NOVEMBER 1982 

ABUNDANCE ESTIMATION OF DOLPHIN STOCKS 

INVOLVED IN THE 

YELLOWFIN TUNA FISHERY DETERMINED FROM 

EASTERN TROPICAL PACIFIC 

AERIAL AND SHIP SURVEYS TO 1979 

Rennie S. Holt 

& 

Joseph E. Powers 

NOAA-TM-NMFS-SWFC-23 

U.S. DEPARTMENT OF COMMERCE 

National Oceanic and Atmospheric Administration 

National Marine Fisheries Service 

Southwest Fisheries Center 
NOAA Technical Memorandum NMFS 

The National Oceanic and Atmospheric Administration (NOAA), organized in 1970, has evolved 

into an agency which establishes national policies an manages and conserves our oceanic, coastal, and 

atmospheric resources. An organizational element within NOAA, the Office of Fisheries is responsible for fisheries policy and the direction of the National Marine Fisheries Service (NMFS). 

In addition to its formal publications, the NMFS uses the NOAA Technical Memorandum series to 

issue informal scientific and technical publications when complete formal review and editorial processing are not appropriate or feasible. Documents within this series, however, reflect sound professional 

work and may be referenced in the formal scientific and technical literature. 
NOAA Technical Memorandum NMFS 

This TM Series IS used lor documentation and timelv communication 01 Dreliminary results, irnterirn repons. Or 

special purpose lntormation and have not received complete formal review editorial control or detailed editing 

NOVEMBER 1982 

ABUNDANCE ESTIMATION OF DOLPHIN STOCKS 

INVOLVED IN THE EASTERN TROPICAL PACIFIC 

YELLOWFIN TUNA FISHERY DETERMINED FROM 

AERIAL AND SHIP SURVEYS TO 1979 

Rennie S. Holt 8 Joseph E. Powers' 

Southwest Fisheries Center 

National Marine Fisheries Service, NOAA 

La Jolla, California 92038 

NOAA-TM-NMFS-SWFC-23 

U.S. DEPARTMENT OF COMMERCE 

Malcolm Baldrige. Secretary 

National Oceanic and Atmospheric Administration 

John V. Byrne. Administrator 

National Marine Fisheries Service 

William G. Gordon, Assistant Administrator for Fisheries 

' Present address: Southeast Fisheries Center. National 

Marine Fisheries Service, NOAA. Miami. Florida 33149. 
CONTENTS 

Page 

ABSTRACT ............................................................. vi 

I . INTRODUCTION .................................................. 1 

I1 . DENSITY OF DOLPHIN SCHOOLS .................................... 5 

Survey design and execution ................................ 5 

Assumptions for 1 ine transect estimation of density ........ 6 

Line transect density estimation theory for aerial data .... 8 

Density estimation theory for research ship data ........... 15 

Density estimates .......................................... 19 

I11 . MEAN SIZE OF DOLPHIN SCHOOLS .................................. 21 

Data 21 

Correction for sighting bias ............................... 22 

School size estimates from aerial photographs .............. 24 

School size estimates from tuna vessels .................... 26 

Choice of mean school size estimate ........................ 28 

sources and possible biases ........................... 

Spatial and temporal bias .................................. 27 

IV . SPECIES PROPORTIONS ........................................... 29 

29 

31 

V . STOCK RANGES .................................................. 33 

Target and nontarget schools ............................... Species proportion of target schools ....................... 

VI . POPULATION SIZE ESTIMATES ..................................... 33 

VI1 . DISCUSSION AND CONCLUSIONS .................................... 35 

LITERATURE CITED ..................................................... 39 

TABLES ............................................................... 41 

FIGURES .............................................................. 68 

APPENDIX 1 AD HOC Committee Members .................................. 76 

APPENDIX 2 Multi-way analysis of variance of school size estimates ... 77 

APPENDIX 3 Estimation of area inhabited .............................. 84 

APPENDIX 4 Estimation of species composition ......................... 93 

i 
LIST OF TABLES 

Tab1 e Page 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

Summary of exponenti a1 power series (EPS) , exponenti a1 

Rolynomial (EP), and Fourier series (FS) estimates of 

f(0) for dolphin schools for inshore aerial sighting 

data stratified by school size categories ..................... 41 

Summary of the Fourier series estimates of t(0) for the 

1979 aerial sighting data in the inshore area, calculated 

at successive truncation points ............................... 42 

Perpendicular sighting distance distributions for 1 arge 

dolphin school s (>14 animal s) observed during vessel 

sighting surveys aboard the Jordan and Cromwell in the 

offshore and calibration areas................................ 43 

Mean perpendicular sighting distance (P) and mean Beaufort 

number (B) for each research vessel sighting, stratified by 

ship, species composition, area, and sighting cue. Sample 

sizes in parentheses .......................................... 44 

Perpendicular sighting distance distributions for 

large dolphin schools (>14 animals) observed during 

aerial sighting surveys in the inshore and calibration areas. 

15,195 nm searched............................................ 45 

Summary of the Fourier series estimates of f(0) for large 

schools (>14 animals) observed during the 1979 aerial 

sighting survey in the inshore area. 

1.05 nm and number of schools observed = llo.................. 46 

Truncation point = 

Number of observed dolphin schools and miles searched 

during the aerial sighting survey in the inshore area. 

Data truncated at 1.05 nm perpendicular distance.. ............ 

Number of large dolphin schools observed per nautical mile 

searched, recorded by observers in 1979 aboard the PBY, 

R/V Jordan and R/V Cromwell in the calibration and 

offsmreas. Ship and aerial sightings were truncated 

at 1.15 nm and 0.95 nm, respectively .......................... 48 

Summary of the Fourier series estimates of f(0) for large 

dolphin schools observed during the aerial sighting survey 

in the calibration area. Truncation point was 0.95 nm and 

number of schools observed was 42............................. 49 

47 

Number of observed dolphin schools and miles searched per 

flight during the aerial sighting survey in the calibration 

area. Data were truncated at 0.95 nm perpendicular distance 

(w=0.95 nm) ................................................... 50 

ii 
LIST OF TABLES-Cont'd 

Tab1 e Page 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

Number of observed dolphin schools and miles searched per 

day from the R/V Cromwell in the calibration area. Data 

were truncated at 1.15 nm perpendicular distance.............. 51 

Number of observed dolphin schools and miles searched per 

day from the R/V Jordan in the calibration area. Data 

were truncated at.nm perpendicul ar distance.. ............ 52 

Number of observed dolphin schools and mires searched per 

day from the R/V Cromwell in the offshore area. Data 

were truncated at 1.15 nm perpendicular distance.............. 53 

Number of observed dolphin schools and miles searched from 

the R/V Jordan in the offshore area. Data were truncated 

at 1.15 nm perpendicular distance............................. 54 

Expected perpendicular sighting di stances ( nm) , with sample 

sizes (n) at different school sizes for data from the 1979 

dolphin sighting surveys on the PBY airplane, and the 

research vessels Jordan and Cromwell...,...................... 55 

Target school size frequency distributions and ratios of 

weighted to unweighted means.................................. 56 

Mean school size estimates for target species (school size 

>14 animals). Mean is weighted for sighting bias ............. 57 

Mean school size estimates for non-target species (school 

size >14 animals), weighted for sighting bias ................. 58 

Proportion of dol phin schools (school size >14 animal s 

which were target schools (Ptarget). See text for 

calculation method............................,................ 59 

Species proportion of target schools (school size >14 

animals), expressed as fraction of individuals of given 

species per target school ..................................... 60 

Pooled estimates of species proportions of target schools 

(school size >14 animals), expressed as fraction of 

individuals of given species per target school................ 

Area inhabited (nm2) by various species/ stocks for the 

inshore, and northern and southern offshore areas 

(Appendix 3) .................................................. 63 

Proportion of eastern and northern whitebelly spinner 

dolphin in the area of their overlap, using tuna vessel 

data for 1978 and 1979.......... .............................. 64 

61 

iii 
LIST OF TABLES-Cont'd 

Tab1 e Page 

24 Estimates of population sizes (in thousands of animals) 

by stock for target species using pooled 1977-79 

tuna vessel and research vessel observer data, using 

pooled 1977 and 1979 research vessel data combined for 

all areas, and using 1979 research vessel data combined 

for all areas. Standard errors shown in parentheses. ......... 65 

25 Estimates of population sizes of spotted, spinner, common, 

and striped dolphin as of January 1, 1974. Estimates are 

in thousands of animals. Note that stock names and 

boundaries are not enti rely equivalent to 1979 estimates.. . . . . 66 

26 Population estimates of spotted, spinner, common, and 

striped dolphin in 1974 and 1979. See Table 25 for 

explanation of the 1974 estimates. 

thousands of animals.......................................... 67 

Estimates are in 

iv 
LIST OF FIGURES 

Figure Page 

1 

2 

3 

4 

5 

Track1 ine for 1979 aircraft and research vessel 

dolphin sighting surveys................................ 68 

Fit of the Fourier series density estimation model 

to the grouped perpendicular distances for dolphin 

school sighted during the 1979 sighting survey on 

the R/V Jordan in the calibration area.................. 69 

Fit of the Fourier series density estimation model 

to the grouped perpendicul ar distances for dol phi n 

schools sighted during the 1979 sighting survey on 

the R/V Cromwell in the calibration area................ 70 

Fit of the Fourier series density estimation model to 

the grouped perpendicul ar distance for dol phin schools 

sighted during the 1979 sighting survey on the PBY 

airplane in the inshore area............................ 71 

Fit of 3- and 4-term Fourier series density estimation 

models to the grouped perpendicul ar di stances for 

dol phi n school s sighted duri ng the 1979 si ghti ng survey 

on the PBY airplane in the calibration area............. 72 

Comparison of school size estimates made visually by 

aeri a1 observers and counted from aeri a1 photographs.. .. 73 

Range of observer and photography estimates of dolphin 

school sizes............................................ 74 

Mean dolphin school size estimates for target species 

(corrected for sighting bias) made by observers and by 

crew members aboard tuna vessels, for each year from 

1974 to 1979. Means are shown, with sample size in 

parentheses, for those dol phi n school s where observers 

made an estimate, where crew members made an estimate, 

and where both observers and crew members made estimates 

(adjacent bars). 

of year................................................. 75 

1979 data include only first six months 

V 
ABSTRACT 

Estimates are developed of the size of several populations of dolphins of 

three species of Stenella, Delphinus delphis and Lagenodelphis hosei in the 

eastern tropical Pacific Ocean, basedmphin sighting surveysonducted 

from January to May 1979. Sighting surveys were made using two research 

vessels and a PBY aircraft, all operated seaward from the coast of Mexico and 

Central and South America. Data collected by scientific observers aboard 

U. S. tuna purse seine vessels were also used. Population size is estimated 

as the product of six parameters: density of schools of dolphins, mean school 

size, proportion of animals of the "target" species, proportion of each 

species in the "target" group, area inhabited by each population of each 

species and the proportion of area occupied by each stock of each target 

species. Estimates of each of these parameters including sampling variability 

are developed, using data available through early 1979. The report represents 

a reference point to which future estimates of population sizes may be 

compared. 

The estimated density of dolphin schools in the nearshore area is 

approximate1 12 schools per 1000 nm2, with a standard deviation of 2 schools 

schools per 1000 nm2, with a standard deviation of 3. The estimated mean 

school size of dolphins of these species is approximately 200 animals, with a 

standard deviation of 27. The estimated proportion of the dolphin schools 

which contained these species is approximately 0.72, with a standard deviation 

of 0.04. The proportion of target schools of each species differed among data 

sets and among areas and years, with S. attenuata and S. coeruleoalba being 

most common. The composite range of alT of these speciescovers approximately 

5.6 million nm2. 

per 1000 nm i! . The density estimate in the offshore area is approximately 6 

Combining these parameter estimates yields estimates of the sizes of the 

populations of each species. The different estimates of species proportions 

from the research vessels and the tuna vessel survey data were used separately 

to explore the variability of the estimates. The ranges of estimates of sizes 

of all populations of each species using the various data sets are 2 million 

to 3 million for S. attenuata, 700,000 to 900,000 for S. longirostris, 600,000 

to 2 million for-S. coeruleoalba, 900,000 to 1 millsn for - D. delphis, and 

20,000 to 120,000 5r L. hosei. 

The estimates of dol phi n popul ation sizes presented are more re1 iabl e 

than earlier estimates (Smith 1981, and references therein) because we used 

more extensive and better survey data and greatly improved analytical 

techniques. Principal improvements which have been made in these estimates 

are: increased re1 iance on research vessel sighting survey data over fishing 

vessel sighting data, increased survey coverage of dolphin ranges, use of more 

robust line transect models for estimating density of schools, and adjusting 

for the effect of dolphin school size on the probability of detecting schools 

during surveys. 

-- 

However, there are a number of uncertainties in these population 

estimates, including: 1) the ability of the aerial observers to estimate the 

size of schools and to estimate school size in less than ideal sea state, 2) 

vi 
the effect of sea state and sun position on the ability of aerial observers to 

detect all schools on the trackline and 3) on the general shipboard sighting 

process, the differences in species proportions in sighting data collected on 

research and tuna vessels and the degree to which the entire historical range 

of each of the populations is occupied at any point in time. Some of these 

sources of uncertainty may be contributing biases in the estimates we present 

and are discussed. 

vii 
I. INTRODUCTION 

The purse seine fishery in the Eastern Tropical Pacific (ETP) Ocean uses 

several species of dolphin as a guide to locating and encircling schools of 

tuna, principally the yellowfin tuna (Thunnus albacares) (Perrin 1968, 

1969). However, in the fishing process manyins become entrapped in the 

net and drown. Under provisions of the Marine Mammal Protection Act of 1972, 

the National Marine Fisheries Service (NMFS) was given the responsibility for 

(1) assessing the impact of the take of marine mammals incidental to 

commercial fishing, and (2) issuing permits and regulations governing that 

take. A ruling by the United States District Court, District of Columbia, 

further defined NMFS' responsibility by stating that NMFS must, among other 

things, make reasonable estimates of 

'I.. .the exi sti ng popul ati on 1 eve1 of each 

species of porpoise affected by the proposed 

regulations, ...I' (Richey 1976)l 

NMFS in 1973 established a research program to assess the impact of 

incidental take of dolphins by tuna purse seiners in the ETP. Two techniques 

for obtaining data to meet the research objectives were developed. One was 

the placement of scientific observers aboard United States purse seine vessels 

to gather information on the biology of the dolphin stocks, the magnitude and 

causes of incidental mortality, and the rate of encounters with dolphin 

aggregations. The second technique was dolphin sighting surveys using 

research vessels and aircraft to gather information on location, size, and 

density of dol phin school s. 

Data from a feasibility study of aerial dolphin sighting surveys and from 

tuna vessel observers and research vessel sighting surveys in 1974 were 

combined to estimate the dolphin population sizes (Smith 1975', 1981). These 

estimates were modified during a workshop on stock assessment of dolphins 

involved in the yellowfin tuna fishery (SWFC 197613 in 1976, and formed the 

basis of a stock assessment and subsequent regulatory and quota regime for the 

1977 fishing season (NMFS 1977)4. There were a number of weaknesses in the 

lRichey, C. R. 1976. Memorandum of opinion. CA NO. 74-1465 and CA NO. 75- 

0227. U. S. District Court, District of Columbia, May 11, 1976. 

(Stenella) in the Eastern Tropical Pacific Ocean. Southwest --- Fish. Cent. Adm. 

- Rep. No. LJ-75-67. 

3SWFC (Southwest Fisheries Center, Nat'l Mar. Fish. Serv., NOAA, La Jolla, CA 

92038). 1976. 

involved in the eastern tropical Pacific yellowfin tuna fishery. Southwest 

Fish. Cent. Adm. Rep. No. LJ-76-29, La Jolla, CA 60 pp. 

2 Smith, T. D. 1975. Estimates of sizes of two populations of porpoise 

La Jolla, CA. 88 pp. 

Report of the workshop on stock assessment of porpoises 

---- 
2 

data on which these population size estimates were based as discussed in SWFC 

(197613, including limited aerial coverage, lack of validation of school size 

estimates, nonrandomness in tuna vessel search patterns, and re1 iance on 

untested analytic methods developed for wild1 i fe studies. 

A second aerial and research vessel sighting survey was conducted in 

1977. The survey design did not include tuna vessel observer sighting data 

because of the possible effect of nonrandom search, and included two research 

vessels operating in areas not accessible to the aircraft. 

After completion of this survey, an ad hoc committee of experts on 

population estimation and line transect theory met in a series of four 

workshops at the Southwest Fisheries Center; the first was held August 30- 

September 1, 1977, with subsequent workshops during December 8-9, 1977, 

October 5-6, 1978, and June 25-26, 1979 (Appendix 1). This committee 

developed new methods of estimating dolphin population size from aerial and 

research vessel sighting surveys. However, probl ems with the 1977 survey data 

such as changes in aircraft and in aircraft speed could not be resolved 

without further field work. 

A third aerial and research vessel survey was therefore conducted from 

January through April 1979. A slower airplane was used, and again two 

research vessels surveyed areas not accessible to the airplane. The survey 

included an area of overlap between the 3 platforms to allow for calibration 

of platforms. Additionally, large format aerial photographs were taken of 

some dolphin schools to allow validation of visual estimates of school size. 

After completion of this survey, the committee met for the last time to 

consider the results, and to advise on appropriate analytic procedures for 

obtaining dolphin population size estimates. 

This report contains recommendations of the commi tee, and includes: (1) 

theoretical developments in estimating density of dolphin schools and in 

adjusting for biases introduced by differential detectability of schools of 

different sizes, (2) description of the selection of a mathematical model for 

estimating density of dolphin schools, (3) description of the selection of 

appropriate data sets for estimating school size, species proportions, and 

area inhabited, and (4) estimates of the population size of each dolphin 

stock. 

The dolphin population size estimates presented in this report should be 

considered as the best available from data available through early 1979. 

Since then, additional data have been collected and further advances have been 

made in understanding procedures for coping with uncertainties in the data. 

In this report we do not present these recent data or findings but discuss 

those that might have a significant effect on our estimates. This report 

‘+NMFS. 1977. Fi nal Environmental Impact Statement. Promul gati on of 

regulations and proposed issuance of permits to commerci a1 fi shermen a1 1 owing 

the taking of marine mammals in the course of yellowfin tuna purse seining 

operations from 1978 through 1980. NMFS, NOAA, Department of Commerce, 

November. 99 pp. 
3 

should be considered a foundation upon which subsequent revised population 

size estimates should be referenced; it should not be viewed as the final word 

on the subject. 

