The use of photographs of individually distinct animal markings to provide data on population dynamics is widespread and likely to increase with improvements in camera and camera trap technology (Sarmento et al. 2010; Sollmann et al. 2011). As the size of the resulting photograph catalogues increases, interest in automated systems for maintaining those catalogues is also increasing (Arzoumanian, Holmberg & Norman 2005; Van Tienhoven et al. 2007). Almost invariably data derived from photo-id studies are analysed as capture–mark–recapture (CMR) data, exploiting the availability of software such as MARK (White & Burnham 1999) to provide the estimates (Carroll et al. 2011; Graham et al. 2011). Data are entered as a capture history matrix with rows of ones and zeroes representing the capture of an individual (in this case on a photograph) or the failure to capture it during successive sampling occasions; in a multi-state model, the ones may be replaced by codes representing the capture of individuals in different states, for example, at different locations (e.g. Nichols & Kendall 1995). However, whereas the history matrix provides sufficient statistics for parameter estimation from CMR data, the same does not hold, in general, for photo-id data where false rejections by the pre-screening software and individuals identified from opposite sides may generate multiple histories from a single individual.
It may be possible to avoid multiple encounter histories by restricting the photographs to those of sufficient quality to eliminate the risk of missing matches and that either all show the same side or are in pairs showing both sides, but only at the cost of reducing the amount of data available (e.g. Arzoumanian, Holmberg & Norman 2005). Furthermore, establishing the criteria by which to select photographs on the basis of quality is complex and any correlation between photograph quality and pattern distinctiveness may lead to selection in favour of a subset of individuals and bias in estimation of population size (Arnbom 1987; Friday et al. 2000, 2008).
Stevick et al. (2001) developed a correction for the Petersen two-sample abundance estimator to account for a measured false rejection rate (FRR), and da Silva (2009) extended the correction for closed populations sampled on more than two occasions by using Bayesian models in an iterative process to suggest likely values for the actual but unknown numbers of different individuals, sample sizes and resightings. Link et al. (2010) also relate observed encounter history frequencies to the underlying ‘latent’ histories in a closed population model, but the relationship is based on the assumption that all false-negative errors lead to single-encounter ‘ghost’ histories (Yoshizaki 2007), which does not hold in general for photo-id.
Morrison et al. (2011) estimate survival in a Cormack–Jolly–Seber model by censoring initial photographs to avoid multiple histories resulting from missed matches. However, their analysis is again based on the assumption that all missed matches are due to low-quality images that cannot be matched to any other image.
In this study, we investigate an alternative solution to dealing with multiple encounter histories resulting from both missed matches and individuals identified from different sides. We use test sets of images of known animals to measure the risk that a randomly selected pair of images showing the same side of the same individual will be falsely rejected by the automated pre-screening process. We then use that ‘pairwise FRR’ in a Jolly–Seber open population model to calculate the expected frequency of each encounter history recognising that, as a result of false rejections, an individual can give rise to more than one history. Furthermore, if the history matrix, although not multi-state in the usual sense, specifies the state of each encounter as being from the left, right or both sides, individuals identified only from different sides can be included by calculating the expected frequency of each aspect-specific history. Corkrey et al. (2008) used the same approach to construct ‘bilateral histories’ from photographs of bottlenose dolphins in north-east Scotland; however, they were able to neglect any risk of false rejection because automated pre-screening was not required with the relatively small population of marked dolphins and ‘only high-quality pictures were used to minimise errors in misidentification’.
We tested our method using photographs of female grey seals taken at a breeding colony on the island of North Rona from 2004 to 2008. They were pre-screened using the ExtractCompare (EC) program originally developed for photographs of grey seals swimming off a haulout (Hiby & Lovell 1990) and used since to maintain photo-id catalogues for a number of other species (e.g. Kelly 2001; Hastings, Hiby & Small 2008; Hiby et al. 2009). Previous studies of this colony have provided a large sample of photographs already known by visual comparison and in a few cases by brands or flipper tags to show the same animals. We used pairs of photographs taken on different dates to measure the FRR of the EC programme on the type of photographs available from the breeding site. Those studies also provided data on longitudinal behavioural ecology and population dynamics at this site (Smout, King & Pomeroy 2011), which has been monitored annually using aerial survey, thus providing trends in abundance as well as previous estimates of population parameters to compare with the results of our analysis.