Size‐dependent variations in the critical buckling height Hcrit and actual height H of plants wer... more Size‐dependent variations in the critical buckling height Hcrit and actual height H of plants were determined for a total of 111 species with self‐supporting stems ranging in diameter between 0.03 cm ≤ D ≤ 3.0m. For each species, experimentally determined values for the physical properties of stems (Young's elastic modulus and bulk tissue density) were used to compute Hcrit. For small species (D < 3 cm), empirically determined critical buckling loads were used to compute Hcrit by means of the Elastica equation and the more traditionally employed Greenhill formula; for larger species (D ≖ 3 cm), Greenhill's formula was used exclusively to estimate Hcrit. Within most of the size‐range examined, the predicted values of Hcrit from the Elastica equation and Greenhill's formula were statistically indistinguishable. Regression analyses showed that the interspecific allometry of Hcrit parallels that of H such that the safety factor against the elastic mechanical failure of stems (i.e., Hcrit/H) under their own biomass was roughly constant. Since the safety factor against elastic buckling is independent of plant size, a general allometric “rule,” Hcrit/H ≈ 4, appears to govern the evolution of plant size.
PREMISE The phenomenon called "diminishing returns" refers to the scaling relationship ... more PREMISE The phenomenon called "diminishing returns" refers to the scaling relationship between lamina mass (M) vs. lamina area (A) in many species, i.e., M ∝ Aα>1 , where αis the scaling exponent exceeding unity. Prior studies have focused on the scaling relationships between lamina dry mass (DM) and A, or between fresh mass (FM) and A. However, the scaling between petiole mass and M and A has seldom been investigated. Here, we examine the scaling relationships among FM, DM, A, and petiole fresh mass (PFM). METHODS FM, DM, A, and PFM were measured for each of 3268 leaves from nine Lauraceae species and their scaling relationships were fitted using reduced major axis regression protocols. The bootstrap percentile method was used to test the significance of the difference in α-values between any two species. RESULTS The phenomenon of diminishing returns was verified between FM vs. A and DM vs. A. The FM vs. A scaling relationship was statistically more robust than the DM vs. A scaling relationship based on bivariate regression r2-values and residual errors. Diminishing returns were also observed for the PFM vs. FM and PFM vs. A scaling relationships. The PFM vs. FM scaling relationship was statistically more robust than the PFM vs. A scaling relationship. CONCLUSIONS "Diminishing returns" was confirmed among the FM, DM, A, and PFM scaling relationships. The data collectively indicate that the petiole scales mechanically more with lamina mass than area, suggesting that static (self) loading takes precedence over dynamic (wind) loading. This article is protected by copyright. All rights reserved.
Size‐dependent variations in the critical buckling height Hcrit and actual height H of plants wer... more Size‐dependent variations in the critical buckling height Hcrit and actual height H of plants were determined for a total of 111 species with self‐supporting stems ranging in diameter between 0.03 cm ≤ D ≤ 3.0m. For each species, experimentally determined values for the physical properties of stems (Young's elastic modulus and bulk tissue density) were used to compute Hcrit. For small species (D < 3 cm), empirically determined critical buckling loads were used to compute Hcrit by means of the Elastica equation and the more traditionally employed Greenhill formula; for larger species (D ≖ 3 cm), Greenhill's formula was used exclusively to estimate Hcrit. Within most of the size‐range examined, the predicted values of Hcrit from the Elastica equation and Greenhill's formula were statistically indistinguishable. Regression analyses showed that the interspecific allometry of Hcrit parallels that of H such that the safety factor against the elastic mechanical failure of stems (i.e., Hcrit/H) under their own biomass was roughly constant. Since the safety factor against elastic buckling is independent of plant size, a general allometric “rule,” Hcrit/H ≈ 4, appears to govern the evolution of plant size.
PREMISE The phenomenon called "diminishing returns" refers to the scaling relationship ... more PREMISE The phenomenon called "diminishing returns" refers to the scaling relationship between lamina mass (M) vs. lamina area (A) in many species, i.e., M ∝ Aα>1 , where αis the scaling exponent exceeding unity. Prior studies have focused on the scaling relationships between lamina dry mass (DM) and A, or between fresh mass (FM) and A. However, the scaling between petiole mass and M and A has seldom been investigated. Here, we examine the scaling relationships among FM, DM, A, and petiole fresh mass (PFM). METHODS FM, DM, A, and PFM were measured for each of 3268 leaves from nine Lauraceae species and their scaling relationships were fitted using reduced major axis regression protocols. The bootstrap percentile method was used to test the significance of the difference in α-values between any two species. RESULTS The phenomenon of diminishing returns was verified between FM vs. A and DM vs. A. The FM vs. A scaling relationship was statistically more robust than the DM vs. A scaling relationship based on bivariate regression r2-values and residual errors. Diminishing returns were also observed for the PFM vs. FM and PFM vs. A scaling relationships. The PFM vs. FM scaling relationship was statistically more robust than the PFM vs. A scaling relationship. CONCLUSIONS "Diminishing returns" was confirmed among the FM, DM, A, and PFM scaling relationships. The data collectively indicate that the petiole scales mechanically more with lamina mass than area, suggesting that static (self) loading takes precedence over dynamic (wind) loading. This article is protected by copyright. All rights reserved.
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