Dear all,
In our romance with MCMCglmm package in R a question arose which we have trouble addressing.
How to properly interpret the "strength" or importance of the phylo effect in our model described as G-structure in numerical values? I'am including below the output of our model. We failed to find any comprehensive information on the proper interpretation of this parameter.
If you would be so kind to give a brief description or reference to materials on the subject I would greatly appreciate it.
DIC: -110.0825
G-structure: ~species
post.mean l-95% CI u-95% CI eff.samp
species 0.05643 6.245e-39 0.1789 1935
R-structure: ~units
post.mean l-95% CI u-95% CI eff.samp
units 0.03674 0.03025 0.04366 712.2
Location effects: log.fat.content ~ log.live.lean.mass.w.chitin + sex * season
post.mean l-95% CI u-95% CI eff.samp pMCMC
(Intercept) -0.03023 -0.69297 0.75244 1005.3 0.86671
log.live.lean.mass.w.chitin 0.53737 0.21619 0.80309 700.3 0.00161 **
sexMale 0.17146 0.10489 0.23529 4959.0 < 2e-04 ***
seasonSpring 0.25401 0.18139 0.33403 4811.3 < 2e-04 ***
sexMale:seasonSpring -0.34973 -0.45863 -0.24046 4959.0 < 2e-04 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Kind regards
Bartosz Schramm
http://www.mpcm-evolution.org/practice/online-practical-material-chapter-11/chapter-11-1-simple-model-mcmcglmm
Dear Bartosz,
Maybe you already know this, but the phylogenetic mixed model is briefly discussed in the Courses notes of MCMCglmm, page 114 of the 2015 version (see first link).
More is explained in Hadfield, J.D. & Nakagawa, S. 2010. General quantitative genetic methods for comparative biology : phylogenies , taxonomies and multi-trait models for continuous and categorical characters. 23: 494–508. (see second link)
Very briefly, from what I got, the interpretation of G is similar to that of an "animal model" from quantitative genetics (considering a phylogenetic tree instead of a pedigree). The parameter "G-structure:species" is the variance in the trait that is explained by the phylogenetic relationships, while the "R-structure:units" is the residual variance after accounting for relatedness and for the fixed effects. If you had no phylogenetic "inertia", then the elements of G would be zero, and all the variance would go to R:units. Therefore, the proportion G/(R+G) gives you a metric similar to a heritability: the proportion of variance explained by the phylogenetic relationships.
I hope this helps.
Best regards,
Timothée Bonnet
https://cran.r-project.org/web/packages/MCMCglmm/vignettes/CourseNotes.pdf
http://onlinelibrary.wiley.com/doi/10.1111/j.1420-9101.2009.01915.x/full
Dear Timothee
Thanks a lot for the detailed description and references. I will most definitely have a look into them in a day or two. Not being much of a statistician myself, I have trouble understanding some of more complex algorithms and terms needed to fully grasp the MCMCglmm concept.
Your bottom description answered some of the questions but one additional question arose.
If in our model both the dependent and independent variables (ie.fat content and body mass) are potentially influenced by phylogeny (which we have to predict) does the MCMCglmm takes this situation into account or it just tests the effect of phylogeny against the dependent variable. We have a strong feeling that the effect of phylogeny on the independent variable is masking the effect on the dependent variable.
Do you have any comments on that? Thanks in advance.
Kind regards
Bartosz Schramm
Dear Bartosz,
Your current models estimates the variance (around the intercept) that is related to phylogeny, therefore it tests the effect of phylogeny only on the dependent variable.
Nevertheless, if there is some phylogenetic covariance between fat and mass, then this will be removed from the estimate of the slope of mass (because this variation is already accounted for by the phylogenetic variance).
In other words, your models gives you the effect of mass on the "phylogeny-corrected fat" and the corrected-for-mass effect of phylogeny on fat.
I don't really know what you are trying to test, so it's difficult to give guidelines (plus I'm a bit out of my zone of comfort), but your current model seems fine if what you wanted was to test for the effect of mass while accounting for the phylogenetic non-independence of the data.
Attached is a very dirty and silly piece of R code with simulations, that I have used to think about the effect of having an independent predictor correlated to the random intercept in your model. I don't know if this one can help at all, but if you are not very clear with what your models do, I recommend you play a bit with such simple simulations until you get how it works.
Best,
Timothée Bonnet
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