spAbundance fits univariate (i.e., single-species) and multivariate
(i.e., multi-species) spatial N-mixture models, hierarchical distance
sampling models, and generalized linear mixed models using Markov chain
Monte Carlo (MCMC). Spatial models are fit using Nearest Neighbor
Gaussian Processes (NNGPs) to facilitate model fitting to large spatial
datasets. spAbundance uses analogous syntax to its “sister package”
spOccupancy (Doser et
al. 2022). Below we provide 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 and the “Articles” tab at the top of the page.
Please also consider joining the spAbundance and spOccupancy users
google group.
You can install the released version of spAbundance from
CRAN with
install.packages("spAbundance")To download the development version of the package, you can use
devtools as follows:
devtools::install_github("biodiverse/spAbundance")Note that because we implement the MCMC in C++, you will need a C++
compiler on your computer to install the package from GitHub. To compile
C++ on Windows, you can install
RTools. To compile
C++ on a Mac, you can install XCode from the Mac app store.
spAbundance Function |
Description |
|---|---|
DS() |
Single-species hierarchical distance sampling (HDS) model |
spDS() |
Single-species spatial HDS model |
msDS() |
Multi-species HDS model |
lfMsDS() |
Multi-species HDS model with species correlations |
sfMsDS() |
Multi-species spatial HDS model with species correlations |
NMix() |
Single-species N-mixture model |
spNMix() |
Single-species spatial N-mixture model |
msNMix() |
Multi-species N-mixture model |
lfMsNMix() |
Multi-species N-mixture model with species correlations |
sfMsNMix() |
Multi-species spatial N-mixture model with species correlations |
abund() |
Univariate GLMM |
spAbund() |
Univariate spatial GLMM |
svcAbund() |
Univariate spatially-varying coefficient GLMM |
msAbund() |
Multivariate GLMM |
lfMsAbund() |
Multivariate GLMM with species correlations |
sfMsAbund() |
Multivariate spatial GLMM with species correlations |
svcMsAbund() |
Multivariate spatially-varying coefficient GLMM with species correlations |
ppcAbund() |
Posterior predictive check using Bayesian p-values |
waicAbund() |
Calculate Widely Applicable Information Criterion (WAIC) |
simDS() |
Simulate single-species distance sampling data |
simMsDS() |
Simulate multi-species distance sampling data |
simNMix() |
Simulate single-species repeated count data |
simMsNMix() |
Simulate multi-species repeated count data |
simAbund() |
Simulate single-species count data |
simMsAbund() |
Simulate multi-species count data |
All model fitting functions allow for Poisson and negative binomial distributions for the abundance portion of the model. All GLM(M)s also allow for Gaussian and zero-inflated Gaussian models. Note the multi-species spatailly-varying coefficient models are only available for Gaussian and zero-inflated Gaussian models.
To get started with spAbundance we load the package and an example
data set. We use data on 16 birds from the Disney Wilderness
Preserve in Central
Florida, USA, which is available in the spAbundance package as the
neonDWP object. Here we will only work with one bird species, the
Mourning Dove (MODO), and so we subset the neonDWP object to only
include this species.
library(spAbundance)
# Set seed to get exact same results
set.seed(500)
data(neonDWP)
sp.names <- dimnames(neonDWP$y)[[1]]
dat.MODO <- neonDWP
dat.MODO$y <- dat.MODO$y[sp.names == "MODO", , ]Below we fit a single-species spatially-explicit hierarchical distance
sampling model to the MODO data using a Nearest Neighbor Gaussian
Process. We use the default priors and initial values for the abundance
(beta) and detection (alpha) coefficients, the spatial variance
(sigma.sq), the spatial decay parameter (phi), the spatial random
effects (w), and the latent abundance values (N). We also include an
offset in dat.MODO to provide estimates of density on a per hectare
basis. We model abundance as a function of local forest cover and
grassland cover, along with a spatial random intercept. We model
detection probability as a function of linear and quadratic day of
survey and a linear effect of wind.
# Specify model formulas
MODO.abund.formula <- ~ scale(forest) + scale(grass)
MODO.det.formula <- ~ scale(day) + I(scale(day)^2) + scale(wind)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 20,000 iterations
split into 800 batches each of length 25. For each chain, we discard the
first 10,000 iterations as burn-in and use a thinning rate of 5 for a
resulting 6,000 samples from the joint posterior. We fit the model using
15 nearest neighbors and an exponential correlation function. Run
?spDS for more detailed information on all function arguments.
