Why Does Not the Leaf Weight-Area Allometry of Bamboos Follow the 3/2-Power Law?

Accelerating leaf area measurement using a volumetric approach

BACKGROUND

Despite the advances in the techniques of indirect estimation of leaf area, the destructive measurement approaches have still remained as the reference and the most accurate methods. However, even utilizing the modern sensors and applications usually requires the laborious and time-consuming practice of unfolding and analyzing the single leaves, separately. In the present study, a volumetric approach was tested to determine the pile leaf area based on the ratio of leaf volume divided by thickness. For this purpose, the suspension technique was used for volumetry, which is based on the simple practice and calculations of the Archimedes' principle.

RESULTS

Wheat volumetric leaf area (VLA), had a high agreement and approximately 1:1 correlation with the conventionally measured optical leaf area (OLA). Exclusion of the midrib volume from calculations, did not affect the estimation error (NRMSE < 2.61%); however, improved the slope of the linear model by about 6%, and also reduced the bias between the methods. The error of sampling for determining mean leaf thickness of the pile, was also less than 2% throughout the season. Besides, a more practical and facilitated version of pile volumetry was tested using Specific Gravity Bench (SGB), which is currently available as a laboratory equipment. As an important observation, which was also expectable according to the leaf 3D expansion (i.e., in a given 2D plane), it was evidenced that the variations in the OLA exactly follows the pattern of the changes in the leaf volume. Accordingly, it was suggested that the relative leaf areas of various experimental treatments might be compared directly based on volume, and independently of leaf thickness. Furthermore, no considerable difference was observed among the OLAs measured using various image resolutions (NRMSE < 0.212%); which indicates that even the superfast scanners with low resolutions as 200 dpi may be used for a precision optical measurement of leaf area.

CONCLUSIONS

It is expected that utilizing the reliable and simple concept of volumetric leaf area, based on which the measurement time might be independent of sample size, facilitate the laborious practice of leaf area measurement; and consequently, improve the precision of field experiments.

Diminishing returns among lamina fresh and dry mass, surface area, and petiole fresh mass among nine Lauraceae species

PREMISE

The phenomenon called "diminishing returns" refers to a scaling relationship between lamina mass (M) vs. lamina area (A) in many species, i.e., M ∝ A^α>1 , where α is the scaling exponent exceeding unity. Prior studies have focused on the scaling relationships between lamina dry mass (DM) and A, or between fresh mass (FM) and A. However, the scaling between petiole mass and M and A has seldom been investigated. Here, we examine the scaling relationships among FM, DM, A, and petiole fresh mass (PFM).

METHODS

For each of 3268 leaves from nine Lauraceae species, FM, DM, A, and PFM were measured, and their scaling relationships were fitted using reduced major axis regression protocols. The bootstrap percentile method was used to test the significance of the difference in α-values between any two species.

RESULTS

The phenomenon of diminishing returns was verified between FM vs. A and DM vs. A. The FM vs. A scaling relationship was statistically more robust than the DM vs. A scaling relationship based on bivariate regression r² -values. Diminishing returns were also observed for the PFM vs. FM and PFM vs. A scaling relationships. The PFM vs. FM scaling relationship was statistically more robust than the PFM vs. A scaling relationship.

CONCLUSIONS

"Diminishing returns" was confirmed among the FM, DM, A, and PFM scaling relationships. The data collectively indicate that the petiole scales mechanically more strongly with lamina mass than with area, suggesting that static (self) loading takes precedence over dynamic (wind) loading.

"Diminishing returns" for leaves of five age-groups of Phyllostachys edulis culms

PREMISE

Leaf mass (M) and lamina surface area (A) are important functional traits reported to obey a scaling relationship called "diminishing returns" (i.e., M ∝ A^α>1 ). Previous studies have focused primarily on eudicots and ignored whether the age of leaves affects the numerical value of the scaling exponent (i.e., α).

METHODS

The effect of age was examined using 1623 Phyllostachys edulis leaves from culms differing in age collected in Nanjing, China. The scaling relationships among leaf A, fresh mass (FM), and dry mass (DM) were evaluated using reduced major axis protocols. The bootstrap percentile method was used to test the significance of differences in α-values.

RESULTS

Overall, the numerical values of α exceeded 1.0. The scaling relationship between FM and A was statistically more robust than that between DM and A. The scaling exponents of FM vs. A exhibited a "high-low-high-low-high" numerical trend from the oldest to the youngest age-group. FM increased linearly as culm age decreased; the leaf DM per unit area (LMA) exhibited a parabolic trend across the age-groups.

CONCLUSIONS

"Diminishing returns" is confirmed for all but one age-group of an important monocot species. The relationship between FM and A was statistically more robust than that between DM and A for each age-group. The FM per unit A decreased with increasing age-groups, whereas the middle age-groups had a greater LMA than the oldest and youngest age-groups. These data are the first to show that the age of shoots affects the scaling relationship between leaf mass and area.

