A Bayesian model-based reduced major axis regression

Reduced major axis (RMA) regression, widely used in the fields of zoology, botany, ecology, biology, spectroscopy, and among others, outweighs the ordinary least square regression by relaxing the assumption that the covariates are without measurement errors. A Bayesian implementation of the RMA regression is presented in this paper, and the equivalence of the estimates of the parameters under the Bayesian and the frequentist frameworks is proved. This model-based Bayesian RMA method is advantageous since the posterior estimates, the standard deviations, as well as the credible intervals of the estimates can be obtained through Markov chain Monte Carlo methods directly. In addition, it is straightforward to extend to the multivariate RMA case. The performance of the Bayesian RMA approach is evaluated in the simulation study, and, finally, the proposed method is applied to analyze a dataset in the plantation.

Biomass allocation and productivity-richness relationship across four grassland types at the Qinghai Plateau

Aboveground biomass (AGB) and belowground biomass (BGB) allocation and productivity-richness relationship are controversial. Here, we assessed AGB and BGB allocation and the productivity-richness relationship at community level across four grassland types based on the biomass data collected from 80 sites across the Qinghai Plateau during 2011-2012. The reduced major axis regression and general linear models were used and showed that (a) the median values of AGB were significantly higher in alpine meadow than in other three grassland types; the ratio of root to shoot (R/S) was significantly higher in desert grassland (36.06) than intemperate grassland (16.60), alpine meadow (13.35), and meadow steppe (19.46). The temperate grassland had deeper root distribution than the other three grasslands, with about 91.45% roots distributed in the top 30 cm soil layer. (b) The slopes between log AGB and log BGB in the temperate grassland and meadow steppe were 1.09 and 1, respectively, whereas that in the desert grassland was 1.12, which was significantly different from the isometric allocation relationship. A competitive relationship between AGB and BGB was observed in the alpine meadow with a slope of -1.83, indicating a trade-off between AGB and BGB in the alpine meadow. (c) A positive productivity-richness relationship existed across the four grassland types, suggesting that the positive productivity-richness relationship might not be affected by the environmental factors at the plant location. Our results provide a new insight for biomass allocation and biodiversity-ecosystem functioning research.

Why Does Not the Leaf Weight-Area Allometry of Bamboos Follow the 3/2-Power Law?

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 ∝ T^b and the weight-area allometry W ∝ A^(b+3)/2 ≈ A^9/8, 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.