# Run the model (Approx run time: 1 min)
out <- spDS(abund.formula = MODO.abund.formula,
det.formula = MODO.det.formula,
data = dat.MODO, n.batch = 800, batch.length = 25,
accept.rate = 0.43, cov.model = "exponential",
transect = 'point', det.func = 'halfnormal',
NNGP = TRUE, n.neighbors = 15, n.burn = 10000,
n.thin = 5, n.chains = 3, verbose = FALSE)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:
#> spDS(abund.formula = MODO.abund.formula, det.formula = MODO.det.formula,
#> data = dat.MODO, cov.model = "exponential", NNGP = TRUE,
#> n.neighbors = 15, n.batch = 800, batch.length = 25, accept.rate = 0.43,
#> transect = "point", det.func = "halfnormal", verbose = FALSE,
#> n.burn = 10000, n.thin = 5, n.chains = 3)
#>
#> Samples per Chain: 20000
#> Burn-in: 10000
#> Thinning Rate: 5
#> Number of Chains: 3
#> Total Posterior Samples: 6000
#> Run Time (min): 0.7582
#>
#> Abundance (log scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) -1.8186 0.3428 -2.5560 -1.8020 -1.1956 1.0692 64
#> scale(forest) -0.1999 0.2056 -0.5818 -0.2102 0.2443 1.0292 160
#> scale(grass) 0.1206 0.1939 -0.2720 0.1244 0.4938 1.0210 229
#>
#> Detection (log scale):
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> (Intercept) -2.5392 0.1196 -2.7602 -2.5436 -2.2815 1.0850 204
#> scale(day) -0.1658 0.0807 -0.3380 -0.1629 -0.0187 1.0341 364
#> I(scale(day)^2) 0.0011 0.0828 -0.1530 -0.0011 0.1648 1.0391 352
#> scale(wind) -0.1352 0.0769 -0.2931 -0.1344 0.0126 1.0037 534
#>
#> Spatial Covariance:
#> Mean SD 2.5% 50% 97.5% Rhat ESS
#> sigma.sq 0.4941 0.2648 0.1725 0.431 1.1929 1.0156 169
#> phi 0.0016 0.0018 0.0003 0.001 0.0072 1.0644 102The function ppcAbund performs a posterior predictive check on the
resulting list from the call to spDS. We provide options to group, or
bin, the data in different ways prior to performing the posterior
predictive check, which can help reveal different types of inadequate
model fit. 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 <- ppcAbund(out, fit.stat = 'freeman-tukey', group = 1)
summary(ppc.out)
#>
#> Call:
#> ppcAbund(object = out, fit.stat = "freeman-tukey", group = 1)
#>
#> Samples per Chain: 20000
#> Burn-in: 10000
#> Thinning Rate: 5
#> Number of Chains: 3
#> Total Posterior Samples: 6000
#>
#> Bayesian p-value: 0.535
#> Fit statistic: freeman-tukeyThe waicAbund function computes the Widely Applicable Information
Criterion (WAIC) for use in model selection and assessment.
waicAbund(out)
#> N.max not specified. Setting upper index of integration of N to 10 plus
#> the largest estimated abundance value at each site in object$N.samples
#> elpd pD WAIC
#> -167.74186 14.03248 363.54866Prediction is possible using the predict function, a set of covariates
at the desired prediction locations, and the spatial coordinates of the
locations. The object neonPredData contains percent forest cover and
grassland cover across the Disney Wildnerness Preserve. Below we predict
MODO density across the preserve, which is stored in the out.pred
object.
# First standardize elevation using mean and sd from fitted model
forest.pred <- (neonPredData$forest - mean(dat.MODO$covs$forest)) /
sd(dat.MODO$covs$forest)
grass.pred <- (neonPredData$grass - mean(dat.MODO$covs$grass)) /
sd(dat.MODO$covs$grass)
X.0 <- cbind(1, forest.pred, grass.pred)
colnames(X.0) <- c('(Intercept)', 'forest', 'grass')
coords.0 <- neonPredData[, c('easting', 'northing')]
out.pred <- predict(out, X.0, coords.0, verbose = FALSE)The vignette("distanceSampling"), vignette("nMixtureModels"), and
vignette("glmm") provide detailed descriptions and tutorials of all
hierarchical distance sampling models, N-mixture models, and generalized
linear mixed models in spAbundance, respectively. Given the similarity
in syntax to fitting occupancy models in the spOccupancy package, much
of the documentation on the spOccupancy
website will also be
helpful for fitting models in spAbundance. Please also consider
joining the spAbundance and spOccupancy users google
group to learn from
others who use the two packages.
Please cite spAbundance as:
Doser, J. W., Finley A. O., Kéry, M., & Zipkin E. F. (2024). spAbundance: An R package for single-species and multi-species spatially explicit abundance models, Methods in Ecology and Evolution. 15, 1024-1033. https://doi.org/10.1111/2041-210X.14332“)
Doser, J. W., Finley, A. O., Kéry, M., and Zipkin, E. F. (2022). 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.