614450 0.04614450
Lag 100 0.04486226 0.04486226
Lag 500 0.04022585 0.04022585
Lag 1000 0.05277963 0.05277963
Lag 5000 0.04252673 0.04252673
traittarsus.2:traittarsus.2.units
Lag 0 0.268960307
Lag 100 0.289158808
Lag 500 0.345252707
Lag 1000 0.323960441
Lag 5000 -0.002082367
, , traittarsus.1:traittarsus.1.units
traittarsus.1:traittarsus.1.animal traittarsus.2:traittarsus.1.animal
Lag 0 -0.7394524 -0.32691256
Lag 100 -0.5906993 -0.20009588
Lag 500 -0.3828210 -0.08127245
Lag 1000 -0.2031251 0.02298348
Lag 5000 -0.0979703 -0.01920779
traittarsus.1:traittarsus.2.animal traittarsus.2:traittarsus.2.animal
Lag 0 -0.32691256 0.23024103
Lag 100 -0.20009588 0.28084172
Lag 500 -0.08127245 0.28272296
Lag 1000 0.02298348 0.28283381
Lag 5000 -0.01920779 0.05177093
traittarsus.1.byear traittarsus.2.byear traittarsus.1.mother
Lag 0 -0.13156159 0.04582166 -0.27455163
Lag 100 -0.05719958 0.04337991 -0.16825519
Lag 500 -0.06997182 0.07140946 -0.07087194
Lag 1000 -0.02088140 0.01426241 0.03955072
Lag 5000 -0.01887279 0.04431921 0.06767122
traittarsus.2.mother traittarsus.1:traittarsus.1.units
Lag 0 -0.1391070 1.00000000
Lag 100 -0.1379410 0.56579808
Lag 500 -0.1301093 0.35250381
Lag 1000 -0.1253506 0.15585076
Lag 5000 -0.0735286 0.05909602
traittarsus.2:traittarsus.1.units traittarsus.1:traittarsus.2.units
Lag 0 0.04896537 0.04896537
Lag 100 0.02746645 0.02746645
Lag 500 0.03218528 0.03218528
Lag 1000 0.05596211 0.05596211
Lag 5000 0.05413531 0.05413531
traittarsus.2:traittarsus.2.units
Lag 0 -0.2610614
Lag 100 -0.3079509
Lag 500 -0.2969894
Lag 1000 -0.2847495
Lag 5000 -0.0427216
, , traittarsus.2:traittarsus.1.units
traittarsus.1:traittarsus.1.animal traittarsus.2:traittarsus.1.animal
Lag 0 -0.030661923 -0.15561461
Lag 100 0.003884354 -0.11920858
Lag 500 0.042099074 -0.08915914
Lag 1000 0.042025296 -0.07981143
Lag 5000 -0.018911064 -0.09774452
traittarsus.1:traittarsus.2.animal traittarsus.2:traittarsus.2.animal
Lag 0 -0.15561461 0.03215520
Lag 100 -0.11920858 0.04834806
Lag 500 -0.08915914 0.05802195
Lag 1000 -0.07981143 0.02656239
Lag 5000 -0.09774452 -0.04245498
traittarsus.1.byear traittarsus.2.byear traittarsus.1.mother
Lag 0 0.06264243 -0.016922288 0.02138992
Lag 100 0.06751797 -0.004991909 0.02085557
Lag 500 0.06731777 -0.030284706 0.05500122
Lag 1000 0.06629827 -0.044495833 0.10333723
Lag 5000 0.08927471 -0.038637660 0.06016204
traittarsus.2.mother traittarsus.1:traittarsus.1.units
Lag 0 0.04614450 0.048965370
Lag 100 0.04880037 0.017340477
Lag 500 0.04329157 -0.013844496
Lag 1000 0.06724925 -0.039591736
Lag 5000 0.04795409 -0.003568665
traittarsus.2:traittarsus.1.units traittarsus.1:traittarsus.2.units
Lag 0 1.0000000 1.0000000
Lag 100 0.9675526 0.9675526
Lag 500 0.9029928 0.9029928
Lag 1000 0.8401123 0.8401123
Lag 5000 0.4663345 0.4663345
traittarsus.2:traittarsus.2.units
Lag 0 -0.04275237
Lag 100 -0.06227874
Lag 500 -0.06672641
Lag 1000 -0.04382724
Lag 5000 0.03699475
, , traittarsus.1:traittarsus.2.units
