TY - JOUR
AU - Puig, P.
AB - ABSTRACT With the objective of verifying the presumed identity of sheep in a traceability study based on visual ear tags and electronic boluses, retinal image recognition was used as an auditing biomarker on 152 lambs of 2 dairy breeds (Manchega, n = 82; Lacaune, n = 70). Lambs were identified with temporary ear tags (birth to weaning), and with official ear tags and electronic mini-boluses (weaning to yearling). At 3 mo of age, 58 lambs were recruited for flock replacement, and the rest were transported to a slaughterhouse. Retinal images (RI) and capturing times (CT) were recorded from the left and right eyes of each lamb in duplicate and by the same operator using an OptiReader device (Optibrand, Fort Collins, CO) at 3, 6, and 12 mo of age in 152, 58, and 58 lambs, respectively. The 3-mo RI were used as reference images and to assess operator training and accuracy of the technique. Intra- and inter-age comparisons were made to obtain the matching score (MS; 0 to 100) of pairs of RI from the same eye, using Optibrand's software. Operator skill improved with training sessions, but MS reached a plateau after the sixth session (264 images; MS = 93.2 ± 1.5). Values of CT also decreased in trained compared with untrained operators (63 ± 5 vs. 144 ± 15 s, respectively; P < 0.001). Training data were eliminated from further analysis. Matching exclusion criteria were estimated from trained operator images at random (804 images) using a nonparametric receiver operating characteristic curve analysis for MS = 70. No breed, eye, or age effects were detected in the MS intra-age comparisons at 3-, 6-, and 12-mo periods, which averaged 96.3 ± 0.3. Capturing time was longer in Lacaune than in Manchega lambs (P < 0.01) and decreased by age (34 ± 4 and 21 ± 2 s, for 6- and 12-mo periods, respectively; P < 0.001). Regarding lamb traceability, 2.8% temporary ear tags were lost from birth to weaning (traceability, 97.2%), but no official ear tag or mini-bolus losses were reported from weaning to yearling (traceability, 100%). Inter-age MS comparison, used as the biomarker for traceability auditing, did not vary by age or breed, on average being 92.6 ± 0.5. Using the 3-mo RI as reference, all 6- and 12-mo RI showed MS >70, which supported 100% lamb traceability. In conclusion, retinal imaging was an accurate technique for auditing the identity of living lambs from weaning to yearling. INTRODUCTION Meat traceability is a complex (i.e., from birth to retail sales) and incompletely solved process (Arana et al., 2002; Caja et al., 2002) requiring the use of identification (ID) devices and of auditing systems (McKean, 2001; Caja et al., 2002). Current livestock ID range from visual to electronic devices, but biometrics (e.g., genetic fingerprinting and retinal imaging) have been proposed to overcome the main limitations of ID devices and for auditing (Caja et al., 2004; Felmer et al., 2006; Barry et al., 2008). The use of retinal images (RI) is based on the uniqueness and invariability of the retinal vascular pattern of each eye. Completion of retina at birth varies according to species precocity, individuals, and diseases (Flower et al., 1985; Hellström et al., 2002). First results point out that sheep clones can be differentiated by RI (Whittier et al., 2003). Barry et al. (2008) reported slight changes in the curvature of retinal vessels of Irish crossbred lambs from 1 to 22 wk of age, which did not affect the matching score (MS) of the RI comparisons between ages. Nevertheless, MS is not a continuous variable, and previous data transformation is required before statistical analysis (Puig et al., 2009). This data transformation was not done in the study by Barry et al. (2008), which made some of their results uncertain. Moreover, there is no information on RI analyses for longer periods, as well as left and right eye relationship and breed effect. The objective of this study was to verify the presumed identity of sheep traced from weaning to yearling by ear tags and electronic boluses, using RI as the auditing biomarker. The adequate discrimination threshold for the effective matching of pairs of RI, the required length of the operator training period, and the repeatability of the methodology between eye duplicates and ages were also investigated in 2 breeds of sheep differing in precocity. A specific model for the treatment of MS data from RI was also developed. MATERIALS AND METHODS The experimental procedures and animal care conditions were approved by the Ethical Committee on Animal and Human Experimentation (reference CEEAH 656/07) of the Universitat Autònoma de Barcelona (Bellaterra, Barcelona, Spain). Animals, Rearing, and Management Manchega and Lacaune weaned lambs (approximately 1 mo of age, 11.5 ± 0.2 kg of BW) born at the Experimental Farm of the S1GCE (Servei de Granges i Camps Experimentals, Universitat Autònoma de Barcelona, Bellaterra, Spain) were used. Manchega and Lacaune are dairy sheep breeds from Spain and France, respectively, differing in precocity, growth speed, and milk yield, but of similar adult frame and BW (Marie et al., 2002; Flores et al., 2008). Lambs were intensively fed with a commercial growth-fattening concentrate (NEg, 1.90 Mcal/kg; CP, 17.4%; as fed), barley straw, and water ad libitum. A total of 152 lambs (Manchega, n = 82; Lacaune, n = 70) reached the slaughter BW as Spanish Recental lambs (approximately 3 mo of age, 23 to 25 kg of BW) and were slaughtered (n = 94; Manchega, n = 54; Lacaune, n = 40) or chosen for replacement of the breeding flock (n = 58; Manchega, n = 28; Lacaune, n = 30). Replacement ewe lambs joined the adult flock at 28 kg of BW and grazed (6 h/d) Italian ryegrass (Lolium multiflorum Lam.) as a unique group and were complemented indoors according to their requirements. Replacement ram lambs were reared separately and fed according to their requirements. Animal ID All lambs were identified with official temporary (lambs traced as a group intended for slaughter) and permanent (lamb individually traced and for replacement) ID devices, according to European Union regulations (EC 21/2004; amended by EC 933/2008) and current Spanish legislation (Real Decreto 947/2005; amended by 1486/2009). The temporary ear tags were inserted at birth in the middle of the left ear of the lambs and consisted of 2 rectangular flags made of polyurethane with a tamper-proof (pin and cup) male-female closing system (2.8 g, 40 × 14.5 mm; Allflex-Azasa, Madrid, Spain). Lambs were also identified at weaning (1 mo of age) with permanent official ear tags attached to the right ear and with electronic