Abstract
Aims of the study: To describe the radial patterns of wood density, and to identify their main sources of variation, and the potential tradeoffs with mean tree growth, in two Eucalyptus species. Area of study: Mesopotamian (Corrientes and Entre Ríos provinces) and Pampean region (Buenos Aires province) of Argentina. Materials and methods: Eucalyptus grandis and Eucalyptus viminalis, growing in genetic trials installed in two sites per species were studied. X-ray wood microdensity profiles were developed from core samples. Each profile was proportionally divided in 10 sections. Mean, maximum, minimum and the standard deviation of wood density, for each section were computed. Mean annual growth was used to study the relationships with wood microdensity variables. A linear mixed-effects model computed the significance of different sources of phenotypic variation. Pearson´s correlation computed the relationships between variables. Main results: The pattern of radial variation in E. grandis showed a decrease in wood density from pith to bark, mainly due to the decrease in minimum wood density, while in E. viminalis, wood density increased towards the outer wood. In both species, the standard deviation of the wood density increased along the radial profile from pith to bark. Significant variation in wood density was explained by site, provenance and clone/family effects. In E. grandis mean, maximum and minimum wood density were negatively correlated with mean growth, whereas in E. viminalis correlations were positive but close to zero. Research highlights: Both the pattern of radial variation of wood density and the relationship between wood density and mean growth were different in the studied Eucalyptus species, and they varied within species depending on the site they were growing and genetic provenance. Keywords: wood microdensity profile; wood properties; wood products; phenotypic plasticity; Eucalyptus grandis; Eucalyptus viminalis.
Highlights
A linear mixed model is characterized by the conditional distribution (Y |U = u) ∼ N (γ(u, θ, β ), σ 2In) where γ(u, θ, β ) = ZΛ (θ )u + Xβ (4.31)
The discrepancy function, d(u|y, θ, β ) = y − γ(u, θ, β ) 2 + u 2, is minimized at the conditional mode, u (θ ), and the conditional estimate, β (θ ), which are the solutions to the sparse, positive-definite linear system
Because one of the factors influencing the choice of implementation for linear mixed models is the extent to which the methods can be applied to other mixed models, we describe several other classes of mixed models before discussing the implementation details for linear mixed models
Summary
Mixed-effects models, like many other types of statistical models, describe a relationship between a response variable and some of the covariates that have been measured or observed along with the response. In mixed-effects models at least one of the covariates is a categorical covariate representing experimental or observational “units” in the data set. In agriculture the experimental units may be the plots of land or the specific plants being studied In all of these cases the categorical covariate or covariates are observed at a set of discrete levels. To make the distinction more concrete, suppose that we wish to model the annual reading test scores for students in a school district and that the covariates recorded with the score include a student identifier and the student’s gender.
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