Single-Species, Multi-Species, and Integrated Spatial Occupancy Models.

spOccupancy

spOccupancy fits single-species, multi-species, and integrated spatial occupancy models using Markov chain Monte Carlo (MCMC). Models are fit using Pólya-Gamma data augmentation. Spatial models are fit using either Gaussian processes or Nearest Neighbor Gaussian Processes (NNGP) for large spatial datasets. The package provides functionality for data integration of multiple single-species occupancy data sets using a joint likelihood framework. For multi-species models, spOccupancy provides functions to account for residual species correlations in a joint species distribution model framework while accounting for imperfect detection. spOccupancy also provides functions for multi-season (i.e., spatio-temporal) single-species occupancy models. Below we give a very brief introduction to some of the package’s functionality, and illustrate just one of the model fitting functions. For more information, see the resources referenced at the bottom of this page.

Installation

You can install the released version of spOccupancy from CRAN with:

install.packages("spOccupancy")

Functionality

Example usage

Load package and data

To get started with spOccupancy we load the package and an example data set. We use data on twelve foliage-gleaning birds from the Hubbard Brook Experimental Forest, which is available in the spOccupancy package as the hbef2015 object. Here we will only work with one bird species, the black-throated blue warbler (BTBW), and so we subset the hbef2015 object to only include this species.

library(spOccupancy)
data(hbef2015)
sp.names <- dimnames(hbef2015$y)[[1]]
btbwHBEF <- hbef2015
btbwHBEF$y <- btbwHBEF$y[sp.names == "BTBW", , ]

Fit a spatial occupancy model using spPGOcc()

Below we fit a single-species spatial occupancy model to the BTBW data using a Nearest Neighbor Gaussian Process. We use the default priors and initial values for the occurrence (beta) and detection (alpha) coefficients, the spatial variance (sigma.sq), the spatial decay parameter (phi), the spatial random effects (w), and the latent occurrence values (z). We assume occurrence is a function of linear and quadratic elevation along with a spatial random intercept. We model detection as a function of linear and quadratic day of survey and linear time of day the survey occurred.

# Specify model formulas
btbw.occ.formula <- ~ scale(Elevation) + I(scale(Elevation)^2)
btbw.det.formula <- ~ scale(day) + scale(tod) + I(scale(day)^2)

We run the model using an adaptive MCMC sampler with a target acceptance rate of 0.43. We run 3 chains of the model each for 10,000 iterations split into 400 batches each of length 25. For each chain, we discard the first 2000 iterations as burn-in and use a thinning rate of 4 for a resulting 6000 samples from the joint posterior. We fit the model using 5 nearest neighbors and an exponential correlation function. We also specify the k.fold argument to perform 2-fold cross-validation after fitting the full model. Run ?spPGOcc for more detailed information on all function arguments.

# Run the model
out <- spPGOcc(occ.formula = btbw.occ.formula,
               det.formula = btbw.det.formula,
               data = btbwHBEF, n.batch = 400, batch.length = 25,
               accept.rate = 0.43, cov.model = "exponential", 
               NNGP = TRUE, n.neighbors = 5, n.burn = 2000, 
               n.thin = 4, n.chains = 3, verbose = FALSE, k.fold = 2)

This will produce a large output object, and you can use str(out) to get an overview of what’s in there. Here we use the summary() function to print a concise but informative summary of the model fit.

summary(out)
#> 
#> Call:
#> spPGOcc(occ.formula = btbw.occ.formula, det.formula = btbw.det.formula, 
#>     data = btbwHBEF, cov.model = "exponential", NNGP = TRUE, 
#>     n.neighbors = 5, n.batch = 400, batch.length = 25, accept.rate = 0.43, 
#>     verbose = FALSE, n.burn = 2000, n.thin = 4, n.chains = 3, 
#>     k.fold = 2)
#> 
#> Samples per Chain: 10000
#> Burn-in: 2000
#> Thinning Rate: 4
#> Number of Chains: 3
#> Total Posterior Samples: 6000
#> Run Time (min): 0.7627
#> 
#> Occurrence (logit scale): 
#>                          Mean     SD    2.5%     50%   97.5%   Rhat ESS
#> (Intercept)            4.0762 0.6183  3.0681  4.0071  5.4855 1.0019 261
#> scale(Elevation)      -0.5203 0.2249 -0.9772 -0.5132 -0.0825 1.0039 984
#> I(scale(Elevation)^2) -1.1806 0.2257 -1.6958 -1.1593 -0.7969 1.0033 244
#> 
#> Detection (logit scale): 
#>                    Mean     SD    2.5%     50%  97.5%   Rhat  ESS
#> (Intercept)      0.6647 0.1155  0.4398  0.6623 0.8955 1.0012 5605
#> scale(day)       0.2899 0.0709  0.1507  0.2900 0.4273 1.0020 6000
#> scale(tod)      -0.0319 0.0697 -0.1680 -0.0327 0.1055 0.9999 6000
#> I(scale(day)^2) -0.0756 0.0867 -0.2476 -0.0752 0.0926 1.0000 6000
#> 
#> Spatial Covariance: 
#>            Mean     SD   2.5%    50%  97.5%   Rhat ESS
#> sigma.sq 1.2610 1.0218 0.2063 0.9694 4.0863 1.0130 101
#> phi      0.0093 0.0085 0.0009 0.0056 0.0294 1.0763  45

