Abstract: 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.

Abstract: Current methods determining biomass yield require sophisticated sensors for in situ measurements or multiple steady-state reactor runs. Determining the yield of specific groups of organisms in mixed cultures in a fast and easy manner remains challenging. This study describes a fast method to estimate the maximum biomass yield (Ymax), based on 13C incorporation during activity measurements. It was applied to mixed cultures containing ammonia oxidizing bacteria (AOB) or archaea (AOA) and nitrite oxidizing bacteria (NOB), grown under mesophilic (1528∘C) and thermophilic (50∘C) conditions. Using this method, no distinction could be made between AOB and AOA co-existing in a community. A slight overestimation of the nitrifier biomass due to 13C redirection via SMP to heterotrophs could occur, meaning that this method determines the carbon fixation activity of the autotrophic microorganisms rather than the actual nitrifier biomass yield. Thermophilic AOA yields exceeded mesophilic AOB yields (0.22 vs. 0.060.11 g VSS g-1 N), possibly linked to a more efficient pathway for CO2 incorporation. NOB thermophilically produced less biomass (0.0250.028 vs. 0.0480.051 g VSS g-1 N), conceivably attributed to higher maintenance requirement, rendering less energy available for biomass synthesis. Interestingly, thermophilic nitrification yield was higher than its mesophilic counterpart, due to the dominance of AOA over AOB at higher temperatures. An instant temperature increase impacted the mesophilic AOB yield, corroborating the effect of maintenance requirement on production capacity. Model simulations of two realistic nitrification/denitrification plants were robust toward changing nitrifier yield in predicting effluent ammonium concentrations, whereas sludge composition was impacted. Summarized, a fast, precise and easily executable method was developed determining Ymax of ammonia and nitrite oxidizers in mixed communities.