traittarsus.1:traittarsus.1.animal traittarsus.2:traittarsus.1.animal
Lag 0 -0.030661923 -0.15561461
Lag 100 0.003884354 -0.11920858
Lag 500 0.042099074 -0.08915914
Lag 1000 0.042025296 -0.07981143
Lag 5000 -0.018911064 -0.09774452
traittarsus.1:traittarsus.2.animal traittarsus.2:traittarsus.2.animal
Lag 0 -0.15561461 0.03215520
Lag 100 -0.11920858 0.04834806
Lag 500 -0.08915914 0.05802195
Lag 1000 -0.07981143 0.02656239
Lag 5000 -0.09774452 -0.04245498
traittarsus.1.byear traittarsus.2.byear traittarsus.1.mother
Lag 0 0.06264243 -0.016922288 0.02138992
Lag 100 0.06751797 -0.004991909 0.02085557
Lag 500 0.06731777 -0.030284706 0.05500122
Lag 1000 0.06629827 -0.044495833 0.10333723
Lag 5000 0.08927471 -0.038637660 0.06016204
traittarsus.2.mother traittarsus.1:traittarsus.1.units
Lag 0 0.04614450 0.048965370
Lag 100 0.04880037 0.017340477
Lag 500 0.04329157 -0.013844496
Lag 1000 0.06724925 -0.039591736
Lag 5000 0.04795409 -0.003568665
traittarsus.2:traittarsus.1.units traittarsus.1:traittarsus.2.units
Lag 0 1.0000000 1.0000000
Lag 100 0.9675526 0.9675526
Lag 500 0.9029928 0.9029928
Lag 1000 0.8401123 0.8401123
Lag 5000 0.4663345 0.4663345
traittarsus.2:traittarsus.2.units
Lag 0 -0.04275237
Lag 100 -0.06227874
Lag 500 -0.06672641
Lag 1000 -0.04382724
Lag 5000 0.03699475
, , traittarsus.2:traittarsus.2.units
traittarsus.1:traittarsus.1.animal traittarsus.2:traittarsus.1.animal
Lag 0 0.2444468 -0.33041768
Lag 100 0.2953169 -0.24524259
Lag 500 0.3257997 -0.12021844
Lag 1000 0.3204576 -0.05040170
Lag 5000 0.1966910 0.07386444
traittarsus.1:traittarsus.2.animal traittarsus.2:traittarsus.2.animal
Lag 0 -0.33041768 -0.9077815
Lag 100 -0.24524259 -0.8410651
Lag 500 -0.12021844 -0.6969304
Lag 1000 -0.05040170 -0.5893775
Lag 5000 0.07386444 -0.1004775
traittarsus.1.byear traittarsus.2.byear traittarsus.1.mother
Lag 0 0.01382634 -0.056471508 0.024297909
Lag 100 0.01730830 -0.030701856 0.017739447
Lag 500 0.03968933 0.004065694 0.010636299
Lag 1000 0.03341332 -0.048898719 -0.028816725
Lag 5000 0.05219060 -0.013503372 -0.005167407
traittarsus.2.mother traittarsus.1:traittarsus.1.units
Lag 0 0.2689603 -0.2610614
Lag 100 0.3013532 -0.3031510
Lag 500 0.3094825 -0.3179085
Lag 1000 0.2400190 -0.2838200
Lag 5000 0.1233946 -0.1252443
traittarsus.2:traittarsus.1.units traittarsus.1:traittarsus.2.units
Lag 0 -0.04275237 -0.04275237
Lag 100 -0.05037125 -0.05037125
Lag 500 -0.01879502 -0.01879502
Lag 1000 0.02100080 0.02100080
Lag 5000 0.10654662 0.10654662
traittarsus.2:traittarsus.2.units
Lag 0 1.00000000
Lag 100 0.87986649
Lag 500 0.70214749
Lag 1000 0.61035106
Lag 5000 0.07522425The cross-sex genetic correlation can estimate form the output of the model. For tarsus length at fledging, sexes shared a lot of genetic variance which is commun for a trait with low sexual dimorphism. If the selection is antagonistic between males and females, sexes can not evolve freely form the other sexes and a sexual conflict appears.
