The unmarked gdistremoval model (Amundson et al. 2014): a single-season
point-count design in which the detected individuals are recorded two ways at
once – their distance band (distance sampling) and the removal period of first
detection (removal sampling). This is NOT the open-population distance model
(distsampOpen); the abundance is static.
Usage
gdistremoval(transect = c("line", "point"), cutpoints = NULL)Details
Site abundance N_i ~ Poisson(lambda_i); the detected birds are
cross-classified by a distance band and a removal period. Writing pdist_i for
the overall distance detection, prem_i for the overall removal detection, the
total detected is a binomial thinning of N_i, and Poisson is closed under
binomial thinning, so the marginal is closed-form:
$$\mathrm{ysum}_i \sim \mathrm{Poisson}(\lambda_i\, p^{dist}_i\, p^{rem}_i),$$
with the distance-band counts and removal-period counts as two conditional
multinomials – the double_observer() Poisson-multinomial pattern, here with
a distance multinomial (half-normal key band integrals) and a depleting-removal
multinomial pi_k = r (1 - r)^{k-1}.
Three site-level arms: log abundance lambda (the tobs() formula), log
distance scale sigma (detection), and logit per-period removal capture r
(removal = ~ ..., default intercept-only).
Inputs
y is an n_sites x n_bins integer matrix of per-distance-band counts;
y_rem an n_sites x n_periods integer matrix of per-removal-period counts.
The per-site row totals must match (the same detected birds cross-classified).
References
Amundson, C. L., Royle, J. A., Handel, C. M. (2014). A hierarchical model combining distance sampling and time removal to estimate detection probability during avian point counts. The Auk 131, 476-494.
Examples
f <- gdistremoval(transect = "point", cutpoints = c(0, 10, 20, 30, 40))
f