Clustering Species With Residual Covariance Matrix in Joint Species Distribution Models

Modeling species distributions over space and time is one of the major research topics in both ecology and conservation biology. Joint Species Distribution models (JSDMs) have recently been introduced as a tool to better model community data, by inferring a residual covariance matrix between species, after accounting for species' response to the environment. However, these models are computationally demanding, even when latent factors, a common tool for dimension reduction, are used. To address this issue, Taylor-Rodriguez et al. (2017) proposed to use a Dirichlet process, a Bayesian nonparametric prior, to further reduce model dimension by clustering species in the residual covariance matrix. Here, we built on this approach to include a prior knowledge on the potential number of clusters, and instead used a Pitman–Yor process to address some critical limitations of the Dirichlet process. We therefore propose a framework that includes prior knowledge in the residual covariance matrix, providing a tool to analyze clusters of species that share the same residual associations with respect to other species. We applied our methodology to a case study of plant communities in a protected area of the French Alps (the Bauges Regional Park), and demonstrated that our extensions improve dimension reduction and reveal additional information from the residual covariance matrix, notably showing how the estimated clusters are compatible with plant traits, endorsing their importance in shaping communities.

Shared environmental effects bias phenotypic estimates of assortative mating in a wild bird

Assortative mating is pervasive in wild populations and commonly described as a positive correlation between the phenotypes of males and females across mated pairs. This correlation is often assumed to reflect non-random mate choice based on phenotypic similarity. However, phenotypic resemblance between mates can also arise when their traits respond plastically to a shared environmental effect creating a (within-pair) residual correlation in traits. Using long-term data collected in pairs of wild blue tits and a covariance partitioning approach, we empirically demonstrate that such residual covariance indeed exists and can generate phenotypic correlations (or mask assortative mating) in behavioural and morphometric traits. These findings (i) imply that residual covariance is likely to be common and bias phenotypic estimates of assortative mating, which can have consequences for evolutionary predictions, (ii) call for the use of rigorous statistical approaches in the study of assortative mating, and (iii) show the applicability of one of these approaches in a common study system.

Assessing components of the model-based mean square error estimator for remote sensing assisted forest applications

Model-based inference is an alternative to probability-based inference for small areas or remote areas for which probability sampling is difficult. Model-based mean square error estimators incorporate three components: prediction covariance, residual variance, and residual covariance. The latter two components are often considered negligible, particularly for large areas, but no thresholds that justify ignoring them have been reported. The objectives of the study were threefold: (i) to compare analytical and bootstrap estimators of model parameter covariances as the primary factors affecting prediction covariance; (ii) to estimate the contribution of residual variance to overall variance; and (iii) to estimate thresholds for residual spatial correlation that justify ignoring this component. Five datasets were used, three from Europe, one from Africa, and one from North America. The dependent variable was either forest volume or biomass and the independent variables were either Landsat satellite image bands or airborne laser scanning metrics. Three conclusions were noteworthy: (i) analytical estimators of the model parameter covariances tended to be biased; (ii) the effects of residual variance were mostly negligible; and (iii) the effects of spatial correlation on residual covariance vary by multiple factors but decrease with increasing study area size. For study areas greater than 75 km2 in size, residual covariance could generally be ignored.

Genotypic parameters for egg production in pure breed hens by using random regression model

ABSTRACT: This study aimed to test different genotypic and residual covariance matrix structures in random regression models to model the egg production of Barred Plymouth Rock and White Plymouth Rock hens aged between 5 and 12 months. In addition, we estimated broad-sense heritability, and environmental and genotypic correlations. Six random regression models were evaluated, and for each model, 12 genotypic and residual matrix structures were tested. The random regression model with linear intercept and unstructured covariance (UN) for a matrix of random effects and unstructured correlation (UNR) for residual matrix adequately model the egg production curve of hens of the two study breeds. Genotypic correlations ranged from 0.15 (between age of 5 and 12 months) to 0.99 (between age of 10 and 11 months) and increased based on the time elapsed. Egg production heritability between 5- and 12-month-old hens increased with age, varying from 0.15 to 0.51. From the age of 9 months onward, heritability was moderate with estimates of genotypic correlations higher than 90% at the age of 10, 11, and 12 months. Results suggested that selection of hens to improve egg production should commence at the ninth month of age.

Examining the Factorial Structure of the T-CRS 2.1

The factor structure of the Teacher–Child Rating Scale (T-CRS 2.1) was examined using confirmatory factor analysis (CFA). A cross-sectional study was carried out on 68,497 children in prekindergarten through Grade 10. Item reduction was carried out based on modification indices, standardized residual covariance, and standardized factor loadings. A higher order model with a general super-ordinate factor fit the data well, and is consistent with the notion of a unidimensional non-cognitive set of learning-related skills. Model-based reliability estimates are provided.