rfm <- model.BivSex$VCV[, "traittarsus.1:traittarsus.2.animal"] / sqrt(model.BivSex$VCV[, "traittarsus.1:traittarsus.1.animal"] * model.BivSex$VCV[, "traittarsus.2:traittarsus.2.animal"])
posterior.mode(rfm) var1
0.9664439 HPDinterval(rfm, 0.95) lower upper
var1 0.4630817 0.992376
attr(,"Probability")
[1] 0.95We can estimate directly the correlation and plot the cross-sex genetic correlation
DvsS <- data.frame(
Trait = colnames(model.BivSex$Sol),
BLUP = posterior.mode(model.BivSex$Sol),
CI = HPDinterval((model.BivSex$Sol))
) %>%
filter(grepl("animal", Trait))
DvsS$ID <- substr(DvsS$Trait, 22, 26)
DvsS$TRAIT <- substr(DvsS$Trait, 6, 13)
summary(factor(DvsS$TRAIT))tarsus.1 tarsus.2
1309 1309 DvsS$Trait <- NULL
BLUPS <- reshape(DvsS, v.names = c("BLUP", "CI.lower", "CI.upper"), idvar = "ID", timevar = "TRAIT", direction = "wide")
nrow(BLUPS)[1] 1309rownames(BLUPS) <- c()
colnames(BLUPS) <- c("ID", "BLUP.btw", "CI.L.btw", "CI.U.btw", "BLUP.tarsus", "CI.L.tarsus", "CI.U.tarsus")
summary(BLUPS) ID BLUP.btw CI.L.btw CI.U.btw
Length:1309 Min. :-4.299559 Min. :-9.4393 Min. : 0.5871
Class :character 1st Qu.:-0.743429 1st Qu.:-5.2018 1st Qu.: 3.5625
Mode :character Median :-0.000879 Median :-4.3976 Median : 4.5287
Mean : 0.024573 Mean :-4.3251 Mean : 4.4753
3rd Qu.: 0.762532 3rd Qu.:-3.4818 3rd Qu.: 5.3499
Max. : 4.546380 Max. : 0.5408 Max. :10.9441
BLUP.tarsus CI.L.tarsus CI.U.tarsus
Min. :-8.75836 Min. :-14.320 Min. :-0.3279
1st Qu.:-1.05441 1st Qu.: -8.156 1st Qu.: 4.9947
Median : 0.07087 Median : -6.720 Median : 6.8749
Mean : 0.07320 Mean : -6.464 Mean : 6.6127
3rd Qu.: 1.17195 3rd Qu.: -4.869 3rd Qu.: 8.3021
Max. :13.71503 Max. : 1.264 Max. :16.7611 plot(BLUP.tarsus ~ BLUP.btw, BLUPS, xlab = "", ylab = "", las = 1.2, bty = "o", col = "white")
arrows(x0 = BLUPS$BLUP.btw, y0 = BLUPS$CI.L.tarsus, x1 = BLUPS$BLUP.btw, y1 = BLUPS$CI.U.tarsus, col = "black", code = 3, angle = 90, length = 0)
arrows(x0 = BLUPS$CI.L.btw, y0 = BLUPS$BLUP.tarsus, x1 = BLUPS$CI.U.btw, y1 = BLUPS$BLUP.tarsus, col = "black", code = 3, angle = 90, length = 0)
points(BLUP.tarsus ~ BLUP.btw, BLUPS, pch = 16, col = rgb(1, 0, 1, 0.2), cex = 1.5)
points(BLUP.tarsus ~ BLUP.btw, BLUPS, pch = 1, col = rgb(1, 0, 1, 0.2), cex = c(1.5))
mtext("Male tarsus (BV±CI)", side = 1, line = 2.4)
mtext("Female tarsus (BV±CI)", side = 2, line = 2, las = 3)
#The B matrix used the same code but in a multivariate animal model framework. Here some example code, however due to the nature of the dataset, the cross-sex genetic covariance for birth weight is hard to estimate making difficulty to fit this multivariate animal model.