mini-boluses recorded with the same individual code. The permanent ear tags had triangular flags made of polyurethane, which were laser recorded, and a tamper-proof (pin and cup) male-female closing system (5.2 g; 38 × 39 mm; Allflex-Azasa, Madrid, Spain). The electronic mini-boluses (19 g, 56.2 × 11.9 mm; Allflex-Azasa) contained a standardized 32 × 3.8-mm half-duplex transponder recorded with a 16-digit code according to the current Spanish legislation (Real Decreto 947/2005; amended by 1486/2009) and with ISO 11784 and 11785 standards on animal electronic ID (ISO, 1996, 2009). Boluses were administered by a trained operator using an adapted balling gun (Rumitag, Espluges de Llobregat, Barcelona, Spain) as described by Ghirardi et al. (2007). Temporary official ear tags for lambs intended for slaughter were removed at 6 mo of age, when replacement lambs joined the breeding flock, and were replaced by the management ID ear tags of the farm. RI The RI were obtained using the OptiReader device (Optibrand, Fort Collins, CO), a commercially available device designed for capturing retinal vascular images in animals. The OptiReader device included a video fundus camera able to capture RI pictures and any other digital image, and a controller with a keyboard, screen, and an embedded global positioning system (GPS) receiver. The controller is a central processing unit that works with the camera to capture and store the RI and other information. The OptiReader device links the images captured with the location and exact time and date, all set by the GPS receiver. All RI were captured in duplicate and by the same operator in morning sessions, done 3 times a week, with 3 to 17 lambs (9.2 ± 1.1 lambs on average), inside a barn and under natural daylight conditions. The operator was a novice at RI capture, but experienced in sheep management and restraint, and previously subjected to a short theoretical and practical course (3-d length) for obtaining the main quality standards required for a novice operator according to the Optibrand operator benchmarks (i.e., collecting only high quality RI with a MS >85 between duplicates and demonstrated thorough understanding of how the OptiReader device worked). Nevertheless, the average proficiency criterion (time for acquiring RI <1 min per eye) was not fulfilled, which was used to evaluate the skill progression of the operator without compromising the RI quality. Lambs were restrained in a self-closing head locker and the operator immobilized the animal head with one hand, while handling the camera with the other. After setting the location, time, and data via the GPS receiver, the operator typed the permanent ear tag ID number into the keyboard of the OptiReader and took a first picture of the ear tag located on the side of the corresponding eye. Left eyes were processed before right eyes. The device automatically captured the best quality RI (e.g., minimum glare and proper focus) according to previously configured parameters on the controller (i.e., animal species, sheep; targeting selectivity, 0). After targeting activation, the camera was directed at the eye of the lamb, positioned at approximately 1 cm from the eye and an angle of 45°, pointing toward the base of the opposite ear of the animal, according to recommendations of the manufacturer (Optibrand). The camera had a light source that illuminated the fundus of the eye (ocular fundus) and allowed the visualization of the retinal vascular pattern on the screen of the controller (Figure 1). An RI was considered acceptable when it showed a contrasted vascular pattern and vertical and horizontal alignment in relation to the screen guidelines, and when there were no black edges, glare, obstructions, or blurriness, as reported in the OptiReader device user guide (Optibrand). Figure 1. View largeDownload slide Left: Capturing a retinal image in a yearling sheep, restrained in a head locker and under natural daylight conditions inside a barn, by using an OptiReader device (CM, camera; ICC, image capturing controller). Right: Retinal images of left and right eyes of 3-mo-of-age fattening lamb. Figure 1. View largeDownload slide Left: Capturing a retinal image in a yearling sheep, restrained in a head locker and under natural daylight conditions inside a barn, by using an OptiReader device (CM, camera; ICC, image capturing controller). Right: Retinal images of left and right eyes of 3-mo-of-age fattening lamb. In addition to GPS coordinates, date, time (to the nearest 0.1 s), and ear tag picture, the capturing time (CT) was also recorded by the device and used to evaluate operator proficiency. The CT was measured to the nearest 10−3 s elapsed between targeting activation and capture of an RI of acceptable quality. This time included the several attempts done until an acceptable RI was obtained. Recorded RI and associated data were stored on a 64-Mb compact flash memory card (SanDisk, Shoot & Store Card, Milpitas, CA) in the form of encrypted binary large object (so-called blob) files, and transferred to a central database online supported by using the Data Management software v. 4.1.3 of Optibrand. Uploaded RI were viewed as JPEG files and used for subsequent matching trials of pairs of images. The Optibrand software matching process used an implemented matching algorithm based on the degree of similarity, size, position, and branch angles of retinal vessels designed to perform about 20 pairs of matches per minute (Allen et al., 2008). The Optibrand Data Management software overlaps the images to compute an MS ranging between 0 and 100. The greater the score, the more likely the images in the pair are from the same eye. To determine when the operator was proficient enough to obtain RI of quality, thereby being considered a trained operator according the Optibrand benchmark criteria (novice operator), the first RI taken from approximately one-half of the lambs at 3 mo of age (33 lambs from each breed, 264 images in total) was used. Training data were analyzed separately from the rest of RI taken during the experiment. A minimum MS threshold was determined as matching decision criteria. With this aim, 2 series of 1-to-1 comparisons of pairs of RI (excluding the data used for studying the training period) were carried out for determining the sensitivity (true positives) and the specificity (true negatives) of the technique. A set of true match comparisons was selected (404 pairs of RI) from different duplicates of the same eye taken at 3, 6, and 12 mo of age. Further, a set of false pairs was selected (400 pairs of RI) from images of eyes of different lambs chosen at