region.ND: Abundance and Density in a region.

In david-borchers/secrgam: Spatially Explicit Capture-Recapture with Generalised Additive Density Models

Description

Estimate the expected and realised populations in a region, using a fitted spatially explicit capture-recapture model. Density is assumed to follow an inhomogeneous Poisson process in two dimensions. Expected N is the volume under a fitted density surface; realised N is the number of individuals within the region for the current realisation of the process (cf Johnson et al. 2010; see Note).

This function is an adapted version of region.N of package secr, to report density as well as abunance, and to accommodate regression spline models for density.

Usage

region.ND(object, region = NULL, spacing = NULL, session = NULL,
  group = NULL, se.N = TRUE, alpha = 0.05, loginterval = TRUE,
  nlowerbound = TRUE, RN.method = "poisson")

Arguments

object	secr object output from secr.fit
region	mask object defining the possibly non-contiguous region for which population size is required, or vector polygon(s) (see Details)
spacing	spacing between grid points (metres) if region mask is constructed on the fly. This argument must be NULL if object is of class sercgam
session	character session
group	group for future use
se.N	logical for whether to estimate SE(N-hat) and confidence interval
alpha	alpha level for confidence intervals
loginterval	logical for whether to base interval on log(N)
nlowerbound	logical for whether to use n as lower bound when computing log interval for realised N
RN.method	character string for method used to calculate realised N (RN) and its sampling variance. 'poisson' or 'MSPE'.

Details

If the density surface of the fitted model is flat (i.e. object$model$D == ~1 or object$CL == TRUE) then E(N) is simply the density multiplied by the area of region, and the standard error is also a simple product. In the conditional likelihood case (not valid for secrgam objects), the density and standard error are obtained by first calling derived.

If, on the other hand, the density has been modelled then the density surface is predicted at each point in region and E(N) is obtained by discrete summation. Pixel size may have a minor effect on the result - check by varying spacing. Sampling variance is determined by the delta method, using a numerical approximation to the gradient of E(N) with respect to each beta parameter.

The region may be defined as a mask object (if omitted, the mask component of object will be used). Alternatively, region may be a SpatialPolygonsDataFrame object (see package sp), and a raster mask will be constructed on the fly using the specified spacing. See make.mask for an example importing a shapefile to a SpatialPolygonsDataFrame.

Note: The option of specifying a polygon rather than a mask for region does not work if the density model in object uses spatial covariates: these must be passed in a mask.

Group-specific N has yet to be implemented.

Population size is adjusted automatically for the number of clusters in 'mashed' models (see mash). However, the population size reported is that associated with a single cluster unless regionmask is specified.

Value

A list with components $Abundance and $Density. If se.N = FALSE, these are the numeric values of expected population size and density, otherwise they each contain a dataframe with rows 'E.N' and 'R.N' for $Abundance, 'E.D' and 'R.D' for $Abundance, with columns as below.

estimate estimate of N (expected or realised, depending on row) SE.estimate standard error of estimated N lcl lower 100(1–alpha) ucl upper 100(1–alpha) n total number of individuals detected

For multiple sessions, a list with one component per session is returned, each component as above.

Examples

## Not run: 
data(Boland.fits1) # get model fitted to Boland leopard data
fit1.a3.dW3 # look at a fitted model

# plot fitted surface:
plot(fit1.a3.dW3, asp=1)
plot(traps(fit1.a3.dW3$capthist), add = TRUE)

# calculate abundance and density estimates on fitting mask:
region.ND(fit1.a3.dW3)

data(Boland.leopards2) # get larger mask
# calculate abundance and density estimates on fitting mask:
region.ND(fit1.a3.dW3,Boland.mask2)

## End(Not run)

david-borchers/secrgam documentation built on May 14, 2019, 9:30 p.m.