Phenylpropanoid Biosynthesis Gene Expression Precedes Lignin Accumulation During Shoot Development in Lowland and Upland Switchgrass Genotypes

Efficient conversion of lignocellulosic biomass into biofuels is influenced by biomass composition and structure. Lignin and other cell wall phenylpropanoids, such as para-coumaric acid (pCA) and ferulic acid (FA), reduce cell wall sugar accessibility and hamper biochemical fuel production. Toward identifying the timing and key parameters of cell wall recalcitrance across different switchgrass genotypes, this study measured cell wall composition and lignin biosynthesis gene expression in three switchgrass genotypes, A4 and AP13, representing the lowland ecotype, and VS16, representing the upland ecotype, at three developmental stages [Vegetative 3 (V3), Elongation 4 (E4), and Reproductive 3 (R3)] and three segments (S1–S3) of the E4 stage under greenhouse conditions. A decrease in cell wall digestibility and an increase in phenylpropanoids occur across development. Compared with AP13 and A4, VS16 has significantly less lignin and greater cell wall digestibility at the V3 and E4 stages; however, differences among genotypes diminish by the R3 stage. Gini correlation analysis across all genotypes revealed that lignin and pCA, but also pectin monosaccharide components, show the greatest negative correlations with digestibility. Lignin and pCA accumulation is delayed compared with expression of phenylpropanoid biosynthesis genes, while FA accumulation coincides with expression of these genes. The different cell wall component accumulation profiles and gene expression correlations may have implications for system biology approaches to identify additional gene products with cell wall component synthesis and regulation functions.

Two symmetric and computationally efficient Gini correlations

Standard Gini correlation plays an important role in measuring the dependence between random variables with heavy-tailed distributions. It is based on the covariance between one variable and the rank of the other. Hence for each pair of random variables, there are two Gini correlations and they are not equal in general, which brings a substantial difficulty in interpretation. Recently, Sang et al (2016) proposed a symmetric Gini correlation based on the joint spatial rank function with a computation cost of O(n2) where n is the sample size. In this paper, we study two symmetric and computationally efficient Gini correlations with the computational complexity of O(n log n). The properties of the new symmetric Gini correlations are explored. The influence function approach is utilized to study the robustness and the asymptotic behavior of these correlations. The asymptotic relative efficiencies are considered to compare several popular correlations under symmetric distributions with different tail-heaviness as well as an asymmetric log-normal distribution. Simulation and real data application are conducted to demonstrate the desirable performance of the two new symmetric Gini correlations.

Measuring the Spatial Dimension of Regional Inequality: An Approach Based on the Gini Correlation Measure

Traditional inequality measures fail to capture the geographical distribution of income. The failure to consider such distribution implies that, holding income constant, different spatial patterns provide the same inequality measure. This property is referred to as anonymity and presents an interesting question about the relationship between inequality and space. Particularly, spatial dependence could play an important role in shaping the geographical distribution of income and could be usefully incorporated into inequality measures. Following this idea, this paper introduces a new measure that facilitates the assessment of the relative contribution of spatial patterns to overall inequality. The proposed index is based on the Gini correlation measure and accounts for both inequality and spatial autocorrelation. Unlike most of the spatially based income inequality measures proposed in the literature, our index introduces regional importance weighting in the analysis, thereby differentiating the regional contributions to overall inequality. Starting with the proposed measure, a spatial decomposition of the Gini index of inequality for weighted data is also derived. This decomposition permits the identification of the actual extent of regional disparities and the understanding of the interdependences among regional economies. The proposed measure is illustrated by an empirical analysis focused on Italian provinces.