California White Shark Abundance SUPPLEMENTAL
Transcription
California White Shark Abundance SUPPLEMENTAL
California White Shark Abundance 1 SUPPLEMENTAL INFORMATION 2 1. SAMPLING METHODS 3 This activity was conducted at known aggregation sites in central California under 4 permit regulations by the California Department of Fish and Game and the National 5 Marine Fisheries Service. 6 To obtain high quality photographs of shark fins, white sharks were attracted to the 7 research vessel using a 1 m long seal-shaped decoy attached by 36 kg test monofilament. 8 A small (<2 kg) piece of flesh obtained from dead marine mammal carcasses (Mirounga 9 angirostris, Physeter catodon or Zalophus californianus) was introduced to the water 10 along the side of the research vessel to create a localized scent. The purpose of using the 11 marine mammal flesh was to sustain a shark’s interest in the areas near the research 12 vessel once it approached the decoy and increase the length of the interaction and, 13 thereby, the probability of successful data collection. The sharks were not offered the bait 14 for consumption and normally surfaced near the decoy. Once the dorsal fin emerged, 15 high-resolution photographs were taken with a Nikon D40X or D90 (55-200 mm lens 16 with 10.1 megapixels). Sharks were lured closer to the boat by slowly retrieving the 17 decoy. Near the boat, individuals were sexed according to the presence (males) or 18 absence (females) of claspers using a SONY HD high-definition underwater camera and 19 sized via reference markings on the gunwale of the boat or parallel reference lasers. If the 20 fin was not presented above the water but water clarity permitted, dorsal fin photographs 21 were recorded from the high-definition video. Once the appropriate data were collected, 22 either the sharks lost interest, or the decoy was removed from the water, and the sharks 23 left the area. California White Shark Abundance 24 25 2. PROCESSING PHOTOGRAPHS 26 Photographs were evaluated to ensure that experts were able to clearly and distinctly 27 distinguish the trailing edge of each fin and no single notch or other single characteristic 28 was used to identify a shark. Some fins are easily identifiable even in low quality photos, 29 while fins with more subtle markings are not. Heterogeneity in the matching probability 30 of fins would essentially produce heterogeneity of capturability, which would violate the 31 assumptions of the mark-recapture model and lead to a negative bias in our estimate. 32 Therefore, we adopted a very strict evaluation scheme, which requires all images display 33 high enough quality that subtle differences/similarities could be used to match every fin. 34 This evaluation process limited heterogeneity in matching (capture) probability, due to 35 photo quality, to a low value. 36 Each photo was evaluated for image quality (maximum score of 8 points) based on 4 37 criteria: 1) Angle- If an image view was nearly lateral (90o) it was given two points. A 38 trailing edge at a non-90o angle but still readable was given one point (e.g. normally 39 >45o). All others were given zero points. 2) Size- If ! " of the fin was photographed then 40 two points were given. If only #-" was photographed then one point was given and zero 41 points were given for < # fin. 3) Focus- Two points were given to a non-pixilated 42 focused photo and one point to a photograph slightly out of focus but still identifiable. 43 Zero points were allocated if subtle notches were unidentifiable because of blurriness or 44 graininess. 4) Contrast- Two points were given for a fin that was distinct from the 45 background. Zero points were given if portions of the fin were not discernable from the 46 background. Any photograph with quality less than seven was removed from the analysis. California White Shark Abundance 47 To determine error rates of identification techniques and insure homogeneity in 48 matching (capture) probabilities, we ran experimental matching trials. Experts (e.g., 49 researchers with extensive experience identifying and matching white shark fins) blindly 50 matched 20 randomly chosen photographs by-eye from 12 sharks with known secondary 51 characteristics (e.g., electronic tags or large scars). Results from each expert were 52 compared to the true matches. Similar techniques were used to assess automated 53 packages DARWIN and FINSCAN. 54 Once it was determined that error rates of by-eye matching were negligible, these 55 experts compared each photograph to all other fin photographs within and across all years 56 simultaneously to determine matches (figure S1). Because animals were found to move 57 between aggregation sites in CCA [1], fin photographs from both locations were pooled. 58 To expedite the matching process from this large dataset, fin images were organized into 59 five groups based on their most obvious markings. This served as a preliminary filter. If a 60 fin did not match another fin within its group it was compared to all other fins in all other 61 groups. 62 63 64 3. ASSUMPTION OF THE MODEL FOR CLOSURE The general assumptions of mark-recapture models discussed below have been 65 presented by a number of authors [2,3]. 