Multilevel maximum likelihood estimation with application to covariance matrices

The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of covariance models to the sample, which is important in data assimilation. The hierarchical maximum likelihood approach is applied to the spectral diagonal covariance model with different parameterizations of eigenvalue decay, and to the sparse inverse covariance model with specified parameter values on different sets of nonzero entries. It is shown computationally that using smaller sets of parameters can decrease the sampling noise in high dimension substantially.     

Foraging in the tropics: relationships among species’ abundances,niche asymmetries and body condition in an urban avian assemblage

Two main theories attempt to explain species coexistence: the neutral theory considers all the species as equivalents so biodiversity is mainly regarded as a function of total available resources (i.e. niche expansion), while the niche theory stresses the relevance of differences in niche use between species (i.e. niche packing). The relative importance of these forces is under discussion and has been largely tested in natural ecosystems. However, few studies have addressed this issue in tropical-urban environments. In this work we studied niche overlap asymmetries among the most common urban resident birds, and the effect of habitat type on this pattern, in a subtropical location of South China (Nanning, Guangxi). We found differences in abundances and niche use among species and urban habitats (parks, streets and orchards). We also recorded strong asymmetries in niche use between species, which we divided into three categories: species with positive asymmetries, which showed highly specific niches and were able to exploit other species’ niches; species with neutral asymmetries, which showed high levels of niche overlap with the rest of species; and species with negative asymmetries, which showed low specificity in their niches and were unable to exploit other species’ niches. These differences in niche use correlated with differences in fat scores. Species from the first group showed higher fat scores than other two groups. Ultimately, niche asymmetries correlated with species’ body condition and mediated their differences in abundance, which supports the view that in this urban context niche theory is more appropriate than neutral theory.