Taylor’s power law of the leaf bilateral symmetry measure of Liriodendron trees

doi:10.3969/j.issn.1000-2006.201808022

SHI Peijian, LIU Mengdi

JOURNAL OF NANJING FORESTRY UNIVERSITY ›› 2019, Vol. 43 ›› Issue (03) : 145-151.

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JOURNAL OF NANJING FORESTRY UNIVERSITY ›› 2019, Vol. 43 ›› Issue (03) : 145-151. DOI: 10.3969/j.issn.1000-2006.201808022

Taylor’s power law of the leaf bilateral symmetry measure of Liriodendron trees

SHI Peijian, LIU Mengdi

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Abstract

【Objective】Taylor’s power law(TPL)is an important biological statistical law that describes the power-law relationship between the mean and variance of a particular biological measure. The leaves of tulip trees exhibit a certain complexity but are bilaterally symmetric. The aim of this study was to examine whether TPL could apply to leaf bilateral symmetry measures.【Method】The leaves of two extant species of tulip trees and their hybrid(Liriodendron chinense, L. tulipifera, and L. chinense ×L. tulipifera)were picked from healthy plants. We will refer to the two species of tulip trees and their hybrid as three species of tulip trees for simplicity. For each species, ≥ 200 leaves were used. For a leaf, 1 000 equidistant strips that are perpendicular to the median axis(i.e., the straight line passing through the apex and base of the leaf)were generated from the apex to base of the leaf, assuming that leaf surface is on a plane. Then, 1 000 areal differences between the intersection(of the left side of the leaf and strips)and that(of the right side of the leaf and strips)were obtained. We calculated the mean and variance of the absolute values of the above 1 000 areal differences, resulting in at least 200 pairs of the data of variance vs. mean(corresponding to 200 leaves)for each species. We used reduced major axis to carry out a linear fit to the log-transformed data of variance vs. mean for each species and also for the pooled data to estimate the slopes of the straight lines(i.e., the exponents of TPL). And then we used the bootstrap percentile method to test whether there was a significant difference in the estimated exponents of TPL among different species.【Result】We found that bilateral symmetry measures of the three species of tulip trees all followed TPL, and there were no significant differences in the estimated exponents of TPL among the three species. The estimated exponent of TPL for the pooled data was equal to 1.777. 【Conclusion】This study shows that leaf area, which has a scaling relationship with leaf weight, can be used for depicting TPL. The goodness of fit for TPL is improved if the scaling relationship of leaf weight vs. area is strong. In addition, there was a large variation in leaf shape across different plant groups. The log-transformed data of variance vs. mean that measured the extent of leaf bilateral symmetry could be well described by a linear equation. Variation in leaf bilateral symmetry is associated with the influence of above-ground plant architecture on light interception and utilization; thus, results of this study can improve our understanding of the effect of above-ground plant topology on the photosynthetic potentials of leaves.

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SHI Peijian, LIU Mengdi. Taylor’s power law of the leaf bilateral symmetry measure of Liriodendron trees[J]. JOURNAL OF NANJING FORESTRY UNIVERSITY. 2019, 43(03): 145-151 https://doi.org/10.3969/j.issn.1000-2006.201808022

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