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Abstract Numerous modelling techniques exist to estimate abundance of plant and animal populations. The most accurate methods account for multiple complexities found in ecological data, such as observational biases, spatial autocorrelation, and species correlations. There is, however, a lack of user‐friendly and computationally efficient software to implement the various models, particularly for large data sets.We developed thespAbundance Rpackage for fitting spatially explicit Bayesian single‐species and multi‐species hierarchical distance sampling models, N‐mixture models, and generalized linear mixed models. The models within the package can account for spatial autocorrelation using Nearest Neighbour Gaussian Processes and accommodate species correlations in multi‐species models using a latent factor approach, which enables model fitting for data sets with large numbers of sites and/or species.We provide three vignettes and three case studies that highlightspAbundancefunctionality. We used spatially explicit multi‐species distance sampling models to estimate density of 16 bird species in Florida, USA, an N‐mixture model to estimate black‐throated blue warbler (Setophaga caerulescens) abundance in New Hampshire, USA, and a spatial linear mixed model to estimate forest above‐ground biomass across the continental USA.spAbundanceprovides a user‐friendly, formula‐based interface to fit a variety of univariate and multivariate spatially explicit abundance models. The package serves as a useful tool for ecologists and conservation practitioners to generate improved inference and predictions on the spatial drivers of abundance in populations and communities.
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Variational determination of the two‐electron reduced density matrix: A tutorial review
Abstract The two‐electron reduced density matrix (2RDM) carries enough information to evaluate the electronic energy of a many‐electron system. The variational 2RDM (v2RDM) approach seeks to determine the 2RDM directly, without knowledge of the wave function, by minimizing this energy with respect to variations in the elements of the 2RDM, while also enforcing knownN‐representability conditions. In this tutorial review, we provide an overview of the theoretical underpinnings of the v2RDM approach and theN‐representability constraints that are typically applied to the 2RDM. We also discuss the semidefinite programming (SDP) techniques used in v2RDM computations and provide enough Python code to develop a working v2RDM code that interfaces to thelibSDPlibrary of SDP solvers. This article is categorized under:Electronic Structure Theory > Ab Initio Electronic Structure MethodsSoftware > Quantum Chemistry
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- Award ID(s):
- 2100984
- PAR ID:
- 10487195
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- WIREs Computational Molecular Science
- Volume:
- 14
- Issue:
- 1
- ISSN:
- 1759-0876
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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