prior2.5 <- list(
G = list(
G1 = list(V = diag(4), nu = 1.002),
G2 = list(V = diag(4), nu = 1.002),
G3 = list(V = diag(4), nu = 1.002)
),
R = list(
V1 = list(V = diag(4), nu = 1.002)
)
)
#
model.MultivSex <- MCMCglmm(cbind(tarsus.1, bwt.1, tarsus.2, bwt.2) ~ trait - 1,
random = ~ us(trait):animal + idh(trait):byear + idh(trait):mother,
rcov = ~ us(trait):units,
family = c("gaussian", "gaussian", "gaussian", "gaussian"),
ginv = list(animal = Ainv), data = gryphon2,
nitt = 130000, thin = 100, burnin = 30000,
prior = prior2.5, verbose = FALSE, pr = TRUE
)
save(model.MultivSex, file = "data/MCMCglmm_model_MultivSex_LongRun.rda")Again we have provided the data from one such run. It can be accessed using the code:
Iterations = 30001:129901
Thinning interval = 100
Sample size = 1000
DIC: 2590.513
G-structure: ~us(trait):animal
post.mean l-95% CI u-95% CI eff.samp
traittarsus.1:traittarsus.1.animal 5.2542 0.6145315 11.414 28.46
traitbwt.1:traittarsus.1.animal 1.2682 -0.7026690 3.298 63.97
traittarsus.2:traittarsus.1.animal 5.9945 0.3482679 13.405 21.59
traitbwt.2:traittarsus.1.animal 1.4467 -0.3853824 4.110 35.84
traittarsus.1:traitbwt.1.animal 1.2682 -0.7026690 3.298 63.97
traitbwt.1:traitbwt.1.animal 1.7891 0.5620761 3.005 97.87
traittarsus.2:traitbwt.1.animal 0.7719 -1.8038433 4.190 22.64
traitbwt.2:traitbwt.1.animal 0.9939 0.0009052 2.069 50.24
traittarsus.1:traittarsus.2.animal 5.9945 0.3482679 13.405 21.59
traitbwt.1:traittarsus.2.animal 0.7719 -1.8038433 4.190 22.64
traittarsus.2:traittarsus.2.animal 12.7341 1.4093961 23.690 28.81
traitbwt.2:traittarsus.2.animal 2.7675 -0.5938976 6.927 20.64
traittarsus.1:traitbwt.2.animal 1.4467 -0.3853824 4.110 35.84
traitbwt.1:traitbwt.2.animal 0.9939 0.0009052 2.069 50.24
traittarsus.2:traitbwt.2.animal 2.7675 -0.5938976 6.927 20.64
traitbwt.2:traitbwt.2.animal 1.5560 0.2002403 3.046 27.21
~idh(trait):byear
post.mean l-95% CI u-95% CI eff.samp
traittarsus.1.byear 3.3123 0.9318 6.450 391.3
traitbwt.1.byear 0.6822 0.2403 1.253 522.1
traittarsus.2.byear 4.2198 1.3966 7.713 245.2
traitbwt.2.byear 1.1743 0.5405 1.992 669.6
~idh(trait):mother
post.mean l-95% CI u-95% CI eff.samp
traittarsus.1.mother 4.858 0.5149 8.841 122.5
traitbwt.1.mother 1.307 0.5752 2.041 369.0
traittarsus.2.mother 5.389 0.7457 9.557 140.4
traitbwt.2.mother 2.003 1.2844 2.770 409.1
R-structure: ~us(trait):units
post.mean l-95% CI u-95% CI eff.samp
traittarsus.1:traittarsus.1.units 14.0783 8.6213 20.698 76.808
traitbwt.1:traittarsus.1.units 4.0764 2.2358 6.357 47.762
traittarsus.2:traittarsus.1.units -3.6471 -16.9514 14.938 4.746
traitbwt.2:traittarsus.1.units -1.3655 -6.7308 4.970 7.185
