Variations In The Law Of Allometric Scaling For Plant Stands Across A Moisture Gradient

According to the metabolic theory, the energy equivalence law of organisms states that the rate of resource use per unit area is independent of the average mass per individual. The -4/3 self-thinning rule is based on this supposition (Enquist et al). However, it has been debated recently whether the self-thinning exponent is -4/3 or -3/2, and whether the allometric exponent of the metabolic rate is 3/4 or 2/3. Therefore it is not known whether these rules are applicable to all species under all growth conditions.To resolve this important issue, (1) field experiments were conducted along a natural moisture gradient/latitude in northwest China (i.e. Lanzhou, Baiyin, Jingtai, Minqin), (2) competition-density (C-D) effect experiments were performed at Yuzhong experimental station of Lanzhou University, and (3) forest data from Tian-xiang Luo also were analyzed across all data sets and along the precipitation level, respectively.As predicted, the absolute values of the allometric exponents of the mass-density relationship (M-N) for the aboveground biomass were less than 4/3 under strong drought stress (Baiyin and Jingtai sites). However, the allometric exponents for the belowground part were not significantly different from -4/3. The allometric exponents were positive for Artemisia desertorum (Minqin) and Salsola passerina Bunge (Jingtai) populations under severe drought conditions. Yet the allometric exponents accorded with the -4/3 power rule when the canopy cover values of the desert populations were transformed to 100%. Finally, most of the most allometric exponents for the shrubs and trees with closed canopy were also close to -4/3 under well watered conditions.The allometric exponents for the spring wheat populations in the low sowing densities (1-1×10³ seeds m^-2) were 0.06 and 0.05 for both the mean leaf area and the mean shoot biomass, respectively. But the 95% CI of the exponents for the mean leaf area indicated that the exponents were not statistically different from 0. And in the high sowing densities, the corresponding allometric exponents were consistent with the values of predicted theory, -1 and -3/2, respectively. The 'trapezia' model was developed to represent the relationship between the mean leaf area and shoot biomass and population stand densities according to our results and the C-D effect. This model estimated that the optimum sowing densities of spring wheat populations for maximal leaf area and shoot biomass per unit ground area were about 1202 and 1072 seeds m^-2, respectively.The allometric exponents of the h-r relationship for the shrubs and trees were close to 2/3, and for the herbages/crops in the dense populations were close to 1 through the analysis of height-diameter (h-r) relationships for these communities.For populations with a closed canopy and well watered conditions, the allometric exponent between the rate of resources use and mean biomass was approximately 0, i.e.β≈0. However, for populations under drought and extreme drought conditions, the values of the exponents wereβ<0,β>0, respectively.Based on these results, the following conclusions are drawn:1, The absolute values of the allometric exponents of the M-N relationship for aboveground biomass decrease with increasing the mean aridity index per year and with decreasing mean cover, compared with the exponents for the belowground biomass which do not vary with the mean aridity and cover in a certain given range. Additionally, individual plant size is positively dependent of population density under the severe drought stress conditions.2, The relationship between the average individual size and population density should follow the corresponding plant geometry principles. The allometric exponents of the h-r relationship vary with plant density and species composition which also influence the allometric exponents of the M-N relationship, i.e., the scaling exponent for the mass-density relationship is variant and can range between -4/3 and -3/2.3, The C-D effect had two boundary lines with growth for annual herbage. In this case, the trapezia model might be developed so as to estimate the optimum population density. 4, The model of energy equivalence, R = N_max(Q|—)∝M⁰, was suitable for the closed-canopy populations, but not for the aboveground biomass of populations growing under drought stress conditions. Furthermore, the variations in the exponents for the M-N relationship indicate that for the limited resource, the efficiency of resource use per unit ground area might decline with growth in the desert populations, but it might be enhanced in populations by a positive interaction under the extreme drought conditions.5, Which resource was limiting, or the type(s) of competition, determine whether the aboveground, belowground part or the whole biomass will scale according to the energy equivalence.6, If plant geometry and metabolic theory taken together, it is predicted that the allometric exponents of the metabolic rate and the mean biomass per plant likely vary in a range of 1/2～3/4 depending on species composition and environmental stresses, and the self-thinning exponents for the populations with closed canopy possibly varies in a range of -2～-3/4.In summary, this research indicates that environmental conditions and species functional-trait differences affect the numerical values of scaling exponents which can vary numerically between 1/2 and 3/4. These results have an important bearing on attempts to improve crop-yields and attempts to develop broad theories concerning plant ecology and allometry relationships.