The dolphin population size estimates presented in this report are 

estimated as the product of six factors: (1) average density of schools in 

the ETP (D), (2) mean school size (SI, (3) proportion of all species of 

interest (i.e., species on which fishing is targeted (Pt)), (4nroportion of 

each species of interest within this "target" group (Pi), (5) total area 

occupied by any species (A),6) proportion of area occupied by each stock 

of each target species. This latter proportion is calculated as the ratio of 

the area occupied by stock j of 'species i (A*.) and the area occupied by 

species i (Ai). Mathematically, the number of ddlphins of stock j of species 

i inhabiting area Aij can be represented as 

Estimates of each of 

seauenti a1 lv and then combi 

these six factors are developed and presented 

ed to produce population size estimate for each 

dol'phin stick. The density of schools and the mean school size are discussed 

in sections I1 and 111, respectively, while the proportions of target schools 

and the proportions of individuals of target species are discussed in Section 

IVY and the total area inhabited and the proportion inhabited by each stock 

are discussed in section V. Population size estimates were calculated 

separately for the inshore area and the northern and southern offshore areas, 

which are described in section VI. These estimates by area were summed to 

yield estimates for dolphin stocks in the ETP, given in section VI. 

Because of the management significance of the material presented and 

because of the new methods used, the paper has undergone extensive peer review 

both within NMFS and by non-government scientists. A brief chronological 

history of this review follows: 

1. April 1979 - Fie1 dwork completed; analysis undertaken. 

2. June 1979 - Population Estimation Workshop reviewed analysis 

and offered advice. 

3. August 1979 - First draft completed as a Status of Porpoise 

Stocks Workshop document (SOPS/79/29). 

4. September 1979 - SOPS 29 sent to Population Estimation Workshop 

menbers for review including Drs. K. Burnham, 

D Chapman, L. Eberhardt, D. Burdick, T. Quinn, 

R. Allen, and K. Pollock. 
4 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 

October 

May 1980 

1979 

November 1980 

January 1981 

July 1981 

August 1981 

Oc to b e r 1 98 1 

October 1981 

February 1982 

April 1982 

June 1982 

June 1982 

July 1982 

August 1982 

There also has 

- Received written reviews from Burnham 

( incorporating Anderson ' s views), Qui nn (a1 so 

reviewing preliminary draft of section of SOPS 

report concerning correcti ng species 

proportions), and Burdick. Verbal comments 

received from Eberhardt. 

- Revised SOPS 29 submitted to SWFC personnel 

including Dr. Smith, Lt. T. Jackson, 

LCDR W. Perryman, and NMFS Technical Editor 

S Sitko, for review. 

- Comments incorporated and manuscript revised. 

- Manuscript to Dr. Smith for Review. 

- Comments incorporated. 

- Revision to Dr. Smith for review. 

- Revised. 

- Draft to Ms. Sitko and Drs. Smith, Reilly, 

DeMaster, Burnham, Eberhardt, and Chapman. A1 so 

to Mr. G. Broadhead (Living Marine Resources). 

- Comments received from Smith, Reilly, DeMaster, 

Eberhardt, Burnham, and Sitko. 

- Revised. 

- Revision to Drs. Smith and Sakagawa. 

- Received comments from Broadhead. 

- Revised. 

- Revised. 

been much useful discussion, both verbal and written, 

among the Population Estimation Workshop members concerning the appropriate 

analysis. The reviews, especially those of Drs. Burdick and Burnham, were 

thorough and very constructive. Their comments were very useful in developing 

the manuscript. 

The original document was scrutinized during the 1980 ALJ Hearings. 

Several alternate and often opposing views were offered in the form of 

testimony. Although testimony was useful, the points must be reconciled in a 

scientific form, which may require further field work, before they can be 

incorporated into the population estimates. 

We appreciate the efforts of the many reviewers and have attempted to 

incorporate their suggestions where, in our opinion, they are appropriate. 
5 

We would like to express our appreciation to the several observers aboard 

the airplane and research ships who unselfishly gathered the data during the 

survey. LCDR Wayne Perryman and Dr. Jay Barlow are thanked for their input 

during the analysis of the data. Dr. Tim Smith provided many suggestions for 

improving this report. Gratitude is also extended to the members of the ad 

hoc committee (see Appendix 1) and the Marine Mammal Monitoring and Assessment 

Program of the Southwest Fisheries Center for their assistance. The several 

drafts of this manuscript were typed by Helen Becker and Cheryl Harless, to 

whom we express our most sincere thanks. This research was funded by the 

Southwest Fisheries Center, La Joll a, Cal i fornia. 

11. DENSITY OF DOLPHIN SCHOOLS 

Survey Design and Execution 

Sightings of dolphins used to calculate the density of dolphin schools 

were made by observers on board an airplane and two research ships. Specific 

in-flight or onboard operating procedures are described by Au (1979)5 and 

Jackson (197916. Only those aspects of the operating procedures pertinent to 

the analysis of these data will be discussed. 

A modified four engine PBY, similar to the two engine PBY used in the 

latter phase of the 1977 survey (SWFC 197817, was used to survey an inshore 

area (Figure 1) which extended from Manzanillo, Mexico, to Lima, Pem 

offshore approximately 600 nm. Nineteen flights were completed in the inshore 

area with one additional flight (Flight 1) in the Gulf of California. This 

latter flight was a ferry and training flight, which generally occurred 

outside the target dolphin stock range; it was not included in the density 

analysi s. 

The two ships traversed an offshore area not accessible by aircraft 

(Figure 1). The R/V Townsend Cromwell, staged from Hawaii, covered the 

western extreme of the dolphin habitat, while the R/V David Starr Jordan, 

originated from San Diego, searched tracklines in the c-7s-n 

offshore regions. 

A calibration area was specified prior to the survey. It extended from 

Manzanillo, Mexico, to Puntarenas, Costa Rica, and extended offshore for 

550 nm (Figure 1); it is a subset of the inshore area. This region was used 

5A~, D. 1979. Cruise Report. Cruises DS-79-01 and TC-79-01, porpoise cruise 

No. 5. 463 and 464. Southwest Fish. Cent., La Jolla, CA 24 pp. 

6Jackson, T. D. 1979. Trip Report: Porpoise population aerial survey of the 

eastern tropical Pacific Ocean, January 22-April 25, 1979, Southwest Fish. 

Cent. Admin. Rep. No. LJ-80-1, La Jolla, CA 74 pp. 

7SWFC (Southwest Fisheries Center, Nat'l Mar. Fish. Serv., NOAA, La Jolla, CA 

92038). 1978. Aerial survey trip report, January-June. 1977. Southwest 

Fish. Cent. Adm. Rep. No. LJ-78-01. 

-- 

--- 

---- 
6 

to calibrate estimates made from ships with those made from the airplane. It 

was selected because, historically, high densities of dolphins occurred in 

this area. There were also several aerodromes adjacent to the coastline from 

which to stage the aircraft. 

The ships spent approximately 50% of their 60-day cruise in the 

calibration area. The PBY was to complete 11 flights in this area, but only 

10 flights were flown, leaving an area in the center of the calibration area 

between Flights 6 and 7 not covered by the airplane. In order to approximate 

coverage of a common area as closely as possible, tracks in this area not 

covered by both the airplane and ships were excluded from the calibration 

data, as were segments of plane tracklines extending outside the calibration 

area. Finally, because of logistical delays, flights were not completed until 

one month after the ship surveys. 

The surveys from the ships and from the airplane were designed to allow 

use of line transect theory in estimating the density of schools. Searching 

was conducted along preselected trackl ines, with legs of searching effort 

defined by changes in sighting conditions. At each sighting, both biological 

and physical data items were collected, including species identification, 

school size estimates, species composition within a school, sea state, sea 

surface water temperature, sun position, Greenwich mean time, and geographic 

position. The perpendicular distance of each school from the trackline was 

recorded for aerial sightings. Sighting angle and radial distance were 

recorded for each shipboard sighting, and the perpendicular distance was then 

c a l c u l ated from these data. 

Assumptions for Line Transect Estimation of Density 

Line transect methods have been used to estimate densities of many 

terrestrial species (Gates et al. 1968; Robinette et al. 1954, 1956) and were 

used in early estimates of dolphin abundance (Smith 1975*, 1981). Burnham, 

Anderson and Laake all participated in the ad hoc committee described above, 

and their monograph (1980) is relied on here. Following their presentation, 

five assumptions must be made in order to estimate the density of dolphin 

schools using the 1 ine transect method. 

1. A trackline of known length was placed randomly in the ETP. 

In practice, airplane trackl ines were placed systematically, subject 

to the location of suitable aerodromes. Ship tracks were plotted to 

systematically traverse the calibration area and, for the remaining 

30 days of their cruise, to search the offshore area while enroute 

to home port. Inside the calibration area, ships followed independent courses (Figure 1). In all cases, line lengths were considered 

fixed (known, not random). Within strata they were placed 

independently of information on areas of local concentrations. 

2. Schools directly on the trackline were never missed. 

The nose of the aircraft used in 1979 was modified with a plexiglass 

bubble which allowed an observer excellent downward and forward 
7 

visibility (Jackson 1979)6. The bow observer was instructed to halt 

the searching effort if he did not feel that he could detect all 

such schools due to reduced visibility. All animals of a small 

school could conceivably be submerged as a plane passed; however, 

the probability of all animals of larger schools being submerged 

decreases, and it was felt that all schools of at least 15 animals 

would always be detected. In addition, school sizes of species 

which are of interest, i.e., target species, seldom occur in schools 

with less than 15 animals. Therefore, only schools with at least 15 

animals were included in the analysis. These schools included those 

whose composition consisted of two or more species if at least one 

of the species was a "dolphin" species. 

3. Schools did not move in response to the sighting platform and 

none were courlted twice on the same trackline. 

For all practical purposes, dolphin schools do not move in response 

to an approaching plane due to the difference in their speeds. In 

fact, dolphins do not appear to be aware of the plane s initial 

approach, but they may exhibit an avoidance behavior towards 

approaching ships (Au and Perryman in press). Some species of 

dolphins appear to be attracted to ships and may ride the bow 

waves. The response of animals to the ships is difficult to 

quantify and, to date, a suitable 

does not exist. The probability 

school on the same trackline is be 

the low density and slow sustained 

survey platforms, and because of 

compared to the narrow detection w 

theory to account for this factor 

of multiple counting of the same 

ieved to be very small because of 

speeds of schools relative to the 

the magnitude of the ocean area 

dth of the survey path. 

4. There were no systematic measurement errors and no rounding errors 

in recording perpendicular and/or radial distances or sighting 

angles. 

Perpendicular distances for schools sighted from the airplane were 

either computed to the nearest 0.1 nm employing a Global Navigation 

System (Jackson 1979)6, or estimated visually to the nearest 0.1 

nm. Generally, distances were estimated vi sual ly when either the 

plane did not divert from the trackline to investigate a sighting or 

the school was observed close to the trackline. Perpendicular 

di stances for the shi p ' s si ghti ngs were c a l c u l ated from the vi sual 

estimates of radial distances and sighting angles. Perpendicular 

distances were then grouped into 0.1 nm intervals. 

In the 1977 and earlier ship sighting surveys, there has been a 

tendency for sighting angles and distances to be estimated in 

multiples of 5 degrees and 0.5 nm, respectively. Attempts were made 

to improve the accuracy of these estimates during the 1979 survey, 

but these were not successful. Therefore, line transect methods 

were not used to analyze ship data. 

I 
8 

5. Sightings were independent events. 

Sightings would not be independent if the probability of making a 

sighting was increased or decreased as the result of making a prior 

sighting. To insure independence, the searching mode was 

immediately discontinued, and any associated sightings were not 

included in the density analysis, once the survey platform diverted 

from the trackline to inspect a school. 

Line Transect Density Estimation Theory for Aerial Data 

If the assumptions for line transect theory are met, the density of 

dolphin schools can be estimated as (Gates et a1 . 1968; Seber 1973; Burnham 

and Anderson 1976) 

11 D =- 

2La 

where D is the density of dolphin schools per nm2, n is the number of 

schools sighted, L is the total track miles searched (nm), and a is an unknown 

parameter related to the probability of detecting a school. 

The estimation of the parameter a has taken many forms (Hayne 1949; Gates 

1969; Anderson et al. 1978; and Eberhardt 1978). Line transect theory is 

based upon the assumption that the probability of a school being detected 

decreases with distance from the track1 ine. Mathematically, this "detection 

function" g(x) can be described (Burnham and Anderson 1976) as the probability 

of observing a dolphin school, given that it is perpendicular distance x from 

the line of travel of the platform. 

For any continuous detection function g(x), one can define a probability 

density function (pdf), say f(x). Burnham and Anderson (1976) show that 

where 

a= 0 g(x) dx. 
9 

Evaluating this expression at x=O, and noting from assumption 3 that g(0) = 1, 

one obtains f(0) = l/a. Rewriting equation (1) yields 

Hence, the critica 

the detecsion function 

estimate f(0) of this q 

problem is one of estimating f(O), the value taken by 

in pdf form at zero perpendicular distance. Given an 

antity as discussed below, the density is estimated as 

The sampling variance of 6 can be estimated using the delta method (Burnham et 

al. 1980) as 

where iar(f(0)) is discussed subsequently. 

empirically using flights or days as replicates for plane or ship data, 

respectively , as 

The iar( n) is determined 

with r = number of line replicates, 

R = nm searched on ith replicate, 

ni 

L = total miles searched on all replicates, and = c R 

n = total number schools observed, and = c n 

i=l i 

= number of schools observed on ith replicate, 

r 

i=l i 

r 
10 

Detection Function Selection 

Density estimates based on a variety of detection functions have been 

published, many of which have been adapted to use with grouped data by Burnham 

et al. (1980). The models considered here include: 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

Kel ker ( Kel ker 1945 

Cox model (Eberhardt 1978) 

nontruncated negative exponential (Burnham et a1 . 1980) 

truncated negative exponential (Burnham et al. 1980) 

truncated exponential polynomial (Burnham et a1 . 1980) 

nontruncated half-normal (Burnham et a1 . 1980) 

truncated ha1 f-normal (Burnham et a1 . 1980) 

exponential power series (Pol lock 1978) 

Fourier series (Crain et al. 1978) 

The Fourier series (FS) model was selected as the most suitable as 

described below, following the four criteria suggested by Burnham et al. 

(1979): (a) model robustness, (b) pooling robustness, (c) shape criterion 

(i.e., f'(O)=O), and (d) relative efficiency. 

(a) model robustness - The ''true" detection curve, g(x), is never 

known. Infact, the shape of g(x) probably varies with dolphin species, sea 

states, and other factors. Hence, one must select a model which can closely 

fit a wide array of true f(x) shapes. In general, a flexible model will not 

require, - a priori, a specific form of f(x). 

The simple parametric negative exponential and ha1 f-normal estimators 

require a specific shape of f(x). The negative exponential model assumes a 

very sharp, rapid fall-off near x=O (i.e., it has f'(O)<O). If, in fact, the 

unknown true pdf does not meet this assumption, a severe upward bias of f(0) 

can occur. The half-normal estimator, as its name implies, requires that a 

pdf model the right half of a normal curve. Use of this model may result in 

biases in estimation of f(O) if the true pdf does not meet this constraint. 

The ''parnmeterless" Cox and Kelker models are model robust in the sense 

that they can be fit to any data. The Kelker model uses only those 

observations in a strip where it is assumed g(x)=l. The Cox model uses 

observations in two intervals out to a distance where the detection function 

drops "sharply". 

f(x) and approximates its area within the two intervals by a linear 

function. Both models are less precise than the Fourier series (FS) model, 

but could be used as a "yardstick" for other estimators. 

It assumes there is some probabil i ty density function (pdf 

Therefore only the exponential polynomial (EP), exponential power series 

(EPS), and the FS models are considered further. 
11 

(b) poolin robustness - The shape of g(x) is influenced both by physical 

factors, --I+ SUC as sun position, Beaufort (sea state) condition, platform, etc., 

and by species-specific biological factors, including animal size, coloration, 

school size, animal behavior, etc. Insufficient sample size prohibits 

stratifying data by each of these factors, Consequently, a suitable model 

must be robust to variations in detection probability for fixed x. Burnham et 

al. (1979) show that an estimator is pooling robust if, given s strata of 

factor p, 

provided that a fixed truncation point (w) and, for the FS model, a fixed 

number of terms (m) are used for all strata. In practice, w and m may not be 

constant among strata but are often determined empirically for each detection 

function in each stratum. 

School size categories were used to examine pooling robustness of the 

three model robust estimators. Specifically, the 1979 PBY dolphin sightings 

were partitioned into two strata: (1) sightings with estimated school size of 

at least 15 but no more than 50 animals and (2) those with school size greater 

than 50 animals. For each model, an estimate of f(0) was obtained for each 

stratum, and for all of the data together (Table 1). Pooling robustness could 

not be tested for the EP estimator because it did not fit the data well for 

the schools of greater than 50 animals, and the maximum likelihood estimate 

could not be obtained. EPS and FS models exhibited similar pooling 

characteristics (Table 1). The estimates obtained by summing the two strata 

in both models were within 20% of the unstratified estimate. Unstratified and 

pooled estimates were only approximately equal because m and w were not 

constant among strata, as sighting distributions were truncated dependent upon 

each specific detection function. In addition, model selection criteria, 

discussed subsequently, indicated that a 3-term FS model for strata (2) data, 

and 4-term models for strata (1) and unstratified distributions, were 

appropriate. Simulation studies (Burnham et al. 1980) with w and rn constant 

show that the EPS and FS models are pooling robust. 

(c) shape criterion - Intuitively, the shape of the true detection curve 

g(x) shoumve a "shoulder" near x=O (Eberhardt 1968). This implies that at 

some, perhaps small, region near the track1 ine, the probability of detection 

is very near l(i.e., g(x)=l) and hence, the derivatives of g(x) and f(x) 

should be nearly 0 at x=O. 

