Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Field evaluation of the dichotomous population estimation technique Wood, Frederick Ernest Allen 1966

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1966_A6_7 W65.pdf [ 4.28MB ]
Metadata
JSON: 831-1.0302525.json
JSON-LD: 831-1.0302525-ld.json
RDF/XML (Pretty): 831-1.0302525-rdf.xml
RDF/JSON: 831-1.0302525-rdf.json
Turtle: 831-1.0302525-turtle.txt
N-Triples: 831-1.0302525-rdf-ntriples.txt
Original Record: 831-1.0302525-source.json
Full Text
831-1.0302525-fulltext.txt
Citation
831-1.0302525.ris

Full Text

A FIELD EVALUATION OF THE DICHOTOMOUS POPULATION ESTIMATION TECHNIQUE  by F.; E. ALLEN WOOD B.Sc,  University of British Columbia, 1964  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE In the Department of Zoology  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA September, 1966  In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study„  I f u r t h e r agree that permission., f o r extensive  copying of t h i s  t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s representatives„  I t i s understood that copying  or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission.  Department The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada ,  A B S T R A C T A f i e l d evaluation of the dichotomous technique was made using 1965 data from the Rivers Inlet sockeye salmon population.  An estimate o f pre-  e x p l o i t a t i o n population size was made with the compositions post-exploitation populations and the catchi the a p p l i c a t i o n of simultaneous  o f the pre- and  The estimate was made through  equations and a maximum l i k e l i h o o d estimator  formulation to changes i n population composition r e s u l t i n g from selective removal.  Biased data was shown to greatly a f f e c t the estimates of popula-  tion size. A wide range o f population estimates was derived from the various dichotomous characters u t i l i z e d *  Graphical analysis of these  estimates  provided an o v e r a l l estimate of the population, ^ . v The p h y s i c a l r e s t r i c t i o n s of the research area made  t h i s estimate of considerable value.  Relative t o most other population estimation techniques, the dichotomous method has wider p o t e n t i a l use because o f i t s l e s s r e s t r i c t i v e basic assumptions.  This f l e x i b i l i t y can be accompanied, however, by a  reduction i n the accuracy o f resultant estimates.  iii T A B L E  OF  C O N T E N T S Page  INTRODUCTION  1  The Dichotomous Method Rivers Inlet Sockeye Salmon  ."  ......  METHODS  1 2 3  The Dichotomous Method Rivers Inlet Survey  3 8  RESULTS  13  Rivers Inlet F i e l d Study ...;  '.. ••  DISCUSSION  13 15  The Dichotomous Method Rivers Inlet Sockeye Salmon F i e l d Evaluation Comparison o f Dichotomous and M a r k - R e c a p t u r e Techniques  15 25 kk  SUMMARY  1*7  LITERATURE CITED  %9  APPENDIX  1.  Derivation o f N  APPENDIX  2.  Pre-exploitation population data ......  APPENDIX  3.  Commercial catch data  APPENDIX  k.  Post-exploitation population data  APPENDIX  5.  Estimated N  Q  Q  estimation equation  50 ..  51  ....  52 53  and i t s variance calculated from  age groupings APPENDIX  6.  Estimated N  Q  5*+  and i t s variance calculated from  3 cm. length groupings APPENDIX  7.  Estimated N  Q  55  and i t s variance calculated from  8 cm. length groupings APPENDIX  8.  Estimated N  Q  57  and i t s variance calculated from  13 cm. length groupings APPENDIX  9.  Different estimates o f N  *. Q  r e s u l t i n g from a  number o f treatments of the data APPENDIX 10.  Overall r e s u l t s  58  59 60  iv L I S T  OF  T A B L E S Page  TABLE  I.  Demonstration of the e f f e c t of sampling bias using hypothetical data  19  V  L I S T  OF  F I G U R E S Page  FIGURE FIGURE  FIGURE  1. 2.  3.  Map showing l o c a t i o n of various landmarks mentioned i n 'the text ...  10  Changes i n the estimated p r e - e x p l o i t a t i o n population size as a r e s u l t o f changes i n the size of catch .......  17  Isopleths o f rate o f net-induced mortality (K) p l o t t e d against natural^mortality (E) and resultant estimated N  22  G i l l n e t s e l e c t i v i t y as demonstrated i n Rivers I n l e t commercial f i s h e r y f o r sockeye salmon (0. nerka)  26  Graphical analysis f o r J u l y 2-29. Estimates of N derived from use of a l l numbers, no extremes, omitting negatives, and absolute values estimates  32  Graphical analysis f o r J u l y 2-8 and J u l y 9-15. Estimates o f W_ derived from use of a l l numbers, no extremes, omitting negatives, and absolute values estimates  33  Q  FIGURE FIGURE  FIGURE  FIGURE  U. 5.  6.  