title: Distance sampling detection functions: 2D or not 2D?
abstract: Conventional distance sampling (CDS) methods assume that animals are uniformly distributed in the vicinity of lines or points. But when animals move in response to observers before detection, or when lines or points are not located randomly, this assumption may fail. By formulating distance sampling models as survival models, we show that using time to first detection in addition to perpendicular distance (line transect surveys) or radial distance (point transect surveys) allows estimation of detection probability, and hence density, when animal distribution in the vicinity of lines or points is not uniform and is unknown. We also show that times to detection can provide information about failure of the CDS assumption that detection probability is 1 at distance zero. We obtain a maximum likelihood estimator of line transect survey detection probability and effective strip half-width using times to detection, and we investigate its properties by simulation in situations where animals are nonuniformly distributed and their distribution is unknown. The estimator is found to perform well when detection probability at distance zero is 1. It allows unbiased estimates of density to be obtained in this case from surveys in which there has been responsive movement prior to animals coming within detectable range. When responsive movement continues within detectable range, estimates may be biased but are likely less biased than estimates from methods that assuming no responsive movement. We illustrate by estimating primate density from a line transect survey in which animals are known to avoid the transect line, and a shipboard survey of dolphins that are attracted to it.
authors.affiliation: Centre for Research into Ecological and Environmental Modelling, The Observatory Buchanan Gardens, University of St Andrews, Fife, KY16 9LZ, Scotland.
authors.forename: David Louis
authors.initials: DL
authors.lastname: Borchers
authors.affiliation: Australian Antarctic Division, Channel Highway Kingston Tasmania 7050, Australia.
authors.forename: Martin James
authors.initials: MJ
authors.lastname: Cox
mesh_terms: D000818:Animals; D011156:Population Density; D011336:Probability; D011795:Surveys and Questionnaires
keywords: Line transect; Point transect; Removal method; Responsive movement; Survival analysis; g(0)=1