Research Articles (Mathematical Sciences)

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Browsing Research Articles (Mathematical Sciences) by Subject "Allometry"

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    Effects of salt stress on the leaf shape and scaling of pyrus betulifolia bunge
    (MDPI, 2019) Yu, Xiaojing; Shi, Peijian; Hui, Cang; Miao, Lifei; Liu, Changlai; Zhang, Qiuyue; Feng, Chaonian
    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.
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    Scaling relationships between leaf shape and area of 12 rosaceae species
    (MDPI, 2019) Yu, Xiaojing; Hui, Cang; Sandhu, Hardev S.; Lin, Zhiyi; Shi, Peijian
    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.
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    Why does not the leaf weight-area allometry of bamboos follow the 3/2-power law?
    (Frontiers Media, 2018) Lin, Shuyan; Shao, Lijuan; Hui, Cang; Song, Yu; Reddy, Gadi V. P.; Gielis, Johan; Li, Fang; Ding, Yulong; Wei, Qiang; Shi, Peijian
    The principle of similarity (Thompson, 1917) states that the weight of an organism follows the 3/2-power law of its surface area and is proportional to its volume on the condition that the density is constant. However, the allometric relationship between leaf weight and leaf area has been reported to greatly deviate from the 3/2-power law, with the irregularity of leaf density largely ignored for explaining this deviation. Here, we choose 11 bamboo species to explore the allometric relationships among leaf area (A), density (ρ), length (L), thickness (T), and weight (W). Because the edge of a bamboo leaf follows a simplified two-parameter Gielis equation, we could show that A ∝ L2 and that A ∝ T2. This then allowed us to derive the density-thickness allometry ρ ∝ Tb and the weight-area allometry W ∝ A(b+3)/2 ≈ A9/8, where b approximates −3/4. Leaf density is strikingly negatively associated with leaf thickness, and it is this inverse relationship that results in the weight-area allometry to deviate from the 3/2-power law. In conclusion, although plants are prone to invest less dry mass and thus produce thinner leaves when the leaf area is sufficient for photosynthesis, such leaf thinning needs to be accompanied with elevated density to ensure structural stability. The findings provide the insights on the evolutionary clue about the biomass investment and output of photosynthetic organs of plants. Because of the importance of leaves, plants could have enhanced the ratio of dry material per unit area of leaf in order to increase the efficiency of photosynthesis, relative the other parts of plants. Although the conclusion is drawn only based on 11 bamboo species, it should also be applicable to the other plants, especially considering previous works on the exponent of the weight-area relationship being less than 3/2 in plants.