secr (version 2.5.0)

region.N: Population Size

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).

Usage

region.N (object, region = NULL, spacing = NULL, session = NULL,
    group = NULL, se.N = TRUE, alpha = 0.05, loginterval = TRUE,
    keep.region = FALSE, 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

session

character session

group

group -- for future use

se.N

logical for whether to estimate SE($\hat{N}$) and confidence interval

alpha

alpha level for confidence intervals

loginterval

logical for whether to base interval on log(N)

keep.region

logical for whether to save the raster region

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'.

Value

• If se.N = FALSE, the numeric value of expected population size, otherwise, a dataframe with rows `E.N' and `R.N', and columns as below. ll{ estimate estimate of N (expected or realised, depending on row) SE.estimate standard error of estimated N lcl lower 100(1--alpha)% confidence limit ucl upper 100(1--alpha)% confidence limit n total number of individuals detected } For multiple sessions, the value is a list with one component per session, each component as above. If keep.region = TRUE then the mask object for the region is saved as the attribute `region' (see Examples).

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, 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.

References

Borchers, D. L. and Efford, M. G. (2008) Spatially explicit maximum likelihood methods for capture--recapture studies. Biometrics 64, 377--385. Efford, M. G. and Fewster, R. M. (2012) Estimating population size by spatially explicit capture--recapture. Oikos http://dx.doi.org/10.1111/j.1600-0706.2012.20440.x Johnson, D. S., Laake, J. L. and Ver Hoef, J. M. (2010) A model-based approach for making ecological inference from distance sampling data. Biometrics 66, 310--318.

See Also

secr.fit, derived, make.mask, expected.n, closedN

Examples

region.N(secrdemo.0)

## a couple more routine examples
region.N(secrdemo.CL)
region.N(ovenbird.model.D)

## region defined as vector polygon
## retain and plot region mask
temp <- region.N(possum.model.0, possumarea, spacing = 40,
    keep.region = TRUE)
temp
plot (attr(temp, "region"), type = 'l')