66 (a) Closed Population 67 Animals were assumed not to enter or to leave the system. Because this study was 68 conducted across a very small proportion of the assumed lifespan of the animals (27+ yrs; 69 [4] and because white sharks have low fecundity and estimated natural mortality [4,5], California White Shark Abundance 70 we assumed the population did not change sufficiently to significantly affect the estimate 71 during the two-year (3 sampling occasion) study period. In addition, targeted fishing for 72 white sharks is not permitted in US waters where these animals spend most of their time. 73 However, tagging studies indicate that sharks move in their yearly migrations through 74 international waters [1,6-8] where unintentional hooking on pelagic longlines set for 75 tunas and other species (swordfish) might occur. Because this gear is not designed to 76 catch large white sharks, we assumed that white sharks would break or cut any leaders 77 used to catch these smaller species. Thus, for this analysis we assumed fishing mortality 78 was negligible. 79 (b) Every individual, marked or unmarked, has equal probability of being caught 80 Klimley and Anderson [9] suggested determination of population abundance using 81 baiting methods has potential to be biased because they heterogeneously attract animals 82 depending on the direction of the odor plume. We did not chum or actively attract sharks 83 with olfactory stimuli and animals were not offered the bait for consumption. The bait 84 that we used created a small, localized scent that acted as a means to overcome an 85 animal’s natural apprehension to approach or remain near the boat once they had 86 investigated the decoy. 87 There is no reason to suspect that the photographing process changed catchability. 88 Sharks did not consume any meat or other material that might cause positive association 89 with the attraction process, thus, we assumed that there was no change in the capture 90 probability. 91 92 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 California White Shark Abundance 93 remain offshore year-round), negatively biasing our estimate. However, though this type 94 of heterogeneity is possible, it is unlikely. These coastal aggregation sites provide white 95 sharks a seasonally and geographically predictable concentration of high caloric prey not 96 available in the open ocean. Often animals are lean upon return to coastal aggregation 97 sites, but quickly increase in mass (TK Chapple pers. obs.). This suggests these 98 aggregations sites are an important seasonal feeding destination and it is unlikely that 99 white sharks would not exploit this resource. Furthermore, the chance that we have 100 missed interacting with or citing a large number of white sharks in the vicinity of CCA is 101 low given the high human population density in the area and the low reports of white 102 shark sightings or historical attacks. 103 Heterogeneity in capture probability can also be present in the processing of the fin 104 photographs. However, our methods of photograph processing (see above) were 105 specifically designed to prevent such heterogeneity. We specified that all photographs 106 were of sufficient quality to identify even subtle differences in fins. Any fin not adhering 107 to these standards was removed from the analysis. This ensured fins with large notches 108 and those with small notches had an equal probability of being matched. Consequently, 109 our experimental matching trials did not indicate any evidence of capture heterogeneity. 110 Although our photograph processing was designed to limit heterogeneity in capture 111 probabilities, we quantitatively explored the potential for such heterogeneity in the data 112 using methods Mo, Mt, and Mh developed by Otis el al. [10] to estimate population 113 abundance assuming no heterogeneity in capture probability, capture probabilities that 114 vary with time and capture probabilities that vary by individual animal, respectively, as 115 well as a method from Chao [11]. The results from methods by Otis et al. [10] were Mo= California White Shark Abundance 116 225 [176, 274], Mt= 220 [173,267] and Mh3= 223 [196,252]. The abundance estimates 117 were very near to estimates from four other analyses based on homogeneous capture 118 probabilities: our Bayesian methods (N=219 [130,275]), the Schnabel method [12] 119 (N=217 [165,320]) and estimates from two methods similar to those previously used by 120 Strong et al. [13] (Jolly-Seber; N= 156 [102,322]) and Cliff et al. [14] (Chapman; N= 213 121 [132,294]) at other locations to estimate white shark abundance (figure S2). The estimate 122 from Chao’s method (N= 328 [222,433]) was larger than our Bayesian estimate, 123 however, it was still within one standard error of our Bayesian estimate (figure S2). The 124 clustering of abundance estimates across different models suggests limited presence of 125 heterogeneity in capture probabilities in our data and supports the robustness of our 126 Bayesian estimate. 127 (c) Marking individuals does not alter their survival probability 128 Photo-identification techniques employed to mark each individual in this study did 129 not alter or affect the sharks in any way. Thus, we assumed there was no survival 130 probability consequence of the photo identification. Some animals were tagged, however, 131 these tags have the capability to indicate mortality and in no case did this occur. Similar 132 studies on epaulette sharks (< 75cm total length) found that tags were not detrimental to 133 the long-term health of the animals [15]. To date, attaching external tags to the 134 significantly larger white sharks has not had any effect on survival probability as 135 measured directly by our pop up satellite tagging program (zero mortality). 136 (d) Individuals do not lose their marks 137 138 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 California White Shark Abundance 139 85% accuracy of fin identification over a short period and Anderson et al. [17] found that 140 dorsal fins were conspicuous and conserved over long time periods (>22 years). Similar 141 techniques have been employed in extensive time-series studies with other marine [18] 142 and terrestrial organisms [19]. 