California White Shark Abundance SUPPLEMENTAL

California White Shark Abundance
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SUPPLEMENTAL INFORMATION
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1. SAMPLING METHODS
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This activity was conducted at known aggregation sites in central California under
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permit regulations by the California Department of Fish and Game and the National
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Marine Fisheries Service.
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To obtain high quality photographs of shark fins, white sharks were attracted to the
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research vessel using a 1 m long seal-shaped decoy attached by 36 kg test monofilament.
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A small (<2 kg) piece of flesh obtained from dead marine mammal carcasses (Mirounga
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angirostris, Physeter catodon or Zalophus californianus) was introduced to the water
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along the side of the research vessel to create a localized scent. The purpose of using the
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marine mammal flesh was to sustain a shark’s interest in the areas near the research
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vessel once it approached the decoy and increase the length of the interaction and,
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thereby, the probability of successful data collection. The sharks were not offered the bait
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for consumption and normally surfaced near the decoy. Once the dorsal fin emerged,
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high-resolution photographs were taken with a Nikon D40X or D90 (55-200 mm lens
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with 10.1 megapixels). Sharks were lured closer to the boat by slowly retrieving the
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decoy. Near the boat, individuals were sexed according to the presence (males) or
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absence (females) of claspers using a SONY HD high-definition underwater camera and
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sized via reference markings on the gunwale of the boat or parallel reference lasers. If the
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fin was not presented above the water but water clarity permitted, dorsal fin photographs
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were recorded from the high-definition video. Once the appropriate data were collected,
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either the sharks lost interest, or the decoy was removed from the water, and the sharks
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left the area.
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2. PROCESSING PHOTOGRAPHS
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Photographs were evaluated to ensure that experts were able to clearly and distinctly
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distinguish the trailing edge of each fin and no single notch or other single characteristic
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was used to identify a shark. Some fins are easily identifiable even in low quality photos,
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while fins with more subtle markings are not. Heterogeneity in the matching probability
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of fins would essentially produce heterogeneity of capturability, which would violate the
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assumptions of the mark-recapture model and lead to a negative bias in our estimate.
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Therefore, we adopted a very strict evaluation scheme, which requires all images display
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high enough quality that subtle differences/similarities could be used to match every fin.
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This evaluation process limited heterogeneity in matching (capture) probability, due to
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photo quality, to a low value.
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Each photo was evaluated for image quality (maximum score of 8 points) based on 4
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criteria: 1) Angle- If an image view was nearly lateral (90o) it was given two points. A
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trailing edge at a non-90o angle but still readable was given one point (e.g. normally
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>45o). All others were given zero points. 2) Size- If ! " of the fin was photographed then
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two points were given. If only #-" was photographed then one point was given and zero
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points were given for < # fin. 3) Focus- Two points were given to a non-pixilated
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focused photo and one point to a photograph slightly out of focus but still identifiable.
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Zero points were allocated if subtle notches were unidentifiable because of blurriness or
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graininess. 4) Contrast- Two points were given for a fin that was distinct from the
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background. Zero points were given if portions of the fin were not discernable from the
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background. Any photograph with quality less than seven was removed from the analysis.
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To determine error rates of identification techniques and insure homogeneity in
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matching (capture) probabilities, we ran experimental matching trials. Experts (e.g.,
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researchers with extensive experience identifying and matching white shark fins) blindly
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matched 20 randomly chosen photographs by-eye from 12 sharks with known secondary
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characteristics (e.g., electronic tags or large scars). Results from each expert were
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compared to the true matches. Similar techniques were used to assess automated
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packages DARWIN and FINSCAN.
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Once it was determined that error rates of by-eye matching were negligible, these
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experts compared each photograph to all other fin photographs within and across all years
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simultaneously to determine matches (figure S1). Because animals were found to move
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between aggregation sites in CCA [1], fin photographs from both locations were pooled.
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To expedite the matching process from this large dataset, fin images were organized into
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five groups based on their most obvious markings. This served as a preliminary filter. If a
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fin did not match another fin within its group it was compared to all other fins in all other
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groups.
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3. ASSUMPTION OF THE MODEL FOR CLOSURE
The general assumptions of mark-recapture models discussed below have been
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presented by a number of authors [2,3].
