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.

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.

The leaves of vines exhibit a high degree of variability in shape, from simple oval to highly dissected palmatifid leaves. However, little is known about the extent of leaf bilateral symmetry in vines, how leaf perimeter scales with leaf surface area, and how this relationship depends on leaf shape. We studied 15 species of vines and calculated (i) the areal ratio (AR) of both sides of the lamina per leaf, (ii) the standardized symmetry index (SI) to estimate the deviation from leaf bilateral symmetry, and (iii) the dissection index (DI) to measure leaf-shape complexity. In addition, we examined whether there is a scaling relationship between leaf perimeter and area for each species. A total of 14 out of 15 species had no significant differences in average ln(AR), and mean ln(AR) approximated zero, indicating that the areas of the two lamina sides tended to be equal. Nevertheless, SI values among the 15 species had significant differences. A statistically strong scaling relationship between leaf perimeter and area was observed for each species, and the scaling exponents of 12 out of 15 species fell in the range of 0.49−0.55. These data show that vines tend to generate a similar number of left- and right-skewed leaves, which might contribute to optimizing light interception. Weaker scaling relationships between leaf perimeter and area were associated with a greater DI and a greater variation in DI. Thus, DI provides a useful measure of the degree of the complexity of leaf outline.

Leaf shape can reflect the survival and development of plants in different environments. In particular, leaf area, showing a scaling relationship with other leaf-shape indices, has been used to evaluate the extent of salt stress on plants. Based on the scaling relationships between leaf area and other leaf-shape indices in experiments at different levels of salt stress, we could examine which leaf-shape indices are also related to salt stress. In the present study, we explored the effects of different salt concentration treatments on leaf dry mass per unit area (LMA), the quotient of leaf perimeter and leaf area (QPA), the quotient of leaf width and length (QWL), the areal quotient (AQ) of left and right sides of a leaf and the standardized index (SI) for bilateral symmetry. We treated Pyrus betulifolia Bunge under NaCl salt solution of 2‰, 4‰ and 6‰, respectively, with fresh water with no salt as the control. The reduced major axis (RMA) was used to fit a linear relationship of the log-transformed data between any leaf trait measures and leaf area. We found that leaf fresh weight and dry weight decrease with salt concentration increasing, whereas the exponents of leaf dry weight versus leaf area exhibit an increasing trend, which implies that the leaves expanding in higher salt environments are prone to have a higher cost of dry mass investment to increase per unit leaf area than those in lower salt environments. Salt concentration has a significant influence on leaf shape especially QWL, and QWL under 6‰ concentration treatment is significantly greater than the other treatments. However, there is no a single increasing or decreasing trend for the extent of leaf bilateral symmetry with salt concentration increasing. In addition, we found that the scaling exponents of QPA versus leaf area for four treatments have no significant difference. It indicates that the scaling relationship of leaf perimeter versus leaf area did not change with salt concentration increasing. The present study suggests that salt stress can change leaf functional traits especially the scaling relationship of leaf dry weight versus leaf area and QWL, however, it does not significantly affect the scaling relationships between leaf morphological measures (including QPA and the extent of leaf bilateral symmetry) and leaf area.

(1) Background: Oaks have achieved notoriety for sufficient levels of sympatric species richness allowing hybridization, thus generating substantial phenotypic variation. Leaf fluctuation asymmetry is an important attribute, as it reflects not only genetic variability but also species buffering capacity. (2) Methods: We investigated the phenotypic diversity of four-oak species (Quercus acutissima, Q. variabilis, Q. fabri, and Q. serrata var. brevipetiolata) using leaf geometric morphometric analysis. Eight leaf morphological indicators (length, width, perimeter, area, left and right areas, areal ratio, and normalized symmetry index) were used to determine the hybridization level, whereas bilateral symmetry indicators were used to assess species environmental adaptation; (3) Results: Phenotypic variation ranged from 1.54 to 29.35 folds and significantly diverged among the studied species. Taxonomically species in Section Quercus (Q. fabri and Q. serrata var. brevipetiolata) are lower than those in Section Cerris (Q. acutissima and Q. variabilis) with good bilateral symmetry. The bilateral symmetry index of Q. variabilis had a larger range of variation, indicating better environmental adaptability; (4) Conclusions: We presume that species in Section Quercus with less leaf fluctuation asymmetry have a high level of genetic heterozygosity; however, this assumption requires further verification. The observed phenotypic diversity reflects a combination of environmental and genetic factors.