Associations between leaf developmental stability, canalization and phenotypic plasticity in an architectural perspective

A completely randomized design was implemented with three density treatments and three replicate plots randomly distributed into nine plots of 2 × 3 m in size. Low, medium and high densities were set up by sowing seeds at three inter-planting distances of 30, 20 and 10 cm, to reach the target plant densities of 12.8, 27.5 and 108.5 plants·m-2 respectively. Plants were sampled at day 50 and 70 of growth after seedling emergence, representing the developmental stages of late vegetative growth or early reproductive growth and mid-late reproductive growth respectively. At each sampling, five to six individuals were randomly chosen from each plot, making the maximum total of 6 individuals × 3 plots × 3 densities × 2 stages = 108 sampling. Each individual was divided into different architectural layers every 10 cm (day 50) or 20 cm (day 70) vertically from bottom to top. Samples from different layers, density treatments and plots were mixed together, and measured in a random sequence. For each layer per individual, we measured all the leaves on the main stem immediately after sampling when they were fresh. For each leaf, we measured the width of right and left halves (from the midrib to the margin) at the widest point of the leaf (perpendicular to the midrib) with a digital caliper (Sheet 1). The width of each side was measured twice successively and immediately after each other. For each leaf, we also calculated the leaf size (LS) as the average width of right and left side, and measured the length and angle (the angle between the petiole and the main stem) of each petiole (Sheet 2). Canalization was evaluated by coefficient of variation (CV, the standard deviation divided by mean value of the trait) among individuals per layer for leaf size, petiole length and angle. For each trait, there were 18 individual values at most for each layer in a total of 5-7 layers (Sheet 5). Plasticity was calculated by simplified Relative Distance Plasticity Index35 for each of leaf size, petiole length and angle, with the abbreviated form of PI and the formula as: PI = (X – Y)/(X + Y) (1-1) where X was the adjusted mean trait value at high or medium density, and Y was the adjusted mean value at low density. We calculated the plasticity both in response to high vs. low density (PIHL) and the plasticity in response to medium vs. low density (PIML). Adjusted mean trait values were produced from one-way ANCOVA on original mean values, with density as effect and plant size (total mass) as a covariate (Sheet 5). We compared various conventional indexes (FA1-FA8 and FA10) in calculating the fluctuating asymmetry (FA) in leaf width, to identify the ones with the highest explanatory powers for our study design (Sheet 3 and 4). All the formulas for FA indexes (Palmer and Strobeck 1986, 1994, 2003) used in this study. R and L were the widths of right and left sides of a leaf, n was the total number of leaves, and LS (leaf size) was calculated by (R+L)/2, MSsj was the mean squares of side × individual interaction, MSm was the mean squares of measurement error, M was the number of replicate measurements per side, from a side × individual ANOVA on untransformed replicate measurements of R and L.Index FormulaFA1 mean│R - L│FA2 mean (│R - L│/ LS)FA3 mean│R - L│/ mean LS FA4 0.798 ×√var (R - L)FA5 0.798 × [ ∑(R - L)2 / n] FA6 0.798×√var [(R - L) / LS] FA7 0.798×√var (R - L) / mean LS FA8 mean│ln(R/L)│FA10 0.798 × √ (MSsj - MSm) / M Different indexes showed little response or similar trends in response to density or architectural layer (Tables S3-S5), thus we adopted FA1, FA2 (with and without effects of leaf size respectively) and FA10 (the only index with measurement error variance partitioned out of the total between-sides variance) in analyses, with the formula as: FA1 = ∑ |R – L| / n (2-1) FA2 = ∑ (|R – L| / LS) / n (2-2) FA10 = 0.798 × √ (MSsj - MSm) / M (2-3) where R and L were the widths of right and left sides of a leaf respectively, n was the total number of leaves, and LS (leaf size) was calculated by (R+L)/2, MSsj was the mean squares of side × individual interaction, MSm was the mean squares of measurement error, M was the number of replicate measurements per side, from a side × individual ANOVA on untransformed replicate measurements of R and L (Sheet 2, 3 and 5). Mean value (MV), CV and PI of leaf size, petiole length and angle and leaf FA were used in statistics. The original data was log-transformed, petiole angles were square root-transformed, before any analysis to minimize variance heterogeneity. All analyses were conducted using SAS statistical software (SAS Institute 9.0 Incorporation 2002). Three-way ANOVA was performed for effects of growth stage, population density, plant layer and their interactions on all variables. Then we used one-way ANOVA for differences among layers for all variables at each density and one-way ANCOVA for effects of density on all variables for each layer or across all layers, with plant total biomass as a covariate. Multiple comparisons used LSD (Least Significant Difference) method in General Linear Model (GLM) program. For each of the three leaf traits at each density and stage, correlations among MV, FA (only results with FA2 were presented due to similar results for different FA indexes), CV and PI across all layers were analyzed with PROC CORR, producing Pearson Correlation Coefficients (PCC) for all correlations and Partial Pearson Correlation Coefficients (PPCC) for correlations among FA, CV and PI, with mean trait value in control in partial correlation analyses (Sheet 5). Explanations for Sheets of 1-5:Sheet 1: individual values of leaf width for all leaves in different layers for each individual plants in three replicate plots for each of three (low, medium and high) densities at two harvests (stages of day 50 and 70);Sheet 2: individual values of leaf size, FA1, FA2 for each individual plants in three replicate plots for each of three (low, medium and high) densities at two harvests (stages of day 50 and 70)Sheet 3: individual values of petiole length and angle for each individual plants in three replicate plots for each of three (low, medium and high) densities at two harvests (stages of day 50 and 70)Sheet 4: FA10 for each layer of all plants in each density treatment at each stage Sheet 5: mean values, CV, PI for leaf size, petiole length and angle and FA indexes for each layer of all plants in each density treatment at each stageLeaf width: for each leaf, we measured the width of right and left halves (from the midrib to the margin) at the widest point of the leaf (perpendicular to the midrib) with a digital caliper.Leaf size (LS): the average width of right and left side for a given leaf.