diff --git a/man/gdistsamp.Rd b/man/gdistsamp.Rd index 1e15cac0..d5d7501a 100644 --- a/man/gdistsamp.Rd +++ b/man/gdistsamp.Rd @@ -1,12 +1,13 @@ \name{gdistsamp} \alias{gdistsamp} \title{ -Fit the generalized distance sampling model of Chandler et al. (2011). + Fit the generalized distance sampling model of Chandler et al. (2011). } \description{ -Extends the distance sampling model of Royle et al. (2004) to estimate -the probability of being available for detection. Also allows abundance -to be modeled using the negative binomial distribution. + Extends the distance sampling model of Royle et al. (2004) to estimate + the probability of being available for detection. Also allows + abundance to be modeled using the negative binomial and zero-inflated + Poisson distributions. } \usage{ gdistsamp(lambdaformula, phiformula, pformula, data, keyfun = @@ -72,49 +73,87 @@ starts, method = "BFGS", se = TRUE, engine=c("C","R"), rel.tol=1e-4, threads=1, bounds} } + \details{ - This model extends the model of Royle et al. (2004) by estimating the - probability of being available for detection \eqn{\phi}{phi}. This - effectively relaxes the assumption that \eqn{g(0)=1}. In other words, - inividuals at a distance of 0 are not assumed to be detected with - certainty. To estimate this additional parameter, replicate distance - sampling data must be collected at each transect. Thus the data are - collected at i = 1, 2, ..., R transects on t = 1, 2, ..., T - occassions. As with the model of Royle et al. (2004), the detections - must be binned into distance classes. These data must be formatted in - a matrix with R rows, and JT columns where J is the number of distance - classses. See \code{\link{unmarkedFrameGDS}} for more information. + + Extends the model of Royle et al. (2004) by estimating the probability + of being available for detection \eqn{\phi}{phi}. To estimate this + additional parameter, replicate distance sampling data must be + collected at each transect. Thus the data are collected at i = 1, 2, + ..., R transects on t = 1, 2, ..., T occassions. As with the model of + Royle et al. (2004), the detections must be binned into distance + classes. These data must be formatted in a matrix with R rows, and JT + columns where J is the number of distance classses. See + \code{\link{unmarkedFrameGDS}} for more information about data + formatting. + + The definition of availability depends on the context. The model is + \deqn{M_i \sim \text{Pois}(\lambda)}{M(i)~Pois(lambda)} + \deqn{N_{i,t} \sim \text{Bin}(M_i, \phi)}{N(i,t)~Bin(M(i), phi)} + \deqn{y_{i,1,t}, \dots, y_{i,J,t} \sim \text{Multinomial}(N_{i,t}, + \pi_{i,1,t}, \dots, \pi_{i,J,t})}{y(i,1,t), ..., y(i,J,t) ~ + Multinomial(N(i,t), pi(i,1,t), ..., pi(i,J,t))} + + If there is no movement, then \eqn{M_i}{M(i)} is local abundance, and + \eqn{N_{i,t}}{N(i,t)} is the number of individuals that are available + to be detected. In this case, \eqn{\phi=g_0}{phi=g(0)}. Animals might + be missed on the transect line because they are difficult to see or + detected. This relaxes the assumption of conventional distance + sampling that \eqn{g_0=1}{g(0)=1}. + + However, when there is movement in the form of temporary emigration, + local abundance is \eqn{N_{i,t}}{N(i,t)}; it's the fraction of + \eqn{M_i}{M(i)} that are on the plot at time t. In this case, + \eqn{\phi}{phi} is the temporary emigration parameter, and we need to + assume that \eqn{g_0=1}{g(0)=1} in order to interpret + \eqn{N_{i,t}}{N(i,t)} as local abundance. See Chandler et al. (2011) + for an analysis of the model under this form of temporary emigration. + + If there is movement and \eqn{g_0<1}{g(0)<1} then it + isn't possible to estimate local abundance at time t. In this case, + \eqn{M_i}{M(i)} would be the total number of individuals that ever use + plot i (the super-population), and \eqn{N_{i,t}}{N(i,t)} would be the + number available to be detected at time t. Since a fraction of the + unavailable individuals could be off the plot, and another fraction + could be on the plot, it isn't possible to infer local abundance and + density during occasion t. + } \note{ - If you aren't interested in estimating phi, but you want to - use the negative binomial distribution, simply set numPrimary=1 when - formatting the data. - } + If you aren't interested in estimating \eqn{\phi}{phi}, but you want + to use the negative binomial or ZIP distributions, set numPrimary=1 + when formatting the data. +} \value{ - An object of class unmarkedFitGDS. - } + An object of class unmarkedFitGDS. +} + \references{ - Royle, J. A., D. K. Dawson, and S. Bates. 2004. Modeling - abundance effects in distance sampling. \emph{Ecology} - 85:1591-1597. - Chandler, R. B, J. A. Royle, and D. I. King. 2011. Inference about + Royle, J. A., D. K. Dawson, and S. Bates. 2004. Modeling abundance + effects in distance sampling. \emph{Ecology} 85:1591-1597. + + Chandler, R. B, J. A. Royle, and D. I. King. 2011. Inference about density and temporary emigration in unmarked - populations. \emph{Ecology} 92:1429--1435. - } + populations. \emph{Ecology} 92:1429--1435. +} + \author{ - Richard Chandler \email{rbchan@uga.edu} - } + Richard Chandler \email{rbchan@uga.edu} +} + \note{ - You cannot use obsCovs, but you can use yearlySiteCovs (a confusing name - since this model isn't for multi-year data. It's just a hold-over - from the colext methods of formatting data upon which it is based.) - } + You cannot use obsCovs, but you can use yearlySiteCovs (a confusing + name since this model isn't for multi-year data. It's just a hold-over + from the colext methods of formatting data upon which it is based.) +} + \seealso{ - \code{\link{distsamp}} - } + \code{\link{distsamp}} +} + \examples{