BARLOW: SHIP SURVEYS OF HARBOR PORPOISE 



Several models were investigated for estimating 

 /(O) from sighting distributions. The FORTRAN pro- 

 gram Transect (Laake et al. 1979) was used to fit 

 2-, 3-, 4-, and 5-parameter Fourier series and 

 2-parameter exponential power series models. The 

 FORTRAN programs Hazard and Hermite (S. Buck- 

 land'') were used to fit the 2-parameter hazard rate 

 model (constrained such that parameter P > 2, 

 Buckland 1985) and the 1-, 2-, 3-, and 4-parameter 

 Hermite polynomial model (Buckland 1985). Of these 

 models, the 2-parameter hazard rate model was 

 selected based on its ability to fit the observed 

 distributions and its lack of dependence on group- 

 ing criteria (Buckland 1985). 



Perpendicular distances were grouped into strata, 

 the size of which increased with perpendicular 

 distance: 0-25 m, 25-50 m, 50-100 m, 100-200 m, 

 200-400 m, 400-800 m, 800-1,600 m, and 1,600- 

 3,200 m. Several alternative groupings were inves- 

 tigated, and the choice of outpoints made very little 

 difference in estimates of /(O). The above strata 

 (increasing with distance) gave lower variances in 

 /(O) than when each stratum was of equal size 

 (possibly because the hazard rate model assumes a 

 distinct shoulder in the sighting distribution, and 

 that shoulder is lost if the first distance strata are 

 large). 



No established criteria exist for choosing an appro- 

 priate perpendicular distance at which to truncate 

 sighting distributions. Burnham et al. (1980) recom- 

 mend that no more than 1-3% of sightings be 

 eliminated by truncation. Using this recommenda- 

 tion, models were not able to adequately fit the 

 observed sighting distributions. In this report, trun- 

 cation distance was chosen in four ad hoc steps: 

 1) The hazard rate model was fit to perpendicular 

 distance data truncated at distances of 400, 800, 

 1,600, and 3,200 m. 2) Truncation distances were 

 identified which gave acceptable x^ values (P > 

 0.1). 3) Of the acceptable truncation distances, the 

 standard error in/(0) was estimated empirically by 

 randomly drawing 10 samples (of the same size as 

 the original sample) from the observed distribution 

 of perpendicular distances and by calculating the 

 standard deviation of/(0) estimated from each ran- 

 dom sample. 4) Truncation distances were chosen 

 as those which gave the lowest coefficient of varia- 

 tion in/(0). 



Variance in R, the number of porpoise seen per 

 kilometer, was estimated using jackknife statistics 



(Efron 1982). Jackknife estimates were calculated 

 by first estimating the value of i? using all data. The 

 value, Rj^, was again estimated excluding the A;th 

 segment of search effort. This process was repeated 

 for each effort segment. To ensure that each kth seg- 

 ment was of equivalent length, effort segments with 

 the same sea state, rain, and fog codes were com- 

 bined in a linear array and were then divided into 

 10 segments of approximately equal length. The 

 variance in the estimate of R was calculated as 



10 



s2 = 



~ • 1 (i?, - Rf 



10 ^=1 



(3) 



Avail, from Southwest Fisheries Center, P.O. Box 271, La Joila, 

 CA 92038. 



^S. Buckland, Inter-American Tropical Tuna Commission, P.O. 

 Box 271, La Jolla, CA 92038, pers. commun. July 1986. 



The variance of D was estimated using the Good- 

 man (1960) product variance formula (assuming no 

 covariance) using this jackknife variance for R and 

 the above Monte Carlo variance for/(0). 



Fraction of Missed Animals 



On survey 4, a second, independent team of 3 

 observers were used to estimate the fraction of 

 harbor porpoise that are missed by the primary 

 team of 5 observers. The fraction of missed animals 

 in a sighting survey is analogous to the fraction of 

 unmarked animals in a mark/recapture experi- 

 ment (Pollock and Kendall 1987). This fraction 

 was estimated using the Chapman (1951) modifica- 

 tion of the Petersen (or Lincoln) index method 

 (Pollock and Kendall 1987). Confidence limits were 

 estimated using Adams' (1951) method, which 

 assumes a binomial sampling distribution. Standard 

 error was estimated using standard binomial 

 formulas. 



Abundance Estimation 



A model was used to estimate the number of har- 

 bor porpoise along the entire coastline based on the 

 density that was observed along the 18 m isobath. 

 In shallow areas, such as the Bering Sea and 

 Georges Bank, harbor porpoise are found a con- 

 siderable distance from land (Gaskin 1984), hence 

 offshore distribution is better modelled as a func- 

 tion of depth than as a function of distance from 

 shore. (Although harbor porpoise are also found in 

 very deep water in fjords and inland waterways of 

 Alaska [Taylor and Dawson 1984], this represents 

 a special case that is not applicable to coastal waters 

 considered here.) The model used to estimate abun- 

 dance was based on data collected on surveys 3 and 

 4 and on data from a ship surveys by La Barr and 



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