random. A total of 608 RI were collected from 152 lambs of 3 mo of age (2 images from both eyes) that were used as reference for further analysis. The replacement lambs were reimaged at 6 and 12 mo of age (464 images). Intra- and inter-age comparisons of pairs of RI for each eye were made, thereby obtaining 1 intra-age (duplicates) and 4 inter-age (3 vs. 6 mo, and 3 vs. 12 mo, taking into account the duplicates) MS for each eye. Intra-age comparisons of pairs of RI were used to set up the working methodology and to evaluate operator training, whereas inter-age comparisons were used to audit the lamb identity assessed by ear tags and electronic mini-boluses for lamb traceability. Statistical Analyses Matching score threshold was determined by means of a nonparametric receiver operating characteristic (ROC) curve analysis using the ROC procedure (SPSS Inc., Chicago, IL). The ROC curve is a graphical method extensively used for assessing the characteristics of a diagnostic test where the true positive rate (sensitivity) is plotted against the false positive rate (1-specificity) for different cut-off points. Each point on the ROC plot represents a sensitivity/specificity pair for a decision threshold. Before the statistical analysis, the MS data were expressed as a proportion variable ranging between 0 and 1 and were analyzed to identify their distribution profile. An excess of values equal to 1 (MS = 100) was observed in the MS data, indicating that the distribution did not correspond to the profile of a continuous distribution such as the beta or the logistic-normal distributions. Consequently, for analyzing this semicontinuous data, the 1-inflated bivariate beta distribution was used, building a specific model for the treatment of MS data from RI. Parameter estimation was done by maximizing the corresponding log-likelihood function using a program made in the free R computing software (http://www.r-project.org; see Appendix). Similar zero-inflated beta models have been recently used for analyzing proportions in finances (Cook et al., 2008). To compare the inter-age images used for identity verification and for auditing the traceability, we also considered random effects models. The models have the special feature of the excess of 1s (1-inflated beta model terms). Logarithmic transformations (log10) for CT data were done. Least squares means of CT were obtained with the MIXED procedure (SAS Inst. Inc., Cary, NC) according to a split-plot model (whole plot = breed; subplot = eye) with repeated measures (age) and including first-order interactions and the error term. The single eye was considered the experimental unit. Interactions that were not significant (P > 0.10) were deleted from the model. The statistical significance and tendency were declared at P < 0.05 and P < 0.10, respectively. RESULTS AND DISCUSSION Determining the MS Threshold The distributions of MS frequencies in the data set used to determine the sensitivity in true positives and the specificity in true negatives of the technique are shown in Figure 2. No images obtained during the training period (sessions 1 to 6, as later indicated) were used to avoid the effect of operator training as recommended by Allen et al. (2008) and Gonzales-Barron et al. (2008). Figure 2. View largeDownload slide Distribution of matching score frequencies for true negative (correct nonmatching, ●) and true positive (correct matching, ○) in lambs after the training period. Matching score was computed by overlapping pairs of images using the Optibrand Data Management software v. 4.1.3 (Optibrand, Fort Collins, CO). The operator was considered as trained when only retinal images with matching score greater than 85 were collected and when the average time to acquire images was less than 1 min per eye. Figure 2. View largeDownload slide Distribution of matching score frequencies for true negative (correct nonmatching, ●) and true positive (correct matching, ○) in lambs after the training period. Matching score was computed by overlapping pairs of images using the Optibrand Data Management software v. 4.1.3 (Optibrand, Fort Collins, CO). The operator was considered as trained when only retinal images with matching score greater than 85 were collected and when the average time to acquire images was less than 1 min per eye. True negatives showed a symmetric distribution and peaked at MS = 55, whereas true positives showed a left-skewed distribution reaching the greatest frequency at MS = 100, indicating that both distributions were distinct and slightly overlapped. Allen et al. (2008) indicated that the suitable threshold varies according to the nature of the forensic application chosen. In our case, the use of RI as the auditing technology for verifying lamb identity implies to discriminate between true and false matches at a stringent level. From the resulting nonparametric ROC curve obtained in our results (Figure 3), the cut-off or threshold MS value estimated to minimize the false matching error and the false nonmatching error to accept or reject a claimed identity, was MS = 70. Estimated false matching error rate for this threshold was 0.5%, whereas the estimated false nonmatching error rate was 1.1%. As a result, the specificity and sensitivity values obtained were 0.995 and 0.989, respectively. This 99.5% accuracy for verifying lamb identity was considered adequate for minimizing the false positives in sheep traceability in practice, being the value greater than obtained in previous implementation studies in which molecular markers were used for auditing lamb traceability (Caja et al., 2007). Figure 3. View largeDownload slide Receiver operating characteristic curve obtained for matching score of retinal images in lambs after the training period of the operator. Matching score was computed by overlapping pairs of images using the Optibrand Data Management software v. 4.1.3 (Optibrand, Fort Collins, CO). The operator was considered as trained when only retinal images with matching score greater than 85 were collected and when the average time to acquire images was less than 1 min per eye. Figure 3. View largeDownload slide Receiver operating characteristic curve obtained for matching score of retinal images in lambs after the training period of the operator. Matching score was computed by overlapping pairs of images using the Optibrand Data Management software v. 4.1.3 (Optibrand, Fort Collins, CO). The operator was considered as trained when only retinal images with matching score greater than 85 were collected and when the average time to acquire images was less than 1 min per eye. Our obtained