Associations between developmental stability, canalization and phenotypic plasticity have been predicted, but rarely supported by direct evidence. Architectural analysis may provide a more powerful approach to finding correlations among these mechanisms in plants. To investigate the relationships among the three mechanisms in architectural perspective, we subjected plants of Abutilon theophrasti to three densities, measured and calculated fluctuating asymmetry (FA), coefficients of variation (CV) and plasticity (PI) of three leaf traits, to analyze the correlations among these variables. As density increased, mean leaf size, petiole length and angle of most layers and mean leaf FA of some layers decreased (at both stages), CV of petiole angle increased (at day 50), and PI of petiole length and angle across all layers decreased (at day 70); leaf FA and CV of traits generally increased with higher layers at all densities. At both stages, there were more positive correlations between FA and CV at lower vs. high densities; at day 50, little correlation of plasticity with FA or CV was found; at day 70, more positive correlations between FA and PI occurred for response to high vs. low density than for response to medium vs. low density, and more positive correlations between CV and PI occurred at lower vs. high densities. Results suggested that developmental instability, decreased canalization and plasticity can be cooperative and the relationships between decreased canalization and plasticity are more likely to be positive if decreased canalization is due to vibrant growth rather than stressful effects. The relationships of plasticity with developmental instability differed from its relationship with decreased canalization in the way of variation. Decreased canalization should be more beneficial for possible plasticity in the future, while canalization may result from already-expressed plasticity.

The experiment was conducted in a research-special field at the Pasture Ecological Research Station of Northeast Normal University, Changling, Jilin province, China (123°44 E, 44°40 N) in 2007. The soil (aeolian sandy soil, pH = 8.3) of the experimental field was a little infertile because of frequent utilization annually, thus we covered the field with a layer of 5-10 cm virgin soil (meadow soil, pH = 8.2) transported from the nearby meadow (with no cultivation history) in the north of the research station, to improve the soil quality (Wang & Zhou 2021b). 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. Seeds were sown on June 7, 2007, and most seeds emerged four days later after sowing. Then seedlings were thinned to the target densities when they reached four-leaf stage. Plots were hand weeded and watered regularly before experiencing drought.

Data collection and calculations of CV and PI

Plants were sampled at day 50 and 70 of growth after seedling emergence. 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 (Wilsey et al. 1998). 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 sides (Palmer & Strobeck 1986; Wilsey et al. 1998), and measured the length and angle (the angle between the petiole and the main stem) of each petiole.

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.

Plasticity was calculated by simplified Relative Distance Plasticity Index (Valladares et al. 2006) 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 (PI_HL) and the plasticity in response to medium vs. low density (PI_ML). 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.

Calculations and analyses of FA

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 (Table A2). Different indexes showed little response or similar trends in response to density or architectural layer (Table A3-A5), 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 (Palmer 1994; Palmer & Strobeck 2003):

FA₁ = ∑ |R – L| / n                                                   (2-1)

FA₂ = ∑ (|R – L| / LS) / n                                              (2-2)

FA₁₀ = 0.798 × √ (MS_sj - MS_m) / 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, MS_sj was the mean squares of side × individual interaction, MS_m 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.

  We measured skew (γ₁) and kurtosis (γ₂) to evaluate whether the leaf asymmetry deviated from normality. To detect the presence of antisymmetry, kurtosis (γ₂) was tested with a t-test of the null hypothesis H₀:γ₂ = 0, where a significant negativeγ₂ indicates possible antisymmetry (Cowart & Graham 1999; Palmer 1994). To test the presence of directional asymmetry, we used two methods: 1) testing (R - L) against 0 with one-sample t-test (the hypothesis H₀:γ₁ = 0); and 2) testing whether the difference between sides (mean squares for side effect [MS_s]) is greater than nondirectional asymmetry (mean squares for side × individual interaction [MS_si]) with factorial ANOVA (Palmer 1994; Wilsey et al. 1998). For layer, density and stage combination, two sets of samples (at day 50) showed leptokurtosis, indicating antiasymmetry; but only one set of samples showed left-dominant directional asymmetry (Table A6, A7). In addition, seven sets of samples at day 50 and ten sets at day 70 also showed greater mean difference between sides (MS_s) than between-sides variation (MS_si; Table A8, A9), indicating directional asymmetry. We regressed |R - L| on LS for all the leaves of individuals per layer at each density and stage to determine the size-dependence of leaf asymmetry, and found several cases of leaf asymmetry were size-dependent (Table A6, A7). We also evaluated whether the between-sides variation is significantly larger than the measurement error (MS_m) in factorial ANOVA (Palmer 1994). The MS_m values for all cases were lower than MS_si values (Table A8, A9).

Statistical analysis

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.