TMB: Automatic Differentiation and Laplace Approximation

TMB is an open source R package that enables quick implementation of complex nonlinear random effect (latent variable) models in a manner similar to the established AD Model Builder package (ADMB, admb-project.org). In addition, it offers easy access to parallel computations. The user defines the joint likelihood for the data and the random effects as a C++ template function, while all the other operations are done in R; e.g., reading in the data. The package evaluates and maximizes the Laplace approximation of the marginal likelihood where the random effects are automatically integrated out. This approximation, and its derivatives, are obtained using automatic differentiation (up to order three) of the joint likelihood. The computations are designed to be fast for problems with many random effects (~10^6) and parameters (~10^3). Computation times using ADMB and TMB are compared on a suite of examples ranging from simple models to large spatial models where the random effects are a Gaussian random field. Speedups ranging from 1.5 to about 100 are obtained with increasing gains for large problems. The package and examples are available at http://tmb-project.org

Volume and Quantizations

The aim of this letter is to indicate the differences between the Rovelli-Smolin quantum volume operator and other quantum volume operators existing in the literature. The formulas for the operators are written in a unifying notation of the graph projective framework. It is clarified whose results apply to which operators and why.Comment: 8 page

Identification of stingless bees (Hymenoptera: Apidae) in Kenya using Morphometrics and DNA barcoding

Stingless bees are important pollinators of wild plants and crops. The identity of stingless bee species in Africa has not been fully documented. The present study explored the utility of morphometrics and DNA barcoding for identification of African stingless bee populations, and to further employ these tools to identify potential cryptic variation within species. Stingless bee samples were collected from three ecological zones, namely Kakamega Forest, Mwingi and Arabuko-Sokoke Forest, which are geographically distant and cover high, medium and low altitudes, respectively. Forewing and hind leg morphometric characters were measured to determine the extent of morphological variation between the populations. DNA barcodes were generated from the mitochondrial cytochrome c-oxidase I (COI) gene. Principal Component Analysis (PCA) on the morphometric measurements separated the bee samples into three clusters: (1) Meliponula bocandei; (2) Meliponula lendliana + Plebeina hildebrandti; (3) Dactylurina schmidti + Meliponula ferruginea black + Meliponula ferruginea reddish brown, but Canonical Variate Analysis (CVA) separated all the species except the two morphospecies (M. ferruginea reddish brown and black). The analysis of the COI sequences showed that DNA barcoding can be used to identify all the species studied and revealed remarkable genetic distance (7.3%) between the two M. ferruginea morphs. This is the first genetic evidence that M. ferruginea black and M. ferruginea reddish brown are separate species