Chapter 21 Functional genomics

21.1 Genotype

We used the following model to asses genetic varaince associated to leaf functional traits once we accounted for ontogenetic variation through DBH:

\[\begin{equation} Trait_{t,p,plot,i} \sim \mathcal{logN}(log(\alpha_{t,p}.a_{t,i}.\delta_{plot}.\frac{DBH_i}{{\beta_{DBH}}_{t,p} + DBH_i}), \sigma_3) \\ a_{t,i} \sim \mathcal{MVlogN}(log(1), \sigma_2.K) \\ \delta_{plot}\sim \mathcal {logN}(log(1),\sigma_3) \tag{21.1} \end{equation}\]

We fitted the equivalent model with following priors:

\[\begin{equation} Trait_{t,p,plot,i} \sim \mathcal{logN}(log(\alpha_{t,p}.\hat{a_{t,i}}.\hat{\delta_{plot}}.\frac{DBH_i}{{\beta_{DBH}}_{t,p} + DBH_i}), \sigma_3) \\ \hat{a_{t,i}} = e^{\sigma_2.A.\epsilon_{1,i}} \\ \hat{\delta_{plot}} = e^{\sigma_3.\epsilon_{2,plot}} \\ \epsilon_{1,i} \sim \mathcal N(0,1) \\ \epsilon_{2,plot} \sim \mathcal N(0,1) \\ ~ \\ \beta_{DBH} \sim \mathcal{logN}(log(1),1) \\ (\sigma_1,\sigma_2,\sigma_3) \sim \mathcal{N}_T^3(0,1) \\ ~ \\ V_P = Var(log(\alpha_{t,p})) \\ V_G = \sigma_2^2 \\ V_{DBH} = Var(log(\frac{DBH_i}{{\beta_{DBH}}_{t,p} + DBH_i})) \\ V_{plot}= \sigma_3^2 \\ V_R = \sigma_1^2 \tag{21.2} \end{equation}\]

Table 21.1: Summary table of the kinship growth model
Variable Parameter Population Estimate \(\sigma\) \(\hat{R}\)
LMA alpha S. globulifera Paracou 1.1807498 0.0578560 1.0009385
LMA alpha S. globulifera Regina 1.0461512 0.0958232 1.0003358
LMA alpha S. sp1 1.3452142 0.0669890 1.0006916
LMA betaDBH S. globulifera Paracou 5.0648601 1.3139445 1.0011020
LMA betaDBH S. globulifera Regina 5.1442279 2.6214540 0.9995415
LMA betaDBH S. sp1 10.2736193 1.5053995 1.0008990
LMA Vp 0.0083969 0.0052189 1.0004351
LMA Vg 0.0038228 0.0050892 1.0323247
LMA Vr 0.0397888 0.0052511 1.0243133
LDMC alpha S. globulifera Paracou 1.0371356 0.0232801 1.0015198
LDMC alpha S. globulifera Regina 1.0609020 0.0354084 1.0007120
LDMC alpha S. sp1 1.1164856 0.0216282 1.0008250
LDMC betaDBH S. globulifera Paracou 2.4684682 0.4964418 1.0002995
LDMC betaDBH S. globulifera Regina 1.1810471 0.6827667 1.0001141
LDMC betaDBH S. sp1 2.2410314 0.3836865 1.0002232
LDMC Vp 0.0013943 0.0008707 0.9997950
LDMC Vg 0.0007099 0.0009889 1.0198329
LDMC Vr 0.0090948 0.0010619 1.0114796
LT alpha S. globulifera Paracou 1.1532006 0.0821860 1.0016910
LT alpha S. globulifera Regina 1.0115487 0.1024935 1.0004089
LT alpha S. sp1 1.1052087 0.0768998 1.0015918
LT betaDBH S. globulifera Paracou 3.6863479 0.9796721 0.9993911
LT betaDBH S. globulifera Regina 7.3115667 2.5529386 0.9997823
LT betaDBH S. sp1 5.8899614 0.9448999 0.9998338
LT Vp 0.0022700 0.0018253 1.0007100
LT Vg 0.0019843 0.0026028 1.0124590
LT Vr 0.0271003 0.0030027 1.0067090
invLA alpha S. globulifera Paracou 0.6465685 0.0626731 1.0003266
invLA alpha S. globulifera Regina 0.9488486 0.0936893 1.0000253
invLA alpha S. sp1 1.4601511 0.1498795 1.0002693
invLA betaDBH S. globulifera Paracou 5.2762936 2.6231096 1.0001882
invLA betaDBH S. globulifera Regina 1.2758801 1.2126296 1.0000454
invLA betaDBH S. sp1 11.6018500 3.2034643 1.0003547
invLA Vp 0.1401222 0.0436246 1.0002158
invLA Vg 0.0083183 0.0122263 1.0134787
invLA Vr 0.1507073 0.0153106 1.0068340
CC alpha S. globulifera Paracou 1.0375996 0.0333635 1.0006473
CC alpha S. globulifera Regina 0.9758495 0.0437684 1.0002397
CC alpha S. sp1 1.1316220 0.0320985 1.0009015
CC betaDBH S. globulifera Paracou 2.4335255 0.7115917 1.0000361
CC betaDBH S. globulifera Regina 1.3971612 0.8966888 0.9996574
CC betaDBH S. sp1 2.6454552 0.5750465 0.9999197
CC Vp 0.0030846 0.0017798 1.0004213
CC Vg 0.0014635 0.0020048 1.0292375
CC Vr 0.0181489 0.0021688 1.0212705
Traceplot.

Figure 21.1: Traceplot.

Genetic variance partitionning.

Figure 21.2: Genetic variance partitionning.