Specifically, this appears realistic for the aerial data. The ability of 

observers to detect "1 argell school s at increasing perpendicular distance 

certainly did not decrease sharply near the trackline (Table 2). In addition, 

Burnham et al. (1980) have shown that both the FS and the EPS estimators can 

model data which have the shoulder effect. 
12 

A 2 

a =- k nw 

(d) efficiency of the estimator - If a group of estimators is model 

robust, pooling robust, and meet the shape requirement, then their relative 

efficiencies should be ComDared. The most efficient model, as measured by its , should then be selected. 

k nx 

n i 

c cos (-1 k=1,2,3, ... i =1 W 

coefficient of variation (kv 

Comparisons of the CV 

pooling tests (Table 1) were 

CV for the EPS estimators 

corresponding FS model. 

of the EPS and FS models for the school size 

used to select the most efficient estimator. The 

n every stratum was at least twice that of the 

In summary, the FS model is model and pooling robust, has the necessary 

shape, and possesses the smal est sampling variance of any model tested. The 

participants at the October 1978 and June 1979 ad hoc committee meetings 

agreed that the FS model was a suitable model and should be used to estimate 

density of dolphin schools. The committee members recognized that other 

suitable models exist; for example, a model developed by Burdick (1979)* 

yields results very similar to the FS. 

Fourier Series Estimator 

The FS expansion was first applied to line transect theory by Crain 

et al. (1978). The reader is referred to their excellent detailed development 

of the FS model. In general for ungrouped data, the unknown pdf is modeled as 

W 

1 

L J 

where w = the perpendicular distance such that all sightings at greater 

di stances are omitted, 

m = the number of terms in the model, 

ak = parameters which must be estimated, where k=l, ..., m, and 

n = total objects observed with corresponding distance xi, 

i=l, ..., n. 

The coefficients ak are estimated as 

*Burdick, D. L. 1979. On estimating the number of porpoise schools. U. S. 

Tuna Foundation Tech. Bull. 124 pp. 
13 

Upon evaluating f(x) at x=O, (5) can be written as 

A mh 1 f(0) = - + c a . w k=l k (7) 

Crain et al. (1978) show that the sampling variance of f(0) is slmply the 

sum of all the variances and covariances of the coefficients of ak. The 

sampling variances of the coefficients are estimated by 

L 

and the sampling covariances (c^OV) of the &Is are estimated by 

A Ah m m AA 

Var(f(0)) = c c COV(a ,a ) . j=l k=l jk 

Equivalently, equation 10 simply expresses the v^ar(f(o)) as the sum of all the 

elements in the m x m matrix of the sampling variances and covariances (from 8 

and 9). 

For grouped data, such as the dolphin survey dgta, no simple explicit 

formula corresponding to (6) is available for the a . Instead, iterative 

al, ..., a and their sampling variances and covariances for any number of 

terms (m) burnham et a1 1980). A computer program (Laake et al. 1979) was 

utilized to calculate these estimators. 

rymerical pethods were used to calculate maximum like 4 ihood (ML) estimators 

The number of terms, in, in the FS model must be selected in a 

nonarbitrary manner. Two measure-of-fit tests were used. The primary test 

was the log likelihood ratio (LLR) test which compares log-likelihood values 

between the m and m+l term models (Burnham et al. 1980). The ML estimates, 

al, ..., a are obtained as above. Then, if in L, represents the log1 i kel i hood ?unction eval uated at the ML estimates, the log-> i kel i hood ratio 

in( Lm/ Lm+l) can be used to test the null hypothesis that E(am+l)=O, versus 
14 

2 the alternative E(a,,i) #O. In practice the test assumes the form of X = 

-2(nn Lm - An Lm 11, with the null hypothesis being distributed as a chisquare variable t~ 2, with 1 degree of freedom. 

If the null hypothesis is rejected, then &+l is a significant term and 

should be included in the model. By failing to reject the null hypothesis, 

the m-term model is accepted as an adequate model. 

If results of the LLR test are inconclusive, i .e. , if the LLR value is 

very close to the critical X2 value of 3.84 (1 degree of freedom, a: = .05), 

then the fit of each model to the data is examined using the chi-square 

goodness-of-fi t test. A general overall fi t i s desi rabl e; however , more 

specifically, the data in the first interval (x=O) must be modeled closely. 

The model is chosen which provides the best fit in the first few intervals, 

provided there is also a good overall fit. 

Aerial Data Characterization 

Prior to data being fitted to any model , it is necessary to make several 

decisions regarding the structure of the input data. Some of these factors 

have already been addressed. Specifically, we used only those sightings which 

were observed while the platform was in a search mode (assumption 5, 

independence of sightings); had an estimated average school size of greater 

than 14 animals (assumption 2, probability of sighting equal 1); and were made 

in the area under investigation. Other more subjective decisions include 

species composition of the sample, selection of interval cutpoints and 

truncation point for the perpendicular sighting distributions. 

(a) species selection - In order to obtain the maximum sample size and to 

ensure imn of all 5 species of interest, all sightings which were 

identified as being dolphin species were included in the school density 

analysis. These incl uded stocks of spotted dol phin (Stenel 1 a attenuata), 

spinner dolphin (S. lon irostris), striped dolphin (S. coeruleoalba), roughtoothed dol Dhi n TSteno -+a- re anensi s ), Ri ssol s dol fii n (Gramws ari seus ). 

Frazi er' s dol phi n (Lagenode1 phi s hosei , common dol phi n ( Dms mj 

bottlenosed dolphin (Tursiops trun*), and "unidentifier dolphins. 

(b) interval selection - Perpendicular sighting distances for schools 

observed from the PBY, as indicated earlier, were either measured or estimated 

to the nearest 0.1 nm. Therefore, data can be considered as grouped into 0.1 

nm intervals. Mid-points between the 0.1 nm measurements were used as 

interval cut points. Dependent upon the truncation point chosen, cut points 

used were 0.0, 0.05, 0.15, 0.25, ..., w nm. (Note that schools were observed 

on either side of the plane but data were "folded over" into the 0.1 nm 

intervals.) 

Observers felt that large schools (>14 animals) could be observed with a 

probability equal to 1.0 in a path directly below and forward of the plane 0.1 

nm wide (i.e., 0.05 nm to either side of the plane). Therefore, due to the 

grouped nature of the data, only those schools recorded with perpendicular 

distance of 0 (i.e., rounded to 0 nm) were considered asabeing on the path 

line and observed with probability of 1. This interval, 0-0.05 nm, includes 

only half the area searched in each of the other "folded-over" intervals. 
15 

(c) data truncation - Aerial surveys may employ a preset maximum 

observationstance (w) perpendicular .. to the track1 ine (Leatherwood et a1 . 1978). However, it is more desirable to record all sightings and then 

truncate data during the analysis stage. No schools need be omitted since w 

may be specified as the largest observed perpendicular distance. However, 

observations noted at extreme perpendicular distances may be considered 

"outliers" and a truncation point selected which will omit these from 

analysis. Because it is f(x) at x=O that must be estimated, observations that 

occur at small perpendicular distances should have the greatest effect; those 

at great distances should have minimal input. The June 1979 ad hoc committee 

suggested that no more than 10% of the observations should be truncated. A 

minimum truncation distance of 0.85 nm is required to include 90% of the PBY 

observations. 

The choice of a truncation point is somewhat subjective and its effect on 

the model is of interest. The aerial data were truncated at successive O.? nm 

increments and subjected to analysis by the FS estimator. Estimates of nf(0) 

calculated at each truncation point did not differ substantially (Table 2). 

Relative effiGiencies, determined by relative sizes of the coefficient of 

variation of f(0) at each point, were very similar for all truncation points 

including at least 90% of the observations, and could not be used to select a 

truncation point. 

It is desirable to include the largest sample size possible while 

selecting a model which includes the smallest number of parameters. For 

example, if a truncation point of 2.05 nm is chosen, six terms are necessary 

to fit the model to the data. Conversely, if 1.05 nm is chosen as the 

truncation point, a 3-term model would fit. The loss in sample size at 1.05 

nm is less than 7% of the total observations. 

In summary, the aeri'al inshore perpendicular sighting distribution was 

truncated at 1.05 nm because it included the minimum 90% of the sightings 

(93%) and because a 3-term model is appropriate, whereas a 4-term model would 

be required if a truncation point of 1.25 nm were selected. For similar 

reasons, the aeri a1 cal i brati on perpendicul ar si gh;i ng di stri bution was 

truncated at 0.95 nm. Again, it should be noted that nf(0) estimates are very 

similar regardless of the truncation point chosen. 

Density Estimation Theory for Research Ship Data 

Radial distances and sighting angles were recorded for observations taken 

aboard the ships. Cal cul ated perpendicul ar di stances were grouped usi ng the 

same intervals as for aerial sightings. As already indicated, these data 

contained serious biases. 

Sighting distributions for dolphin schools observed from research ships 

both in the calibration area and in the offshore area indicate that an 

inordinately high number of schools were recorded as being directly on the 

trackline (Table 3). This was most pronounced for the Jordan data, where 20% 

of all "large" school sightings were recorded bet- and 0.05 nm 

perpendicular distance; only 4% of the sightings were recorded in the next 

interval 10.06 through 0.15 nm). Again, note that the second interval 

included twice the amount of area searched as the on-track interval. The 

percentage of the observations for the Cromwell data recorded in the first and 

second intervals were 12 and 6%, respectively. 
16 

Sighting distributions which exhibit a pronounced shoulder very close or 

directly on the line, with a sharp decrease in the adjacent interval, would be 

expected to have a very short "tail"; i.e., visibility should decrease rapidly 

and few sightings should be observed at great distances from the trackline. 

But sighting distributions for both ships had very long tails (Table 3). 

Schools actually located adjacent to, but not on, the trackline very possibly 

could have been recorded as being on track. This "heaping effect", if it 

occurs, may be due to an inability for the unaided eye to accurately discern 

small angles (say 0' to 10') at large distances; mean radial distance for the 

35 schools was 2.4 nm. 

This problem is very complex and not well understood. It may possibly be 

related to movement of the dolphin schools (assumption 3, above). Avoidance 

trajectories of dolphins observed from helicopters have been studied by Au and 

Perryman (in press), but sufficient data do not exist to quantify this. In 

addition, the specific motion of a ship will affect sighting abilities. This 

includes the degree of a ship's roll, pitch, and yaw. Even in relatively calm 

waters, one or more of these factors may occur and can affect accurate data 

acqui si ti on. 

Regardless of causal factors, neither the FS model nor any other model 

tested fit the ship-sighting distributions. A marginal fit by the FS model 

could be obtained for both ships' data by grouping the data into 9 or fewer 

broad equal-intervals [Figures 2 and 3). However, the smoothing effect (and 

thus the estimate of f(0)) is highly dependent on the interval width chosen 

when abnormalities in the distribution occur close to the origin. 

The 1979 survey was designed to determine a correction factor (K) for the 

avoidance phenomenon and for other unknown biases for each of the two ships 

separately, by relating ship data to plane data in a common area such that 

= estimated density of schools in the calibration area 

based on 1979 aerial line transect data, and 

ssc = estimated density of schools in the calibration 

area based on 1979 ship line transect data (either 

ship). 

where: 6pc 

However, f(0) for ship data could not be estimated because of the failure of 

the models to fit the data. Therefore, alternate analyses were completed. 

Let: 9 =ratio of the number of sightings (n) per track mile 

h =ratio of the number of sightings (n) per track mile 

'so = 

searched (L) from a ship in the calibration area, 

searched (L) from a ship in the offshore area, 

estimated density of schools in the offshore area based on 

ship data. 

I 
17 

Then for some constant C, 

A 

h D c = -pc- . (11) 

Azsuming the ratio is independent of area, the density in the offshore area 

(Dso) can be calculated by 

A I 

= Ch SO 

or 

A hi = *c-. 

9 so (12) 

The sampl i ng variance 

(Seber 1973) as 

of is0 is approximated using the delta method 

The asymptotic sampling variance of 6 is given by (3) while the 

variance for the terms g and h can be expresseicas 

where n is the number of sightings, iar(n) is given by (4), and L is line 

1 ength searched. 
18 

Estimated density for the offshore area was calculated by weighting the 

Jordan and Cromwell density estimates by their respective track miles searched 

as 

A A 

A D L+D L = Jo4~ro-CoLJo + LCo 

to 

where: ita = estimated density in the offshore area based 

= estimated density in the offshore area based 'J o 

on weighted ship estimates, 

on Jordan data and equation (121, 

GCo = estimated density in the offshore area based 

on Cromwell data and equation (12), 

number of track miles searched from the Jordan LJo = in the offshore area, and 

Lco = number of track miles seached from the Cromwell 

in the offshore area. 

Sampl ing variance is given by 

(15) 

As already noted, (12) is based upon the assumption that sighting 

efficiencies (i .e., detection functions) are constant over area and are 

therefore independent of density. Two factors which may introduce biases are 

relative sea state conditions (measured by the Beaufort scale) and sighting 

cue differences. These factors were examined by the 1979 Status of Porpoise 

Stocks (SOPS) Workshop (Smith 197919. 

For comparative purposes, research ship effort data were recorded by 

utilizing techniques employed by tuna vessel observers (Au 197912. This 

approach did not allow stratification of effort by Beaufort. Specifically, 

Beaufort number was recorded at the beginning of each searching leg, which 

gSmith, T. D. 

27-31, 1979) Southwest Fish. Cent. Adm. Rep. No. LJ-79-41, La Jolla, CA 

1979. Report of the status of porpoise stocks workshop (Aug. 

---- 120 pp. 
19 

represents a constant unit of effort, but searching legs were not changed when 

Beaufort changed. 

The SOPS Workshop members (Smith 1979) suggested that Beaufort numbers 

recorded at the time of sightings be averaged for inshore and offshore areas 

to determine if sea state conditions were comparable. The average Beauforts 

at which schools were observed were very similar in the two areas (Table 4). 

The SOPS Workshop participants therefore concluded that weather was not a 

significant factor. This assumption is also used herein. However, it should 

be noted that the average Beaufort at time of sighting does not incorporate 

the amount of searching effort and thus it is simply the average Beaufort when 

a sighting was observed. 

Birds associated with porpoise schools are used by observers as sighting 

cues. It was noted that the proportion of sightings associated with birds was 

greater in the inshore area than the offshore areas (Table 4). This would 

introduce bias because bird-associated schools are observed at greater 

perpendicular distances than are schools which are not associated with 

birds. Examination of the average perpendicular distances for schools on the 

inshore versus offshore areas indicated that sighting distances of birdassociated school s and school s without birds were different (Table 4). 

However, it should be noted that the number of bird-associated schools 

observed from both vessels in the offshore area was small. Large sample sizes 

in the offshore area are only present for schools not associated with birds 

observed from the Jordan; the average perpendicular distance for these schools 

is equal to that ominshore schools. The SOPS Workshop suggested that all 

ship sightings observed at a perpendicular distance greater than 1.15 nm be 

omitted from the analysis. This "correction" is used in this report. 

Density Estimates 

Inshore Area 

A total of 15,195 nm was searched while completing 19 flights in the 

PBY. Dolphins were observed in 

every 0.1 nm interval out to 1.0 nm; only eight schools were reported beyond 

this point (Table 5). The maximum perpendicular distance recorded for any 

school was 3.8 nm. As indicated, schools observed at a greater distance than 

1.05 nm were omitted from analysis (w=1.05 nm). 

Observers recorded 118 large dolphin schools. 

A 3-term FS model was selected as the appropriate model based upon 

results of the LLR test and the X2 goodness-of-fit test (Table 6). 

provided an excellent fit to the data (Figure 4). 

The model 

Equation (7) therefore was 

1.2890 + 0.7489 + 0.3299 = 3.32 1 

1.05 

i(0) = - + 

The density of schools in the inshore area using equation (2) was 0.01202 

schools per nm2. The standard deviation of n from Table 7 and equation (4) 
20 

was 17.197. 

coefficient of variation of D is 16.8%. 

The standard deyiation for 6 from equation (3) was 0.00202. The 

For comparative purposes, the Cox and Kelker models provided very similar 

estimates to the FS model. Their standard deviations, however, were larger 

than those of the FS. The density of schools determined by the Cox and Kelker 

models were 0.01397 and 0.01316 schools per nm2, respectively. Associated 

standard deviations were 0.002779 and 0.002895, respectively. 

Calibration Area 

Observers aboard the Jordan, Cromwell , and PBY recorded 77, 37, and 42 

large schools of dolphins imcalibration area while searching 2718, 2157, 

and 6240 nm, respectively (Table 8). Both vessels surveyed approximately the 

same number of track miles in the offshore area as in the calibration area; 

however, substantially fewer schools were observed in the offshore area. 

A 4-term FS model (Table 9) was used to determine school density for the 

aerial data in the calibration area. The log-likelihood ratio test for 

selection between a 3- or 4-term model was inconclusive; the ratio value was 

3.36 versus a critical X2 value of 3.84 (df=l, a =.05). The X2 goodness-offit tests were then examined; the 4-term model was selected because it 

generally provided a better overall fit and specifically fit better in the 

first interval (Figure 5). 

h 

Substituting the ML estimates, a, (m=1, ..., 41, into equation (7) 

1 

0.95 

t(0) = - + 1.322 + 0.890 + 0.661 + 0.366 = 4.29 

The density of doljhin schools determined from aerial sightings in the 

calibration area (D from equation (2) was 0.01444 schools per nm2. 

The sampling varianc8Cqf n from Table 10 and equation (4) was 81.55. The 

standard deviation for Dpc from equation (3) was 0.0035. 

Off shore Area 

The total number of observed dolphin schools and nautical miles searched 

by the ships in the calibration and offshore areas are given in Table 8 as are 

the associated standard deviations for each n/L ratio, calculated using Tables 

11-14 and equation (14). 

and Cromwell (ice) data in the 

offshore area from equation (12) were 0.0&24 and 0.00335 4 schools per nm2, 

respectively. Respective associated standard deviatiop using equation (13) 

were 0.00496 and 0.00101. The total offshore density (D and its associated 

standard deviation from equations (15) and (16) were 0.686458 schools per nm2 

and 0.00262, respectively. 

Density estimates for the Jordan (6 
21 

111. MEAN SIZE OF DOLPHIN SCHOOLS 

In the next step of the analysis estimates for the density of dolphin 

schools (calculated in the previous sections) were expanded by estimates of 

mean school size to obtain density of individuals. In this section, 

techniques for determining the mean school size estimate are presented. 