Posterior predictive check

The function ppcOcc performs a posterior predictive check on the resulting list from the call to spPGOcc. For binary data, we need to perform Goodness of Fit assessments on some binned form of the data rather than the raw binary data. Below we perform a posterior predictive check on the data grouped by site with a Freeman-Tukey fit statistic, and then use the summary function to summarize the check with a Bayesian p-value.

ppc.out <- ppcOcc(out, fit.stat = 'freeman-tukey', group = 1)
summary(ppc.out)
#> 
#> Call:
#> ppcOcc(object = out, fit.stat = "freeman-tukey", group = 1)
#> 
#> Samples per Chain: 10000
#> Burn-in: 2000
#> Thinning Rate: 4
#> Number of Chains: 3
#> Total Posterior Samples: 6000
#> 
#> Bayesian p-value:  0.4828 
#> Fit statistic:  freeman-tukey

Model selection using WAIC and k-fold cross-validation

The waicOcc function computes the Widely Applicable Information Criterion (WAIC) for use in model selection and assessment (note that due to Monte Carlo error your results will differ slightly).

waicOcc(out)
#>       elpd         pD       WAIC 
#> -679.88774   22.96844 1405.71235

Alternatively, we can perform k-fold cross-validation (CV) directly in our call to spPGOcc using the k.fold argument and compare models using a deviance scoring rule. We fit the model with k.fold = 2 and so below we access the deviance scoring rule from the 2-fold cross-validation. If we have additional candidate models to compare this model with, then we might select for inference the one with the lowest value of this CV score.

out$k.fold.deviance
#> [1] 1414.417

Prediction

Prediction is possible using the predict function, a set of occurrence covariates at the new locations, and the spatial coordinates of the new locations. The object hbefElev contains elevation data across the entire Hubbard Brook Experimental Forest. Below we predict BTBW occurrence across the forest, which are stored in the out.pred object.

# First standardize elevation using mean and sd from fitted model
elev.pred <- (hbefElev$val - mean(btbwHBEF$occ.covs[, 1])) / sd(btbwHBEF$occ.covs[, 1])
coords.0 <- as.matrix(hbefElev[, c('Easting', 'Northing')])
X.0 <- cbind(1, elev.pred, elev.pred^2)
out.pred <- predict(out, X.0, coords.0, verbose = FALSE)

Learn more

The vignette("modelFitting") provides a more detailed description and tutorial of the core functions in spOccupancy. For full statistical details on the MCMC samplers for core functions in spOccupancy, see vignette("mcmcSamplers"). In addition, see the introductory spOccupancy paper that describes the package in more detail (Doser et al. 2022). For a detailed description and tutorial of joint species distribution models in spOccupancy that account for residual species correlations, see vignette("factorModels"), vignette("mcmcFactorModels"), and our open-access paper (Doser et al. 2023). For a description and tutorial of multi-season (spatio-temporal) occupancy models in spOccupancy, see vignette("spaceTimeModels"). For a tutorial on spatially-varying coefficient models in spOccupancy, see vignette("svcModels") and vignette(mcmcSVCModels) and our associated papers that describe the methods (Doser et al. 2024A) and applications to ecology (Doser et al. 2024B) in much more detail.

References

Doser, J. W., Finley, A. O., Kery, M., and Zipkin, E. F. (2022a). spOccupancy: An R package for single-species, multi-species, and integrated spatial occupancy models. Methods in Ecology and Evolution. 13(8) 1670-1678. https://doi.org/10.1111/2041-210X.13897.

Doser, J. W., Finley, A. O., and Banerjee, S. (2023). Joint species distribution models with imperfect detection for high-dimensional spatial data. Ecology, 104(9), e4137. https://doi.org/10.1002/ecy.4137.

Doser, J. W., Finley, A. O., Saunders, S. P., Kéry, M., Weed, A. S., & Zipkin, E. F. (2024A). Modeling complex species-environment relationships through spatially-varying coefficient occupancy models. Journal of Agricultural, Biological and Environmental Statistics. https://doi.org/10.1007/s13253-023-00595-6.

Doser, J. W., Kéry, M., Saunders, S. P., Finley, A. O., Bateman, B. L., Grand, J., Reault, S., Weed, A. S., & Zipkin, E. F. (2024B). Guidelines for the use of spatially varying coefficients in species distribution models. Global Ecology and Biogeography, 33, e13814. https://doi.org/10.1111/geb.13814