traittarsus.1:traitbwt.1.units 4.0764 2.2358 6.357 47.762
traitbwt.1:traitbwt.1.units 1.7295 0.7344 2.785 57.968
traittarsus.2:traitbwt.1.units -1.1455 -5.8008 4.672 6.837
traitbwt.2:traitbwt.1.units -0.4245 -2.3300 1.630 7.646
traittarsus.1:traittarsus.2.units -3.6471 -16.9514 14.938 4.746
traitbwt.1:traittarsus.2.units -1.1455 -5.8008 4.672 6.837
traittarsus.2:traittarsus.2.units 10.8365 0.5947 19.576 26.795
traitbwt.2:traittarsus.2.units 3.7358 -0.1168 6.848 25.426
traittarsus.1:traitbwt.2.units -1.3655 -6.7308 4.970 7.185
traitbwt.1:traitbwt.2.units -0.4245 -2.3300 1.630 7.646
traittarsus.2:traitbwt.2.units 3.7358 -0.1168 6.848 25.426
traitbwt.2:traitbwt.2.units 1.7825 0.2691 2.916 28.817
Location effects: cbind(tarsus.1, bwt.1, tarsus.2, bwt.2) ~ trait - 1
post.mean l-95% CI u-95% CI eff.samp pMCMC
traittarsus.1 20.424 19.488 21.324 484.6 <0.001 ***
traitbwt.1 6.143 5.686 6.550 596.7 <0.001 ***
traittarsus.2 20.487 19.421 21.461 587.3 <0.001 ***
traitbwt.2 8.247 7.744 8.741 876.7 <0.001 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1autocorr(model.MultivSex$VCV), , traittarsus.1:traittarsus.1.animal
traittarsus.1:traittarsus.1.animal traitbwt.1:traittarsus.1.animal
Lag 0 1.0000000 0.6872795
Lag 100 0.8646238 0.6023267
Lag 500 0.6217623 0.4701016
Lag 1000 0.4759845 0.3306117
Lag 5000 0.1189988 0.1665003
traittarsus.2:traittarsus.1.animal traitbwt.2:traittarsus.1.animal
Lag 0 0.6821642 0.5157628
Lag 100 0.5837197 0.4557449
Lag 500 0.4393984 0.3819538
Lag 1000 0.3626317 0.3277211
Lag 5000 0.1659171 0.2490413
traittarsus.1:traitbwt.1.animal traitbwt.1:traitbwt.1.animal
Lag 0 0.6872795 0.2316436
Lag 100 0.6023267 0.1917562
Lag 500 0.4701016 0.1506507
Lag 1000 0.3306117 0.1026122
Lag 5000 0.1665003 0.1840457
traittarsus.2:traitbwt.1.animal traitbwt.2:traitbwt.1.animal
Lag 0 0.4371184 0.2363148
Lag 100 0.3790517 0.1969987
Lag 500 0.3316844 0.1943316
Lag 1000 0.2706112 0.1653149
Lag 5000 0.2226417 0.2722600
traittarsus.1:traittarsus.2.animal traitbwt.1:traittarsus.2.animal
Lag 0 0.6821642 0.4371184
Lag 100 0.5837197 0.3790517
Lag 500 0.4393984 0.3316844
Lag 1000 0.3626317 0.2706112
Lag 5000 0.1659171 0.2226417
traittarsus.2:traittarsus.2.animal traitbwt.2:traittarsus.2.animal
Lag 0 0.10780644 0.12397199
Lag 100 0.07023035 0.10315317
Lag 500 0.03867618 0.09153994
Lag 1000 0.03903023 0.09577409
Lag 5000 0.21464371 0.32154133
traittarsus.1:traitbwt.2.animal traitbwt.1:traitbwt.2.animal
Lag 0 0.5157628 0.2363148
Lag 100 0.4557449 0.1969987
Lag 500 0.3819538 0.1943316
Lag 1000 0.3277211 0.1653149
Lag 5000 0.2490413 0.2722600
traittarsus.2:traitbwt.2.animal traitbwt.2:traitbwt.2.animal
Lag 0 0.12397199 0.07790198