Data Sources and Possible Biases 

School size estimates are available from data sets collected by (1) 

scientific observers aboard the aerial survey aircraft, (2) scientific 

observers aboard the research vessels, (3) observers placed aboard tuna purse 

seiners, (4) crew members of observed tuna purse seiners, and (5) aerial 

observers using photography during the aerial survey. With the exception of 

the aerial photography, the school size estimates are simply visual 

assessments of the number of dolphin present and are subject to unknown 

errors. 

Each of the above data sets is subject to two forms of possible bias: in 

the estimate of an individual school's size (measurement bias), and in the 

sample of schools measured (size biased sampling). Very few data exist to 

test the first form of bias directly because only two actual counts of the 

total number of dolphins within a school have ever been done in the ETP purse 

seine fishery, neither of which were in conjunction with a research vessel or 

aircraft (DeBeer 198Ol1O. Reasons for possible measurement bias in the data 

are (1) not all of the dolphins are seen at one time, (2) a vague multiplying 

factor is often used on tuna vessels to adjust for animals not seen 

underwater, (3) aerial photography may not record all of the dolphins 

underwater, (4) adverse sighting conditions, such as heavy seas, may reduce 

the view of the school, and (5) observers aboard tuna vessels may consistently 

alter their estimates in relation to the crew, assuming the crew's estimates 

are biased and the crew may be altering their estimates in the opposite 

direction. These possible biases are mostly unknown and may lead to downward 

or upward errors in estimation. 

Sampling bias can take many forms. First, it is likely that the 

probability of sighting a school is increased with large schools. Therefore, 

the sample of observed schools is biased toward large schools. Second, tuna 

vessels are concentrating their effort on dolphin schools which aggregate with 

tuna. These schools are likely to be large relative to schools without tuna, 

even within the same dolphin species. Third, since the main course of 

business aboard the tuna seiner is catching fish, the presence of smaller 

schools which do not affect the fishing operation may not be communicated to 

the observer. 

l0DeBeer, John. 1980. Cooperative dedicated vessel research program on the 

tuna porpoise problem: overview and final report. Final Report to the U. S. 

Mar. Mammal Comm. 43 pp. 
22 

Another set of sampling biases may occur for the research platforms 

(vessels and aircraft). The aircraft can only search the inshore waters to 

approximately 750 nm from the coast. If there are differences in school size 

between the inshore and offshore areas, the aircraft sample extrapolated to 

offshore areas may be biased. Similarly, the research vessels cover 

relatively small areas of the ocean. Their sample may not be representative 

of the total area. Finally, the schools photographed may be considered to be 

a sample for calculation of the mean. However, choice of schools to be 

photographed may be made on the basis of size. Smaller schools of less than 

30 or 40 individuals may have a lower chance of being photographed. 

The analysis of school size was divided into "target'l and "non-target'' 

species groupings. As previously indicated, the "target'' species are those on 

which fishing effort is directed; i.e., it is known that yellowfin tuna 

aggregate with these species from time to time. These target species include 

spotted dolphin, spinner dolphin, common dolphin, striped dolphin, and 

Fraser's dolphin. By including Fraser's dolphin in this group, the more 

general identification of "unidentified whitebelly" could a1 so be included 

with the target species, raising the sample size. Unidentified whitebellies 

in the ETP can be Fraser's, common, striped, or spinner dolphin. Therefore, a 

school of animals of the target species was one in which striped, spotted, 

common, spi nner, Fraser' s, or uni denti f i ed whi tebel ly occurred. The other 

group (non-target species) includes a1 1 other dolphin school s. The school 

size analysis was based upon these two groups. 

Correction for Si ghti ng Bi as 

The ad hoc committee participants pointed out that school size and the 

probabi 1 i ty of sighting were posi ti vely correl ated. A1 though the estimator of 

school density is robust to pooling over school size classes, the estimation 

of the mean school size is not. The school size must be weighted inversely to 

the probability of it being sighted. Several committee participants addressed 

the question of an appropriate correction factor by noting that 

n 

c f(0lS.) s i =1 ii 

E(S) = 9 (17) n 

c f(OlS.1 i =1 1 

where S is the school size and f(0lSi) is the probability density for the 

sighting function, given a particular school size S- and evaluated at the 

perpendicul ar si ghti ng di stance equal to zero. The empi rical weighting 

formulae were developed using an exponential power series model for f(XlS). 

The choice of this model is one of convenience in order to obtain the weights, 

but it has sufficient generality to model many school size distributions, 

i .e., it includes curves with both negative exponential and ha1 f-normal 

shapes. Therefore, let f(XlS) be equal to an exponential power series. 
23 

Then 

where the scale parameter h(S) is an appropriate function of school 

size, r is the gama function, and p is a shape parameter (Pollock 1978). 

Thus, 

1 

where C' is a constant. 

distance given a particular school size is 

The expected value of the perpendicular 

Assuming curve shape (p) is relatively constant and only the scale 

parameter (A) is affected by school size, then h is modeled as a function of 

school size (S) but p is independent of S. The above equation then reduces to 

where C is a constant equal to 
24 

Using equations (17) and (18) 

n S 

At this point an appropriate characterization for 

The log-linear function was postulated, i.e., 

h(Si) had to be chosen. 

E(XIS) = C h(S) = a+b ln(S). (20) 

If it is assumed that parameter a is equal to zero in equation (201, then 

the corrected estimator becomes 

an estimator which is independent of the value of the parameter b. 

Equation (20) was fitted to school size interval data (Table 15) using 

weighted 1 inear regression separately for aerial and research vessel data, and 

the estimate of the parameter a was not significantly different from zero. 

The proportional model was fitted, yielding estimates of the parameter b of 

0.08, 0.24, and 0.25 for the aerial , Jordan, and Cromwell data, 

respectively. The model fit the data well, withcorrelation coefficients 

ranging from 0.81 to 0.95 for the three platforms. Note that this correlation 

is between the expected value of x given S and the correlation of x with 

Ins. Thus, there are only 6 degrees of freedom for the fit. The effect of 

utilizing the corrected mean is to reduce the mean school size to about 80 

percent of the uncorrected value (Table 16). 

School Size Estimates from Aerial Photographs 

The aerial photographs were taken with 2-1/4" x 2-1/4" and 9" x 9" 

formats. At the time the photographs were taken the observer at the camera 

station recorded the aircraft's speed and altitude. He also made notes on the 

shape of the school, the probability that the entire school was photographed, 

and whether any portion of the school was seen to dive out of sight as the 

photographic over-flight was in progress. 
25 

After the transparencies were processed, they were reviewed on a light 

table with a hand-held magnifying lens; photographs that did not include the 

entire school or were judged to be of inferior quality were eliminated. The 

2-1/4" square slides were then projected against a large sheet of paper where 

individual animals were marked. The 9" transparencies were taken to the NASA 

test facility at Bay St. Louis, Mississippi, where they were enlarged and 

analyzed on Variscan Mark I1 projectors. A sheet of clear plastic was 

attached to the projector screen, and individual animals were marked as 

described above. 

Three experienced aerial observers with know1 edge of aerial photography 

of porpoise schools made independent counts and estimates from each of the 

selected photographs. They were instructed to mark all the animals that they 

could see in the photographs and to use this count, their impression of the 

quality of the photograph, notes taken by the photographer, and information 

available from any other transparency of the same format of the same school , to derive their estimate of the school size. Since the two formats were 

analyzed separately, only photographs of the same format would be used for 

comparison in making an estimate. 

Each observer devel oped hi s own technique for marking and estimating. 

One technique was to mark every possible image as an animal and then allow 

very few animals as missed when generating the estimate. Another was to mark 

more conservatively and to allow a larger percentage as possibly missed. For 

each transparency the observer made notes as to the quality of the slide, his 

estimation technique, and his confidence in his estimate. After all the 

acceptable photographs were analyzed, the 2-1/4" and 9" results were compared, 

and the photograph with the largest estimate was selected as the best 

photograph of that school. The largest estimate was selected because 

photographs can only provide minimum counts. The average estimate from the 

three observers was used as the best school size estimate for that school. 

The sample of usable photographs included 15 from the 1979 aerial survey 

(11 target schools, 4 nontarget), 4 from the 1977 aerial survey, and 4 taken 

from he1 icopter photography and observation associated with a research vessel 

in 1976 aboard the R/V Surveyor. The control of the photographic analysis of 

the latter two groups was not as refined as that of 1979; therefore, more 

weight was placed on the 1979 sample. 

The mean school size estimates generated from the photographs correlated 

quite closely with the mean of the aerial observer estimates for that sighting 

(Figure 6). For all of the photographed schools (n = 231, the correlation 

coefficient between observer and photographic estimates was 0.96. The 

correlation coefficient was 0.97 for the target species (n = 11) in 1979. The 

photographs also allowed estimation to become more precise. The range of 

estimates from the photographs was always smaller than the range from aerial 

observers (Figure 7). 

The sample of 11 target schools yielded a weighted mean of 343.91 and 

306.95 animals from the aerial observer and photographic estimates, 

respectively. This does not differ significantly from the weighted mean from 

all target species in the 1979 aerial survey (Table 16). The small sample of 

photographs resulted in a very large standard error. In addition, after 

discussions with the aerial survey personnel, it was concluded that aerial 
26 

photographs were probably a biased sample in that schools of less than 40 

animal s were examined but not photographed. Therefore, the photographic 

estimates were used for comparison and not as a random sample. 

The possibility also exists that the aerial observer estimates of schools 

not photographed were biased downward due to sighting conditions. Using the 

Beaufort number as an index of sea state, the photographed target schools had 

a mean Beaufort number of 1.73 (standard error = 0.271, while the 

unphotographed target schools had a mean of 2.81 (standard error = 0.10). 

As expected, this shows that the photographs were either not taken or did 

not process well when there was a higher sea state. However, this comparison 

does not indicate that the estimates by aerial observers become biased 

downward during choppy sea conditions: there are not data from which to 

conclude that such a bias exists. But if heavy seas do cause such a bias, the 

estimate of size from the sample of unphotographed schools would accordingly 

be biased downward. 

The effect upon the school size estimate of increasing the length of time 

during which a school is viewed was studied in a controlled experiment during 

a flight of the 1977 aerial survey in the Gulf of California. This study 

showed that observation times of 3, 7, and 9 minutes did not result in 

significant increases or decreases in the school size estimate (Brazier 

1978) ll. 

In summary, the mean school size estimated from photographs correl ated 

closely with the mean of aerial observer estimates for each particular 

sighting. In addition, photographs yielded a mean estimate which did not 

differ significantly from the mean school size for all target schools. 

However, we conclude that aerial photographs are probably a biased sample and 

should not be used as an independent estimate of average school size, but 

rather as corroboration for the visual estimates. 

School Size Estimates from Tuna Vessels 

Examination of school size estimates of target species by EIMFS observers 

and crew members on tuna vessels produced some interesting results. First, to 

avoid possible sampling bias introduced by concentrations of fishing effort 

(and sightings) in areas of larger schools, the sample was reduced to only 

those target schools which were sighted while the observer was on marine 

mammal watch, i.e., when he was in a search mode and the vessel was searching 

or running to new grounds. The data were further grouped into schools where 

(1) the observer made estimates of size, (2) the crew made estimates and (3) 

both the observer and a crew member made estimates. Note that these are not 

exclusive categories. 

llBrazier, E. B. 

estimation data from the eastern tropical Pacific. Copley Int'l Gorp., La 

Jolla, CA 117 pp. 

1978. A statistical analysis of porpoise school size 
27 

The results (Figure 8) show that each year the observer estimates 

consistently had a larger sample size and a smaller mean than the crew member 

estimates. The observer obtains information on the presence of a dolphin 

school from his own observation and from communication with the crew when they 

make a sighting. The data indicated that some schools which the observer made 

estimates of were either ignored by the crew or the crew was not aware of 

them. Apparently the crew member estimates recorded were biased toward 1 arger 

schools. The crew member may not notice or may not care to venture an opinion 

about schools which do not affect fishing. Thus, the observer made estimates 

on a larger number of schools, the difference being the smaller aggregations 

of target species. Conversely, there may be sightings of which the crew are 

aware and the observer is not. We do not have data on this form of sampling 

bias, if such schools would indeed cause bias. 

The difference between observer and crew member estimates when both were 

made (Figure 8) tended to increase during 1977 through 1979. This may have 

occurred due to increased training of observers on school size estimation 

procedures. 

It is, therefore, concluded that the crew member estimates result in a 

sample that is biased toward larger schools. No data exist to detect 

corresponding sampling bias in the observer estimates. In addition, because 

the estimations of neither observer nor crew have been calibrated by 

photographs or other means, there has not been an independent verification of 

the tuna vessel estimates. 

Spatial and Temporal Bias 

The impact of variables such as geographical area and time of the year on 

school si ze estimates from aircraft , research vessel s , and tuna vessel s were 

investigated by Brazier (1978) l1 using one-way analysis of variance. This 

approach was extended (Appendix 2) to look at the factors jointly, i.e., with 

mu1 ti-way analysis of variance. The results indicated that some regional and 

seasonal differences in school sizes exist, but also that the cause for this 

may arise from a variety of sources including bias in the estimates from the 

various platforms. Therefore, the util ization of this information to adjust 

for seasonal or regional sampling bias was investigated. 

Aerial photography supported the bel ief that aerial observations produced 

measurements of school size with little bias. The aerial surveys did not, 

however, cover the entire range of the dolphin stocks. For this reason, an 

extrapolation would be necessary to estimate school sizes in the areas not 

covered. An extrapolation util izing available tuna vessel data and the basic 

analysis of variance model is one possibility: 

'ijk = X + =i + pj + aij + 'ijk 

The mean school size for regional area i, during quarter of the year j, 

as estimated from platform k, can be expressed as the grand mean for all areas 
28 

and seasons and a sum of the effects due to area, quarter, arealquarter 

interactions, and platform. Note that an interaction between platform and any 

other factor would invalidate this extrapolation method. 

Using mu1 ti -way analysi s of variance (Appendix 2 ) , regional area could 

not be shown to be significant in its effect on school size as estimated from 

tuna vessels. This point sheds doubt on the potential value in any 

extrapolation of school size estimates by area. Nevertheless, this model 

could be of some value if there was substantial agreement between tuna vessel 

and aerial observations at the same time of the year for the same area. But 

there is no strong agreement between school sizes as estimated from a tuna 

boat and as estimated from the air (Appendix 2). In conclusion, there seems 

to be no basis for using tuna vessel data to extrapolate aerial survey 

estimates of school size into areas not covered by the survey. 

Choice of Mean School Size Estimate 

Weighted means for data from the aircrgft, research vessels, and tuna 

vessel s were c a l c u l ated using equation (21 1, i .e., 

Jacknife techniques were employed to calculate standard error (SEI estimates 

of s. 

The resulting estimates (Table 17) show that point estimates differ 

markedly between research platforms and tuna vessels both in 1977 and 1979 

survey years. This occurs even in the well-defined calibration area. The 

evidence of the photographic analysis and the demonstrated bias of the tuna 

vessel data led all but one of the ad hoc committee participants12 to conclude 

that the estimates of school size from tuna vessels should be rejected. There 

was no statistical difference between estimates from aircraft and research 

vessels. However, these estimates were not combined because the corroborative 

evidence of the photographs were for the aircraft and not for the research 

vessels. Therefore, it was concluded that the mean school size should be 

derived solely from the aircraft data. The aircraft estimates for 1977 and 

1979 for the target species are in Table 17. The 1977 and 1979 estimates for 

the nontarget species are in Table 18. 

120ne workshop participant expressed doubt as to the validity of excluding 

from the school size analysis tuna vessel observer estimates without ''at least 

a small body of accurate representative tuna vessel school size data" which 

could be compared to other platforms. 
29 

IV. SPECIES PROPORTIONS 

The estimate of the total number of dolphins is divided among the several 

species in two steps. First, the proportion of those dolphins sighted which 

belong to the "target" group is determined (Pt in the Introduction), based on 

the data from the research platforms. Second, the proportion of these target 

dolphins of each species is determined (Pi in the Introduction), based on 

either the research vessel or, alternately, the tuna vessel and research 

vessel data pooled. 

Target and Nontarget School s 

School size is likely to be related to species. Because the sightability 

of larger schools is greater, the estimated species proportion based on 

sighting data may be biased accordingly. To adjust for this suspected bias, 

the proportions must be weighted by the probability that a particular school 

size (and thus a particular species group) is seen. The weighting factors 

developed for correction of the mean school size are considered appropriate 

for this correction (see Appendix 4 for development): 

n 1 

c 

i=l m S P - - i 

where 

= the proportion of the density of schools 

= the number of target schools, 

which are target species schools, 'target 

n 

m = the number of nontarget schools, and 

Si = the school size. 

This weighting scheme assumes that the ratio of unidentified target 

schools to all unidentified schools is the same as the ratio of identified 

target schools to all identified schools. 

In discussions with aerial survey personnel it was verified that one 

nontarget species was especially easy to identify. Risso's dolphin (Grampus 

griseus) was probably identified in all cases from the air; thus, the 
30 

unidentified schools should not include this species. Therefore, the 

proportion of target species as calculated from aerial data used the equation 

(developed in Appendix 4): 

P 

target 

where n = number of target schools, 

Risso's dolphin occurs), 

m = number of nontarget schools (excluding those in which 

g = number of schools of Risso's dolphin, and 

u = number of schools that are unidentified. 

To estimate the variance of the estimate of Ptar t, the data were 

separated into units of effort, days for the ships, a% flights for the 

aircraft. An estimate of Ptar et was calculated for each day or flight using 

equations (22) or (231, respecavely. The variance of the estimate of Ptarget 

was estimated from the variability of these rep1 icates. 

The Townsend Cromwell data resulted in higher estimates of Ptar et than 

the data Tor the other research vessel, David Starr Jordan, or the airsraft in 

both 1977 and 1979 (Table 19). The Cromnswincludes the more westerly 

area of the ETP, which may have a lower density of nontarget schools. When 

the data from all of the research platforms were pooled, the estimate of 

was very consistent between 1977 and 1979. Therefore, the pooled 

es Ptarae€ 1 a e of Ptar e was used in proportioning the density for both the aerial 

and research vesaf density estimates. 

