secrdesign (version 2.5.5)

Lambda: Expected Detections

Description

Compute the expected number of detections as a function of location (Lambda), and the expected total numbers of individuals \(n\), recaptures \(r\) and movements \(m\) for a population sampled with an array of detectors (Enrm).

Usage

Lambda(traps, mask, detectpar, noccasions, detectfn = c("HHN", "HHR", "HEX", 
    "HAN", "HCG", 'HN', 'HR', 'EX'))
Enrm(D, ...)
minnrRSE(D, ..., CF = 1.0, distribution = c("poisson","binomial"))

Arguments

traps

traps object

mask

mask object

detectpar

a named list giving a value for each parameter of detection function

noccasions

integer number of sampling occasions

detectfn

integer code or character string for shape of detection function -- see detectfn

D

population density animals / hectare; may be scalar or vector of length nrow(mask)

…

arguments passed to Lambda

CF

numeric correction factor

distribution

character distribution of \(n\)

Value

Lambda -- mask object with covariates `Lambda' (\(\Lambda(x)\)), `sumpk' and `sumq2' (intermediate values for computation of expected counts - see ../doc/expectedcounts.pdf) Enrm -- numeric vector of length 3, the values of E(\(n\)), E(\(r\)) and E(\(m\)).

minnrRSE -- rule-of-thumb RSE(D-hat)

Details

The detector attribute of traps may be `multi', `proximity' or `count'. It is assumed that detectpar and detector type do not differ among occasions.

The calculation is based on an additive hazard model. If detectfn is not a hazard function (`HHN', `HEX', `HHR', `HAN' and `HCG') then an attempt is made to approximate one of the hazard functions (HN -> HHN, HR -> HHR, EX -> HEX). The default is `HHN'.

For hazard function \(\lambda(d)\) and \(S\) occasions, we define \(\Lambda(x) = \sum_s \sum_k \lambda(d_k(x))\).

Formulae for expected counts are given in secrdesign-Enrm.pdf.

minnrRSE has mostly the same inputs as Enrm but returns sqrt(CF/min(n,r)). The correction factor CF may be used to adjust for systematic bias (e.g., for a line of detectors CF = 1.4 may be appropriate). The default distribution = 'poisson' is for Poisson-distributed \(N\) and \(n\). To adjust the prediction for fixed \(N\) (binomial \(n\)) use distribution = 'binomial' (see ../doc/secrdesign-tools.pdf Appendix 2).

See Also

getdetectpar, optimalSpacing, scenarioSummary

Examples

# NOT RUN {
tr <- traps(captdata)
detector(tr) <- "multi"
msk <- make.mask(tr, buffer = 100, type = 'trapbuffer')

L <- Lambda(tr, msk, list(lambda0 = 0.2, sigma = 20), 5)
nrm <- Enrm(D = 5, tr, msk, list(lambda0 = 0.2, sigma = 20), 5)
nrm

plot(L, cov = "Lambda", dots = FALSE)
plot(tr, add = TRUE)
mtext(side = 3,  paste(paste(names(nrm), round(nrm,1)), collapse = ", "))

# }