value of MS threshold agreed with that reported by Gonzales-Barron et al. (2008; MS = 70) in adult sheep, despite the difference in age with our lambs, although their specificity and sensitivity values were 0.992 and 0.998, respectively. Allen et al. (2008) graphically chose an inspection threshold of MS = 75 in cattle of different ages, but no specificity and sensitivity data were calculated. MS Data Treatment A careful examination of the data set showed an inflated distribution of values at MS = 100. This fact was a consequence of the matching algorithm used by the Optibrand Data Management Software, which was designed for a high throughput (approximately 20 pair matches/min). Although the exact algorithm used in this software is unknown, the most plausible explanation was that each image was partially analyzed at the beginning of the process, and if the agreement was satisfactory, the algorithm finalized the calculations and attributed a MS = 100. Otherwise, the algorithm would continue analyzing the RI and give an estimated and specific MS value. Consequently, this algorithm provided inflated MS values of 100, with a nonequal probability (nonzero probability), and we decided to use the 1-inflated bivariate beta distribution and to build a specific model for the treatment of MS data from RI as proposed previously by Puig et al. (2009) and detailed in the Appendix. Training Period Using MS and CT values as decision criteria, the training period was considered as completed when the MS reached a plateau (P > 0.10; Figure 4). Simultaneously the operator achieved the image collection proficiency stated in the Optibrands benchmarks of 1 min per eye, on average. This occurred after the sixth training session (MS = 93.2 ± 1.5; CT = 91.3 ± 15.8 s) in which the RI of both eyes of a total of 66 lambs (33 lambs of each breed) were collected in duplicate (264 images in total). Figure 4. View largeDownload slide Changes in matching score (●) and capturing time (∆) values of retinal images in lambs according to the experience accumulated by the operator across the working sessions carried out. At each working session, done 3 times a week, the operator collected the retinal images of both eyes from 9.2 ± 1.1 lambs, on average. Matching score was computed by overlapping pairs of images using the Optibrand Data Management software v. 4.1.3 (Optibrand, Fort Collins, CO). The dashed line represents the session at which the operator was considered as trained. a–hMean values in the same series with different letters differ (P < 0.05). Figure 4. View largeDownload slide Changes in matching score (●) and capturing time (∆) values of retinal images in lambs according to the experience accumulated by the operator across the working sessions carried out. At each working session, done 3 times a week, the operator collected the retinal images of both eyes from 9.2 ± 1.1 lambs, on average. Matching score was computed by overlapping pairs of images using the Optibrand Data Management software v. 4.1.3 (Optibrand, Fort Collins, CO). The dashed line represents the session at which the operator was considered as trained. a–hMean values in the same series with different letters differ (P < 0.05). Operator training has been shown to be a key factor for collecting quality RI using the OptiReader device (Whittier et al., 2003; Allen et al., 2008), although no experimental data have been reported to show differences between untrained and trained operators. Allen et al. (2008) and Gonzales-Barron et al. (2008) proposed a 2- to 3-wk period of training, which agreed with the results of our study if 3 half-day sessions per week were carried out. Values of MS during the considered training period (sessions 1 to 6) ranged between 90.1 and 93.4 (i.e., 3-mo-old Lacaune lambs and untrained operator in Table 1), being on average less than the rest of the MS data sets used (Table 1; P < 0.01). No eye side or breed effects were detected during the training period (P > 0.10). Table 1. Intra-age1 comparisons of matching scores2 of retinal image according to operator skill, breed (Manchega, Lacaune), and eye side (left, right) at different ages in lambs (values are means ± SE) Operator skill  Age, mo  Manchega  Lacaune  Overall  Left  Right  Left  Right  Untrained  3  92.5 ± 1.9  92.5 ± 2.2  90.1 ± 1.8  93.4 ± 1.7  92.1 ± 1.1a      (33)3  (33)  (33)  (33)  (132)  Trained4  3  97.2 ± 0.7  97.9 ± 0.7  94.4 ± 1.3  95.3 ± 1.2  96.4 ± 0.5b      (49)  (49)  (37)  (37)  (172)    6  98.0 ± 0.5  94.4 ± 1.5  98.2 ± 0.6  94.1 ± 1.5  96.2 ± 0.6b      (28)  (28)  (30)  (30)  (116)    12  96.9 ± 1.1  95.8 ± 1.8  96.1 ± 1.0  96.5 ± 1.0  96.3 ± 0.6b      (28)  (28)  (30)  (30)  (116)    Overall  97.3 ± 0.4  96.4 ± 0.7  96.1 ± 0.6  95.3 ± 0.7  96.3 ± 0.3b      (105)  (105)  (97)  (97)  (404)  Operator skill  Age, mo  Manchega  Lacaune  Overall  Left  Right  Left  Right  Untrained  3  92.5 ± 1.9  92.5 ± 2.2  90.1 ± 1.8  93.4 ± 1.7  92.1 ± 1.1a      (33)3  (33)  (33)  (33)  (132)  Trained4  3  97.2 ± 0.7  97.9 ± 0.7  94.4 ± 1.3  95.3 ± 1.2  96.4 ± 0.5b      (49)  (49)  (37)  (37)  (172)    6  98.0 ± 0.5  94.4 ± 1.5  98.2 ± 0.6  94.1 ± 1.5  96.2 ± 0.6b      (28)  (28)  (30)  (30)  (116)    12  96.9 ± 1.1  95.8 ± 1.8  96.1 ± 1.0  96.5 ± 1.0  96.3 ± 0.6b      (28)  (28)  (30)  (30)  (116)    Overall  97.3 ± 0.4  96.4 ± 0.7  96.1 ± 0.6  95.3 ± 0.7  96.3 ± 0.3b      (105)  (105)  (97)  (97)  (404)  a,bWithin a column, values with different superscripts differ (P < 0.01). No differences between ages for the trained operator were observed (P > 0.10), and no effects of eye side, breed, and their interactions were detected in all cases (P > 0.10). 1Comparisons between image duplicates of the same lamb and eye taken at the same age. 2Computed overlapping score of a pair of images (ranging from 0 to 100), obtained by the Optibrand Data Management software v. 4.1.3 (Optibrand, Fort Collins, CO). 3Values in parentheses are number of eyes studied. 