Year target Standard Error 

1977 0.7291 

1979 0.7105 

0.0447 

0.0338 
31 

Conversely, the proportion of nontarget schools (P ontarget) was calculated as 

on ar et = 1 - Ptarget and standard error of pnontarget was equal to the 

s p€ an 2 ar il error of Ptarget. 

Year nontarget Standard Error 

1977 0.2709 

1979 0.2895 

0.0447 

0.0338 

Species Proportions of Target School s 

Once a school was sighted from the aircraft, research vessel, or tuna 

vessel, the proportion of each species occurring in that school was recorded 

as a fraction. Each school, therefore, had a proportion associated with each 

species. The values of these fractions ranged from zero to one, 

inclusively. The target schools could thus be prorated to the categories: 

spotted dol phi n, spi nner dol phi n, common dol phi n, striped dol phi n, Fraser ' s 

dolphin, and other cetaceans, based upon the mean values of the fractions from 

the sample. 

There is, however, a correlation between size of the school and the 

species occurring in it. Therefore, the proportional representation of each 

species, the species distribution, is affected by the size of schools seen and 

by the sighting bias caused by larger schools being seen more often than 

expected. One can attempt to correct this bias by applying the same weighting 

factor used for calculating both the mean school size and the expected 

proportion of target schools. The weighting factor, the inverse of the 

logarithm of school size, can be incorporated into the estimate as 

n 

c 

i=l 

P= 

j n 

iz1 [Ai] 

where 

si = the school size for sightings of target schools 

(i=l, 2, ..., n) 

school size i 

Pij 

'j 

Species distributions were calculated separately for the inshore area, 

northern offshore area, and southern offshore area, using equation (24) and 

sighting data collected from aircraft, research vessels, and tuna vessels. 

The assumption was made that the distributions of perpendicular sighting 

distances among research ships or among tuna vessels were not greatly 

different. 

= the proportion of individuals of species j in 

= the estimated proportion of individuals of species j 

in all target schools. 

The areas corresponded to the estimation methods for density of 
32 

schools and provided strata for which gross differences in species 

distributions could be detected. The results indicated that the distributions 

of species varied with the data set chosen (Table 20). 

Based on discussions with aerial survey personnel, it was concluded that 

the species distribution from that platform may be biased due to a 

differential ability to identify species within the target school group. In 

particular, common dolphin are relatively easy to identify whereas some of the 

other species are not. This factor, coupled with the small sample size for 

aerial data (Table 201, indicated that little reliance should be placed on 

this data set for estimating species proportions. 

The ad hoc committee members also felt that the research vessels provided 

a better platform for identification within target school s. These vessel s 

would follow the school until an adequate identification was made, unless sea 

or weather conditions precluded it. Research vessel observers felt that the 

probability of this occurring was independent of the species. However, the 

research vessels searched relatively few nautical miles. Therefore, the 

distributions of species depend upon the location of searching effort. For 

example, in the inshore area, the 1979 research vessel surveys concentrated in 

the middle of the inshore area while the 1977 research vessels searched 

further south within that area, which resulted in a differing account of 

species distribution (Table 20). In addition, the coverage by research 

vessels in the northern offshore area in both 1977 and 1979 was relatively 

sparse and concentrated toward the east. Use of the research vessel species 

distributions may thus be biased in these regards. 

The other alternative data set is the tuna vessel data. In general, this 

data set provides fairly extensive coverage of the three areas. Only 

prel iminary 1979 data, which were concentrated primarily within the inshore 

area (Table 201, were included in this analysis. The tuna vessel data were 

relatively extensive in 1977 and 1978 and comparable between years, suggesting 

that data for 1977 through 1979 be pooled. The disadvantage to this is the 

presumption that the relative population sizes have not altered over the span 

of years. In addition, these data may be biased due to the concentration of 

fishing effort on particular species. Although they may cover a wide area of 

the ocean, the tuna vessels could be sampling primarily in areas of spotted 

and spinner dolphin. However, the only comparable data available are research 

vessel data, which are not as widely dispersed through the areas. 

Another source of tuna vessel bias in species distributions is that 

identification may not be equally reliable among the species of target 

schools. If the school shows no indication that tuna is present or if there 

are no birds associated with the school, then it may not be approached for 

further investigation. The species within this school would then be more 

likely to remain unidentified. For species which are less likely to occur 

with tuna, such as the striped dolphin, this would reduce the percentage of 

these species si ghti ngs and proportional ly raise the percentage of the others. 

With the above caveats in mind, three alternatives for determining 

species distributions were devel oped. The first simply uses the 1979 research 

vessel data pooled for all areas. This assumes the distribution to be 
33 

independent of area. The second alternative uses the 1977 and 1979 research 

vessel data pooled over all areas. This assumes the distribution is 

independent of years and area but increases the sample size. The third 

alternative utilizes the pooled data from 1977 and 1979 research vessels and 

the 1977 through 1979 tuna vessel data within each area. This alternative 

assumes the distribution is independent of platform and years but not among 

areas. Because of the disparately large sample sizes from tuna vessel data, 

the third distribution is dominated by the tuna vessel distributions. The 

estimated proportions and standard errors for each distribution are given in 

Tab1 e 21. Popul ation estimates were devel oped using each a1 ternative. 

V. STOCK RANGES 

A dolphin stock is defined as a species subgroup which occupies a 

distinct oceanographic region and differs biologically from other subgroups of 

the same species. Stock boundaries for spotted, spinner, common, and striped 

dolphins were drawn, based upon historical sightings of dolphins by tuna 

vessel and research vessel observers, oceanographic features, and biological 

data taken from animals killed in the fishing process (Au, D, W. L. Perryman, 

and W. Perrin 1979)13. Maps depicting the range of each stock are presented 

in Appendix 3 and summarized in Table 22. 

The boundaries between stock ranges within a species do not overlap, with 

the exception of the sympatric stocks of eastern and northern whitebelly 

spinner dol phins. Two additional areas were defined in order to account for 

this overlap: the overlapping area in the inshore area and overlapping area in 

the northern offshore area. The area inhabited by each spinner stock in the 

overlap area is also included in Table 22. The proportions of individuals 

represented by eastern and northern whitebelly spinners in relation to all 

spinners in the two new areas were calculated using tuna vessel data (Table 

23). Because the offshore overlap area was not well sampled in 1979, and 

because the point estimates were very similar to those of 1978, the data were 

pooled (Table 23) and the pooled proportions were employed. 

VI. POPULATION SIZE ESTIMATES 

Population estimates for target species are based on the above developed 

estimates of the density of schools, proportion of target and non-target 

schools, mean school size, proportion of individuals of a species within the 

target schools, and total area inhabited. To obtain estimates for each stock, 

the estimates for each species must be expanded by the proportion of area 

inhabited by each stock of each species, assuming that the density of a 

particular species is constant within an area. Therefore, the number of 

individuals in a stock, in relation to other stocks of the same species, is 

l3Au, D., W. L. Perryman, and W. Perrin. 1979. Dolphin distribution and the 

relationship to environmental features in the eastern tropical Pacific, 

Southwest Fish. Cent. Status of Porpoise Stocks working paper SOPS/79/36. La 

Jolla, CA mp.- 
34 

defined by the relative size of the area inhabited by those individuals within 

a given area. The formula for calculating the abundance of stocks in target 

schools is 

A 

i jk ik 

3A 

N =(P 1 (S 1 c (D )(P, )(A /A. 1 (A ) + (PI )(Aijkjl , ij target target k=l k ik k ik 

where Nij = abundance of target species i, stock j, 

Ptarget = proportion of dolphin schools which are 

target school s, 

- 

'target = mean size of target schools, 

'k 

pi k 

"ik 

Aik 

Ak 

*ijk 

A'ijk 

= density of dolphin schools in area k 

with D^i=densi ty inshore area; 

62=63=densi ty offshore. 

= proportion of individuals of species i in 

target schools in area k, 

= proportion of individuals of species i in 

target schools in overlap region of area k, 

= area inhabited by species i in area k, 

= total area inhabited by all species in area k. 

= area inhabited by species i, stock j, in area k, and 

= area inhabited by species i, stock j, in overlap 

region of area k. 
35 

The variance calculated as a Taylor series expansion is 

AA A 

Var(N..) = Var(S 1 

1J target 

+ Var(P 1 

target 

aN. . 

ai 

-1 J 

target 

+ Var(P 1 

target 

aN. . -1 J - 

nc 

UJ I 

target I 

A AA 

2 

COV D D aN. . 4- -1J ,'J 1' offshore 

aD aD offshore 1 offshore 

Although little is known about the boundaries to the range of Fraser's 

dolphin, estimates of their population size were made for the three areas: 

inshore, northern offshore, and southern offshore. The size of the areas 

(nm2) used for computing the estimates for the latter two areas were assumed 

to be the same as those of the spotted dolphin. Since survey coverage of 

these areas was sparse, and since it is not known if Fraser's dolphin inhabits 

the entire area, the estimates may be biased upward. However, the inshore 

area is relatively uniformly sampled and should provide an unbiased estimate 

of Fraserls dolphin within -- that area. Results are given for all areas 

separately. 

The estimates derived from the 1979 survey data of population size for 

the stocks of spotted, spinner, comnon, striped, and Fraser's dolphin are 

presented in Table 24. Estimates are given using species proportions from (1) 

pooled research vessel and tuna vessel data, (2) pooled 1977 and 1979 research 

vessel data combined over area, and (3) 1979 research vessel data pooled over 

area. 

VII. DISCUSSION AND CONCLUSIONS 

The present estimates of dolphin population sizes are improvements over 

previously avail ab1 e estimates (SWFC 1976 3). In general , the magnitude of 

these estimates is smaller than those of previous estimates (SWFC 19763) which 

are given in Table 25. However, several factors, including new data on stock 

definitions, have made direct comparisons difficult. Therefore the species 

estimates (sums of stock estimates within a species) are given in Table 26. 
36 

The disparity between the 1974 and 1979 estimates were caused by a 

variety of factors. The differences in the estimation methods which could 

have caused the disparity are: 

1. Mean school size was corrected for sighting bias in 1979; in 1974 it 

was not. 

2. The 1974 methods used both observer and crew member tunaboat 

estimates of school size; the 1979 estimates were from aerial observers. 

3. The 1974 density of spotted and spinner dolphin was derived from both 

aerial and tunaboat data; the 1974 density of common and striped dolphin was 

from tunaboat data alone. The 1979 estimates of density of all dolphin 

species were from aerial and research vessel data. 

4. Species distributions in 1974 were based upon tunaboat sampling rates 

which were uncorrected for the effect of school size on sampling bias. The 

species distributions of 1979 were a combination of tunaboats and research 

vessel s corrected for the effect of school size sampl i ng bias. 

5. The 1974 estimates included extrapolation of densities to areas not 

covered by the aircraft or tuna vessels - a large portion of the range. The 

1979 surveys covered more of that area by research vessel. However, offshore 

data were sparse for both years. 

6. The 1974 estimates were the average of two estimates using expanded 

and unexpanded range of the spotted and spinner dolphins. The 1979 estimates 

were based upon ranges which were quite close to the 1974 expanded range. 

The difference in methods between 1974 and 1979 was the result of 

development and refinement of techniques, obtaining new data from new sources, 

and from critically addressing some of the assumptions of the 1974 estimate 

(see SWFC 19763: Appendix 2). The 1979 estimates (Table 24) are the best 

assessment of population sizes of these stocks for dolphins. 

However, the estimates of population sizes we present are based on 

several sources of data, collected under a variety of conditions. Not all of 

the data were collected under suitably controlled conditions, and in some 

instances the data have been more sparse than desirable. We make estimates of 

the six parameters which are combined to produce the population size estimates 

using a variety of analytic methods, some with rather stringent assumptions 

and some developed to deal with specific problems with the data sets used. 
37 

Most of the problems in the data were reviewed by the ad hoc committee 

and analytic procedures to correct the problems were discussed at great 

length. Adjustments reflected in this paper reflect some of the advice from 

the committee, but for some situations no suitable resolution of the problems 

was possible. Several of the more important probl erns are currently receiving 

considerable experimental and analytic attention, and the results of these 

studies could eventually be used to adjust our data or improve our analysis. 

One area of particular concern is the applicability of line transect 

model s to dol phin surveys, both aeri a1 and shipboard. A1 though these methods 

have been applied to aerial data before (Smith 19811, there have been no 

experimentally control led studies to demonstrate the appl icabil i ty, especially 

under varyi ng si ghti ng conditions. Thus the re1 i abi 1 i ty of these methods for 

analysis of aerial survey data needs testing. Similarly, we designed this 

study to allow use of line transect models to the research vessel dolphin 

sighting data. The probl ems di scussed here of apparently imprecise 

measurements of angles and distances at the time of sighting, which precluded 

our use of these methods, weakened the overall reliability of our results as 

the effects of the variability of sighting conditions are not adequately 

accounted for. 

We have conducted additional experimental work on both of these problems 

in 1980 and 1981, focusing on gathering information to improve the design of 

future studies. Results from these studies are in preparation. Additionally, 

we completed additional sighting surveys in 1980 aimed at improving the 

coverage further offshore. These data, while still suffering from precision 

in the angle and distance measurements, increase the coverage sufficiently and 

allow better consideration of the effects of sea state (e.g., Beaufort Scale) 

and sighting cues (e.g., bird distributions). 

Another general area of concern is the visual estimation of dolphin 

school size. The validity of these estimates has been partially tested by 

comparison to counts made from aerial photographs; since 1979 additional data 

have been collected which will allow testing of the validity of the visual 

estimates for larger schools. However, good aerial photographs have not been 

taken under less ideal sighting conditions, so the problem cannot yet be fully 

evaluated. In addition, further study of school size estimates including data 

collected since 1979 will be required to better define relative biases in the 

data. These investigations will aid us in selecting the best source of data 

for calculating the mean school size of the dolphins in the ETP. 

The estimates of the proportion of the dolphins of each species in an 

area are affected by the degree that available data are representative of the 

population. Different estimates are presented for proportions estimated from 

tuna vessel and from research vessel data, which are markedly different for 

some species. Further study of the tuna vessel searching process is needed to 

determine more precisely the types and degrees of sampling biases which may be 

present. Also, additional research vessel sighting data is being collected to 

evaluate the stability of these proportions over time. 
Finally, the area of the historical ranges of these dolphin populations 

has been used as an approximation to the actual areas inhabited at the time of 

the survey. These areas are subject to the uncertainties of including regions 

of potentially very low density along the margins of the ranges, including 

regions not occupied at all at the time of the surveys, and including regions 

occupied by separate but perhaps similar animals of different populations. 

This problem is especially significant in the present situation because 

1 ogistic 1 imitations have precl uded complete coverage of the historical ranges 

at one point in time, and the use of maximal ranges tends to bias the 

resul ti ng popul ation size estimates upward. Additional data and analyses are 

needed to improve our understanding of the temporal fluctuations in dolphin 

ranges in order to estimate actual inhabited range at the time of a survey. 

In summary, these estimates of dolphin population sizes are the best 

avail ab1 e using data avail ab1 e through early 1979. These estimates represent 

vast improvements over previous estimates. Several 1 imitations on data and 

analytic methods are discussed. Analysis of data collected since 1979 and 

improved analytic methods may result in upward adjustments of some estimates 

of the various parameters and downward adjustments of others. This report 

represents a reference point to which future comparisons may be made. 
39 

LITERATURE CITED 

Anderson, D. R., K. P. Burnham, and B. R. Crain. 1978. A log-linear model 

approach to estimation of population size using the line transect 

sampl i ng method. Ecol ogy 59 ( 1 ) : 190-193. 

Au, D. and W. L. Perryman. In press. Movement and speed of dolphin schools 

responding to an approaching ship. Fish. Bull ., U.S. 

Bialek, E. L. 1966. Handbook of oceanographic tables. U.S. Naval 

Oceanographic Office, Washington, D.C. 427pp. 

-- -- 

Burnham, K. P. and D. R. Anderson. 1976. Mathematical models for 

nonparametric inferences from line transect data. Biometrics 32(2): 325- 

336. 

Burnham, K. P., D. R. Anderson, and J. L. Laake. 1979. On robust estimation 

Burnham, K. P., D. R. Anderson, and J. L. Laake. 1980. Estimation of densit-y 

from line transect data. -- J. Wildl. Manage. 43(4): 992-996. 

from 1 i ne- transect sampl i ng of biological popul ations. -- J. Wi 1 dl . ManageMonogr. No. 72. 202pp. 

Crain, B. R., K. P. Burnham, D. R. Anderson and J. L. Laake. 1978. A Fourier 

series estimator of population density for line transect sampling. Utah 

State University Press, Logan. 25pp. 

Dixon, W. J. and M. B. Brown (eds.). 1977. Biomedical Computer Programs PEberhardt, L. L.. 1968. A preliminary appraisal of line transects. - J. 

Series, BMDP-77 University of California Press, Los Angeles, CA. 880 pp. 

Wildl. Manage. 32:82-88. 

Eberhardt, L. L. 1978. Transect methods for population studies. J. Wildl. -- Manage. 42(1): 1-31. 

Gates, C. E. 1969. Simulation study of estimators for the line transect 

sampling method. Biometrics 25(2): 317-328. 

Gates, C. E., W. H. Marshall, and D. P. Olson. 1968. Line transect method of 

estimating grouse population densities. Biometrics 24(1): 135-145. 

Hayne, D. W. 1949. An examination of the strip census method for estimating 

animal populations. -- J. Wildl. Manage. 13(2): 145-57. 

Kelker, G. H. 1945. Measurement and interpretation of forces that determine 

populations of managed deer. Ph.D. Dissertation. Univ. of Mich., Ann 

Arbor, MI. 422 pp. 

Laake, J. L., K. P. Burnham, and D. R. Anderson. 1979. User's Manual for 

Program TRANSECT. Utah State University Press, Logan. 26 pp. 
40 

Leatherwood, S., J. R. Gilbert, and D. G. Chapman. 1978. An evaluation of 

some techniques for aerial censuses of bottl enosed dol phi ns. J. Wi 1 dl . Manage. 42(2): 239-250. -- 

Perrin, W. F. 1968. The porpoise and the tuna. -- Sea Front 14:166-174. 

Perrin, W. F.. 1969. Using porpoise to catch tuna. World -- Fish. 

18(6):42-45. 

Pollock, K. H. 1978. A family of density estimators for line-transect 

sampling. Biometrics 34(3): 475-478. 

