Influence of the physical dimension of leaf size measures on the goodness of fit for Taylor's power law using 101 bamboo taxa

The mean and variance of ecological measures usually follow a power-law relationship, referred to as Taylor's power law (TPL). Leaves are important organs for photosynthesis, and leaf size is closely related to photosynthetic potential. Leaf size has different physical measures, such as leaf length, area, and fresh or dry weight. However, it has not been reported whether these leaf size measures follow TPL and whether the estimates of the TPL exponent reflect basic topological constraints. Considering that the variation of leaf size can affect the photosynthetic capacity of leaves and plant competitive abilities in communities, we examined the effects of different physical dimensions of leaf size (including leaf length, area, and fresh and dry weight) on the estimate of the scaling exponent and the goodness of fit of TPL for 101 bamboo species, varieties, forms, and cultivars, using 90-100 leaves for each type of plant. All leaf size measures follow TPL. However, the goodness of fit increases with the physical dimension of the leaf size measure (e.g., from 1D leaf length to 3D leaf weight). Interestingly, no significant differences in the estimates of the TPL exponent were detected among any of the physical dimensions (1D to 3D) because the 95% confidence intervals of the differences between any two groups of bootstrap replicates of the exponents of TPL obtained from different leaf size measures did not include 0. In other words, the TPL exponents of leaf size measures from the different physical dimensions could be deemed identical. We found that leaf dry weight provides the best fit of TPL and the most reliable estimate of the exponent among the four leaf size measures used in this study, perhaps because it is the best representative of the energy allocated to individual leaves.