Aims The fractal-like network model of plants (the WBE model) considers that the branching exponents 1/a and 1/b determine the metabolic exponent θ in plants. However, the constant 3/4 metabolic exponent does not completely reflect the plant metabolic scaling. Price, Enquist and Savage extended the WBE model by assuming that branching exponents are not constant but covary with each other, and developed the branching traits covariation model of plants (the PES model). In this paper, we study and compare branching exponents and metabolic exponents in seven woody plants based on leaf area and leaf biomass by using the PES model.
Methods To test the PES model, data on leaf area and leaf biomass of seven woody species were used to determine the values of branching and metabolic exponents. Standardized major axis (SMA) regression protocols were used to determine the numerical values of scaling exponents and normalization constants for each species and across the seven species using the software SMATR. Furthermore, test of a common slope across all species and comparisons between the estimated values and theoretical values proposed by the WBE model were also performed by using the SMATR. Specifically, if the value of p exceeds a critical level, then it is considered that there would be no significant differences among the groups compared and that a common slope can be determined; if the value of p is below the critical level, then it would indicate that the estimated value would be significantly different from the theoretical value.
Important findings Significant allometric relationships between leaf area and leaf biomass were verified within and across species. Specifically, leaf area scaled as 0.86-power of leaf biomass across the entire data sets. Therefore, values of branching and metabolic exponents were determined by using leaf biomass and leaf area separately. Values of the branching exponent 1/a and the metabolic exponent θ based on leaf area were statistically indistinguishable among the seven woody species. On the contrary, values of the branching exponents 1/a and 1/b and the metabolic exponent θ based on leaf biomass differed significantly among the seven woody species. Values of the branching exponents and the metabolic exponent estimated from both leaf area and leaf biomass across the entire data set were all statistically indistinguishable from the theoretical values. Furthermore, compared with the value of metabolic exponent based on leaf biomass, the value of metabolic exponent based on leaf area was statistically more comparable to the theoretical value. The effect of allometric relationship between leaf area and leaf biomass on metabolic rate and relative functional traits of plants should be paid more attention in future research.