143 (e) Sampling time is instantaneous 144 The sampling period was a small fraction of the time allowed for mixing of marked 145 and unmarked individuals. Sampling occurred from September through January. 146 Individuals were allowed to mix for the remainder of the year before the next sampling 147 period occurred. 148 (f) Animals do not leave the population and return 149 Previous observations of mature females have suggested that they are present at 150 coastal aggregation sites every other year [20]. During our brief study period we saw no 151 significant evidence of a two year cycle. Ultrasonic tags allowed us to passively monitor 152 the presence of the sharks [1]. All animals that were passively detected in year one and 153 three were also detected in year two. We assumed that these animals were representative 154 of the population; there were no animals that left the population and later returned. 155 156 157 4.BAYESIAN FRAMEWORK Below, we briefly outline the key steps and assumption in the use of Bayes’ theorem 158 in a mark-recapture framework adapted from Gazey and Staley [3]. This method was 159 initially adapted for mark-recapture estimates with a low number of recaptures [3]. 160 We assumed the population was closed (see above). Because individuals were not 161 counted more than once in each year, sampling was without replacement, hence we used California White Shark Abundance 162 the hypergeometric distribution. The number of recaptures, Rt, contained in a sample of 164 size Ct at a given population abundance, Ni, was be expressed by 166 (1) 168 169 170 Where Mt is the total number of marked animals in the population at time, t. 171 Assuming each sample was independent over sampling periods, T, we can determine 172 the likelihood (or sampling distribution) of drawing all the observed Rt’s at a givcn value 173 of Ni 175 177 (2) 179 180 181 If we assume no prior information about the distribution of the population size over K 182 values of N, we can use a uniform uninformative prior distribution, 183 (3) 185 186 187 except that the population must be at least as large as the number of animals marked in 188 the population (Ni ! Mt). 189 Using Bayes’ theorem, from equations 2 and 3 we can write the posterior distribution. 190 This posterior distribution can then be combined with equation 1 into Bayes’ theorem to 191 represent sampling with the hypergeometric distribution California White Shark Abundance 192 193 (4) 194 195 196 The total number of sessions in which recaptures are possible, T, equals 2 in this case 197 and N1=130. Following Gazey and Staley [3] we ran initial trials of the model to 198 determine where the posterior probability of values <N1 and >NK, the realistic ceiling of 199 the population abundance (NK=401), were small, to establish a suitable range for the 200 prior. If the posterior probabilities N1 and NK are small, there will be negligible 201 differences in estimated population abundances from alternative initial priors. The initial 202 posterior distribution calculated from the uninformative prior was used as the prior for 203 the subsequent calculation. From the final posterior we determined the mode of this 204 distribution, which is the maximum likelihood estimate of abundance at each time (figure 205 S3). The resolution of the estimate was governed by K (=272). The Bayesian posterior 206 interval (credible interval) was calculated such that b-a is a minimum and P(a $ N $ b) = 207 1-!. 208 209 210 211 212 213 214 215 216 217 218 219 220 221 REFERENCES 1. Jorgensen S. J., Reeb C., Chapple T. K., Anderson S. D., Perle C., Van Sommeran S., Fritz-Cope C., Brown A., Klimley A. P., Block B. A. 2010 Philopatry and migration of Pacific white sharks. P. R. Soc. B. 277, 679-688. (doi:10.1098/rspb.2009.1155) 2. Seber G. A. F. 1973 The Estimation of Animal Abundance and Related Parameters. London: Griffin. 3. Gazey W. J., Staley M. J. 1986 Population estimation from mark-recapture experiments using a sequential Bayes algorithm. Ecology. 67, 941–951. 4. Cailliet G. M., Natanson L. J., Welden B. A., Ebert D. 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D., Pyle P. 2003 A temporal, sex-specific occurrence pattern among white sharks at the South Farallon Islands, California. Cal. Fish Game 89, 96–101. Figure Legends 291 292 Figure S1. 293 (b) are from the same tagged shark in 2007 and 2008, respectively. The trailing edge is 294 identical between the years. (c) Is a photograph from a different shark in 2008 showing 295 how distinct the trailing edge of the fin is between sharks. Three dorsal fin photographs used in this analysis. Fin photographs (a) and 296 297 Figure S2. A summary of estimates of the white shark population using three closed 298 population multiple mark-recapture methods (Bayesian, Schnabel, Mo), an open 299 population multiple mark-capture method (Jolly-Seber; JS) and the average of two single 300 mark-recapture closed population estimates for each year (Chapman) based on 301 homogeneous capture probabilities and three closed population multiple mark-recapture California White Shark Abundance 302 models based on heterogeneous capture probabilities (Mt, Mh3, Chao). Error bars describe 303 the 95% confidence intervals (or credible intervals). 304 305 Figure S3. 306 used as a prior for future calculations. The solid line represents the final frequency 307 distribution (2008) with all data (N=219 and Nk=401). The initial posterior (--) calculated from the first recapture period (2007) is 500 450 Population Size 400 350 * 300 * 250 * 200 150 100 50 0 Bayes Schnabel Mo JS !"#$%&'(()& Chapman Mt Mh3 Chao