Application of an Ovate Leaf Shape Model to Evaluate Leaf Bilateral Asymmetry and Calculate Lamina Centroid Location

Leaf shape is an important leaf trait, with ovate leaves common in many floras. Recently, a new leaf shape model (referred to as the MLRF equation) derived from temperature-dependent bacterial growth was proposed and demonstrated to be valid in describing leaf boundaries of many species with ovate leaf shape. The MLRF model's parameters can provide valuable information of leaf shape, including the ratio of lamina width to length and the lamina centroid location on the lamina length axis. However, the model wasn't tested on a large sample of a single species, thereby limiting its overall evaluation for describing leaf boundaries, for evaluating lamina bilateral asymmetry and for calculating lamina centroid location. In this study, we further test the model using data from two Lauraceae species, Cinnamomum camphora and Machilus leptophylla, with >290 leaves for each species. The equation was found to be credible for describing those shapes, with all adjusted root-mean-square errors (RMSE) smaller than 0.05, indicating that the mean absolute deviation is smaller than 5% of the radius of an assumed circle whose area equals lamina area. It was also found that the larger the extent of lamina asymmetry, the larger the adjusted RMSE, with approximately 50% of unexplained variation by the model accounted for by the lamina asymmetry, implying that this model can help to quantify the leaf bilateral asymmetry in future studies. In addition, there was a significant difference between the two species in their centroid ratio, i.e., the distance from leaf petiole to the point on the lamina length axis associated with leaf maximum width to the leaf maximum length. It was found that a higher centroid ratio does not necessarily lead to a greater investment of mass to leaf petiole relative to lamina, which might depend on the petiole pattern.

Scaling Relationships between Leaf Shape and Area of 12 Rosaceae Species

Leaf surface area (A) and leaf shape have been demonstrated to be closely correlated with photosynthetic rates. The scaling relationship between leaf biomass (both dry weight and fresh weight) and A has been widely studied. However, few studies have focused on the scaling relationship between leaf shape and A. Here, using more than 3600 leaves from 12 Rosaceae species, we examined the relationships of the leaf-shape indices including the left to right side leaf surface area ratio (AR), the ratio of leaf perimeter to leaf surface area (RPA), and the ratio of leaf width to length (RWL) versus A. We also tested whether there is a scaling relationship between leaf dry weight and A, and between PRA and A. There was no significant correlation between AR and A for each of the 12 species. Leaf area was also found to be independent of RWL because leaf width remained proportional to leaf length across the 12 species. However, there was a negative correlation between RPA and A. The scaling relationship between RPA and A held for each species, and the estimated scaling exponent of RPA versus A approached −1/2; the scaling relationship between leaf dry weight and A also held for each species, and 11 out of the 12 estimated scaling exponents of leaf dry weight versus A were greater than unity. Our results indicated that leaf surface area has a strong scaling relationship with leaf perimeter and also with leaf dry weight but has no relationship with leaf symmetry or RWL. Additionally, our results showed that leaf dry weight per unit area, which is usually associated with the photosynthetic capacity of plants, increases with an increasing A because the scaling exponent of leaf dry weight versus A is greater than unity. This suggests that a large leaf surface area requires more dry mass input to support the physical structure of the leaf.

Leaf Fresh Weight Versus Dry Weight: Which is Better for Describing the Scaling Relationship between Leaf Biomass and Leaf Area for Broad-Leaved Plants?

Leaf dry mass per unit area (LMA) is considered to represent the photosynthetic capacity, which actually implies a hypothesis that foliar water mass (leaf fresh weight minus leaf dry weight) is proportional to leaf dry weight during leaf growth. However, relevant studies demonstrated that foliar water mass disproportionately increases with increasing leaf dry weight. Although scaling relationships of leaf dry weight vs. leaf area for many plants were investigated, few studies compared the scaling relationship based on leaf dry weight with that based on leaf fresh weight. In this study, we used the data of three families (Lauraceae, Oleaceae, and Poaceae, subfamily Bambusoideae) with five broad-leaved species for each family to examine whether using different measures for leaf biomass (i.e., dry weight and fresh weight) can result in different fitted results for the scaling relationship between leaf biomass and area. Reduced major axis regression was used to fit the log-transformed data of leaf biomass and area, and the bootstrap percentile method was used to test the significance of the difference between the estimate of the scaling exponent of leaf dry weight vs. area and that of leaf fresh weight vs. area. We found that there were five species across three families (Phoebe sheareri (Hemsl.) Gamble, Forsythia viridissima Lindl., Osmanthus fragrans Lour., Chimonobambusa sichuanensis (T.P. Yi) T.H. Wen, and Hibanobambusa tranquillans f. shiroshima H. Okamura) whose estimates of the scaling exponent of leaf dry weight to area and that of leaf fresh weight to area were not significantly different, whereas, for the remaining ten species, both estimates were significantly different. For the species in the same family whose leaf shape is narrow (i.e., a low ratio of leaf width to length) the estimates of two scaling exponents are prone to having a significant difference. There is also an allometric relationship between leaf dry weight and fresh weight, which means that foliar water mass disproportionately increases with increased leaf dry weight. In addition, the goodness of fit for the scaling relationship of leaf fresh weight vs. area is better than that for leaf dry weight vs. area, which suggests that leaf fresh mass might be more able to reflect the physiological functions of leaves associated with photosynthesis and respiration than leaf dry mass. The above conclusions are based on 15 broad-leaved species, although we believe that those conclusions may be potentially extended to other plants with broad and flat leaves.

