Digital processing and statistical analysis

We used Adobe Photoshop® software (Adobe Systems, San Jose, CA) to set pictures to a single optical plane for perspective correction. ImageJ® software [24] was used for measuring the traits, by transforming the scale from pixels to metric units [21]. We measured modular traits: (1) the vertical length variation by measuring the variation in length of the main axis, (2) horizontal length variation by haphazardly selecting secondary branches (1688 branches, x¯=9.4 per segment) and measuring the variation in length at both time points, and (3) new branches promotion generated after injury, in the growing apical segment as well as branches on old secondary branches.

Linear mixed-effects models (LMMs) were constructed to explain the variance in the traits measured between morphotypes and habitats. With this model, we assessed the effect of the response variables both separately and jointly over trait performances. Response variables (vertical length, horizontal length, and new branch promotion) were regressed on the predictors morphotype (two levels, bushy and deep) and target habitat (two levels, shallow and deep) as well as on their interactions. Location (Hospital Point and Crawl Key) was included as a random effect to account for environmental differences, as well as the internal variance of morphotypes (genotypes nested into morphotypes). The significance of the model terms was assessed using Akaike information criterion (AIC) and calculated with the “dredge” function [25]. AIC value below two suggests substantial evidence for the model, values between 3 and 7 means that the model has considerably less support, and values over ten indicates that the model is very unlikely [26]. Fixed variables from all models with AIC values below two, were examined for Beta, t-student and p-values to test for significant relationships. The significance values of Beta, t-student and p-values supported the analysis of AIC test for a better interpretation across each predictor assessed. In addition, the normality of data was examined with exploratory graphics of quantile-quantile plots.

A statistical significant morphotype effect indicates that genotype differences may explain the response. A significant target habitat effect on trait variation implies plasticity, indicating consistent variation in the trait with the environment. A significant morphotype by target habitat interaction indicates a genotype by environment effect on the response (G X E), where variation in the degree of plasticity between morphs is detected. A graphical approach to joint statistical analysis was performed using reaction norms of the three assessed traits using the median values (M) and Median Absolute Deviation (MAD) keeping in mind the asymmetric distributions of the resulting variance. Reaction norms for new branches promotions were constructed using a density of branches (number of branches over a length of the main axis) to get appropriate slopes in cases of null promotion. All statistical analyses were performed in R version 3.2.3 [27] using the lme4 package [28].