Fitting statistical distributions to seaduck count data: Implications for survey design and abundance estimation

Zipkin, Elise F.
Leirness, Jeffery B.
Kinlan, Brian P.
O’Connell, Allan F.
Silverman, Emily D.
USGS Patuxent Wildlife Research Center
USFWS -Migratory Bird Management - Laurel MD.
University Delaware, Entomology and Wildlife Ecology
National Oceanic and Atmospheric Administration (NOAA)
Consolidated Safety Services Inc. Fairfax VA
Publication Date: 

Determining appropriate statistical distributions for modeling animal count data is important for accurate estimation of abundance,distribution,and trends.In the case of
seaducks along the U.S.Atlantic coast,managers want to estimate local and regional abundance to detect and track population declines, to define
areas of high and low use, and to predict the impact of future habitat change on populations. In this paper, we used a modified marked point process to model survey data that recorded flock sizes of Common eiders, Long-tailed ducks, and Black, Surf, and White-winged scoters. The data come from an experimental aerial
survey, conducted by the United States Fish & Wildlife Service (USFWS) Division of Migratory Bird Management, during which
east-west transects were flown along the Atlantic Coast from Maine to Florida during the winters of 2009–2011.To model the number of flocks per transect (the points), we compared the fit of four statistical distributions (zero-inflated Poisson,zero-inflated geometric, zero-inflated negative binomial and negative binomial)
to data on the number of species-specific seaduck flocks that were recorded for each transect flown. To model the flock sizes (the marks), we compared the fit of flock size data for each species to seven statistical distributions: positive Poisson, positive negative binomial, positive geometric, logarithmic, discretized log normal,
zetaand Yule–Simon.Akaike’sInformation Criterion and Vuong’s closeness tests indicated that the negative binomial and discretized
lognormal were the best distributions for all species for the points and marks, respectively. These findings have important
implications for estimating seaduck abundances as the discretized log normal is a more skewed distribution than the Poisson and
negative binomial, which are frequently used to model avian counts; the lognormal is also less heavy-tailed than the power
law distributions (e.g.,zetaand Yule–Simon), which are becoming increasingly popular for group size modeling. Choosing appropriate
statistical distributions for modeling flock size data is fundamental to accurately estimating population summaries, determining
required survey effort, and assessing and propagating uncertainty through decision-making processes

Citation Information: 
E.F.Zipkin etal./StatisticalMethodology17(2014)67–81