Many criteria for statistical parameter estimation, such as maximum likelihood, are formulated as a nonlinear optimization problem. Automatic Differentiation Model Builder (ADMB) is a programming framework based on automatic differentiation, aimed at highly nonlinear models with a large number of parameters. The benefits of using AD are computational efficiency and high numerical accuracy, both crucial in many practical problems. We describe the basic components and the underlying philosophy of ADMB, with an emphasis on functionality found in no other statistical software. One example of such a feature is the generic implementation of Laplace approximation of high-dimensional integrals for use in latent variable models. We also review the literature in which ADMB has been used, and discuss future development of ADMB as an open source project. Overall, the main advantages of ADMB are flexibility, speed, precision, stability and built-in methods to quantify uncertainty.

Aim Spatial analysis of the distribution and density of species is of continuing interest within theoretical and applied ecology. Species distribution models (SDMs) are being increasingly used to analyse count, presence–absence and presence‐only data sets. There is a growing literature on dynamic SDMs (which incorporate temporal variation in species distribution), joint SDMs (which simultaneously analyse the correlated distribution of multiple species) and geostatistical models (which account for similarity between nearby sites caused by unobserved covariates). However, no previous study has combined all three attributes within a single framework. Innovation We develop spatial dynamic factor analysis for use as a ‘joint, dynamic SDM’ (JDSDM), which uses geostatistical methods to account for spatial similarity when estimating one or more ‘factors’. Each factor evolves over time following a density‐dependent (Gompertz) process, and the log‐density of each species is approximated as a linear combination of different factors. We demonstrate a JDSDM using two multispecies case studies (an annual survey of bottom‐associated species in the Bering Sea and a seasonal survey of butterfly density in the continental USA), and also provide our code publicly as an R package. Main conclusions Case study applications show that that JDSDMs can be used for species ordination, i.e. showing that dynamics for butterfly species within the same genus are significantly more correlated than for species from different genera. We also demonstrate how JDSDMs can rapidly identify dominant patterns in community dynamics, including the decline and recovery of several Bering Sea fishes since 2008, and the ‘flight curves’ typical of early or late‐emerging butterflies. We conclude by suggesting future research that could incorporate phylogenetic relatedness or functional similarity, and propose that our approach could be used to monitor community dynamics at large spatial and temporal scales.

. 2000. Including predation mortality in stock assessments: a case study for Gulf of Alaska walleye pollock. -ICES Journal of Marine Science, 57: 279-293.A separable catch-age stock assessment model that accommodates predation mortality is applied to the Gulf of Alaska walleye pollock (Theragra chalcogramma) assessment. Three predators are incorporated in the model: arrowtooth flounder (Atheresthes stomias), Pacific halibut (Hippoglossus stenolepis), and Steller sea lion (Eumetopias jubatus). The effect of these predators is examined by defining the predation mortality as a type of fishery. The model is used to quantify changes in the relative fit to the survey, fishery, and predator data when the assumption of constant natural mortality is relaxed. Specifically, we examine the effect of assumptions regarding the functional feeding response, residual naturaly mortality, and uncertainty in predator biomass on stock assessment. Total natural mortality rates (including predation) tended to be higher than estimated from life history characteristics of the stock. Models that did not account for uncertainty in natural mortality underestimated uncertainty in current stock biomass by as much as 20%. Our results indicate that independent estimates of survey selectivity, additional food habits data, and estimates of the feeding responses of predators to different prey densities are all needed to improve our ability to develop stock assessment models that address ecosystem concerns. 2000 International Council for the Exploration of the Sea