7. Graphical analysis f o r J u l y 16-22 and July 23-29. Estimates of N derived from use of a l l . numbers, no extremes, omitting negatives, and absolute values estimates ..-  FIGURE  8.  D i s t r i b u t i o n o f estimated N  FIGURE  9.  Mean number o f days t o recovery s i t e o f f i s h tagged at the mouth of Goose Bay (x)  FIGURE 10.  Q  and catch through time  ......  Modal number o f days t o recovery s i t e o f f i s h tagged at the mouth of Goose Bay (x) ...................  3^ 37  39  kO  A C K N O W L E D G M E N T S The author would l i k e t o express h i s gratitude t o Dr. N.J..Wilimovsky, who supervised the writing o f the t h e s i s , f o r h i s invaluable c r i t i c i s m and advice.  Thanks are due to Drs. J.F. Bendell, J.T. McFadden and J.E. P h i l l i p s  who reviewed the manuscript and made many h e l p f u l suggestions. I wish to thank the Canada Department of Fisheries f o r providing the necessary f i n a n c i a l assistance, f a c i l i t i e s and equipment, without which the problem could not have been undertaken.  Thanks are also due to  the commercial f i s h i n g companies and fishermen i n the study area, i n p a r t i c u l a r B r i t i s h Columbia Packers L t d . and The Canadian Fishing Co. Ltd., f o r t h e i r assistance and cooperation. I am indebted t o a l l those persons who gave encouragement and assistance throughout the study.  1INTRODUCTION The Dichotomous Method The determination of stock size is a general problem in a population study.  A specialized case of indirect count method of  population estimation is the "dichotomous" (Chapman, 195*0 or "change of composition" method.  "If a population Is classifiable in two or more ways,  and harvesting from i t is selective with respect to this classification, then i t i s possible to make a population estimate from knowledge of the original composition, the f i n a l composition, and the composition of the harvested catch" (Ricker, 1958).  Factors such as age, colour, sex, size,  species, etc., may be used for classification of the population.  The ease  of classification by sex and, in many instances, age (i.e., juveniles or adults), and the marked selectivity of k i l l (as a result of legal restriction or animal behaviour) has permitted relatively wide use of this technique for population estimates of game birds and mammals. The procedure has been used mainly for pheasant (Allen, 19^2) and deer (Kelker, 19^0, 19^2; and Daman, I9U3J  Riordan, l^kB;  Petrides, 19^9j  Rasmussen  Dasmann, 1952) populations  because their environments and modes of l i f e generally meet most of the requirements of this form of study.  Although this system of population  estimation i s known among fishery biologists, there Is l i t t l e documented use of i t .  The method has been used by Vaughn (1955) for estimating  populations of chinook salmon on the Taku Rlverj  i t has been t r i e d also for  racial studies of the Bristol Bay sockeye salmon stocks. As both of these studies had only limited success, i t was proposed to use the dichotomous principles to make a population estimate of the sockeye salmon (Oncorhynchus nerka) stocks passing through Rivers Inlet.  2 Rivers Inlet Sockeye Salmon Work was This area was  carried out i n 1965  i n the Rivers Inlet area (see Figure l ) .  ehosen because the i n l e t i s r e l a t i v e l y long (26 miles) and  narrow (maximum of 2 miles), and as a l l sockeye i n the i n l e t enter the Wannock River at the head of the i n l e t , they must migrate the f u l l length of the i n l e t .  The commercial f i s h e r y during the sockeye season, by  regulation, i s l i m i t e d to g i l l n e t and t r o l l gear, the g i l l n e t f i s h e r y being the only one operable during the season.  The l o c a t i o n of the  commercial f i s h e r y , predominantly within the i n l e t , permits sampling at or near the mouth of the i n l e t of what would be b a s i c a l l y an unexploited population.  The l o c a t i o n of the f i s h i n g boundary 3.5  miles from the head  of the i n l e t provided an area of pooling and mixing of schools from which the " a f t e r - f i s h e r y " population could be sampled.  The short (3 miles)  Wannock River flows from Owikeno Lake to the head of Rivers I n l e t ; most of the major spawning areas (except the Wannock River which i s a l a t e stock) are located considerable distances from the outlet of the lake (closest i s 6 miles) and i t was planned therefore to sample near the outlet of the lake f o r a second sample of the post-exploitation population.  METHODS The Dichotomous Method There are at present two basic procedures f o r making population estimates by change of composition method:  simultaneous equations  (Model I) and maximum l i k e l i h o o d estimators (Model I I ) . Both of these forms of estimation t r e a t the populations as binomial populations. That i s , f o r any one i n d i v i d u a l there are two possible categories, only one of which i t can occupy.  