Spatio-temporal analysis of univariate or multivariate data, e.g., standardizing data for multiple species or stages
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  • Is an R package for implementing a spatial delta-generalized linear mixed model (delta-GLMM) for multiple categories (species, size, or age classes) when standardizing survey or fishery-dependent data.
  • Builds upon a previous R package SpatialDeltaGLMM (public available here), and has unit-testing to automatically confirm that VAST and SpatialDeltaGLMM give identical results (to the 3rd decimal place for parameter estimates) for several varied real-world case-study examples
  • Has built in diagnostic functions and model-comparison tools
  • Is intended to improve analysis speed, replicability, peer-review, and interpretation of index standardization methods


  • This tool is designed to estimate spatial variation in density using spatially referenced data, with the goal of habitat associations (correlations among species and with habitat) and estimating total abundance for a target species in one or more years.
  • The model builds upon spatio-temporal delta-generalized linear mixed modelling techniques (Thorson Shelton Ward Skaug 2015 ICESJMS), which separately models the proportion of tows that catch at least one individual ("encounter probability") and catch rates for tows with at least one individual ("positive catch rates").
  • Submodels for encounter probability and positive catch rates by default incorporate variation in density among years (as a fixed effect), and can incorporate variation among sampling vessels (as a random effect, Thorson and Ward 2014) which may be correlated among categories (Thorson Fonner Haltuch Ono Winker In press).
  • Spatial and spatiotemporal variation are approximated as Gaussian Markov random fields (Thorson Skaug Kristensen Shelton Ward Harms Banante 2014 Ecology), which imply that correlations in spatial variation decay as a function of distance.


Regions available in the example script: alt text and see for visualization of results for regions with a public API for their data.

Installation Instructions

Build Status DOI

This function depends on R version >=3.1.1 and a variety of other tools.

First, install the "devtools" package from CRAN

# Install and load devtools package

Second, please install the following:

Note: at the moment, TMB and INLA can be installed using the commands

# devtools command to get TMB from GitHub
# source script to get INLA from the web

Next, please install the geostatistical_delta-GLMM package from this GitHub repository using a function in the "devtools" package:

# Install package
# Load package

Known installation/usage issues


Example code

Please see examples folder for single-species and multi-species examples of how to run the model. This folder also contains a User Manual

This code illustrates how to loop through different default model configurations, plot diagnostics for each model, and obtain the AIC for each model.

Please also read the instructions from the single-species SpatialDeltaGLMM package, Guidelines for West Coast users wiki page, which is a living document and will evolve over time as best practices become apparent.

Description of package

Please cite if using the software

Description of individual features

Correlated spatio-temporal variation among species

  • Thorson, J.T., Ianelli, J.N., Larsen, E., Ries, L., Scheuerell, M.D., Szuwalski, C., and Zipkin, E. 2016. Joint dynamic species distribution models: a tool for community ordination and spatiotemporal monitoring. Glob. Ecol. Biogeogr. 25(9): 1144–1158. doi:10.1111/geb.12464. url:
  • Thorson, J.T., Scheuerell, M.D., Shelton, A.O., See, K.E., Skaug, H.J., and Kristensen, K. 2015. Spatial factor analysis: a new tool for estimating joint species distributions and correlations in species range. Methods Ecol. Evol. 6(6): 627–637. doi:10.1111/2041-210X.12359. url:

Index of abundance

  • Thorson, J.T., Shelton, A.O., Ward, E.J., Skaug, H.J., 2015. Geostatistical delta-generalized linear mixed models improve precision for estimated abundance indices for West Coast groundfishes. ICES J. Mar. Sci. J. Cons. 72(5), 1297–1310. doi:10.1093/icesjms/fsu243. URL:

Standardizing samples of size/age-composition data

Range shift metrics

Effective area occupied metric

Spatio-temporal statistical methods

Accounting for fish shoals using robust observation models

  • Thorson, J. T., I. J. Stewart, and A. E. Punt. 2012. Development and application of an agent-based model to evaluate methods for estimating relative abundance indices for shoaling fish such as Pacific rockfish (Sebastes spp.). ICES Journal of Marine Science 69:635–647. URL:
  • Thorson, J. T., I. Stewart, and A. Punt. 2011. Accounting for fish shoals in single- and multi-species survey data using mixture distribution models. Canadian Journal of Fisheries and Aquatic Sciences 68:1681–1693. URL:

Accounting for variation among vessels

Accounting for fisher targetting in fishery-dependent data

  • Thorson, J.T., Fonner, R., Haltuch, M., Ono, K., and Winker, H. In press. Accounting for spatiotemporal variation and fisher targeting when estimating abundance from multispecies fishery data. Can. J. Fish. Aquat. Sci. doi:10.1139/cjfas-2015-0598. URL:

Bias-correction of estimated indices of abundance

Estimating and attributing variation in size-structured distribution

  • Kai, M., Thorson, J. T., Piner, K. R., and Maunder, M. N. 2017. Spatio-temporal variation in size-structured populations using fishery data: an application to shortfin mako (Isurus oxyrinchus) in the Pacific Ocean. Canadian Journal of Fisheries and Aquatic Sciences. doi:10.1139/cjfas-2016-0327. URL:
  • Thorson, J. T., Ianelli, J. N., and Kotwicki, S. 2018. The relative influence of temperature and size-structure on fish distribution shifts: A case-study on Walleye pollock in the Bering Sea. Fish and Fisheries. doi:10.1111/faf.12225. URL:

Estimating fishing impacts using spatial surplus production modelling

Estimating species interactions using multispecies Gompertz model

Funding and support for the tool

  • Ongoing: Support from Fisheries Resource Analysis and Monitoring Division (FRAM), Northwest Fisheries Science Center, National Marine Fisheries Service, NOAA
  • Ongoing: Support from Danish Technical University (in particular Kasper Kristensen) for development of Template Model Builder software, URL:
  • Generous support from people knowledgeable about each region and survey! Specific contributions are listed here.
  • Thorson, J., Ianelli, J., and O’Brien, L. 2015. Distribution and application of a new geostatistical index standardization and habitat modeling tool for stock assessments and essential fish habitat designation in Alaska and Northwest Atlantic regions. Habitat Assessment Improvement Plan 2014 RFP. URL: