The principle of similarity (Thompson, 1917) states that the weight of an organism follows the 3/2-power law of its surface area and is proportional to its volume on the condition that the density is constant. However, the allometric relationship between leaf weight and leaf area has been reported to greatly deviate from the 3/2-power law, with the irregularity of leaf density largely ignored for explaining this deviation. Here, we choose 11 bamboo species to explore the allometric relationships among leaf area (A), density (ρ), length (L), thickness (T), and weight (W). Because the edge of a bamboo leaf follows a simplified two-parameter Gielis equation, we could show that A ∝ L2 and that A ∝ T2. This then allowed us to derive the density-thickness allometry ρ ∝ Tb and the weight-area allometry W ∝ A(b+3)/2 ≈ A9/8, where b approximates −3/4. Leaf density is strikingly negatively associated with leaf thickness, and it is this inverse relationship that results in the weight-area allometry to deviate from the 3/2-power law. In conclusion, although plants are prone to invest less dry mass and thus produce thinner leaves when the leaf area is sufficient for photosynthesis, such leaf thinning needs to be accompanied with elevated density to ensure structural stability. The findings provide the insights on the evolutionary clue about the biomass investment and output of photosynthetic organs of plants. Because of the importance of leaves, plants could have enhanced the ratio of dry material per unit area of leaf in order to increase the efficiency of photosynthesis, relative the other parts of plants. Although the conclusion is drawn only based on 11 bamboo species, it should also be applicable to the other plants, especially considering previous works on the exponent of the weight-area relationship being less than 3/2 in plants.

Key messageThe mean and variance of developmental rates of bamboos at different temperatures follow a power law. The rate isomorphy hypothesis, demonstrated in insects and mites, does not hold in bamboos. Abstract The developmental time of plants and poikilotherms can be significantly affected by temperature. Developmental rate (i.e. the reciprocal of developmental time) of arthropods and germination rate of some plant seeds have been demonstrated to follow a linear function with temperature. The rate isomorphy hypothesis in entomology suggests a lower developmental threshold below which development of all life stages terminates. If this hypothesis also holds for plants, the estimated lower threshold for one development stage could be used for predicting thresholds of other stages. Here, we tested this hypothesis to compare the developmental time of seedling emergence and the time from seedling emergence to the unfolding of the third leaf in two bamboo species. We used five constant thermal environments from 18.5 to 28.5 °C with an increment of 2.5 °C. Both species showed a linear relationship between temperature and developmental rate, with the mean and variance of developmental rates following a power law. Using the bootstrap percentile method, we showed that the isomorphy hypothesis does not hold for both species. The effect of temperature on the survival rate at the time of seedling emergence differed significantly between the two species.

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