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(a) Closed Population
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Animals were assumed not to enter or to leave the system. Because this study was
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conducted across a very small proportion of the assumed lifespan of the animals (27+ yrs;
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[4] and because white sharks have low fecundity and estimated natural mortality [4,5],
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we assumed the population did not change sufficiently to significantly affect the estimate
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during the two-year (3 sampling occasion) study period. In addition, targeted fishing for
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white sharks is not permitted in US waters where these animals spend most of their time.
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However, tagging studies indicate that sharks move in their yearly migrations through
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international waters [1,6-8] where unintentional hooking on pelagic longlines set for
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tunas and other species (swordfish) might occur. Because this gear is not designed to
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catch large white sharks, we assumed that white sharks would break or cut any leaders
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used to catch these smaller species. Thus, for this analysis we assumed fishing mortality
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was negligible.
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(b) Every individual, marked or unmarked, has equal probability of being caught
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Klimley and Anderson [9] suggested determination of population abundance using
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baiting methods has potential to be biased because they heterogeneously attract animals
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depending on the direction of the odor plume. We did not chum or actively attract sharks
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with olfactory stimuli and animals were not offered the bait for consumption. The bait
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that we used created a small, localized scent that acted as a means to overcome an
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animal’s natural apprehension to approach or remain near the boat once they had
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investigated the decoy.
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There is no reason to suspect that the photographing process changed catchability.
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Sharks did not consume any meat or other material that might cause positive association
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with the attraction process, thus, we assumed that there was no change in the capture
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probability.
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Capture probability may also be affected if there is a section of the population that is
not available to sampling (e.g., sharks do not travel to these coastal aggregation sites or
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remain offshore year-round), negatively biasing our estimate. However, though this type
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of heterogeneity is possible, it is unlikely. These coastal aggregation sites provide white
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sharks a seasonally and geographically predictable concentration of high caloric prey not
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available in the open ocean. Often animals are lean upon return to coastal aggregation
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sites, but quickly increase in mass (TK Chapple pers. obs.). This suggests these
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aggregations sites are an important seasonal feeding destination and it is unlikely that
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white sharks would not exploit this resource. Furthermore, the chance that we have
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missed interacting with or citing a large number of white sharks in the vicinity of CCA is
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low given the high human population density in the area and the low reports of white
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shark sightings or historical attacks.
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Heterogeneity in capture probability can also be present in the processing of the fin
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photographs. However, our methods of photograph processing (see above) were
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specifically designed to prevent such heterogeneity. We specified that all photographs
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were of sufficient quality to identify even subtle differences in fins. Any fin not adhering
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to these standards was removed from the analysis. This ensured fins with large notches
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and those with small notches had an equal probability of being matched. Consequently,
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our experimental matching trials did not indicate any evidence of capture heterogeneity.
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Although our photograph processing was designed to limit heterogeneity in capture
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probabilities, we quantitatively explored the potential for such heterogeneity in the data
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using methods Mo, Mt, and Mh developed by Otis el al. [10] to estimate population
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abundance assuming no heterogeneity in capture probability, capture probabilities that
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vary with time and capture probabilities that vary by individual animal, respectively, as
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well as a method from Chao [11]. The results from methods by Otis et al. [10] were Mo=
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225 [176, 274], Mt= 220 [173,267] and Mh3= 223 [196,252]. The abundance estimates
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were very near to estimates from four other analyses based on homogeneous capture
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probabilities: our Bayesian methods (N=219 [130,275]), the Schnabel method [12]
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(N=217 [165,320]) and estimates from two methods similar to those previously used by
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Strong et al. [13] (Jolly-Seber; N= 156 [102,322]) and Cliff et al. [14] (Chapman; N= 213
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[132,294]) at other locations to estimate white shark abundance (figure S2). The estimate
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from Chao’s method (N= 328 [222,433]) was larger than our Bayesian estimate,
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however, it was still within one standard error of our Bayesian estimate (figure S2). The
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clustering of abundance estimates across different models suggests limited presence of
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heterogeneity in capture probabilities in our data and supports the robustness of our
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Bayesian estimate.
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(c) Marking individuals does not alter their survival probability
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Photo-identification techniques employed to mark each individual in this study did
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not alter or affect the sharks in any way. Thus, we assumed there was no survival
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probability consequence of the photo identification. Some animals were tagged, however,
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these tags have the capability to indicate mortality and in no case did this occur. Similar
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studies on epaulette sharks (< 75cm total length) found that tags were not detrimental to
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the long-term health of the animals [15]. To date, attaching external tags to the
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significantly larger white sharks has not had any effect on survival probability as
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measured directly by our pop up satellite tagging program (zero mortality).
