Accounting for matching uncertainty in two stage capture–recapture experiments using photographic measurements of natural marks

We propose a Bayesian hierarchical modeling approach for estimating the size of a closed population from data obtained by identifying individuals through photographs of natural markings. We assume that noisy measurements of a set of distinctive features are available for each individual present in a photographic catalogue. To estimate the population size from two catalogues obtained during two different sampling occasions, we embed the standard two-stage $$M_t$$ capture–recapture model for closed population into a multivariate normal data matching model that identifies the common individuals across the catalogues. In addition to estimating the population size while accounting for the matching process uncertainty, this hierarchical modelling approach allows to identify the common individuals by using the information provided by the capture–recapture model. This way, our model also represents a novel and reliable tool able to reduce the amount of effort researchers have to expend in matching individuals. We illustrate and motivate the proposed approach via a real data set of photo-identification of narwhals. Moreover, we compare our method with a set of possible alternative approaches by using both the empirical data set and a simulation study.

[1]  James D Nichols,et al.  Assessing tiger population dynamics using photographic capture-recapture sampling. , 2006, Ecology.

[2]  Jens B. Lund,et al.  Models for point processes observed with noise , 2000 .

[3]  M. Humphries,et al.  Encounter frequencies and grouping patterns of narwhals in Koluktoo Bay, Baffin Island , 2009, Polar Biology.

[4]  S. Creel,et al.  Population size estimation in Yellowstone wolves with error‐prone noninvasive microsatellite genotypes , 2003, Molecular ecology.

[5]  Arnaud Doucet,et al.  Particle methods for maximum likelihood estimation in latent variable models , 2008, Stat. Comput..

[6]  William E. Winkler,et al.  Data quality and record linkage techniques , 2007 .

[7]  Peter J. Green,et al.  Bayesian alignment using hierarchical models, with applications in protein bioinformatics , 2005 .

[8]  William A Link,et al.  Uncovering a Latent Multinomial: Analysis of Mark–Recapture Data with Misidentification , 2010, Biometrics.

[9]  G. Seber.  The estimation of animal abundance and related parameters , 1974 .

[10]  Babak Nadjar Araabi,et al.  Computer-assisted photo-identié cation of individual marine vertebrates: a multi-species system , 2003 .

[11]  Pierre Dutilleul,et al.  Statistical analysis of animal observations and associated marks distributed in time using Ripley’s functions , 2010, Animal Behaviour.

[12]  David R. Anderson,et al.  Statistical inference from capture data on closed animal populations , 1980 .

[13]  Tim D. Smith,et al.  Errors in identification using natural markings: rates, sources, and effects on capture-recapture estimates of abundance , 2001 .

[14]  W. A. Ericson.  Subjective Bayesian Models in Sampling Finite Populations , 1969 .

[15]  F. Al-Shamali,et al.  Author Biographies. , 2015, Journal of social work in disability & rehabilitation.

[16]  Matthew A. Jaro,et al.  Advances in Record-Linkage Methodology as Applied to Matching the 1985 Census of Tampa, Florida , 1989 .

[17]  S. Ravela,et al.  Multi‐scale features for identifying individuals in large biological databases: an application of pattern recognition technology to the marbled salamander Ambystoma opacum , 2007 .

[18]  H. Whitehead,et al.  Nicks and notches of the dorsal ridge: Promising mark types for the photo-identification of narwhals , 2009 .

[19]  Zaven Arzoumanian,et al.  An astronomical pattern-matching algorithm for computer-aided identification of whale sharks Rhincodon typus , 2005 .

[20]  Raymond A. Webster,et al.  Modeling misidentification errors in capture-recapture studies using photographic identification of evolving marks. , 2009, Ecology.

[21]  Stephen E. Fienberg,et al.  Discrete Multivariate Analysis: Theory and Practice , 1976 .

[22]  A. C. Davison,et al.  Statistical models: Name Index , 2003 .

[23]  Sam H. Ridgway,et al.  River dolphins and the larger toothed whales , 1989 .

[24]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[25]  Brunero Liseo,et al.  Bayesian estimation of population size via linkage of multivariate normal data sets , 2011 .

[26]  Bayesian analysis to correct false-negative errors in capture–recapture photo-ID abundance estimates , 2009 .

[27]  Jean-Michel Marin,et al.  Bayesian Core: A Practical Approach to Computational Bayesian Statistics , 2010 .

[28]  C. Langtimm,et al.  SURVIVAL ESTIMATES FOR FLORIDA MANATEES FROM THE PHOTO‐IDENTIFICATION OF INDIVIDUALS , 2004 .

[29]  Matthew R. Schofield,et al.  Incorporating Genotype Uncertainty into Mark–Recapture‐Type Models For Estimating Abundance Using DNA Samples , 2009, Biometrics.

[30]  P. Green,et al.  Alignment of Multiple Configurations Using Hierarchical Models , 2009 .

[31]  Brunero Liseo,et al.  A hierarchical Bayesian approach to record linkage and population size problems , 2010, 1011.2649.

[32]  E. Woehler,et al.  FORUM: Is flipper banding of penguins a problem? , 2005 .

[33]  Hal Whitehead,et al.  Computer-assisted photo-identification of narwhals , 2011 .

[34]  Shen-Ming Lee,et al.  BAYES ESTIMATION OF POPULATION SIZE FROM CAPTURE-RECAPTURE MODELS WITH TIME VARIATION AND BEHAVIOR RESPONSE , 2003 .

[35]  N. Ebrahimi,et al.  Bayesian capture-recapture methods for error detection and estimation of population size: Heterogeneity and dependence , 2001 .

[36]  J. York,et al.  Bayesian methods for estimation of the size of a closed population , 1997 .

[37]  E. Woehler,et al.  IS FLIPPER BANDING OF PENGUINS A PROBLEM ? , 2006 .