Applications and Extensions of Chao's Moment Estimator for the Size of a Closed Population

• Published in: Biometrics 2007-12, Vol.63 (4), p.999-1006
• Main Authors: Rivest, Louis-Paul, Baillargeon, Sophie
• Format: Article
• Language: English
• Subjects: Algorithms; Animal Identification Systems - methods; Animal populations; Animals; Biometrics; Biometry - methods; Chaos theory; Computer Simulation; Data Interpretation, Statistical; Estimation bias; Estimation methods; Estimators; Log-convexity; Loglinear models; Mathematical independent variables; Measurement techniques; Mixture models; Modeling; Models, Biological; Models, Statistical; Monte Carlo simulation; Multinomial distribution; Parametric models; Poisson regression; Population Density; Population Dynamics; Population estimates; Population size; Research methodology; Robust design; Sample Size
• ISSN: 0006-341X; 1541-0420
• DOI: 10.1111/j.1541-0420.2007.00779.x

This article revisits Chao's (1989, Biometrics 45, 427-438) lower bound estimator for the size of a closed population in a mark-recapture experiment where the capture probabilities vary between animals (model Mh). First, an extension of the lower bound to models featuring a time effect and heterogeneity in capture probabilities ($M_{th}$) is proposed. The biases of these lower bounds are shown to be a function of the heterogeneity parameter for several loglinear models for$M_{th}$. Small-sample bias reduction techniques for Chao's lower bound estimator are also derived. The application of the loglinear model underlying Chao's estimator when heterogeneity has been detected in the primary periods of a robust design is then investi- gated. A test for the null hypothesis that Chao's loglinear model provides unbiased abundance estimators is provided. The strategy of systematically using Chao's loglinear model in the primary periods of a robust design where heterogeneity has been detected is investigated in a Monte Carlo experiment. Its impact on the estimation of the population sizes and of the survival rates is evaluated in a Monte Carlo experiment. /// Cet article$r\acute{e}\acute{e}tudie$l'estimateur de la limite$inf\acute{e}rieure$de Chao (1989) pour l'effectif d'une population$ferm\acute{e}e$, pour des données de marquage-recapture avec$h\acute{e}t\acute{e}rog\acute{e}ndit\acute{e}$des$probabilit\acute{e}s$de capture entre individus ($mod\grave{e}le$Mh). Dans un premier temps, nous proposons une$g\acute{e}n\acute{e}ralisation}$de la limite$inf\acute{e}rieure$aux$mod\acute{e}les$comprenant à la fois un effet du temps et de$l'h\acute{e}t\acute{e}rog\acute{e}neit\acute{e}$de capture ($M_{th}$). Nous montrons que les biais de ce type d'estimateurs$d\acute{e}pendent$du$parametr\grave{e}$ $d'h\acute{e}t\acute{e}rog\acute{e}n\acute{e}it\acute{e}$, pour plusieurs$modul\grave{e}s$log-$lin\acute{e}aires$de forme$M_{th}$. Nous proposons des techniques de$r\acute{e}duction$du biais pour petits échantillons, pour l'estimateur de la limite$infir\acute{e}eure$de Chao. Nous$\acute{e}tudions$ensuite l'application du$mod\grave{e}le$ $log-lin\acute{e}aire$de Chao, dans le cas d'un plan$d'exp\acute{e}rience$robuste où une$h\acute{e}t\acute{e}rog\acute{e}n\acute{e}it\acute{e}$de capture dans les$p\acute{e}riodes$principales a$\acute{e}t\acute{e}$ $d\acute{e}tect\acute{e}e$. Nous proposons un test de l'hypothèse nulle que le$mod\grave{e}le$ $log-lin\acute{e}aire$de Chao fo