Robinette, W. L., D. A. Jones, J. S. Gashwiler, and G. M. Aldous. 1954. 

Methods for censuing winter-lost deer. Trans. N. Am. Wildl. Conf. ----- 19~511-525. 

Robinette, W. L., D. A. Jones, J. S. Gashwiler, and G. M. Aldous. 1956. 

Further analysis of methods for censuing winter-lost deer. J. Wildl. 

Manage. 20(1): 75-78. 

Seber, G. A. F. 1973. The Estimation of Animal Abundance. Hafner, New York. 

506 pp. 

-- 

Smith, T. D. 1981. Line-transect techniques for estimating density of 

porpoise schools. -- J. Wildl . Manage. 45(3):650-657. 
41 

Tab1 e 1. Summary of exponenti a1 power series (EPS) , $xponen ti a1 pol ynomi a1 

(EP), and Fourier series (FS) estimates of f(0) for dolphin schools 

for inshore aerial sighting data stratified by school size 

categories. 

~~ 

School 

size 

(SI 

EPS 

(1) 15<S<50 -- 

(2) 950 

(3) Sum (1)+(2) 

(4) Unstratified 

EP 

(1) 15<S<50 

(2) s>50** 

(3) Sum (1)+(2) 

(4) Unstratified** 

-- 

FS 

(1) 15<S<50 

(2) 950 

(3) Sum (1)+(2) 

(4) Unstratified 

-- 

Coef f i - 

Number Trunca- cient of 

meters distance schools tip of goodness 

para- ti on Number varia- X2* 

(m) (W) (n) 4%) f(0) of fit nP(0) 

2 0.75 51 5.625 0.300 0.395 286.875 

2 1.35 62 3.247 0.389 0.245 201 314 

488.189 

2 1.35 114 5.359 0.314 0.417 610.926 

2 0.75 51 5.724 0.262 0.435 291.924 

4 0.75 51 5.75 0.151 0.910 284.325 

3 1.35 62 2.385 0.097 0.432 147.870 

432.195 

4 1.35 114 3.207 0.063 0.981 365.598 

* Denotes the achieved significance level of the test. 

** Maximum likelihood estimates of parameters could not 

be obtained by the iterative algorithm used. 
42 

Table 2. Summary of the Fourier series estimates of f(0) for 

the 1979 aerial sighting data in the inshore area, 

c a l c u l ated at successi ve truncation points. 

Trunca- Number 

tion of Sampl e 

point terms size 

(W) m) (n) ?(o) s.e.(?(o)) cv(f0)) x'* nT(0) 

0.25 

0.45 

0.65 

0.85 

1.05 

1.25 

1.45 

1.65 

2.05 

77 

96 

101 

107 

110 

112 

114 

116 

117 

5.18 

3.85 

3.68 

3.24 

3.32 

3.29 

3.05 

3.10 

3.02 

0.670 

0.252 

0.291 

0.168 

0.205 

0.237 

0.177 

0.201 

0.191 

0.129 

0.065 

0.079 

0.052 

0.062 

0.072 

0.058 

0.065 

0.063 

.914 

.840 

.894 

.914 

.959 

.953 

.941 

.972 

.957 

398.86 

369.60 

371.68 

346.68 

365.20 

368.48 

347.70 

359.60 

353.34 

*Denotes the achieved significance level of the test. 
43 

Table 3. Perpendicular sighting distance distributions for large dolphin 

school s (>14 animal s 1 observed during vessel si ghti ng surveys aboard 

the Jordan and Cromwell in the offshore and calibration areas. 

~~ ~~ ~ 

Number Of Schools Sighted 

Perpendicular Jordan Cromwell 

di stance 

interval Offshore Calibration Offshore Calibration 

(nm) area area area area 

0.00-0.05 

0.06-0.15 

0.16-0.25 

0.26-0.35 

0.36-0.45 

0.46-0.55 

0.56-0.65 

0.66-0.75 

0.76-0.85 

0.86-0.95 

0.96-1.05 

1.06-1.15 

1.16-1.25 

1.26-1.35 

1.36-1.45 

1.46-1.55 

1.56-1.65 

1.66-1.75 

1.76-1.85 

1.86 -1.95 

1.96-2.05 

2.06-2.15 

2.16-2.25 

2.26-2.35 

2.36-2.45 

2.46-2.55 

2.56-2.65 

2.66-2.75 

2.76-2.85 

2.86-2.95 

2.96-3.05 

3.06-3.15 

3.16-3.35 

3.36-3.45 

3.46-3.55 

3.56-3.65 

3.66-3.95 

3.96-4.15 

4.16-4.25 

4.26-4.75 

4.76-7.15 

18 17 

7 

4 

6 

7 

13 

1 8 

4 

2 

6 

1 

3 

2 

2 

1 

1 

1 

1 

2 

2 

2 

3 

2 

4 

2 

1 

4 

4 

3 

1 

1 

1 

1 

1 

7 

4 

8 

1 

2 2 

1 

3 

5 

1 2 

1 

1 

1 

2 

1 1 

1 

1 

1 

1 

1 

1 

1 

Total si ghti ngs 52 121 9 62 
44 

Table 4. Mean perpendicular sighting distance (PI and mean 

Beaufort number* (B) for each research vessel sighting, 

stratified by ship, species composition, area, and 

sighting cue. Sample sizes in parentheses. 

Sighting Cue 

Ship Species Area Birds Not Birds 

Jordan 

A1 1 

Spotted 

Spinner 

and 

Cromwell Inshore 

A1 1 

Spotted 

and 

Spinner 

Inshore P 1.6 (38) 

B 1.9 (38) 

Offshore P 0.5 (3) 

B 2.0 (3) 

Inshore P 1.7 (26) 

B 2.0 (26) 

Offshore P 0.8 (2) 

B 2.0 (2) 

P 1.5 (41) 

B 2.5 (41) 

Offshore P 1.0 (3) 

B 2.3 (3) 

Inshore P 1.4 (35) 

B 2.4 (35) 

Offshore P 0.8 (1) 

B 3.0 (1) 

0.8 (97) 

1.8 (97) 

0.8 (83) 

2.0 (83) 

0.4 (12) 

2.1 (12) 

0.9 (12) 

1.8 (12) 

0.9 (26) 

2.5 (26) 

0.4 (4) 

2.5 (4) 

0.5 (5) 

2.2 (5) 

0.5 (1) 

3.0 (1) 

*Note these are Beaufort numbers at the time 

of sighting, not during sighting effort. 
45 

Table 5. Perpendicular sighting distance distributions for large 

dolphin school s (>14 animals) observed during aerial 

sighting surveys in the inshore and calibration areas. 

15,195 nm searched. 

Perpendicular 

distance interval 

(nm) 

Number of Schools Sighted 

Inshore Area Cal ibration Area 

0.00-0.05 

0.06-0.15 

0.16-0.25 

0.26-0.35 

0.36-0.45 

0.46-0.55 

0.56-0.65 

0.66-0.75 

0.76-0.85 

0.86-0.95 

0.96-1.05 

1.06-1.15 

1.16-1.25 

1.26-1.35 

1.36-1.45 

1.46-1.55 

1.56-1.65 

1.66-2.05 

2.06-3.85 

To tal ob serva t i ons 

20 

33 

24 

11 

8 

3 

2 

2 

4 

2 

1 

2 

2 

2 

1 

1 

118 

9 

15 

7 

2 

2 

2 

2 

1 

1 

1 

2 

1 

45 
46 

Table 6. Summary of the Fourier series estimates of f(0) 

for large schools (>14 animals) observed during 

the 1979 aerial sighting survey in the inshore 

area. Truncation point = 1.05 nm and number of 

schools observed = 110. 

Coefficient 

Number Standard of Log likeliof para- grror var i,a ti o n hood (XLL) Ratio 

meters ?(o) f(O) f(O) X** value XL L 

1 1.87 0.055 0.030 0.000 -229.424 

2 2.65 0.128 0.048 0.123 -216.120 

3 3.32 0.205 0.062 0.959 -210.493 

26.61 

11.25 

0.00 

1.09 

0.05 

4 3.33 0.322 0.097 0.917 -210.493 

5 3.61 0.403 0.111 0.966 -209.947 

6 3.67 0.485 0.132 0.924 -209.922 

*Denotes the achieved significance level of the test 
47 

Table 7. Number of observed dolphin schools and miles searched 

during the aerial sighting survey in the inshore area. 

Data truncated at 1.05 nm perpendicul ar di stance. 

Number of Miles 

schools searched 

F1 ight n nm 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

Total 

4 

2 

3 

6 

5 

5 

5 

2 

8 

11 

10 

2 

10 

15 

5 

0 

4 

5 

8 

110 

804.30 

956.46 

638.40 

796.75 

866.86 

939.91 

1136.10 

522.83 

1003.09 

572.46 

629.70 

590.99 

783.02 

979.68 

740.74 

607.34 

1025.34 

994.86 

606.06 

151 94.89 
48 

Table 8. Number of large dolphin schools observed per nautical 

mile searched, as recorded by observers in 1979 

aboard the PBY, R/V Jordan and R/V Cromwell in 

the cal i bration and -re areas. Ship and aerial 

sightings were truncated at 1.15 nrn and 0.95 nm, 

respectively. 

Nautical Standard 

Number mi 1 es devi a tion 

P1 atform schools (n) searched (L) n/L of (n/L) 

Calibration Area 

PB Y 42 6239.8 

Jordan 77 2717.6 .0283 .0052 

Cromwell 37 2157.1 . 01 72 .0036 

Off shore Area 

Jordan 

Cromwel 1 

38 2033.3 .0187 .0079 

8 2008.1 .0040 .0017 
49 

Table 9. Summary of the Fourier series estimates of i(0) for large 

dolphin schools observed during the aerial sighting survey 

in the calibration area. Truncation point was 0.95 nm and 

number of schools observed was 42. 

Coefficient Log Number Standard of Goodness likeliparameters srro r var i,a ti on of fit hood Ratio 

(m) +(O) f (0) f (0) X2" (XLL 1 XLL 

1 2.01 0.127 0.152 0.017 -86.567 

8.79 

5.72 

3.36 

0.28 

0.00 

2 2.76 0.268 0.097 0.259 -82.170 

3 3.53 0.388 0.109 0.750 -79.308 

4 4.29 0.513 0.119 0.995 -77.627 

5 4.55 0.685 0.150 0.997 -77.489 

6 4.55 0.872 0.192 0.987 -77.489 

*Denotes the achieved significance level of the test 
50 

Table 10. Number of observed dolphin schools and miles searched per 

flight during the aerial sighting survey in the calibration 

area. 

(w=O.95 nm). 

Data were truncated at 0.95 nm perpendicular distance 

No. of 

school s 

F1 i ght (n) 

Mi 1 es 

searched 

(nm) 

3 

4 

5 

6 

7 

8 

9 

11 

12 

13 

2 

3 

6 

5 

5 

3 

2 

11 

3 

2 

792.1 

483.8 

666.9 

866.9 

939.9 

482.2 

409.3 

572.5 

435.2 

591.0 

Total 42 6239.8 
51 

Table 11. Number of observed dolphin schools and miles searched 

per day from the R/V Cromwell in the calibration area. 

Data were truncated at 1.15 nm perpendicular distance. 

No. of Miles 

Date school s searched 

(1979) (n) (nm) 

Jan 30 

31 

Feb 1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

0 

1 

1 

1 

2 

2 

3 

1 

2 

4 

1 

0 

1 

1 

3 

6 

0 

0 

1 

0 

2 

2 

0 

3 

103.1 

109.0 

102.4 

70.5 

105.3 

86.6 

95.6 

72.1 

79.0 

110.9 

107.6 

113.5 

113.0 

98.1 

86.8 

80.6 

92.2 

88.0 

89.0 

67.7 

67.0 

66.5 

84.7 

68.3 

Total 37 2157.1 
52 

Table 12. Number of observed dolphin schools and miles searched 

per day from the R/V Jordan in the calibration area. 

Data were truncated am nm perpendicular distance. 

No. of Miles 

Date school s searched 

(1979) (n) (nm) 

Total 

Jan 30 

31 

Feb 1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

11 

0 

5 

3 

1 

3 

4 

4 

3 

5 

4 

0 

0 

1 

5 

5 

2 

2 

1 

1 

1 

7 

2 

2 

5 

77 

99.3 

112.0 

75.1 

98.7 

22.2 

108.9 

107.7 

101.8 

111.5 

117.7 

114.9 

122.9 

119.1 

110.6 

124.2 

63.5 

112.6 

118.5 

116.4 

105.7 

113.3 

109.8 

114.8 

110.2 

106.2 

2717.6 
53 

Table 13. Number of observed dolphin schools and miles searched 

per day from the R/V Cromwell in the offshore area. 

Data were truncated at 1.15 nm perpendicular distance. 

No. of Mi 1 es 

Date schools searched 

(1979) (n) (nm) 

Jan 7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

March 4 

5 

6 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0 

1 

3 

1 

1 

1 

126.4 

95.3 

91.1 

110.1 

122.4 

109.1 

120.0 

118.4 

115.9 

115.7 

116.3 

125.1 

121.7 

102.8 

105.7 

109.7 

96.0 

106.4 

Total 8 2008.1 
54 

Table 14. Number of observed dolphin schools and miles searched from 

the R/V Jordan in the offshore area. Data were truncated 

at 1.15 nm perpendicul ar distance. 

No. of Miles 

Date school s searched 

(1979) (n) (nm) 

Jan 5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

Mar 5 

6 

7 

8 

0 

2 

1 

0 

0 

0 

0 

1 

3 

2 

8 

13 

3 

0 

1 

87.1 

114.0 

115.2 

124.1 

100.5 

115.8 

111.1 

104.3 

107.9 

89.8 

91.0 

88.8 

94.8 

120.8 

120.2 

108.3 

115.6 

108.9 

115.2 

Total 38 2033.4 
55 

Table 15. Expected perpendicular sighting distances (nm), with 

sample sizes (n) at different school sizes for data 

from the 1979 dolphin sighting surveys on the PBY 

airpl ane, and the research vessel s Jordan and 

Cromwell . 

School 

size 

PBY Jordan Cromwell 

E(XIS) n E(XIS) n E(XIS) n 

<15 

15 - 29 

30 - 59 

60 - 119 

120 - 239 

240 - 479 

480 - 959 

960 - 1919 

0.08 4 0.67 

0.18 5 0.70 

0.28 12 0.88 

0.38 16 0.93 

0.36 18 1.00 

0.44 13 1.99 

0.41 9 0.94 

1.60 3 2.62 

9 

10 

46 

28 

18 

15 

6 

1 

0.48 5 

0.93 10 

1.10 12 

1.22 13 

1.60 13 

1.45 12 

0.76 5 

2.29 1 
56 

Table 16. Target school size frequency distributions 

and ratios of weighted to unweighted means. 

1979 1979 1979 

School Size Aeri a1 Jordan Cromwell 

Interval Frequency Frequency Frequency 

15 - 29 5 

30 - 59 12 

60 - 119 16 

120 - 239 18 

240 - 479 13 

480 - 959 9 

960 - 1919 3 

S unweighted = 250.01 

S weighted* = 201.34 

S weighted 

S unweighted = 0.81 

10 

46 

28 

18 

15 

6 

1 

144.70 

115.26 

0.80 

10 

12 

13 

13 

12 

5 

1 

189.94 

150.78 

0.79 

*See text, equation 21. 

. 
57 

Table 17. Mean school size estimates for target species (school 

size >14 animals). Mean is weighted for sighting bias. 

Data Source 

Standard 

error Sample 

Weighted mean of mean si ze 

1977 observers 

Aerial 

Jordan 

Cromwell 

Tuna vessel 

1979 observers 

Aerial 

Jordan 

Cromwell 

Tuna vessel 

179.16 

188.65 

156.80 

884.01 

201.34 

115.26 

150.78 

521.54 

1979 Cal ibration Area observers* 

Aeri a1 

Jordan 

Cromwell 

Tuna vessel 

195.40 

166.10 

187.92 

583.45 

29.81 

32.53 

65.06 

17.55 

26.96 

11.90 

20.55 

25.51 

48.32 

23.48 

26.80 

53.87 

47 

61 

18 

4223 

76 

124 

66 

6 94 

31 

62 

49 

167 

*Area used in calibration of the density of the research vessels 

in relation to the aircraft. 
58 

Table 18. Mean school size estimates for non-target species 

(school size >14 animal s) , weighted for sighting 

bias. 

Data Source 

Standard 

Weighted error of Sample 

mean mean* si ze 

1979 Aerial observers 42.02 7.33 49 

1977 Aerial observers 70.93 32.53 57 

*Approximation: See text 
59 

Table 19. Proportion of dolphin schools (school size >14 

animals) which were target schools (Ptarget). 

See text for calculation method. 

Number 

days or 

Standard fl ights w/ Number 

error of i denti fi ed identified 

school s school s Survey 'target Ptarget 

1979 Aerial 0.6873 0.0629 18 

1979 Jordan 0.6635 0.0569 40 

1979 Cromwell 0.8484 0.0463 30 

Pool ed 0.7105 0.0338 88 

1977 Aerial 0.6229 0.0933 19 

1977 Jordan 0.8097 0.0515 30 

108 

167 

75 

3 50 

89 

66 

1977 Cromwell 0.9589 0.0320 14 

Pooled 0.7291 0.0447 63 

18 

173 
60 

Table 20. Species proportion of target schools (school size >14 

animals) , expressed as fraction of individual s of given 

species per target school. 