4Training period images excluded. The operator was considered trained when only retinal images with matching score greater than 85 were collected and when the average time to acquire images was less than 1 min per eye. View Large Table 1. Intra-age1 comparisons of matching scores2 of retinal image according to operator skill, breed (Manchega, Lacaune), and eye side (left, right) at different ages in lambs (values are means ± SE) Operator skill  Age, mo  Manchega  Lacaune  Overall  Left  Right  Left  Right  Untrained  3  92.5 ± 1.9  92.5 ± 2.2  90.1 ± 1.8  93.4 ± 1.7  92.1 ± 1.1a      (33)3  (33)  (33)  (33)  (132)  Trained4  3  97.2 ± 0.7  97.9 ± 0.7  94.4 ± 1.3  95.3 ± 1.2  96.4 ± 0.5b      (49)  (49)  (37)  (37)  (172)    6  98.0 ± 0.5  94.4 ± 1.5  98.2 ± 0.6  94.1 ± 1.5  96.2 ± 0.6b      (28)  (28)  (30)  (30)  (116)    12  96.9 ± 1.1  95.8 ± 1.8  96.1 ± 1.0  96.5 ± 1.0  96.3 ± 0.6b      (28)  (28)  (30)  (30)  (116)    Overall  97.3 ± 0.4  96.4 ± 0.7  96.1 ± 0.6  95.3 ± 0.7  96.3 ± 0.3b      (105)  (105)  (97)  (97)  (404)  Operator skill  Age, mo  Manchega  Lacaune  Overall  Left  Right  Left  Right  Untrained  3  92.5 ± 1.9  92.5 ± 2.2  90.1 ± 1.8  93.4 ± 1.7  92.1 ± 1.1a      (33)3  (33)  (33)  (33)  (132)  Trained4  3  97.2 ± 0.7  97.9 ± 0.7  94.4 ± 1.3  95.3 ± 1.2  96.4 ± 0.5b      (49)  (49)  (37)  (37)  (172)    6  98.0 ± 0.5  94.4 ± 1.5  98.2 ± 0.6  94.1 ± 1.5  96.2 ± 0.6b      (28)  (28)  (30)  (30)  (116)    12  96.9 ± 1.1  95.8 ± 1.8  96.1 ± 1.0  96.5 ± 1.0  96.3 ± 0.6b      (28)  (28)  (30)  (30)  (116)    Overall  97.3 ± 0.4  96.4 ± 0.7  96.1 ± 0.6  95.3 ± 0.7  96.3 ± 0.3b      (105)  (105)  (97)  (97)  (404)  a,bWithin a column, values with different superscripts differ (P < 0.01). No differences between ages for the trained operator were observed (P > 0.10), and no effects of eye side, breed, and their interactions were detected in all cases (P > 0.10). 1Comparisons between image duplicates of the same lamb and eye taken at the same age. 2Computed overlapping score of a pair of images (ranging from 0 to 100), obtained by the Optibrand Data Management software v. 4.1.3 (Optibrand, Fort Collins, CO). 3Values in parentheses are number of eyes studied. 4Training period images excluded. The operator was considered trained when only retinal images with matching score greater than 85 were collected and when the average time to acquire images was less than 1 min per eye. View Large A progression of operator skill was observed from 1 to 6 sessions with increased proficiency for collecting RI of acceptable quality and a CT reduction. Capturing time decreased logarithmically (y = 61.9 ln x + 200; R2 = 0.83; P < 0.05) from 210 ± 50 s, at session 1, to 53 ± 8 s, at session 7 (P < 0.001; Figure 4), but no differences were reported thereafter (P > 0.10). On average, 2.6 ± 0.2 images were rejected until a RI of acceptable quality was obtained, during the training period. In contrast, CT during the training period ranged between 75 and 181 s and its overall mean was longer than the means from other periods in the trained operator (Figure 4; P < 0.001). In this case, an eye side effect was detected on CT, the time required being less for the right eye than for the left eye (P = 0.004), which may be a consequence of processing the left eye first according to our methodology; the lamb being more stressed just after capturing and restraining. A tendency was also observed by breed during the training period, the Manchega lambs showing shorter CT than the Lacaune lambs (122 ± 15 vs. 164 ± 27 s, respectively; P = 0.054), which may be consequence of the greater age of the Manchega lambs to reach the slaughter age. Of the 132 pairs of RI compared in the training period, 127 pairs (96.2%) were over the previously determined MS threshold (MS ≥70) and were considered as being from the same lamb. When eyes were analyzed separately, no differences in percentage of RI over the threshold were detected between the left and right eye RI (97.0 vs. 95.5%, respectively; Table 2; P = 0.78), allowing the left or the right eye to be used indistinctly for verifying lamb identity. Table 2. Percentage of retinal images showing matching scores1 (MS) greater than the threshold of acceptance (MS ≥ 70) according to operator skill, breed (Manchega, Lacaune), and eye side (left, right) at different ages in lambs Image comparison  Age, mo  Operator skill  Manchega  Lacaune  Overall  Left  Right  Left  Right  Left  Right  Intra-age2  3  Untrained  97.0  93.9  97.0  97.0  97.0  95.5        (33)3  (33)  (33)  (33)  (66)  (66)    3  Trained4  100  100  97.3  97.3  98.8  98.8        (49)  (49)  (37)  (37)  (86)  (86)    6  Trained4  100  96.4  100  96.7  100  96.6        (28)  (28)  (30)  (30)  (58)  (58)    12  Trained4  100  96.4  100  100  100  98.3        (28)  (28)  (30)  (30)  (58)  (58)  Inter-age5  3 vs. 66  Trained  100  100  100  100  100  100        (27)  (26)  (30)  (25)  (57)  (51)    3 vs. 127  Trained  100  100  100  100  100  100        (27)  (26)  (30)  (26)  (57)  (52)  Image comparison  Age, mo  Operator skill  Manchega  Lacaune  Overall  Left  Right  Left  Right  Left  Right  Intra-age2  3  Untrained  97.0  93.9  97.0  97.0  97.0  95.5        (33)3  (33)  (33)  (33)  (66)  (66)    3  Trained4  100  100  97.3  97.3  98.8  98.8        (49)  (49)  (37)  (37)  (86)  (86)    6  Trained4  100  96.4  100  96.7  100  96.6        (28)  (28)  (30)  (30)  (58)  (58)    12  Trained4  100  96.4  100  100  100  98.3        (28)  (28)  (30)  (30)  (58)  (58)  Inter-age5  3 vs. 66  Trained  100  100  100  100  100  100        (27)  (26)  (30)  (25)  (57)  (51)    3 vs. 127  Trained  100  100  100  100  100  100        (27)  (26)  (30)  (26)  (57)  (52)  1Computed overlapping score of a pair of images (ranging from 0 to 100), obtained by the Optibrand Data Management software v. 4.1.3 (Optibrand, Fort Collins, CO). 2Comparisons between image duplicates of the same lamb and eye taken at the same age. 3Values in parentheses are number of eyes studied. 4Training period images excluded. The operator was considered trained when only retinal images with MS > 85 were collected and when the average time to acquire images was less than 1 min per eye. 5Comparisons between images of the same eye and lamb, taken at different ages. 6A total of 8 images were incorrectly declared unmatched by the software (false negative) and were excluded. 7A total of 7 images were incorrectly declared unmatched by the software (false negative) and were excluded. View Large Table 2. Percentage of retinal images showing matching scores1 (MS) greater than the threshold of acceptance (MS ≥ 70) according to operator skill, breed (Manchega, Lacaune), and eye side (left, right) at different ages in lambs Image comparison  Age, mo  Operator skill  Manchega  Lacaune  Overall  Left  Right  Left  Right  Left  Right  Intra-age2  3  Untrained  97.0  93.9  97.0  97.0  97.0  95.5        (33)3  (33)  (33)  (33)  (66)  (66)    3  Trained4  100  100  97.3  97.3  98.8  98.8        (49)  (49)  (37)  (37)  (86)  (86)    6  Trained4  100  96.4  100  96.7  100  96.6        (28)  (28)  (30)  (30)  (58)  (58)    12  Trained4  100  96.4  100  100  100  98.3        (28)  (28)  (30)  (30)  (58)  (58)  Inter-age5  3 vs. 66  Trained  100  100  100  100  100  100        (27)  (26)  (30)  (25)  (57)  (51)    3 vs. 127  Trained  100  100  100  100  100  100        (27)  (26)  (30)  (26)  (57)  (52)  Image comparison  Age, mo  Operator skill  Manchega  Lacaune  Overall  Left  Right  Left  Right  Left  Right  Intra-age2  3  Untrained  97.0  93.9  97.0  97.0  97.0  95.5        (33)3  (33)  (33)  (33)  (66)  (66)    3  Trained4  100  100  97.3  97.3  98.8  98.8        (49)  (49)  (37)  (37)  (86)  (86)    6  Trained4  100  96.4  100  96.7  100  96.6        (28)  (28)  (30)  (30)  (58)  (58)    12  Trained4  100  96.4  100  100  100  98.3        (28)  (28)  (30)  (30)  (58)  (58)  Inter-age5  3 vs. 66  Trained  100  100  100  100  100  100        (27)  (26)  (30)  (25)  (57)  (51)    3 vs. 127  Trained  100  100  100  100  100  100        (27)  (26)  (30)  (26)  (57)  (52)  1Computed overlapping score of a pair of images (ranging from 0 to 100), obtained by the Optibrand Data Management software v. 4.1.3 (Optibrand, Fort Collins, CO). 