Intercropping can improve yield and nitrogen use efficiency in organic vegetable production by pairing crops with complementary resource use. An intercrop field experiment was conducted to determine yield, root growth and nitrogen (N) dynamics using faba bean (Vicia faba L.) grown as a vegetable and pointed cabbage (Brassica oleracea var. capitata cv. conica). Both crops were grown in monocropping (MC) and intercropping systems (IC). Minirhizotrons were used to measure root growth. Yield of pointed cabbage per metre row was 28% higher under the IC system than under MC, whereas faba bean yield as fresh seeds did not differ. The land equivalent ratio was 1.06, showing that improved yield under IC resulted from efficient land resource use. Even though MC cabbage had the highest aboveground biomass, total N accumulation was higher under IC and MC faba bean systems. Both root frequency and intensity were greater under IC faba bean rows compared with MC faba bean because of the presence of cabbage roots in faba bean rows. Monocropped cabbage had the highest root intensity and the lowest amount of soil mineral N in the 0–1.5 m depth after harvest. Monocropped cabbage was efficient in assimilating N, whereas MC faba bean was efficient in exporting N as harvestable yield. The nitrogen use efficiency using the IC system (75%) was higher than growing faba bean (44%) and cabbage (65%) alone. Thus, faba bean as an intercrop in organic cabbage production systems improves land and N use efficiency by complementary root growth.
We propose a method for inference in generalised linear mixed models (GLMMs) and several extensions of these models. First, we extend the GLMM by allowing the distribution of the random components to be non-Gaussian, that is, assuming an absolutely continuous distribution with respect to the Lebesgue measure that is symmetric around zero, unimodal and with finite moments up to fourth-order. Second, we allow the conditional distribution to follow a dispersion model instead of exponential dispersion models. Finally, we extend these models to a multivariate framework where multiple responses are combined by imposing a multivariate absolute continuous distribution on the random components representing common clusters of observations in all the marginal models.Maximum likelihood inference in these models involves evaluating an integral that often cannot be computed in closed form. We suggest an inference method that predicts values of random components and does not involve the integration of conditional likelihood quantities. The multivariate GLMMs that we studied can be constructed with marginal GLMMs of different statistical nature, and at the same time, represent complex dependence structure providing a rather flexible tool for applications.
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