Spatial factor analysis: a new tool for estimating joint species distributions and correlations in species range

James T. Thorson, Mark D. Scheuerell, Andrew O. Shelton, Kevin E. See, Hans J. Skaug, Kasper Kristensen

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Abstract

1. Predicting and explaining the distribution and density of species is one of the oldest concerns in ecology. Species distributions can be estimated using geostatistical methods, which estimate a latent spatial variable explaining observed variation in densities, but geostatistical methods may be imprecise for species with low densities or few observations. Additionally, simple geostatistical methods fail to account for correlations in distribution among species and generally estimate such cross-correlations as a post hoc exercise.
2. We therefore present spatial factor analysis (SFA), a spatial model for estimating a low-rank approximation to multivariate data, and use it to jointly estimate the distribution of multiple species simultaneously. We also derive an analytic estimate of cross-correlations among species from SFA parameters.
3. As a first example, we show that distributions for 10 bird species in the breeding bird survey in 2012 can be parsimoniously represented using only five spatial factors. As a second case study, we show that forward prediction of catches for 20 rockfishes (Sebastes spp.) off the U.S. West Coast is more accurate using SFA than analysing each species individually. Finally, we show that single-species models give a different picture of cross-correlations than joint estimation using SFA.
4. Spatial factor analysis complements a growing list of tools for jointly modelling the distribution of multiple species and provides a parsimonious summary of cross-correlation without requiring explicit declaration of habitat variables. We conclude by proposing future research that would model species cross-correlations using dissimilarity of species' traits, and the development of spatial dynamic factor analysis for a low-rank approximation to spatial time-series data.
Original languageEnglish
JournalMethods in Ecology and Evolution
Volume6
Issue number6
Pages (from-to)627-637
ISSN2041-210X
DOIs
Publication statusPublished - 2015

Keywords

  • ECOLOGY
  • DISTRIBUTION MODELS
  • HIERARCHICAL-MODELS
  • TIME-SERIES
  • COUNT DATA
  • COOCCURRENCE
  • ABUNDANCE
  • SELECTION
  • WORLD
  • factor analysis
  • Gaussian process
  • Gaussian random field
  • geostatistics
  • habitat envelope model
  • hierarchical model
  • joint species distribution models
  • mixed-effects model
  • spatial factor analysis

Cite this

Thorson, James T. ; Scheuerell, Mark D. ; Shelton, Andrew O. ; See, Kevin E. ; Skaug, Hans J. ; Kristensen, Kasper. / Spatial factor analysis: a new tool for estimating joint species distributions and correlations in species range. In: Methods in Ecology and Evolution. 2015 ; Vol. 6, No. 6. pp. 627-637.
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abstract = "1. Predicting and explaining the distribution and density of species is one of the oldest concerns in ecology. Species distributions can be estimated using geostatistical methods, which estimate a latent spatial variable explaining observed variation in densities, but geostatistical methods may be imprecise for species with low densities or few observations. Additionally, simple geostatistical methods fail to account for correlations in distribution among species and generally estimate such cross-correlations as a post hoc exercise. 2. We therefore present spatial factor analysis (SFA), a spatial model for estimating a low-rank approximation to multivariate data, and use it to jointly estimate the distribution of multiple species simultaneously. We also derive an analytic estimate of cross-correlations among species from SFA parameters. 3. As a first example, we show that distributions for 10 bird species in the breeding bird survey in 2012 can be parsimoniously represented using only five spatial factors. As a second case study, we show that forward prediction of catches for 20 rockfishes (Sebastes spp.) off the U.S. West Coast is more accurate using SFA than analysing each species individually. Finally, we show that single-species models give a different picture of cross-correlations than joint estimation using SFA. 4. Spatial factor analysis complements a growing list of tools for jointly modelling the distribution of multiple species and provides a parsimonious summary of cross-correlation without requiring explicit declaration of habitat variables. We conclude by proposing future research that would model species cross-correlations using dissimilarity of species' traits, and the development of spatial dynamic factor analysis for a low-rank approximation to spatial time-series data.",
keywords = "ECOLOGY, DISTRIBUTION MODELS, HIERARCHICAL-MODELS, TIME-SERIES, COUNT DATA, COOCCURRENCE, ABUNDANCE, SELECTION, WORLD, factor analysis, Gaussian process, Gaussian random field, geostatistics, habitat envelope model, hierarchical model, joint species distribution models, mixed-effects model, spatial factor analysis",
author = "Thorson, {James T.} and Scheuerell, {Mark D.} and Shelton, {Andrew O.} and See, {Kevin E.} and Skaug, {Hans J.} and Kasper Kristensen",
year = "2015",
doi = "10.1111/2041-210X.12359",
language = "English",
volume = "6",
pages = "627--637",
journal = "Methods in Ecology and Evolution",
issn = "2041-210X",
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Spatial factor analysis: a new tool for estimating joint species distributions and correlations in species range. / Thorson, James T.; Scheuerell, Mark D.; Shelton, Andrew O.; See, Kevin E.; Skaug, Hans J.; Kristensen, Kasper.