2Comparisons between image duplicates of the same lamb and eye taken at the same age. 3Values in parentheses are number of eyes studied. 4Training period images excluded. The operator was considered trained when only retinal images with MS > 85 were collected and when the average time to acquire images was less than 1 min per eye. 5Comparisons between images of the same eye and lamb, taken at different ages. 6A total of 8 images were incorrectly declared unmatched by the software (false negative) and were excluded. 7A total of 7 images were incorrectly declared unmatched by the software (false negative) and were excluded. View Large Intra-Age Comparisons The MS values of the RI duplicates obtained from the same eye were compared intra-age using the purged data set after excluding the training period images (sessions 7 to 16; 808 images). No differences by breed (P = 0.69) or between the left and right eyes (P = 0.98) were observed for trained operator data, and consequently, their MS values were pooled and the overall mean calculated (Table 1). Correlation between values of MS for the left and right eye were extremely low (R2 = 0 to 0.06; P = 0.85). As a consequence, indistinct use of the left or the right eye may be done for verifying lamb identity. At 3 mo of age, the MS mean values for trained operator ranged between 94.4 and 97.9 across breed and eye. No breed or eye effect was detected (P > 0.10; Table 1). On average, 98.8% of RI showed a MS ≥70 (data not shown), which was a greater percentage than the results obtained in the training period. With regard to CT, values at 3 mo of age were approximately one-half of those obtained in the training period, ranging between 37 and 83 s according to breed and eye (Table 3 and Figure 4). Left and right eye CT values tended to differ (P = 0.052; Table 3), the interaction of breed × eye being significant (P = 0.035) and the Manchega lambs showing greater CT for the left than the right eye. On average, 2.5 ± 0.2 images were rejected by the trained operator at 3 mo of age. Table 3. Capturing time (s) of retinal images according to operator skill, breed (Manchega, Lacaune), and eye side (left, right) at different ages in lambs (values are means ± SE) Operator skill  Age, mo  Manchega  Lacaune  Overall  Left  Right  Left  Right  Left  Right  Untrained1  3  168 ± 24a  75 ± 12b  148 ± 22a  181 ± 37a  158 ± 16e,x  128 ± 20f,w      (33)2  (33)  (33)  (33)  (66)  (66)  Trained3  3  66 ± 10a  37 ± 6b  83 ± 14a  75 ± 12a  73 ± 8y  53 ± 6x      (49)  (49)  (37)  (37)  (86)  (86)    6  27 ± 3  30 ± 4  34 ± 6  42 ± 9  31 ± 3z  36 ± 5y      (28)  (28)  (30)  (30)  (58)  (58)    12  18 ± 2ab  14 ± 2b  30 ± 6a  21 ± 4ab  24 ± 3e,z  18 ± 2f,z      (28)  (28)  (30)  (30)  (58)  (58)  Operator skill  Age, mo  Manchega  Lacaune  Overall  Left  Right  Left  Right  Left  Right  Untrained1  3  168 ± 24a  75 ± 12b  148 ± 22a  181 ± 37a  158 ± 16e,x  128 ± 20f,w      (33)2  (33)  (33)  (33)  (66)  (66)  Trained3  3  66 ± 10a  37 ± 6b  83 ± 14a  75 ± 12a  73 ± 8y  53 ± 6x      (49)  (49)  (37)  (37)  (86)  (86)    6  27 ± 3  30 ± 4  34 ± 6  42 ± 9  31 ± 3z  36 ± 5y      (28)  (28)  (30)  (30)  (58)  (58)    12  18 ± 2ab  14 ± 2b  30 ± 6a  21 ± 4ab  24 ± 3e,z  18 ± 2f,z      (28)  (28)  (30)  (30)  (58)  (58)  a,bWithin a row, mean values between eye and breed with different superscripts differ (P < 0.05). e,fWithin a row, overall mean values with different superscripts differ (P < 0.05). w–zWithin a column, overall mean values with different superscripts differ (P < 0.05). 1Corresponding to sessions 1 to 6 in which 264 retinal images were collected. 2Values in parentheses are number of eyes studied. 3Training period images excluded. The operator was considered trained when only retinal images with matching score greater than 85 were collected and when the average time to acquire images was less than 1 min per eye. View Large Table 3. Capturing time (s) of retinal images according to operator skill, breed (Manchega, Lacaune), and eye side (left, right) at different ages in lambs (values are means ± SE) Operator skill  Age, mo  Manchega  Lacaune  Overall  Left  Right  Left  Right  Left  Right  Untrained1  3  168 ± 24a  75 ± 12b  148 ± 22a  181 ± 37a  158 ± 16e,x  128 ± 20f,w      (33)2  (33)  (33)  (33)  (66)  (66)  Trained3  3  66 ± 10a  37 ± 6b  83 ± 14a  75 ± 12a  73 ± 8y  53 ± 6x      (49)  (49)  (37)  (37)  (86)  (86)    6  27 ± 3  30 ± 4  34 ± 6  42 ± 9  31 ± 3z  36 ± 5y      (28)  (28)  (30)  (30)  (58)  (58)    12  18 ± 2ab  14 ± 2b  30 ± 6a  21 ± 4ab  24 ± 3e,z  18 ± 2f,z      (28)  (28)  (30)  (30)  (58)  (58)  Operator skill  Age, mo  Manchega  Lacaune  Overall  Left  Right  Left  Right  Left  Right  Untrained1  3  168 ± 24a  75 ± 12b  148 ± 22a  181 ± 37a  158 ± 16e,x  128 ± 20f,w      (33)2  (33)  (33)  (33)  (66)  (66)  Trained3  3  66 ± 10a  37 ± 6b  83 ± 14a  75 ± 12a  73 ± 8y  53 ± 6x      (49)  (49)  (37)  (37)  (86)  (86)    6  27 ± 3  30 ± 4  34 ± 6  42 ± 9  31 ± 3z  36 ± 5y      (28)  (28)  (30)  (30)  (58)  (58)    12  18 ± 2ab  14 ± 2b  30 ± 6a  21 ± 4ab  24 ± 3e,z  18 ± 2f,z      (28)  (28)  (30)  (30)  (58)  (58)  a,bWithin a row, mean values between eye and breed with different superscripts differ (P < 0.05). e,fWithin a row, overall mean values with different superscripts differ (P < 0.05). w–zWithin a column, overall mean values with different superscripts differ (P < 0.05). 1Corresponding to sessions 1 to 6 in which 264 retinal images were collected. 2Values in parentheses are number of eyes studied. 