Species 

Re search 

Aer i a1 vessel Tuna vessel 

1977 1979 1977 1979 1977 1978 1979 

1979 Inshore area 

Spotted 

Spinner 

Common 

Striped 

Fraser I s 

Other 

n 

1979 Offshore area 

north of equator 

Spotted 

Spinner 

Common 

Striped 

Fraser I s 

Other 

n 

1979 Offshore area 

south of equator 

Spotted 

Spinner 

Common 

Stri ped 

Fraser I s 

Other 

n 

0.3739 0.2216 0.3001 0.4420 0.5920 

0.1711 0.0940 0.1664 0.1197 0.1282 

0.4035 0.5557 0.1959 0.1461 0.2277 

0.0504 0.1043 0.2929 0.2782 0.0369 

0 0.0221 0.0378 0 0.0007 

0.0056 0.0025 0.0069 0.0140 0.0144 

38 55 28 137 2126 

0.4411 0.4717 0.1724 0.6381 

0.0519 0.2365 0.0828 0.1652 

0.3805 0.0649 0.2382 0.1489 

0.1265 0.1782 0.4885 0.0297 

0 0.0506 0.0136 0.0054 

0 0.0036 0.0066 0.0127 

9 50 44 2018 

0.2148 0 0.3575 

0.2145 0 0.1347 

0 0 0.2636 

0.5275 0.9693 0.2325 

0.0166 0 0.0009 

0.0265 0.0307 0.0109 

38 7 79 

0.5261 0.5914 

0.1475 0.1281 

0.2275 0.1886 

0.0769 0.0754 

0 0.0013 

0.0220 0.0152 

1099 605 

0.4714 0.4285 

0.1301 0.0332 

0.3349 0.4600 

0.0409 0.0623 

0.0035 0 

0193 0.0160 

71 5 72 

0.5291 0.2381 

0.1806 0.0476 

0.1062 0.5002 

0.1612 0.1664 

0.0141 0.0425 

0.0087 0.0051 

52 17 
61 

Table 21. Pooled estimates of species proportions of target schools 

(school size >14 animals), expressed as fraction of 

individuals of given species per target school. 

Inshore Area Northern Offshore Area 

Pooled research vessel Pool ed research vessel 

(77+79) and tuna (77+79) and tuna 

Species vessel (77-79) vessel (77-79) 

Standard Standard 

Proportion error Proportion error 

Spotted 

Spinner 

Common 

Striped 

Fraserls 

Other 

n 

0.5675 0.0078 0.5775 0.0092 

0.1306 0.0046 0.1491 0.0059 

0.2187 0.0068 0.2075 0.0085 

0.0661 0.0046 0.0461 0.0046 

0.0009 0.0005 0.0060 0.0014 

0.0162 0.0017 0.0139 0.0018 

3977 2881 

Southern Off shore Area 

Pooled research vessel 

(77+79) and tuna 1979 Research Vessel 

Species vessel (77-79) pooled all areas 

Standard Standard 

Proportion error Proporti on error 

Spotted 

Spinner 

Common 

Stri ped Fraserl s 

Other 

n 

0.3482 0.0340 0.3599 0.0343 

0.1481 0.0235 0.1062 0.0194 

0.1786 0.0296 0.1629 0.0278 

0.2975 0.0372 0.3618 0.0369 

0.0122 0.0068 0.0033 0.0033 

0.0154 0.0066 0.0059 0.0028 

185 188 
62 

Table 21. (Continued) 

Spec i es 

1977 and 1979 

Research vessel 

Pooled all areas 

Standard 

Propor ti on error 

Spotted 

Spinner 

Common 

Striped 

Fraser ' s 

Other 

n 

0.3431 0.0288 

0.1348 0.0185 

0.1397 0.0221 

0.3551 0.0313 

0.0180 0.0074 

0.0094 0.0036 

2 60 
63 

Table 22. Area inhabited (nm2) by various species/stocks for the inshore, and northern and southern 

offshore areas (Appendix 3). 

Species/Stock 

Offshore, Offshore, 

north of south of 

Inshore equator e qua tor 

area (nm2) (nm2) (nm2) 

Spotted 

Coastal 

N. offshore 

S. offshore 

To tal 

158,983 

1,244,164 

286,727 

1,689,874 

$pi nner 

N. whi tebel ly 

non-over1 ap 14,353 

Eastern, non-over1 ap 582,764 

E. and N. whitebelly area 

of overlap 704,504 

S. whi tebel ly 339,568 

Costa Rican 38,614 

Total 1,679,803 

Common 

N. tropical 149,128 

E. central tropical 1,013,799 

W. central tropical 3,832 

S. tropical 488,173 

Total 1,654,932 

Striped 

N. tropical 220,904 

E. central tropical 1,027,023 

W. central tropical 

Southern tropical 432,558 

To tal 1,680,485 

Maximum area occupied 1,753,826 

44,326 

2,251,058 

645,799 

2,295,384 

1,602,804 

287,204 

599,438 

797,068 

2,489,446 

401,329 

126,447 

1,007,297 

191,550 

1,726,623 

307,348 

310,064 

840,342 

486,232 

1,943,986 

2,801,084 

12,677 

758,476 

797,068 

142,380 

142,380 

994,989 

994,989 

1,075,545 
64 

Table 23. Proportion of eastern and northern whitebelly spinner 

dolphin in the area of their overlap, using tuna vessel 

data for 1978 and 1979. 

Spinner 

dol phi n 

Inshore Area Off shore Area 

Standard Standard 

Proportion error n Proportion error n 

1979 

Eastern 0.5121 

Northern whi tebel ly 0.4879 

1978 

Eastern 0.5175 

Northern whi tebel ly 0.4825 

1978-79 Pool ed 

Eastern 0.5161 

Northern whi tebel ly 0.4839 

0.0925 0.3504 

0.0990 0.6496 

3 52 

0.0535 0.3670 

0.0554 0,6331 

988 

0.0462 0.3663 

1340 

0.0483 0.6337 

0.3862 

0.4630 

9 

0.0632 

0.0636 

370 

0.0623 

0.0634 

379 
65 

Table 24. Estimates of population sizes (in thousands of animals) by stock 

for target species using pooled 1977-79 tuna vessel and research 

vessel observer data, using pooled 1977 and 1979 research vessel 

data combined for all areas, and using 1979 research vessel data 

combined for all areas. Standard errors shown in parentheses. 

Speci es/Stoc k 

Pooled 1977-79 tuna 1977+79 1979 

vessel and 1977+79 Research Research 

research vessel vessel vessel 

Spotted 

Coastal 

Northern offshore 

Southern offshore 

To tal 

Spinner 

Costa Rican 

Eastern 

Northern whi tebel ly 

Southern whi tebel ly 

Total 

Common 

Northern tropical 

East central tropical 

West central tropical 

Southern tropical 

To tal 

Striped 

Northern tropical 

East central tropical 

West central tropical 

Southern t rop i c a1 

Total 

189.8 

2775.0 

584.6 

3549.4 

9.0 

292.9 

380.4 

226.6 

908.9 

184.1 

443.1 

314.6 

431.3 

1373.1 

45.0 

140.8 

51.5 

376.5 

613.8 

Fraser' s 

Fraser' s (inshore area) 2.7 

Fraserls (outside, N. of equator)* 15.5 

Fraserls (outside, S. of equator)* 12.1 

To tal 30.3 

(40.0) 

(761.4) 

(156.2) 

(946.8) 

(2.0) 

(64.4) 

(134.9) 

(73.0) 

(263.4) 

(58.1) 

(94.8) 

(135.3) 

(122.4) 

(368.9) 

(11.2) 

(30.9) 

(22.7) 

(147.4) 

( 196.8 ) 

(1.6) 

(7.6) 

(8.5) 

(14.3) 

114.4 (25.5) 

1682.0 (471.8) 

465.5 (141.1) 

2261.9 (629.1) 

9.3 (2.4) 

292.7 (71.0) 

354.2 (128.4) 

216.0 (67.4) 

872.2 (254.3) 

121.9 (41.4) 

284.4 (72.9) 

211.7 (96.6) 

303.0 (92.0) 

921.0 (267.4) 

285.9 (74.5) 

800.5 (179.1 ) 

397.0 (174.2) 

851.8 (273.5) 

2341.2 (652.3) 

54.3 (25.3) 

46.6 (27.7) 

17.9 (10.6) 

118.8 (44.4) 

120.0 (27.1) 

1764.0 (497.9) 

488.3 (148.9) 

2372.3 (663.3) 

7.4 (2.1) 

230.6 (60.2) 

279.0 (104.7) 

170.2 (55.2) 

687.2 (207.1) 

142.2 (48.8) 

331.6 (87.2) 

246.9 (113.7) 

353.3 ( 108.2) 

1074.0 (314.7) 

291.3 (79.6) 

815.6 (185.8) 

404.5 (178.7) 

874.0 (280.0) 

2385.4 (668.9) 

9.9 (10.2) 

8.5 (9.3) 

3.3 (3.6) 

21.7 (14.8) 

*Assumes range to be the same as spotted dolphin. 
66 

Table 25. Estimates of population sizes of spotted, spinner, 

common, and striped dolphin as of January 1, 1974*. 

Estimates are in thousands of animals. Note that 

stock names and boundaries are not entirely equivalent 

to 1979 estimates. 

Spec i e s/Stock 

Spotted 

Coastal 

Offshore and 

Total 

southwestern 

Spinner 

Costa Rican 

Eastern 

Whi tebel ly & southwestern 

To tal 

Common 

Northern 

Central 

Southern 

Total 

Striped 

Northern 

North equatorial 

Total 

3500 

3 500 

- 

1200 

1600 

400** 

400 

230 

800 

1430 

18 

230 

2 48 

500 

500 

- 

200 

55 

207 

45 

75 

75 

115 

7 

60 

60 

*Source: Stock assessment Workshop , La Jol 1 a , Cal i fornia , July 27-31 , 1976 (SWFC 197613. 

**Subsequent to the workshop new data were obtained which increased 

the January 1, 1977 projected estimate of whitebelly spinners to 

approximately 690,000 animal s. 
67 

Table 26. Population estimates of spotted, spinner, common, 

and striped dolphin in 1974 and 1979. See Table 

25 for explanation of the 1974 estimates. 

are in thousands of animals. 

Estimates 

1977-79 Tuna 

vessel and 

1977+1979 1977+1979 1979 

re search Research Research 

Species 1974 vessel vessel vessel 

Spotted 3500 3549 2262 2372 

Spinner 1600 909 872 687 

1430 1373 92 1 1074 

248 614 2341 2385 

Common 

Striped 
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76 

APPENDIX 1 

AD HOC COMMITTEE MEMBERS 

Participants in the series of four workshops ((1) August 30-September 1, 

1977; (2) December 8-9, 1977; (3) October 5-6, 1978; (4) June 25-26, 1979) 

were : 

Dr. Robin Allen 

Inter-American Tropical 

Tuna Commission 

La Jolla, CA (1,2,3) 

Dr. David Anderson 

Utah Cooperative Wi 1 dl i fe Unit 

Utah State University 

Logan, Utah (1,2,3) 

Dr. David Burdick 

Porpoise Rescue Foundation and 

San Diego State University 

San Diego, CA (1,2,3,4) 

Dr. Kenneth Burnham 

United States Fish 

Fort Collins, CO (1,2,3,4) 

and Wildlife Service 

Dr. Douglas Chapman 

Marine Mammal Commission and 

Coll ege of Fi sheries 

University of Washington 

Seattle, WA (3) 

Dr. Brad Crain 

Department of Mathematics 

University of Oklahoma 

Norman, OK (1) 

Southwest Fisheries Center Staff 

Dr. Rennie Holt 

Dr. Joseph Powers 

Dr. David Au 

Dr. Eric Barham 

LT Terrance Jackson 

Mr. Ernest Brazier 

( Co-c hai rman and Edi tor) 

(Co-chai rman and Edi tor) 

Dr. Lee Eberhardt 

Marine Mammal Commi ssion and 

Battell e Northwest Laboratories 

Rich1 and, WA (1,2,3,4) 

Mr. Jeffrey Laake 

Inter-American Tropical 

Tuna Commission 

La Jolla, CA (4) 

Dr. Terrance Quinn 

I'nternational Pacific 

Halibut Commission 

University of Washington 

Seattle, WA (1,2,4) 

Dr. Kenneth Pollock 

Department of Statistics 

N. Carol ina State University 

Raleigh, NC (3) 

Mr. Patrick Tom1 inson 

In ter-Ameri can Tropical 

Tuna Commi ssion 

La Jolla, CA (1) 

Dr. Nancy Lo 

Dr. William Perrin 

LCDR Wayne Perryman 

Dr. Tim Smith 

Dr. Warren Stuntz 

Mr. Jay Barlow 

Ms. Jacqueline Jennings 

(Copley International Corp., La Jolla, CA. 

Contracted to the Southwest Fisheries Center) 
77 

APPENDIX 2 

MULTI-WAY ANALYSIS OF VARIANCE OF SCHOOL SIZE ESTIMATES 

Estimates of mean dolphin school size may be biased by the platform from 

which the observations took place. In addition to platform, other factors 

which may influence the mean school size estimates include year, quarter of 

the year, and geographical area. Previous analysis uti7 izing one-way analysis 

of variance (Brazier 1978l) examined the influence of these three factors as 

well as several others. Significant variability between years was found for 

aerial observations and for observations by NMFS personnel on tuna vessels. 

In 1975 and 1976 the mean school sizes, as estimated by all observers 

stationed on tuna vessel s, were significantly different between quarters of 

the same year. Four geographical areas (Figure A2.1) were used to examine 

regional effects. The mean school sizes for the four areas were found to be 

significantly different in 1974 and 1976 for observations made by tunaboat 

crews only. 

The one-way analysis of variance used in the above-mentioned analysis has 

some drawbacks. First, since samples must be stratified with respect to other 

significant factors, sample size is reduced and multiple testing becomes a 

consideration. Secondly, the significance of interactions between factors 

cannot be tested. An example of such an interaction might be if seasonality 

in school size varied by geographical area. Multi-way analysis of variance 

provides a means of testing the significance of such interactions between 

factors. 

Although it might be desirable to test all possible interactions between 

platform, year, quarter, and area, there was the limitation of available 

data. Incomplete factorial design and grossly unequal cell sizes confound any 

attempt to look simultaneously at all interactions of the above factors. The 

very 1 arge sample size for tuna vessel observations dominate any interaction 

that does not consider observation platform. It was not possible, however, to 

look for platform interactions with year, quarter, or area due to insufficient 

data. For these reasons, interaction effects were examined on a subset of the 

total data set. 

To examine the effects of area, quarter of the year, and the interaction 

of area and quarter, tuna vessel observations made by crew and NMFS personnel 

were considered separately. The data from 1974 to 1977 (the same data set 

utilized by Brazier (1978)l) were lumped. The analysis of variance model was 

thus 

Xijk = x t ct i ' Pj 

lBrazier, E.B., 1978. A statistical analysis of porpoise school size 

estimation data from the eastern tropical pacific. Copley Intl. Corp., 

La Jolla, CA. 117pp. 
78 

where: = size of the kth school found in area i 

and quarter of the year j, 'ijk 

X = mean school size, 

ai = deviation from mean school size due to 

area effects, 

pj = deviation from mean school size due to quarter 

of the year effects, 

aij = interaction effect of area and quarter, and 

Ejjk = residual variance. 

The assumptions of the above model are: 1) error terms are normally 

distributed and independent, and 2) variance shows homoskedaci ty. 

The hypotheses tested were: 

1) The mean school sizes in each of the four areas were not 

statistically different, 

2) The mean school sizes in each of the four quarters of the year were 

not stati stical ly different, and 

3) The mean school sizes in each of the possible combinations of area 

and quarter were not statistically different. 

Each of the above null hypotheses was tested at an effective significance 

level of a= .05. Testing all three hypotheses simultaneously reduces the 

actual rejection criteria by approximately one-third (01 = .05/3 = .017). 

Program P2V of Biomedical Computers Program' s P-Series (Di xon and Brown 1977) 

was used to calculate the analysis of variance. 

The cell, column, and row means for school size estimates are given in 

Tables A2.1 and A2.2. The results of the analysis of variance (ANOVA) are 

summarized in Tables A2.3 and A2.4. 

For observations made by NMFS personnel from tuna vessels, the mean 

school sizes by area and quarter of the year did not show significant 

differences (p >.017). The interaction effect of quarter and area was shown 

to be significant, thus the third hypothesis above can be rejected 

(p <.017). Similarly, the mean school size as estimated by tuna vessel crew 

members did not show significant differences between areas or quarters of the 

year (p >>.017). Again, however, the interaction effect of area and quarter 

was found to be significant (p <.017). 

The ANOVA test has indicated that the observed effects of area/quarter 

interactions are unlikely to have arisen from chance alone. The actual cause 

of the differences in mean estimates is subject to conjecture. The 

differences may reflect real changes in school size or they could reflect 

regional and seasonal differences in the bias of the school size estimates. 

Care must therefore be taken to avoid confusing analysis of variance with an 

analysis of cause. 
79 

Table A2.1. Cell means, sample sizes, and standard deviations for 

school size estimates by observers on tuna vessels. 

Row 

Area 1 Area 2 Area 3 Area 4 means 

1st Qtr 40 804 930 

n=l n=380 n=1287 

S.D.=O S. D. =1295 

2nd Qtr 1095 919 1009 

n=347 n=198 n=1201 

S. D. =1316 S. D. =1243 

3rd Qtr 1048 722 858 

n=948 n=54 n=775 

S. D. =1435 S. D. =778 

4th Qtr 1450 1496 828 

n=45 n=46 n=187 

S. D. =1440 S. D. =1953 

Col umn 

means 1073 878 936 

9 95 

n=2129 

S. D. =1295 

93 9 

n=1757 

S. D. =1432 

1041 

n=7 78 

S. D. =lo47 

1023 

n=256 

S. D. =1290 

954 

S. D. =1555 

97 7 

S. D. =1399 

981 

S. D. =1787 

1031 

S. D. =1653 

984 97 3 
80 

Table A2.2. Cell means, sample sizes, and standard deviations 

for school size estimates by tuna vessel crews. 

Row 

Area 1 Area 2 Area 3 Area 4 means 

1st Qtr 900 1518 1328 

n=l n=151 n=767 

S. D. =O S. D. =1558 

2nd Qtr 1418 1120 1308 

n=282 n=150 n=863 

S.D.=1608 S.D.=1522 

3rd Qtr 1342 871 1054 

n=715 n=31 n=730 

S. D. =1692 S. D. =706 

4th Qtr 1476 1343 1193 

n=26 n=28 n=162 

S. D. 4279 S. D. =1262 

Col umn 

means 1366 1283 1233 

1230 

n=975 

S. D. =1515 

1188 

n=1083 

S. D. =1624 

1346 

n-632 

S. D. =1326 

1211 

n=178 

S. D. =1244 

1239 

1292 

S. D. =1407 

1255 

S. D. =1570 

1237 

S. D. =2086 

1230 

S. D.=1706 

1258 
81 

Table A2.3. ANOVA results from observer estimates of school size. 