Lag 100 0.10315317 0.07045248
Lag 500 0.09153994 0.07781235
Lag 1000 0.09577409 0.07872349
Lag 5000 0.32154133 0.36408510
traittarsus.1.byear traitbwt.1.byear traittarsus.2.byear
Lag 0 -0.0001991343 0.02533600 0.027261984
Lag 100 0.0100119397 0.03699313 0.023145145
Lag 500 0.0417069693 0.01039048 0.001545709
Lag 1000 0.0504304342 0.06238542 -0.035646379
Lag 5000 0.0318527577 0.07041675 0.069731639
traitbwt.2.byear traittarsus.1.mother traitbwt.1.mother
Lag 0 -0.01231264 -0.150788349 0.10750858
Lag 100 -0.02806645 -0.118379074 0.11004526
Lag 500 0.01040024 -0.006641147 0.07412673
Lag 1000 -0.02300762 0.007943789 0.04372918
Lag 5000 -0.01416454 0.056559933 -0.06110098
traittarsus.2.mother traitbwt.2.mother
Lag 0 0.01502226 0.050820670
Lag 100 0.01411095 0.039228813
Lag 500 0.05290822 0.008673539
Lag 1000 0.06760176 -0.017960145
Lag 5000 0.02399980 -0.029552126
traittarsus.1:traittarsus.1.units traitbwt.1:traittarsus.1.units
Lag 0 -0.6964793 -0.5806661
Lag 100 -0.6332557 -0.5256332
Lag 500 -0.5006482 -0.4211229
Lag 1000 -0.3965468 -0.3341455
Lag 5000 -0.1551518 -0.1703888
traittarsus.2:traittarsus.1.units traitbwt.2:traittarsus.1.units
Lag 0 0.1834123 0.1843936
Lag 100 0.1989318 0.1972224
Lag 500 0.2183849 0.2244201
Lag 1000 0.2393546 0.2533883
Lag 5000 0.1874294 0.2352808
traittarsus.1:traitbwt.1.units traitbwt.1:traitbwt.1.units
Lag 0 -0.5806661 -0.2972330
Lag 100 -0.5256332 -0.2627074
Lag 500 -0.4211229 -0.1975278
Lag 1000 -0.3341455 -0.1864674
Lag 5000 -0.1703888 -0.1779074
traittarsus.2:traitbwt.1.units traitbwt.2:traitbwt.1.units
Lag 0 0.1148525 0.1045202
Lag 100 0.1322561 0.1205853
Lag 500 0.1661494 0.1609281
Lag 1000 0.2078063 0.2097516
Lag 5000 0.2120391 0.2411848
traittarsus.1:traittarsus.2.units traitbwt.1:traittarsus.2.units
Lag 0 0.1834123 0.1148525
Lag 100 0.1989318 0.1322561
Lag 500 0.2183849 0.1661494
Lag 1000 0.2393546 0.2078063
Lag 5000 0.1874294 0.2120391
traittarsus.2:traittarsus.2.units traitbwt.2:traittarsus.2.units
Lag 0 -0.09279221 -0.09066377
Lag 100 -0.06552157 -0.08137057
Lag 500 -0.03120806 -0.06842888
Lag 1000 -0.04688856 -0.07652447
Lag 5000 -0.22692538 -0.31476665
traittarsus.1:traitbwt.2.units traitbwt.1:traitbwt.2.units
Lag 0 0.1843936 0.1045202
Lag 100 0.1972224 0.1205853
Lag 500 0.2244201 0.1609281
Lag 1000 0.2533883 0.2097516
Lag 5000 0.2352808 0.2411848
traittarsus.2:traitbwt.2.units traitbwt.2:traitbwt.2.units
Lag 0 -0.09066377 -0.04305989
Lag 100 -0.08137057 -0.04967401
Lag 500 -0.06842888 -0.06533316
Lag 1000 -0.07652447 -0.05918369
Lag 5000 -0.31476665 -0.34290345
, , traitbwt.1:traittarsus.1.animal
traittarsus.1:traittarsus.1.animal traitbwt.1:traittarsus.1.animal