3Training period images excluded. The operator was considered trained when only retinal images with matching score greater than 85 were collected and when the average time to acquire images was less than 1 min per eye. View Large Comparison of RI at 6 mo of age showed similar MS results to those obtained at 3 mo of age; on average, 98.3% had MS ≥70 (data not shown); no breed (P = 0.89) or eye effects were detected in MS at 6 mo of age (Table 1; P = 0.96). Capturing time at 6 mo of age continued decreasing with respect to 3 mo of age (P < 0.05), according to the greater operator skill, and ranged between 27 and 42 s (Table 3; P = 0.48). Although the CT was shorter in Manchega than Lacaune lambs, the difference was not significant in this case (29 ± 3 vs. 38 ± 6 s; P = 0.74). On average, 1.4 ± 0.1 images were rejected at 6 mo of age, showing an improvement of operator skill (44%) from the 3-mo-of-age period. Finally, at 12 mo of age, MS values steadied and were similar to those of 3 and 6 mo of age (Table 1; P = 0.98), although the percentage of RI with MS ≥70 reached the greatest value (99.1%). No differences by breed or eye were detected (Table 1; P > 0.10). With regard to CT at 12 mo of age, mean value was shorter than at 3 and 6 mo of age and did not exceed 30 s per eye (Table 3; P < 0.001). As previously indicated, CT in Manchega lambs were shorter than in Lacaune (16 ± 1 vs. 26 ± 4 s; P = 0.014), this difference between breeds being consistent across all periods but without an apparent reason. Moreover, CT values of the right eye were shorter (P = 0.032) than those of the left eye, agreeing with the results obtained during the training period. The overall CT obtained at 12 mo of age was markedly shorter (21 ± 2 s) than reported previously by Rusk et al. (2006; 56 s) and Gonzales-Barron et al. (2008; 50 s) in adult ewes, which agreed with the low rate of rejected images for a RI of acceptable quality achieved in our data at 12 mo of age (0.7 ± 0.1 images), and a marked improvement of the operator skill was achieved when compared with the 3-mo-of-age data (72%). Nevertheless, there is no information available on the subjective criteria used by different authors for excluding or accepting sheep RI at different ages. Lamb Traceability Lamb traceability by artificial markers was assessed by calculating the retention rate of ear tags and electronic mini-boluses. At the start of the experimental period, 2.8% of the lambs had lost the official temporary ear tags (97.2% traceability). No losses of electronic mini-boluses or permanent official ear tags, both applied at weaning, were reported throughout the experiment, showing 100% traceability from weaning to yearling under intensive fattening and grazing conditions. Traceability auditing of lamb identity obtained from electronic mini-boluses or permanent official ear tags data, was done by comparing the RI from the same lamb eye at different ages and using the 3-mo-of-age RI as reference. Table 4 shows the 2 types of inter-age comparisons done: 3 vs. 6 mo and 3 vs. 12 mo of age. Table 4. Matching scores1 of retinal images compared inter-age2 according to breed (Manchega, Lacaune) and eye side (left, right) in lambs (values are means ± SE) Age comparison  Manchega  Lacaune  Overall  Left  Right  Left  Right  Left  Right  3 vs. 6 mo3  94.6 ± 1.4  93.2 ± 1.5  94.3 ± 1.1  91.9 ± 1.4  94.5 ± 0.9  92.6 ± 1.0  (27)4  (26)  (30)  (25)  (57)  (51)  3 vs. 12 mo5  93.7 ± 1.3  93.7 ± 1.2  91.5 ± 1.3  92.5 ± 1.2  92.5 ± 0.9  93.1 ± 0.8  (27)  (26)  (30)  (26)  (57)  (52)  Age comparison  Manchega  Lacaune  Overall  Left  Right  Left  Right  Left  Right  3 vs. 6 mo3  94.6 ± 1.4  93.2 ± 1.5  94.3 ± 1.1  91.9 ± 1.4  94.5 ± 0.9  92.6 ± 1.0  (27)4  (26)  (30)  (25)  (57)  (51)  3 vs. 12 mo5  93.7 ± 1.3  93.7 ± 1.2  91.5 ± 1.3  92.5 ± 1.2  92.5 ± 0.9  93.1 ± 0.8  (27)  (26)  (30)  (26)  (57)  (52)  1Computed overlapping score of a pair of images (ranging from 0 to 100), obtained by the Optibrand Data Management software v. 4.1.3 (Optibrand, Fort Collins, CO). 2Comparisons between images of the same eye and lamb obtained by the trained operator at different ages. No effects of age, eye side, breed, and their interactions were detected (P > 0.05). 3A total of 8 images were incorrectly declared unmatched by the software (false negative) and were excluded. The failure was repeatable, but visual verification led to the conclusion that they came from the same lamb. 4Values in parentheses are number of eyes studied. 5A total of 7 images were incorrectly declared unmatched by the software (false negative) and were excluded. The failure was repeatable, but visual verification led to the conclusion that they came from the same lamb. View Large Table 4. Matching scores1 of retinal images compared inter-age2 according to breed (Manchega, Lacaune) and eye side (left, right) in lambs (values are means ± SE) Age comparison  Manchega  Lacaune  Overall  Left  Right  Left  Right  Left  Right  3 vs. 6 mo3  94.6 ± 1.4  93.2 ± 1.5  94.3 ± 1.1  91.9 ± 1.4  94.5 ± 0.9  92.6 ± 1.0  (27)4  (26)  (30)  (25)  (57)  (51)  3 vs. 12 mo5  93.7 ± 1.3  93.7 ± 1.2  91.5 ± 1.3  92.5 ± 1.2  92.5 ± 0.9  93.1 ± 0.8  (27)  (26)  (30)  (26)  (57)  (52)  Age comparison  Manchega  Lacaune  Overall  Left  Right  Left  Right  Left  Right  3 vs. 6 mo3  94.6 ± 1.4  93.2 ± 1.5  94.3 ± 1.1  91.9 ± 1.4  94.5 ± 0.9  92.6 ± 1.0  (27)4  (26)  (30)  (25)  (57)  (51)  3 vs. 12 mo5  93.7 ± 1.3  93.7 ± 1.2  91.5 ± 1.3  92.5 ± 1.2  92.5 ± 0.9  93.1 ± 0.8  (27)  (26)  (30)  (26)  (57)  (52)  1Computed overlapping score of a pair of images (ranging from 0 to 100), obtained by the Optibrand Data Management software v. 4.1.3 (Optibrand, Fort Collins, CO). 2Comparisons between images of the same eye and lamb obtained by the trained operator at different ages. No effects of age, eye side, breed, and their interactions were detected (P > 0.05). 3A total of 8 images were incorrectly declared unmatched by the software (false negative) and were excluded. The failure was repeatable, but visual verification led to the conclusion that they came from the same lamb. 4Values in parentheses are number of eyes studied. 