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(d) Individuals do not lose their marks
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Marking an individual involves visually identifying the unique characteristic on the
trailing edge of the dorsal fin. Gubili et al. [16] used genetic data and photo ID’s to show
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85% accuracy of fin identification over a short period and Anderson et al. [17] found that
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dorsal fins were conspicuous and conserved over long time periods (>22 years). Similar
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techniques have been employed in extensive time-series studies with other marine [18]
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and terrestrial organisms [19].
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(e) Sampling time is instantaneous
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The sampling period was a small fraction of the time allowed for mixing of marked
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and unmarked individuals. Sampling occurred from September through January.
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Individuals were allowed to mix for the remainder of the year before the next sampling
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period occurred.
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(f) Animals do not leave the population and return
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Previous observations of mature females have suggested that they are present at
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coastal aggregation sites every other year [20]. During our brief study period we saw no
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significant evidence of a two year cycle. Ultrasonic tags allowed us to passively monitor
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the presence of the sharks [1]. All animals that were passively detected in year one and
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three were also detected in year two. We assumed that these animals were representative
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of the population; there were no animals that left the population and later returned.
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4.BAYESIAN FRAMEWORK
Below, we briefly outline the key steps and assumption in the use of Bayes’ theorem
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in a mark-recapture framework adapted from Gazey and Staley [3]. This method was
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initially adapted for mark-recapture estimates with a low number of recaptures [3].
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We assumed the population was closed (see above). Because individuals were not
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counted more than once in each year, sampling was without replacement, hence we used
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the hypergeometric distribution. The number of recaptures, Rt, contained in a sample of
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size Ct at a given population abundance, Ni, was be expressed by
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(1)
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Where Mt is the total number of marked animals in the population at time, t.
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Assuming each sample was independent over sampling periods, T, we can determine
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the likelihood (or sampling distribution) of drawing all the observed Rt’s at a givcn value
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of Ni
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(2)
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If we assume no prior information about the distribution of the population size over K
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values of N, we can use a uniform uninformative prior distribution,
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(3)
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except that the population must be at least as large as the number of animals marked in
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the population (Ni ! Mt).
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Using Bayes’ theorem, from equations 2 and 3 we can write the posterior distribution.
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This posterior distribution can then be combined with equation 1 into Bayes’ theorem to
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represent sampling with the hypergeometric distribution
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(4)
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The total number of sessions in which recaptures are possible, T, equals 2 in this case
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and N1=130. Following Gazey and Staley [3] we ran initial trials of the model to
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determine where the posterior probability of values <N1 and >NK, the realistic ceiling of
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the population abundance (NK=401), were small, to establish a suitable range for the
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prior. If the posterior probabilities N1 and NK are small, there will be negligible
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differences in estimated population abundances from alternative initial priors. The initial
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posterior distribution calculated from the uninformative prior was used as the prior for
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the subsequent calculation. From the final posterior we determined the mode of this
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distribution, which is the maximum likelihood estimate of abundance at each time (figure
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S3). The resolution of the estimate was governed by K (=272). The Bayesian posterior
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interval (credible interval) was calculated such that b-a is a minimum and P(a $ N $ b) =
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1-!.
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Long-term Individual Identification and Site Fidelity of Great White Sharks,
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Figure Legends
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Figure S1.
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(b) are from the same tagged shark in 2007 and 2008, respectively. The trailing edge is
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identical between the years. (c) Is a photograph from a different shark in 2008 showing
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how distinct the trailing edge of the fin is between sharks.
Three dorsal fin photographs used in this analysis. Fin photographs (a) and
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Figure S2.
A summary of estimates of the white shark population using three closed
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population multiple mark-recapture methods (Bayesian, Schnabel, Mo), an open
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population multiple mark-capture method (Jolly-Seber; JS) and the average of two single
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mark-recapture closed population estimates for each year (Chapman) based on
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homogeneous capture probabilities and three closed population multiple mark-recapture
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models based on heterogeneous capture probabilities (Mt, Mh3, Chao). Error bars describe
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the 95% confidence intervals (or credible intervals).
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Figure S3.
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used as a prior for future calculations. The solid line represents the final frequency
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distribution (2008) with all data (N=219 and Nk=401).
The initial posterior (--) calculated from the first recapture period (2007) is
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Population Size
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Bayes
Schnabel
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JS !"#$%&'(()&
Chapman
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Mh3
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