Proportional Relationship between Leaf Area and the Product of Leaf Length and Width of Four Types of Special Leaf Shapes

The leaf area, as an important leaf functional trait, is thought to be related to leaf length and width. Our recent study showed that the Montgomery equation, which assumes that leaf area is proportional to the product of leaf length and width, applied to different leaf shapes, and the coefficient of proportionality (namely the Montgomery parameter) range from 1/2 to π/4. However, no relevant geometrical evidence has previously been provided to support the above findings. Here, four types of representative leaf shapes (the elliptical, sectorial, linear, and triangular shapes) were studied. We derived the range of the estimate of the Montgomery parameter for every type. For the elliptical and triangular leaf shapes, the estimates are π/4 and 1/2, respectively; for the linear leaf shape, especially for the plants of Poaceae that can be described by the simplified Gielis equation, the estimate ranges from 0.6795 to π/4; for the sectorial leaf shape, the estimate ranges from 1/2 to π/4. The estimates based on the observations of actual leaves support the above theoretical results. The results obtained here show that the coefficient of proportionality of leaf area versus the product of leaf length and width only varies in a small range, maintaining the allometric relationship for leaf area and thereby suggesting that the proportional relationship between leaf area and the product of leaf length and width broadly remains stable during leaf evolution.

A General Leaf Area Geometric Formula Exists for Plants—Evidence from the Simplified Gielis Equation

Plant leaves exhibit diverse shapes that enable them to utilize a light resource maximally. If there were a general parametric model that could be used to calculate leaf area for different leaf shapes, it would help to elucidate the adaptive evolutional link among plants with the same or similar leaf shapes. We propose a simplified version of the original Gielis equation (SGE), which was developed to describe a variety of object shapes ranging from a droplet to an arbitrary polygon. We used this equation to fit the leaf profiles of 53 species (among which, 48 bamboo plants, 5 woody plants, and 10 geographical populations of a woody plant), totaling 3310 leaves. A third parameter (namely, the floating ratio c in leaf length) was introduced to account for the case when the theoretical leaf length deviates from the observed leaf length. For most datasets, the estimates of c were greater than zero but less than 10%, indicating that the leaf length predicted by the SGE was usually smaller than the actual length. However, the predicted leaf areas approximated their actual values after considering the floating ratios in leaf length. For most datasets, the mean percent errors of leaf areas were lower than 6%, except for a pooled dataset with 42 bamboo species. For the elliptical, lanceolate, linear, obovate, and ovate shapes, although the SGE did not fit the leaf edge perfectly, after adjusting the parameter c, there were small deviations of the predicted leaf areas from the actual values. This illustrates that leaves with different shapes might have similar functional features for photosynthesis, since the leaf areas can be described by the same equation. The anisotropy expressed as a difference in leaf shape for some plants might be an adaptive response to enable them to adapt to different habitats.

Taylor’s Power Law for Leaf Bilateral Symmetry

Leaf shape and symmetry is of interest because of the importance of leaves in photosynthesis. Recently, a novel method was proposed to measure the extent of bilateral symmetry in leaves in which a leaf was divided into left and right sides by a straight line through the leaf apex and base, and a number of equidistant strips were drawn perpendicular to the straight line to generate an equivalent number of differences in area between the left and right parts. These areal differences are the basis for a measure of leaf bilateral symmetry, which was then examined to see how well it follows Taylor’s power law (TPL) using three classes of plants, namely, 10 geographical populations of Parrotia subaequalis (H.T. Chang) R.M. Hao et H.T. Wei, 10 species of Bambusoideae, and 10 species of Rosaceae. The measure of bilateral symmetry followed TPL for a single species or for a class of closely related species. The estimate of the exponent of TPL for bamboo plants was significantly larger than for the dicotyledonous trees, but its goodness of fit was the best among the three classes of plants. The heterogeneity of light falling on branches and leaves due to above-ground architectural patterns is an important contributor to leaf asymmetry.