5A total of 7 images were incorrectly declared unmatched by the software (false negative) and were excluded. The failure was repeatable, but visual verification led to the conclusion that they came from the same lamb. View Large Obtained results showed that 8 (6.9%) and 7 (6.0%) RI comparisons by the Optibrand software of 3 vs. 6 mo and 3 vs. 12 mo of age, respectively, failed to match at the chosen threshold (6.9% on average). The matching failure for the same pair of images was repeatable. Nevertheless, visual verification of these images by 2 observers led to the conclusion that these images were of high quality (contrasted vascular pattern, vertical and horizontal alignments in relation to the screen guidelines, and without black edges, glare, obstructions, or blurriness) and came from the same lamb, and their MS values were eliminated from the comparison, as reported in Table 4. This fact did not occur in the intra-age comparisons. Although reasons for these false negatives were unknown, we discarded that they were due to a RI-deficient quality and we attributed it to an incorrect overlapping made by the software. Further research on this issue is warranted. Purged inter-age values of MS were, on average, less than previously reported intra-age values, ranging between 91.5 and 94.6 (Table 4). No breed, eye, or age effects were detected, being the last 93.5 ± 0.8 and 92.6 ± 0.7, on average for 3 vs. 6 mo and 3 vs. 12 mo of age, respectively (P = 0.43). Mean MS values obtained in our results were slightly less than reported by Barry et al. (2008; 96.0), in lambs from 8 to 22 wk of age, and by Gonzales-Barron et al. (2008; 95.6) in adult ewes under indoors conditions, which may be a consequence of a more restricted criteria of RI acceptance. Despite the decreased MS value obtained in our results, the RI inter-age comparison made confirmed the 100% traceability of the lambs from weaning to yearling obtained by the permanent official ear tags and the electronic mini-boluses. Conclusions The use of retinal imaging was a useful technique for verifying the presumed identity of live lambs from 3 to 12 mo of age. To accept or reject a claimed lamb identity, the use of RI collected at 3 mo of age as a reference and a cut-off MS value of 70 provided enough specificity and sensitivity to achieve 100% traceability in fattening and yearling lambs. No eye side and breed effects were detected in MS. Nevertheless, an extra percentage of approximately 7% of pairs of images considered by the software as not matching were false negative, so we recommended the visual checking of rejected pairs of images. Moreover, we detected an inflated distribution of MS values at 100, which seems to be a consequence of the matching algorithm used by the data management software of the equipment, making necessary the use of a specific model for the treatment of MS data. No mention of these facts was previously reported. Under similar conditions to those used in this study, the use of RI is an accurate technique for verifying the identity of living sheep, mainly overcoming the retention and readability limitations associated with the use of ID devices. Moreover, retinal imaging may be a real-time alternative to currently available biomarkers requiring the collection of samples for laboratory analysis with the aim of auditing the traceability of sheep. LITERATURE CITED Allen A. Golden B. Taylor M. 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Accessed Dec. 15, 2010. http://www.asas.org/western03/data/1000936.pdf. APPENDIX An excess of matching values equal to 1 (MS = 100), not corresponding to the profile of a continuous distribution between 0 and 1, were detected in the whole MS data set used. Consequently, for analyzing these semicontinuous data, the 1-inflated beta distribution and the 1-inflated bivariate beta distribution were used. The 1-inflated beta distribution, defined over xε [0; 1], has a probability density function (PDF) of the form  Here Φ is a parameter of dispersion, and I(x) is an indicator function; that is, I(1) = 1 and I(x) = 0 for x ≠ 1. The right part of this PDF, which corresponds to the classical beta distribution, was parameterized according to Ferrari and Cribari-Neto (2004). This model is equivalent to the zero-inflated beta distribution if each observation x is replaced by 1 − x. We also assumed that for x ≠ 1, the corresponding population mean μi depended linearly on the covariates by means of an appropriate link function like the logit. Then, in our data sets we assumed that  where β0 and β1 were the intercept of the slope, and Ζi was a dichotomic variable indicating the lamb breed (Manchega, 1; Lacaune, 2). The 1-inflation parameter pi was also modeled in terms of μi to reflect the empirical fact that greater values of μi are accompanied by a greater proportion of 1s. Thus, we assumed that pi= μiγ, where γ is a parameter to be estimated from the data. For studying the inter-eye images, bivariate models were also considered. These models have the special feature of the 1-inflated terms. For instance, let (x, y) be the 2-dimensional random vector that represents the MS observations from the left and right eyes of the same animal. The 1-inflation phenomenon was more complicated for these bivariate patterns because the 1s can appear in only one component or in both. The PDF of the 1-inflated bivariate beta distribution that we have considered can be written as follows:  Here p11, px1, and p1y indicated the proportion of observations of the form (1, 1), (x, 1), and (1, y) respectively. Moreover, f(x; μx, c) and f(y; μy, c) were the PDF of the classical beta distribution with population means μx and μy, and the same dispersion parameter c. The bivariate PDF f(x, y; μx, μy, c) was just the PDF of the bivariate beta distribution of Olkin and Liu (2003). It had the following expression:  More details can be found in Puig et al. (2009). For parameter estimation, we have maximized the corresponding log-likelihood function and the asymptotic SE were calculated from the Hessian of the log-likelihood at the maximum. With this aim, a program made in R was used and is available from the authors upon request. Footnotes 1 This work was done in the frame of the Plan Nacional I+D+i (research projects AGL-2007-64541 and MTM-2009-10893), funded by the Spanish Ministry of Science and Innovation (MCINN, Madrid, Spain) and by a research scholarship to María Alejandra Rojas-Olivares from the Agencia Española de Cooperación Internacional y Desarrollo (AECID, Madrid, Spain). The authors are grateful to Alan Clark, Fred Kerst, and Chad Smith (Optibrand, Fort Collins, CO) for their technical support, to Ramon Costa and the team of the Servei de Granges i Camps Experimentals of the Universitat Autònoma de Barcelona (Bellaterra, Spain) for the care of the animals, and to Nic Aldam for the English revision of the manuscript. American Society of Animal Science
TI - Retinal image recognition for verifying the identity of fattening and replacement lambs
JF - Journal of Animal Science
DO - 10.2527/jas.2010-3197
DA - 2011-08-01
UR - https://www.deepdyve.com/lp/oxford-university-press/retinal-image-recognition-for-verifying-the-identity-of-fattening-and-mU9g0H9NpL
SP - 2603
EP - 2613
VL - 89
IS - 8
DP - DeepDyve
ER -