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## Similar protocols

## Protocol publication

[…] To estimate the population quantitative genetic differentiation (QST), we first estimated additive genetic variance and between population variance following a similar approach as in [] using the animal model []. Within and between population quantitative genetic variation were estimated using REML approach in ASReml-R[] as follows: y = Xβ + Zp + Za + ε where X and Z–incidence matrices assigning fixed and random effects to measurements in vector y, β –the vector of the fixed effects of growth chamber climate and any other unspecific chamber effects, p~N(0,Iσp2)–the vector of random population effects, with σp2 –between population variance and I is identity matrix, a~N(0, 2Gσa2)–the vector of random individual plant genetic effects, with σa2—within population (additive genetic) variance and G–Loisselle’s kinship coefficient [] matrix estimated in **SPAGeDi** 1.5 [] using the four microsatellite markers of this study (). Since trait plasticity was calculated as the difference of trait values measured for a single genotype grown in different growth chambers, within and between population quantitative genetic variation of trait plasticity was estimated with the model y = Xβ + Zp + Za + ε Narrow-sense QST was then calculated for trait values and plasticity as QST=σ^p2σ^p2+σ^a2 with σ^p2 and σ^a2 being the REML estimates of between and within-population genetic variance.Kinship coefficient estimates based on four loci could be imprecise and downwardly bias the estimates of within-population variance, resulting in an overestimate of QST. We thus estimated the lower bound of QST through the population phenotypic differentiation index (PST) as defined in []. Within and between population variation were estimated using a general mixed model as follows: y = β + b + ε, where β –the vector of the fixed effects of growth chamber and any other unspecific chamber effects, b~N(0,σb2)–the vector of random population effects, with σb2 the variance of random population effects, and ε~N(0, σw2)–the vector of residuals, with σw2 the residual population variance. We then calculated PST for trait values and plasticity as PST=ch2σ^b2c^h2σb2+σ^w2 with σ^b2 and σ^w2 being the estimates of within and between population variation, c the proportion of between population variance that is due to additive genetic factors only, and h2 trait heritability, or the proportion of within-population genetic variance that is due to additive genetic factors. We assume c = h2
= 1, meaning that all of the observed phenotypic variance is due to additive genetic factors only []. The assumption c = 1 plausible in our study, given that all populations are grown in a common environment, which reduces between population differences that can be due to environmental factors. Assuming h2
= 1 is clearly an overestimate of the additive genetic component of σw2, but it is relevant in our case because we want to estimate the lower boundary of PST, which is done by maximising the within-population variance.To test for the effects of selection on population divergence in quantitative traits, we used the method described in [] as implemented in an R script available from []. In brief, a neutral QST-FST (PST-FST) distribution was simulated using the Lewontin-Krakauer distribution [], and the estimates of FST (from molecular markers), and of σ^p2 and σ^a2 for QST (of σ^b2 and σ^w2 for PST). The quantile of the observed Q^ST−F^ST(P^ST−F^ST) value compared against the neutral distribution was obtained in order to determine the p-value of the null hypothesis that QST (PST) equals FST. This method was particularly suitable for our data set, as it gives reliable results when used with relatively few neutral molecular markers, when population differentiation in molecular markers is low, and when the number of populations is relatively high (ten or higher). Given that microsatellite data can have mutation rates that are higher than migration rates, microsatellite based FST can be downwardly biased. To avoid this, we also made QST—RST comparisons, with RST being an FST analogue based on allele size, calculated following []. RST should not be affected by the microsatellite mutation rate, provided that microsatellite size variance is proportional to their genetic distance [,]. [...] Coinertia analysis is a multivariate ordination method that measures the concordance between two data sets. The goal of a COA is to find a multidimensional projection of the two data sets which is a compromise between the maximal variance of each data set and the maximal covariance between the two data sets [,]. COA can be used to explore the shared structure between genetic diversity as estimated by molecular markers and phenotypic traits []. We used COA analyses to simultaneously examine the relationship between differentiation of molecular markers, phenotypic traits (or plasticity). If this relationship was significant, we further tested how the covariation between traits and markers was affected by environmental variation, instead of proceeding by pairwise comparisons between the three data sets. A significant effect of the environment would confirm that the observed joint population differentiation in traits and markers can be at least partly predicted by the environment, and thus the molecular markers could be used as indicators of the phenotypic value of the individuals of the studied populations.COA was made using the projections of the first two axes of Principal Component Analysis (PCA) for trait values (or plasticity) and molecular markers. For phenotypic trait values PCA we used the Euclidian distance matrices based on the trait values averaged across growth chambers calculated by the R package ade4 [], and for molecular markers PCA we used Nei-distances calculated by the R package **adegenet** []. The significance of the correlation between the matrix of phenotypic trait values (or plasticities) and that of neutral genetic patterns was assessed by 999 bootstraps. COA with trait means and individual genetic differentiation will be further referred to as COAmean, and COA with trait plasticity and individual genetic differentiation will be referred to as COAplast.If significant coinertia was detected between trait values (or plasticities) and molecular markers, we then tested how are the individual projections on the main COA axis (COA axis 1) affected by climate variation. For this, we used ANOVA with temperature and precipitation of origin and their interaction as fixed, quantitative, explanatory variables. Significance levels were estimated using Fisher’s F statistic. A significant ANOVA result meant that the molecular marker variation which was associated with variation of trait value (or plasticity) was also influenced by climate variation. If such a relationship existed, we further tested for alleles that were associates with specific trait values, or which were characteristic for some populations (see below). Note that if allelic frequencies were influenced by phenotypic trait values and/or environmental variables, it does not mean that they were under selection, as microsatellite loci are by default considered to be neutral markers. This association could have been caused by pure genetic drift, or non-random mating patterns. Independent of the causes of the association, the alleles associated with phenotypic traits and climatic variables could further be used to identify individuals with specific phenotypes or thriving in specific climates. [...] We tested for isolation by distance (IBD) and isolation by adaptation (IBA) by estimating the proportion of genetic differentiation between populations explained by geographical and environmental distances, respectively, using Mantel tests (R package **vegan**). The genetic distance matrix was based on Bruvo distances (R package polysat,[]), and the geographic and environmental (combining temperature and precipitation data) distances were based on Euclidean distances. Significance testing was made with 999 bootstraps. In addition to testing the effect of geographical and environmental distances on their own, we used partial Mantel test to examine the effect of environmental distance after accounting for geographical structure, and of geographical distances after accounting for environmental structure.We also tested the relationship between population genetic diversity and population trait means or plasticity using Pearson’s product moment correlations. Since the estimate of genetic diversity in hexaploid organisms is not straightforward because complete information about allelic frequencies cannot be obtained [,], several different estimators were used: number of alleles, number of effective alleles, allelic richness and expected heterozygosity and Pons and Petit’s index of population genetic diversity of non-ordered alleles relationship between individual genotypes []. All of these estimators were calculated with SPAGeDi 1.5 []. Being based on expected rather than observed allele frequencies, these estimators are informative about the population effective size. Thus a significant correlation between genetic diversity and trait means could indicate that populations with a lower effective size are phenotypically highly differentiated, possibly because of the effects of IBD or IBA []. […]

## Pipeline specifications

Software tools | SPAGeDi, adegenet, vegan |
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Applications | Phylogenetics, Population genetic analysis |