Example of PointedSDMs for the solitary tinamou

Load data

Firstly, we load in the datasets and objects required for this vignette. The SolitaryTinamou dataset attached to this package contains a list of four objects; for ease of use, we make new objects for the items in this list.

data('SolitaryTinamou')
projection <- CRS("+proj=longlat +ellps=WGS84")

datasets <- SolitaryTinamou$datasets
covariates <- SolitaryTinamou$covariates
region <- SolitaryTinamou$region
mesh <- SolitaryTinamou$mesh
mesh$crs <- projection

The first item is a list of three datasets: eBird, Gbif and Parks. The first two are data.frame objects containing only two variables: X and Y describing the latitude and longitude coordinates of the species location respectively. As a result of this, these two datasets are considered to be present only datasets in our integrated model.

The other dataset (Parks) is also a data.frame object. It contains the two coordinate variables present in the first two datasets, but contains two additional variables: Present, a binary variable describing the presence (1) or absence (0) of the species at the given coordinates, and area describing the area of the park. Since we have information on the presences and absences of the species in this dataset, we consider it a presence absence dataset.

Region is a SpatialPolygons object which give the boundary of the park containing the species; it was used in the mesh construction and for the plots in this vignette.

str(datasets)
class(region)

The next object is covariates, a list of Raster objects of the covariates (Forest, NPP and Altitude) describing the area of the parks. We stack these three objects together using the stack function, and then scale them.

covariates <- scale(stack(covariates))
crs(covariates) <- projection
plot(covariates)

Finally we require a Delaunay triangulated mesh for the construction of the spatial field. A plot of the mesh used for this vignette is provided below.

plot(mesh)

Base model

To set up an integrated species distribution model with PointedSDMs, we initialize it with the intModel function – which results in an R6 objects with additional slot functions to further customize the model. The base model we run for these data comprises of the spatial covariates and an intercept term for each dataset.

base <- intModel(datasets, spatialCovariates = covariates, Coordinates = c('X', 'Y'),
                 Projection = projection, responsePA = 'Present', Offset = 'area',
                 Mesh = mesh, pointsSpatial = NULL)

Using the .$plot function produces a gg object of the points used in this analysis by dataset; from this plot, we see that most of the species locations are found towards the eastern and south-central part of the park.

base$plot(Boundary = FALSE) + 
  gg(region) +
  ggtitle('Plot of the species locations by dataset')

In this model, we also include prior information for the Forest effect using $priorsFixed.

base$priorsFixed(Effect = 'Forest', mean.linear = 0.5, prec.linear = 0.01)

To run the integrated model, we use the runModel function with the data argument as the object created with the intModel function above.

baseModel <- runModel(data = base)
baseModel

Model with spatial fields

Spatial fields are fundamental in our spatial species distribution models, and so we include them in the model by setting pointsSpatial = TRUE in intModel. Furthermore, we will remove the intercept terms by specifying pointsIntercept = FALSE

fields <- intModel(datasets, Coordinates = c('X', 'Y'),
                   Projection = projection, Mesh = mesh, responsePA = 'Present', 
                   Offset = 'area',
                   pointsIntercept = FALSE)

To specify the spatial field in the model, we use the slot function $specifySpatial. This in turn will call R-INLA’s inla.spde2.pcmatern function, which is used to specify penalizing complexity (PC) priors for the parameters of the field. If we had set PC = FALSE in this function, our shared spatial field would be specified with R-INLA’s inla.spde2.matern function.

fields$specifySpatial(sharedSpatial = TRUE, prior.range = c(1,0.01), 
                      prior.sigma = c(0.75, 0.05))

We furthermore include an additional spatial field (deemed the bias field) for our citizen science eBird observations with the $addBias slot function.

fields$addBias('eBird')

Finally we run the integrated model, again with runModel but this time we specify options with R-INLA’s empirical Bayes integration strategy to help with computation time.

fieldsModel <- runModel(fields, options = list(control.inla = list(int.strategy = 'eb')))

Prediction of the spatial fields

If we wanted to make predictions of the shared spatial random field across the map, we set spatial = TRUE in the generic predict function.

spatial_predictions <- predict(fieldsModel, mesh = mesh,
                       mask = region, 
                       spatial = TRUE,
                       fun = 'linear')

And subsequently plot using the generic plot function.

plot(spatial_predictions)

However if we wanted to make predictions of the bias field, we would do this by setting biasfield = TRUE.

bias_predictions <- predict(fieldsModel, 
                    mesh = mesh, 
                    mask = region, 
                    biasfield = TRUE,
                    fun = 'linear')

plot(bias_predictions)

Dataset out cross-validation

The last function of interest is datasetOut, which removes a dataset out of the full model, and then calculates a cross-validation score with this reduced model. In this case, we try the function out by removing the eBird dataset.

eBird_out <- datasetOut(model = fieldsModel, dataset = 'eBird')

eBird_out