2.6 Within-Family Broad-Sense Heritability
(H2) Calculation
Surveys of the Melampsora sp. leaf rust, S. musiva leaf
spot and counts of the Phyllocolpa sp. galls had within-garden
microsite variation removed using thin-plate spline regression
(fields R package). Residuals of the spatial correction were
added to the mean of each survey dataset for each tree observation to
spatially correct and rescale the values. These corrected values were
then used to calculate the proportion of variance in the fungal and
insect distributions that was due to genotype using a linear-mixed model
(lmer function of the lme4 R package) with insect counts
and fungal scores as the response, tree genotype as the predictor, and
stem diameter biomass estimates as a covariate where applicable.
Broad-sense heritability was calculated
as\(\ H^{2}=\ \delta_{g}^{2}/{(\delta}_{g}^{2}+\delta_{e}^{2})\),
where \(\delta_{g}^{2}\) is the genetic variance due to genotype
and \(\delta_{e}^{2}\) is the residual variance. Rapid, simulation-based
exact likelihood ratio tests were used to evaluate the significance of
variation due to genotype for each linear model (exactRLRTfunction of the RLRsim R package).
SAS software version 9.4 (2013) was used to test for the normality of
all data sets and for all subsequent statistical analyses,
transformations were conducted when necessary. Data from all chemical
assays were analyzed by single-factor ANOVAs (PROC GLM) to test for
differences between low and high Phyllocolpa sp. abundance.