(Eqn.
1)
Where L E and L I is leaf
area at t E - and t I,respectively.
The difference t E – t Ireflects the 84 days between the start of the treatment phase
(t I) and the day of the final harvest
(t E).
Drought tolerance was defined as the capacity of a genotype to maintain
its growth under drought stress (restricted-water) and was computed per
genotype as the ratio of the trait mean in restricted-water to the trait
mean in ample-water across blocks.
Data analysis
Linear mixed effect models were applied to test the effects of water
treatment on selected growth traits across (i) cultivation status, (ii)
genetic group or (iii) location. Linear mixed-effect models were used
because mixed models account for unbalanced, nested designs (such as
varying numbers of genotypes by cultivation status, genetic groups and
location) that occurred in our data (Bates et al. , 2015) . To
estimate the impact of water shortage on plant traits across cultivation
status, genetic groups and locations, genotypes were considered a random
effect both in terms of the intercept: i.e ., the absolute trait
value in ample-water, and the slope: i.e ., the response to
drought (difference between the trait value in ample and
restricted-water conditions). To account for the heterogeneity of
variance in the observations, variances in the traits were dependent on
the cultivation status, genetic group or location (Zuur, Ieno and
Elphick, 2010) .
The model with cultivation status had 12 parameters: three levels of
cultivation status (CS) and two water treatments (making six
parameters), three parameters of the random effect to model differences
across genotypes: (i) a parameter to model the variation of traits in
ample-water conditions (intercept), (ii) a parameter related to the
variation in the treatment effect (slope), and (iii) a parameter that
models the correlation between the intercept and the slope, and three
parameters to account for a different residual variance per cultivation
status (see Model 1 in Appendix Data Box A.1.). The model with the
genetic group had 18 parameters: two for each genetic group (making 10)
and three parameters of the random effect to model differences across
genotypes: (i) a parameter to model the variation of traits in
ample-water conditions (intercept), (ii) a parameter related to the
variation in the effect of the treatment effect (slope), and (iii) a
parameter that models the correlation between the intercept and the
slope, and five parameters to account for a different residual variance
per genetic group (see Model 2 in Appendix Data Box A.1.). Note that
while testing the genetic group effect, all genotypes that were
misclassified and/or hybrids were not considered.
Factor location analysis tests for differences in terms of the
environment but also for genetic basis, and therefore, indirectly for
putative local adaptation. Therefore, the model with location had in
total 24 parameters, two for each location (14) and three parameters of
the random effect to model differences across genotypes: a parameter to
model the variation of traits in control (intercept), a parameter
related to the variation in the treatment effect (slope), a parameter
that models the correlation between the intercept and the slope, and
seven parameters to account for a different residual variance per
location (see Model 3 in Appendix Data Box A.1.).
Post-hoc Tukey tests were performed to determine whether: (i) drought
had significant effects on performance (RGRA) of
genotypes across cultivation status, genetic groups and location; (ii)
genotypes of different cultivation status, genetic groups or location
responded significantly differently to drought and (iii) absolute
performance of genotypes in ample-water and restricted-water conditions
differed across cultivation status, genetic groups and locations. Tukey
adjustment to p-values was done in case of multiple comparisons. The
analyses were performed in R version 3.5.0 Statistical Software using
“me”, “emmeans” and “ggplot2” packages. For all the analyses, any
effect with p < 0.05 was considered statistically significant
and non-significant at p > 0.05.
Multivariate analysis of growth-related traits
To explore the multivariate dependency between the measured traits, a
principal component analysis was performed on the genotypic means. Only
genotypes were included for which there were at least two replicates
available. All variables were centred to a mean of zero and scaled to
unit variance before the analysis contained both treatments. Next, to
test whether location and cultivation significantly affected the suite
of traits, a multivariate analysis was performed using a PERMANOVA. This
PERMANOVA tests, similar to a classical multivariate ANOVA, whether the
dissimilarities between genotypes from the same location, status and
treatment are smaller than the dissimilarities between genotypes across
locations, status and treatment (Anderson, 2001). We used Euclidean
distances between the centred and scaled observations, and 999
permutations.
Drought tolerance performance trade-off
Type (II) major axis regression was performed to determine the
relationship between the genotypic average growth trait in ample water
versus restricted water. Type II regression was used to account for both
measurement errors in the independent and the dependent variable (David
and Neville, 2002) and to test whether the slope and intercept were
different from each other. The analysis was performed in R version 3.5.0
Statistical Software using the packages “smatr”.
Drought tolerance climate relationship
In addition, a weighted linear regression analysis was performed to
determine the relationship between drought tolerance based on
RGRA, TNL and TLDW and
wetness index (WI). The analysis was performed in R version 3.5.0
Statistical Software. Because the number of replicates varied across
genotypes in locations, we introduced weights for replicates in the
analysis. In this weighted linear regression analysis, we excluded
genotypes from Kawanda and Kituza because the genotypes in these
collections were sourced from different origins and assembled asex-situ collections at NARO institutes, and therefore, we could
not retrieve the WI of these genotypes. The probability of rejecting the
null hypothesis that there is no relationship between performance in
low-water conditions and wetness index (WI) or no relationship between
drought tolerance and wetness index (WI) was set at p-value
> 0.05. The weighted linear regression models were fitted
with lm () functions in R version 3.5.0 Statistical Software.
RESULTS
The study results are presented in hierarchical order starting with: (i)
the effect of experimental treatments on the grand mean of growth
response traits (i.e., lumping genotypes together), (ii) the main
effects of factors, i.e. cultivation status, genetic groups and location
on growth response traits, (iii) the detailed synthesis of the effect of
drought on RGRA as our proxy trait for plant
performance, (iv) the relationship between performance under ample and
restricted-water conditions, (v) the relationship between performance
under restricted-water conditions and wetness index of the locations and
(vi) the relationship between drought tolerance and wetness index of the
locations.