Degrees 

of Tai 1 

Source freedom F-Ratio probability 

Mean 

Quarters 

Area 

Quarters/area 

103.3 

2.98 

1.59 

2.48 

. 000 

.030 

.189 

.008 

Deci si on 

- 

Fail to reject 

Fail to reject 

Reject 

Error 10373 - - - 
82 

Table A2.4. ANOVA results from crew estimates of school size 

Degrees 

of Tai 1 

Source freedom F-Ratio probabil i ty Decision 

Mean 1 136.9 . 000 - 

Quarters 3 .60 .613 Fail to reject 

Area 3 .07 .975 Fail to reject 

Quarters/Area 9 2.39 .Oll Reject 

Error 6758 - - - 
83 

40' 

30' 

20' 

IO' 

0' 

IO' 

I 

20;i'Oo 160" I 50" 140" 130" I 20" I100 100" 90" 80" 

Figure A2.1. Geographical stratification for school size multi-way analysis 

of variance (after Brazier 1979'). 
84 

APPENDIX 3 

Estimation of Area Inhabited 

Boundaries for each dolphin stock, based on the maximum historical range 

(Au et al. 197911, were partitioned into inshore, northern offshore, and 

southern offshore subareas, as shown in Figures A3.1 to A3.4 for spotted, 

spinner, common, and striped dolphin, respectively. 

The square nautical miles inhabited by a species/stock in a subarea was 

determined by first counting the number of 1" quadrilateral squares within the 

stock range at each degree of latitude; partial squares were approximated. 

Next the number of 1" squares were multiplied by the area in a 1" square. 

Si nce 1 ongi tudi nal 1 engths decrease at increasing distance from the equator 

square, a corrected area for each 1" square latitude was used (Bialek 1966). 

The total area inhabited in a subarea was found by summing the appropriate 1" 

latitude areas (Tables A3.1-A3.4). The details of these calculations are 

shown in Tables A3.1 to A3.4 for spotted, spinner, common, and striped 

dol phi ns , respec ti vely . 

lAu, D., W. L. Perryman and W. Perrin. 1979. Dolphin distribution and the 

relationship to environmental features in the eastern tropical Pacific, 

Southwest Fish. Cent., Status of Porpoise Stocks working paper SOPS/79/36. La 

Jolla, CA mp.- 
Table A3.1. kumber of 1" square quadrilaterals deterrliined by subareas for 

southern offshore (SS), northern offshore (NS), and Coastal (C) 

spotted dolphin stocks in the inshore (I), northern offshore 

(NO), and southern offshore (SO) areas. A-SS stock, SO area; 

B=SS stock, I area; C=NS stock, NO area; 0=NS stock, I area; 

E=NS stock, SO area; F=C stock, I area; and G=C stock, NO area. 

Area of 

1' lat. 

R long. Stock Subarea 

Degrees quadrilat. lateral A 8 C D E F G 

North 

27-26 

26-25 

25-24 

24-23 

23-22 

22-21 

21-20 

20-19 

19-18 

18-17 

17-16 

16-15 

15-14 

14-13 

13-12 

12-11 

11-10 

10- 9 

9- 8 

8- 7 

7- 6 

6- 5 

5- 4 

4- 3 

3- 2 

2- 1 

1- 0 

South 

0- 1 

1- 2 

2- 3 

3- 4 

4- 5 

5- 6 

6- 7 

7- 8 

8- 9 

9-10 

10-11 

11-12 

3220.22 

3247.14 

3273.08 

3298.04 

3322 .OO 

3344.96 

3366.91 

3387.85 

3407.78 

3426.68 

3444.56 

3461.41 

3471.23 

3492.01 

3505.74 

3518.43 

3530.08 

3540.67 

3550.21 

3558.70 

3566.14 

3572.50 

3577.82 

3582.07 

3585.26 

3587.39 

3588.45 

3588.45 

3587.39 

3585.26 

3582.07 

3577.82 

3572.50 

3566.14 

3550.21 

3540.67 

3530.08 

3518.43 

3558.70 

29.4 

27.3 

25.6 

23.4 

20.7 

18.2 

15.1 

11.5 

7.2 

2.3 

3.1 

6.9 

8.8 

8.2 

8.1 

8.7 

8.9 

8.7 

8.5 

8.1 

2.5 

1 .8 

5.4 

9.1 0.3 

11.5 1.5 

16.7 3.1 

20.4 6 .O 

23.0 8.6 

25.9 11.7 

27.8 i6.8 

30.3 18.0 

32.5 19.7 

33.9 22.2 

36.0 22.4 

37 .O 22.6 

37.2 23.3 

36.9 24.5 

37.5 25.2 

37.6 24.3 

40.4 22.8 

34.6 19.9 

34.1 16.5 

35.0 12.9 

33.5 10.7 

9.8 31.4 

6.2 

2.4 

2.1 

2.0 

2.5 

2.8 

2.8 

0.8 1.2 

1 .o 0.1 

0.9 

1.3 

2.0 

2 .o 

4.6 

1.1 

3.4 

1.9 

1.2 

1.0 

1.8 

2.9 

3.4 

2.0 

1 .o 

1.1 

1.3 

1.1 

1.3 

1.1 

1.1 

0.9 

1.1 

1.3 

0.9 

0.9 

0.8 

Tota area 645799 286727 2251058 1244164 112677 158983 44326 i! (nm 1 
86 

Table A3.2. Number of 1" square quadrilaterals determined by subareas for 

northern whitebelly (NU) ,southern whitebelly (SW), eastern (E) 

and Costa Rican (CR) spinner dolphin stocks in the inshore (I), 

northern offshore (NO), and southern offshore (SO) areas. A=NW 

stock non-overlap NO area; B=NW stock, non-overlap I area; C=NW 

and E stocks, overlap I area; D=NW and E stocks, overlap NO 

area; E=E stock non-overlap I area; F=E stock, non-overlap NO 

area; G=SW stock SO area; H=SW stock, I area; J=M stock, I area. 

Area of 

1' lat. 

& long. Stock Subarea 

Degrees quadri- lat. lateral A B C D E F G H J 

North 

25-24 

24-23 

23-22 

22-21 

21-20 

20- 19 

19-18 

18-17 

17-16 

16-15 

15-14 

14-13 

l? 12 

12-11 

11-10 

10- 9 

9- 8 

8- 7 

7- 6 

6- 5 

5- 4 

4- 3 

3- 2 

2- 1 

1- 0 

South 

0- 1 

1- 2 

2- 3 

3- 4 

4- 5 

5- 6 

6- 7 

7- 8 

8- 9 

9-10 

10-11 

11-12 

12-13 

13-14 

Totaj area 

(nm ) 

3273.08 

3298.04 

3322 .OO 

3334.96 

3366.91 

3387.85 

3407.78 

3426.68 

3444.56 

3461.41 

3477.23 

3492.01 

3505.74 

3518.43 

3530.08 

3540.67 

3550.21 

3558.70 

3566.14 

3572.50 

3577.82 

3582.07 

3585.26 

3587.39 

3588.45 

3588.45 

3587.39 

3585.26 

3582.07 

3577.82 

3572.50 

3566.14 

3558.70 

3550.21 

3540.67 

3530.08 

3518.43 

3505.74 

3492.01 

4.6 

10.5 

14.9 

17.9 

20.5 

22.2 

24.1 

26.1 

27.4 

29.4 

31.3 

33.3 

35.1 

40.7 

38.0 

36.8 0.5 

38.1 3.5 

1602804 14353 

1.4 

4.3 

6.4 

8.9 

11.3 

15.9 

17.5 

22.2 

22 .o 

20.4 

18.6 

16.8 

14.4 

11 .o 

6.8 

2.1 

6.1 

0.1 8 .O 

0.9 8.0 

1.2 9.1 

2.2 10 .o 

5 .O 12.0 

7.9 13.0 

1.8 11.1 11.5 

8.1 16.2 5.0 

14.0 16.8 

15.0 16.1 

15.5 16.3 

15.9 14.3 

15.6 12.1 

15.3 8 .O 

14.2 7.7 

13.3 3.7 

12.3 5.0 

11.5 6.0 

10.8 5.3 

6.4 4.2 

0.1 2.4 

2.5 

1.4 

704504 599438 582764 287204 

0.2 

1.1 

1.2 

1.1 

1.5 

1.4 

2.4 

2.0 

32.1 9.5 

29.7 8.8 

27.2 8.0 

24.5 7.6 

21.8 7.2 

19.1 6.9 

16.5 7.2 

13.7 7.5 

11.0 7.8 

8.1 8.1 

5.5 8.3 

3.0 8.4 

8.2 

2.8 

797068 339568 38614 
Table A3.3. Number of 1" square quadrilaterals determined by subareas for 

area occupied by northern tropical (NT), west central tropical 

(WC), eastern central tropical (EC) and southern tropical (ST) 

common dolphin stocks in the inshore (I), northern offshore (NO) 

and southern offshore (SO) areas. A=NT stock, NO area; B=NT 

stock, I area; C=WC stock, NO area; U=WC stock, I wed; E=EC 

stock, NO area; F=EC stock, I area; G=ST stock, NO area; H=ST 

stock, I area; J=ST stock, SO area. 

Degrees 

1 at. 

North 

28-27 

27-26 

26-25 

25-24 

24-23 

23-22 

22-21 

21-20 

20-19 

19-18 

18-17 

17-16 

16-15 

15-14 

14-13 

13-12 

12-11 

11-10 

10- 9 

9- 8 

8- 7 

7- 6 

6- 5 

5- 4 

4- 3 

3- 2 

2- 1 

1- 0 

South 

0- 1 

1- 2 

2- 3 

3- 4 

4- 5 

5- 6 

6- 7 

7- 8 

8- 9 

9-10 

Area of 

1' lat. 

& long. 

quadri1 ateral 

3192.32 

3220.22 

3247.14 

3273.08 

3298.04 

3322 .OO 

3344.96 

3366.91 

3387.85 

3407.78 

3426.68 

3444.56 

3461.41 

3477.23 

3492.01 

3505.74 

3518.43 

3530.08 

3540.67 

3550.21 

3558.70 

3566.14 

3572.50 

3577.82 

3582.07 

3587.39 

3588.45 

3588.45 

3587.39 

3585.26 

3582.07 

3577.82 

3572.50 

3566.14 

3558.70 

3550.21 

3540.67 

3585.26 

Tota area h (nm ) 

Stock Subarea 

A B C D E F G H J 

6.3 

6.9 

8.1 

8.7 

11.4 

12.9 

13.2 

11.9 

10.7 

9.3 

8.0 

6.7 

6.1 

401329 

0.6 

1.5 

2.4 

4.9 

7.5 

11 .o 

15.5 8.7 

21.3 

27.2 

28.6 

30.2 

30.7 

31.6 

32.5 

32.5 

24.4 

8 .O 

5.5 

4.2 

149128 1007297 

0.7 

0.3 

0.1 

0.4 

0.8 

1.2 

1.5 

1.8 

3.5 

6.1 

8.9 

11.2 

17.9 

20.0 

22.9 

22.3 

23.3 

24.0 

26.5 

29.0 

29 .O 

26.6 

23.7 

21 .o 

17.0 16.7 

18.1 14.2 

18.3 11.6 

10.1 16.6 

10.2 8.9 

10.0 8.7 

10.0 3.6 

9.0 1.6 

9.0 0.3 

8.7 

9.0 

9 .o 

9 .o 

3832 126447 1013799 191550 488173 142380 
Table A3.4. Number of 1" square quadrilaterals determined by subareas for 

northern tropical (NT), west central tropical (K), eastern 

central tropical (NT), west central tropical (WC), eastern 

stocks in the inshore (I), northern offshore (NO) and southern 

offshore (SO) areas. A=NT stock, NO area; B=UT stock, I area; 

C=WC stock, NO area; D=EC stock, NO area, E=€C stock, I area; 

F=ST stock, SO area; G=ST stock, I area and H=ST stock. ?@ area. 

Area of 

1' lat. 

& long. Stock Subarea 

Degrees quadrilat. lateral A B C D E F G H 

North 

26-25 

25-24 

24-23 

23-22 

22-21 

21-20 

20-19 

19-18 

18-17 

17-16 

16-15 

15-14 

14-13 

13-12 

12-11 

11-10 

10- 9 

9- 8 

8- 7 

7- 6 

6- 5 

5- 4 

4- 3 

3- 2 

2- 1 

1- 0 

South 

0- 1 

1- 2 

2- 3 

3- 4 

4- 5 

5- 6 

6- 7 

7- 8 

8- 9 

9-10 

3247.14 

3273.08 

3298.04 

3322 .OO 

3344.96 

3366.91 

3387.85 

3407.78 

3426.68 

3444.56 

3461.41 

3477.23 

3492.01 

3505.74 

3518.43 

3530.08 

3540.67 

3550.21 

3558.70 

3566.14 

3572.50 

3577.82 

3582.07 

3585.26 

3587.39 

3588.45 

3588.45 

3587.39 

3585.26 

3582.07 

3577.82 

3572 -50 

3566.14 

3558.70 

3550.21 

3540.67 

Tota area h (mn ) 

1 .o 

3.3 

5.1 

6.7 

7.4 

7.9 

9.2 

9.5 

10.1 

9 .o 

7.1 

6.4 

7.7 

307348 

0.8 

1.4 

2.7 

4.9 

7.5 

10.7 

14.0 

11.6 

10.4 

220904 

9.2 

17.6 

23.9 9.9 

26.4 10.4 

28.4 10.8 

30.4 10.9 

31.5 11.4 

32.5 11.6 

31.8 13.7 

6.0 8.8 

840342 310064 

0.2 

2.7 

5.2 

9.6 

23.3 

23.4 

25.3 

22.i 

25.2 

26.7 

28.8 

26.7 

16.6 7 .O 12.3 

14.7 6.2 17.5 

12.2 5.1 25.1 

9.9 4.1 37.5 

7 .O 4.8 43.2 

4.6 45.0 5.9 

2.7 45.5 7.4 

1.5 44.9 8.9 

0.3 42.5 10.2 

30.6 9 .o 

22.5 9 .o 

18.0 9.9 

13.5 10.6 

9.5 11.2 

6.0 11.8 

1027023 994989 432558 486232 
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93 

APPENDIX 4 

ESTIMATION OF SPECIES COMPOSITION 

Let p be the proportion of porpoise schools within an area of the ocean 

which consists of species j. Then, for a survey of line length L, 

D. n.f.(O)/;ZL - n.f .(O) 

D nf(0)/2L nf(0) 

- -J-J- P = -J = -J-J 

where 

D = density of all schools, 

n 

f(0) 

= the number of schools observed, 

= sighting pdf for all schools evaluated at the origin, 

= density of schools of species j, 

= number of species j schools observed, and 

= sighting pdf for schools of species j evaluated at the 

Dj 

fj(0) 

origin 

We assume that at the origin, the detectability of a given species will 

not be affected by the species directly. However, we expect that certain 

species will have inherently different school sizes than other species. Since 

the detectability of a school depends on the school size, this may introduce 

bias into the estimation of p. Thus, we say that 

(A4-1) 

Note that the numerator of (A4-1) is the expected number of schools of 

species j, size Si in the surveyed area while the denominator is the expected 

total number of schools of size Si. 
94 

In the body of this paper, we adjusted the sighting pdf of school size 

using equations (18) and (191, i.e., 

where C' is a constant. This was based upon an exponential power series 

model for f(xlS). It was assumed there that only the scale parameter 1. S)) 

was affected by school size and not the shape parameter. Thus, C' is constant 

for all school sizes and species. This gives 

E [ c':(si)] 

We showed (equation (20)) that h(S) was well modeled by 

Then 

Finally, the expected proportion becomes 
95 

This is equivalent to (22) in the text. 

However, the unidentified species must be prorated and included in this 

DroDortion. The Droration assumDtion was that unidentified schools occur in I. 

the same species distribution as the identifieds 

dolphin). Therefore, the expected number of schools of 

unidentifieds is E(uj 1. Then 

and 

( excl udi ng Ri ssol s 

species j among the 

where u is the number of unidentifieds. 

Therefore, the proportion of species j in the identifieds - and 

unidentifieds is ply and its expected value is 

where g is the number of Rissols schools observed. This becomes 

(A4-2) 

Equation (A4-2) is equivalent to equation (23) in the text. 

the method used for species proration of the schools. 

This was 
RECENT TECHNICAL MEMORANDUMS 

Copies of this and other NOAA Technical Memorandums are available from the National Technical 

Information Service, 5285 Port Royal Road, Springfield, VA 22167. Paper copies vary in price. 

Microfiche copies cost $3.50. Recent issues of NOAA Technical Memorandums from the NMFS 

Southwest Fisheries Center are listed below: 

NOAA-TM-NM FS-SW FC- 13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

Planning double-tagging experiments. 

J. A. WETHERALL and M. Y. Y. YONG 

(May, 1981 

Histological gonad analyses of late summer-early winter collections of 

bigeye tuna, Thunnus obesus, and yellowfin tuna, Thunnus albacares, 

from the Northwest Atlantic and the Gulf of Mexico. 

S. R. GOLDBERG and H. HERRING-DYAL 

(June, 1981) 

Status reports on world tuna and billfish stocks. 

STAFF, SWFC 

(July, 1981 

An evaluation of tagging, marking, and tattooing techniques for 

M. J. WHITE, JR., J. G. JENNINGS, W. F. GANDY and L. H. 

CORN ELL 

(November 1981 

Local stability in maximum net productivity levels for a simple model 

T. POLACHECK 

(April 1981) 

Environmental data contouring program EDMAP2. 

L. EBER 

(April 1982) 

The relationship between changes in gross reproductive rate and the 

current rate of increase for some simple age structured models. 

T. POLACHECK 

(May 1982) 

Testing methods of estimating range and bearing to cetaceans 

T. D. SMITH 

(1 982) 

"An annotated bibliography of the ecology of co-occurring tunas 

(Katsuwonus pelamis. Thunnus albacares) and dolphins (Stenella 

attenuata, Stenella longirostris and Delphinus delphis in the 

eastern tropical Pacific" 

small delphinids. 

of porpoise population sizes. 

aboard the R/V 0. S. Jordan. 

S. D. HAWES 

(November 1982) 

Structured flotsam as fish aggregating devices. 

R. S. SHOMURA and W. M. MATSUMOTO 

(