Lag 0 0.6872795 1.0000000
Lag 100 0.5870266 0.8045048
Lag 500 0.4080911 0.4908098
Lag 1000 0.3227808 0.3613161
Lag 5000 0.1778345 0.1860991
traittarsus.2:traittarsus.1.animal traitbwt.2:traittarsus.1.animal
Lag 0 0.3863431 0.5234222
Lag 100 0.3311212 0.4545868
Lag 500 0.2390588 0.3427345
Lag 1000 0.2351271 0.3004179
Lag 5000 0.1671396 0.1589172
traittarsus.1:traitbwt.1.animal traitbwt.1:traitbwt.1.animal
Lag 0 1.0000000 0.7001005
Lag 100 0.8045048 0.5457846
Lag 500 0.4908098 0.3331394
Lag 1000 0.3613161 0.2645656
Lag 5000 0.1860991 0.1481314
traittarsus.2:traitbwt.1.animal traitbwt.2:traitbwt.1.animal
Lag 0 0.4680554 0.4293517
Lag 100 0.3667985 0.3303034
Lag 500 0.2878690 0.2612182
Lag 1000 0.2588194 0.2248089
Lag 5000 0.2468277 0.2268437
traittarsus.1:traittarsus.2.animal traitbwt.1:traittarsus.2.animal
Lag 0 0.3863431 0.4680554
Lag 100 0.3311212 0.3667985
Lag 500 0.2390588 0.2878690
Lag 1000 0.2351271 0.2588194
Lag 5000 0.1671396 0.2468277
traittarsus.2:traittarsus.2.animal traitbwt.2:traittarsus.2.animal
Lag 0 0.096601163 0.14997594
Lag 100 0.063514030 0.11517198
Lag 500 0.007343656 0.08445112
Lag 1000 0.062005867 0.13299248
Lag 5000 0.138711493 0.22091811
traittarsus.1:traitbwt.2.animal traitbwt.1:traitbwt.2.animal
Lag 0 0.5234222 0.4293517
Lag 100 0.4545868 0.3303034
Lag 500 0.3427345 0.2612182
Lag 1000 0.3004179 0.2248089
Lag 5000 0.1589172 0.2268437
traittarsus.2:traitbwt.2.animal traitbwt.2:traitbwt.2.animal
Lag 0 0.14997594 0.14180302
Lag 100 0.11517198 0.11177118
Lag 500 0.08445112 0.09651159
Lag 1000 0.13299248 0.13501835
Lag 5000 0.22091811 0.25836873
traittarsus.1.byear traitbwt.1.byear traittarsus.2.byear
Lag 0 0.06781216 -0.04857154 -0.001115860
Lag 100 0.05744185 -0.04365919 -0.003028122
Lag 500 0.04182580 -0.01683610 -0.013871766
Lag 1000 0.08409670 0.04075709 -0.088936973
Lag 5000 0.07211397 0.04755605 0.061879136
traitbwt.2.byear traittarsus.1.mother traitbwt.1.mother
Lag 0 -0.026101857 0.015326642 -0.015001711
Lag 100 -0.026229006 0.004791955 -0.002553299
Lag 500 -0.004795139 0.018197593 -0.001734987
Lag 1000 -0.025567829 -0.014419690 -0.054320480
Lag 5000 -0.011401634 -0.003782365 -0.012255190
traittarsus.2.mother traitbwt.2.mother
Lag 0 0.05171415 -0.01155255
Lag 100 0.04549989 -0.01648838
Lag 500 0.09888411 -0.02579001
Lag 1000 0.07526847 -0.03519968
Lag 5000 0.07495551 -0.03929467
traittarsus.1:traittarsus.1.units traitbwt.1:traittarsus.1.units
Lag 0 -0.5374156 -0.7822168
Lag 100 -0.4631107 -0.6561709
Lag 500 -0.3115622 -0.4297448
Lag 1000 -0.2502951 -0.3378405
Lag 5000 -0.1757000 -0.1812141
traittarsus.2:traittarsus.1.units traitbwt.2:traittarsus.1.units
Lag 0 0.1247101 0.1399193