In: Methods in Ecology and Evolution, Vol. 6, No. 6, 2015, p. 627-637.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Spatial factor analysis: a new tool for estimating joint species distributions and correlations in species range

AU - Thorson, James T.

AU - Scheuerell, Mark D.

AU - Shelton, Andrew O.

AU - See, Kevin E.

AU - Skaug, Hans J.

AU - Kristensen, Kasper

PY - 2015

Y1 - 2015

N2 - 1. Predicting and explaining the distribution and density of species is one of the oldest concerns in ecology. Species distributions can be estimated using geostatistical methods, which estimate a latent spatial variable explaining observed variation in densities, but geostatistical methods may be imprecise for species with low densities or few observations. Additionally, simple geostatistical methods fail to account for correlations in distribution among species and generally estimate such cross-correlations as a post hoc exercise. 2. We therefore present spatial factor analysis (SFA), a spatial model for estimating a low-rank approximation to multivariate data, and use it to jointly estimate the distribution of multiple species simultaneously. We also derive an analytic estimate of cross-correlations among species from SFA parameters. 3. As a first example, we show that distributions for 10 bird species in the breeding bird survey in 2012 can be parsimoniously represented using only five spatial factors. As a second case study, we show that forward prediction of catches for 20 rockfishes (Sebastes spp.) off the U.S. West Coast is more accurate using SFA than analysing each species individually. Finally, we show that single-species models give a different picture of cross-correlations than joint estimation using SFA. 4. Spatial factor analysis complements a growing list of tools for jointly modelling the distribution of multiple species and provides a parsimonious summary of cross-correlation without requiring explicit declaration of habitat variables. We conclude by proposing future research that would model species cross-correlations using dissimilarity of species' traits, and the development of spatial dynamic factor analysis for a low-rank approximation to spatial time-series data.

AB - 1. Predicting and explaining the distribution and density of species is one of the oldest concerns in ecology. Species distributions can be estimated using geostatistical methods, which estimate a latent spatial variable explaining observed variation in densities, but geostatistical methods may be imprecise for species with low densities or few observations. Additionally, simple geostatistical methods fail to account for correlations in distribution among species and generally estimate such cross-correlations as a post hoc exercise. 2. We therefore present spatial factor analysis (SFA), a spatial model for estimating a low-rank approximation to multivariate data, and use it to jointly estimate the distribution of multiple species simultaneously. We also derive an analytic estimate of cross-correlations among species from SFA parameters. 3. As a first example, we show that distributions for 10 bird species in the breeding bird survey in 2012 can be parsimoniously represented using only five spatial factors. As a second case study, we show that forward prediction of catches for 20 rockfishes (Sebastes spp.) off the U.S. West Coast is more accurate using SFA than analysing each species individually. Finally, we show that single-species models give a different picture of cross-correlations than joint estimation using SFA. 4. Spatial factor analysis complements a growing list of tools for jointly modelling the distribution of multiple species and provides a parsimonious summary of cross-correlation without requiring explicit declaration of habitat variables. We conclude by proposing future research that would model species cross-correlations using dissimilarity of species' traits, and the development of spatial dynamic factor analysis for a low-rank approximation to spatial time-series data.

KW - ECOLOGY

KW - DISTRIBUTION MODELS

KW - HIERARCHICAL-MODELS

KW - TIME-SERIES

KW - COUNT DATA

KW - COOCCURRENCE

KW - ABUNDANCE

KW - SELECTION

KW - WORLD

KW - factor analysis

KW - Gaussian process

KW - Gaussian random field

KW - geostatistics

KW - habitat envelope model

KW - hierarchical model

KW - joint species distribution models

KW - mixed-effects model

KW - spatial factor analysis

U2 - 10.1111/2041-210X.12359

DO - 10.1111/2041-210X.12359

M3 - Journal article

VL - 6

SP - 627

EP - 637

JO - Methods in Ecology and Evolution

JF - Methods in Ecology and Evolution

SN - 2041-210X

IS - 6

ER -