[R-sig-ME] Bivariate random regression model in MCMCglmm to estimate selection on reaction norm slopes

Jarrod Hadfield j.hadfield at ed.ac.uk
Sat Mar 28 08:47:52 CET 2015

Hi Phillip,

The correct syntax (assuming fitness is an annual measure so you have  
repeat records?) is:




Quoting Phillip Gienapp <phillip.gienapp at helsinki.fi> on Wed, 18 Mar  
2015 11:25:07 +0100:

> Dear all,
> First a bit of background: I currently work on an anlysis of  
> phenotypic plasticity of avian phenology in response to temperature.  
> Using a random regression model I found that individual reaction  
> norms (defined by slope and intercept) vary among individuals, i.e.  
> some individuals change their phenology more strongly in response to  
> temperatures than others and also that some individuals have a  
> consistently earlier phenology than others.
> I now want to test whether there is selection on reaction norm  
> slopes, i.e. whether individuals with steeper/shallower slope have a  
> higher/lower fitness. This means I have to fit a bivariate random  
> regression model but only one trait (phenology) should be regressed  
> against temperature. For the random effects part this should give me  
> a 3x3 covariance matrix with variation in slopes, intercepts,  
> fitness plus all the covariances and then the covariance between  
> slope and fitness indicates selection on reaction norm slopes.
> I figured how to regress only phenology and not fitness against  
> temperature for the fixed effects part but am still struggling with  
> the syntax for the random effects part.
> The univariate random regression model (omitting obvious syntax parts) is:
> phenology~age + temp, random=~us(1+temp):individual
> For the multivariate model I came up with:
> cbind(phenology,fitness)~trait:age + at.level(trait,1):temp,  
> random=~us(at.level(trait,1):(1+mt2):at.level(trait,2):1):individual,  
> rcov=~us(trait):units
> but curiously this fits only a single variance for individual and  
> not the desired 3x3 matrix...
> I hope I managed to explain my problem clearly enough (maybe there  
> was too much non-technical detail...). Any ideas to fit the desired  
> model are highly welcome!
> Best,
> Phillip
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