Lag 100 0.1426212 0.1604774
Lag 500 0.1604094 0.2063094
Lag 1000 0.1703454 0.2249688
Lag 5000 0.1859265 0.1911673
traittarsus.1:traitbwt.1.units traitbwt.1:traitbwt.1.units
Lag 0 -0.7822168 -0.6444049
Lag 100 -0.6561709 -0.5391921
Lag 500 -0.4297448 -0.3429426
Lag 1000 -0.3378405 -0.2744658
Lag 5000 -0.1812141 -0.1591715
traittarsus.2:traitbwt.1.units traitbwt.2:traitbwt.1.units
Lag 0 0.1003793 0.1067549
Lag 100 0.1314503 0.1404067
Lag 500 0.1658186 0.1981668
Lag 1000 0.1899850 0.2354607
Lag 5000 0.2090708 0.1964048
traittarsus.1:traittarsus.2.units traitbwt.1:traittarsus.2.units
Lag 0 0.1247101 0.1003793
Lag 100 0.1426212 0.1314503
Lag 500 0.1604094 0.1658186
Lag 1000 0.1703454 0.1899850
Lag 5000 0.1859265 0.2090708
traittarsus.2:traittarsus.2.units traitbwt.2:traittarsus.2.units
Lag 0 -0.09677793 -0.12847847
Lag 100 -0.06212434 -0.10051402
Lag 500 -0.01671120 -0.07130994
Lag 1000 -0.07460059 -0.11790351
Lag 5000 -0.16171357 -0.21125583
traittarsus.1:traitbwt.2.units traitbwt.1:traitbwt.2.units
Lag 0 0.1399193 0.1067549
Lag 100 0.1604774 0.1404067
Lag 500 0.2063094 0.1981668
Lag 1000 0.2249688 0.2354607
Lag 5000 0.1911673 0.1964048
traittarsus.2:traitbwt.2.units traitbwt.2:traitbwt.2.units
Lag 0 -0.12847847 -0.10947233
Lag 100 -0.10051402 -0.09309607
Lag 500 -0.07130994 -0.08545450
Lag 1000 -0.11790351 -0.11149356
Lag 5000 -0.21125583 -0.23203853
, , traittarsus.2:traittarsus.1.animal
traittarsus.1:traittarsus.1.animal traitbwt.1:traittarsus.1.animal
Lag 0 0.682164176 0.38634307
Lag 100 0.591700877 0.34935277
Lag 500 0.451559860 0.32828629
Lag 1000 0.378373002 0.27249926
Lag 5000 0.004289439 0.08293975
traittarsus.2:traittarsus.1.animal traitbwt.2:traittarsus.1.animal
Lag 0 1.00000000 0.78206164
Lag 100 0.87865696 0.70110541
Lag 500 0.69161215 0.56910648
Lag 1000 0.56265051 0.44347532
Lag 5000 -0.04003226 0.01712343
traittarsus.1:traitbwt.1.animal traitbwt.1:traitbwt.1.animal
Lag 0 0.38634307 0.09679049
Lag 100 0.34935277 0.10017661
Lag 500 0.32828629 0.12775760
Lag 1000 0.27249926 0.11433423
Lag 5000 0.08293975 0.09000388
traittarsus.2:traitbwt.1.animal traitbwt.2:traitbwt.1.animal
Lag 0 0.71265304 0.46511587
Lag 100 0.64354820 0.41849123
Lag 500 0.54967619 0.35510793
Lag 1000 0.45077032 0.27846473
Lag 5000 0.02763651 0.08826768
traittarsus.1:traittarsus.2.animal traitbwt.1:traittarsus.2.animal
Lag 0 1.00000000 0.71265304
Lag 100 0.87865696 0.64354820
Lag 500 0.69161215 0.54967619
Lag 1000 0.56265051 0.45077032
Lag 5000 -0.04003226 0.02763651
traittarsus.2:traittarsus.2.animal traitbwt.2:traittarsus.2.animal
Lag 0 0.5942621 0.5613010
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