Research Articles (Mathematical Sciences)

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

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    Leaf bilateral symmetry and the scaling of the perimeter vs. the surface area in 15 vine species
    (2020-02-23) Shi, Peijian; Niinemets, Ulo; Hui, Cang; Niklas, Karl J.; Yu, Xiaojing; Holscher, Dirk
    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.
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    Leaf fresh weight versus dry weight : which is better for describing the scaling relationship between leaf biomass and leaf area for broad-leaved plants
    (MDPI, 2019-02-13) Huang, Weiwei; Ratkowsky, David A.; Hui, Cang; Wang, Ping; Su, Jialu; Shi, Peijian
    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.