For example, the f i s h can be male or  female, i t usually cannot be both.  Although characters such as age  and  length give r i s e to a multinomial population, the method of treatment of data such that a single category i s compared to a l l other categories changes t h i s to an e s s e n t i a l l y binomial s i t u a t i o n . The estimation of population size through the use of simultaneous equations i s achieved by equating the actual proportion of individuals i n the escapement having a chosen character to the expected proportion as calculated from the catch and o r i g i n a l population.  With knowledge  of the absolute size of one of these populations, generally catch, an estimate of the size of the other two populations can be made.  The  Model I method of population estimation can be demonstrated through the use of the following parameters of a hypothetical population: SEX CLASSES % males' % females  SEX SAMPLES  SAMPLE SIZE  ORIGINAL POPULATION  50$  50$  2500  CATCH  k0%  60f«  5000  ESCAPEMENT  6V?o  k0%  2500  SIZE OF CATCH (500,000)  200,000  300,000  Assuming unbiased sampling, l e t X be the number of f i s h i n the unexploited population.  As removal (commercial catch) i s 5 0 0 , 0 0 0 , then  escapement i s X - 500,000.  Fifty per cent of the unexploited population  is composed of males; the number of males in that population i s .5X. The incidence of males in the escapEment i s 60 per cent so the number escaping i s .6(X - 500,000).  As the number of males in the catch i s 200,000,  the number of males i n the escapement must also equal ,5X - 200,000.  Setting  the values of male escapement equal to each other and solving for X provides an estimate of the size of the original population. .6X - 300,000  =  .5X - 200,000  .IX  .  100,000  X  =  1,000,000  The original population size i s equal to 1,000,000 f i s h .  The  estimate i s based on the proportion of males in the population. Additional estimates of the size of that same population could be based on the proportion of females, different age classes, and length groupings.  An  indication of the r e l i a b i l i t y of the resultant estimates can be derived from the size of the variances of the individual estimates. A crude estimate of the variances of estimates derived from the simultaneous equations method i s obtained by summing the variances of the three binomial populations involved.  "The variance of a binomial population  is equal to the product of the relative frequencies of successes and failures"  ( L i , 1964).  For example: u  =  relative frequency of successes in the population  n  =  sample size u  variance  original population  .5  .25  catch  .k  .2k  escapement  .6  ,2k  variance  =  u ( l •— u)  5 estimate variance  =  .25 + .24 + ,2k  =  + 73% (including catch)  =  .25 + .24  =  + k9% (excluding catch)  As the absolute size of the removal i s known, i t s variance i s not considered to contribute s i g n i f i c a n t l y to the variance of the o v e r a l l estimate of variance, therefore i t i s not added into the estimate variance.  Rather than  adding the variances i t may be considered desirable to estimate a weighted average of the variances, i . e . , weighted average variance  =  (n —  x  (n  - l ) ^ + (n :—r : x  -  2  - l ) u + (n~ - l ) u r *—r * 2  y  1) + (ng - 1) + ( n - l ) 3  Using the above data the weighted average variance i s 47.7  per cent;  excluding catch data i t i s 55 per cent. The simultaneous  equations method i s r e l a t i v e l y simple, but with  t h i s s i m p l i c i t y comes reduced r e l i a b i l i t y i n the r e s u l t s .  Failure to  account f o r sample size and poor variance estimates are major weaknesses of t h i s method. The second method of population estimation based on-the change of composition method u t i l i z e s equations derived as moment estimates from the product of the binomial representations of the pre- and p o s t - e x p l o i t a t i o n population c h a r a c t e r i s t i c s (Chapman,  1954). (See Appendix 1 f o r algebraic  derivation. The following notation i s used i n these estimates: =  population size at time t ^ ( i = 0,  l ) made up of two  classes X and Y which are defined by the characters upon which s e l e c t i o n acts, NQ  =  the size of the o r i g i n a l (unexploited) population  N X.,Y.  = =  the size of the escapement population size of classes X and Y at times t . I  =  size of classes X and Y i n the o r i g i n a l population  -  size of classes X and Y i n the escapement  2  i '  i  X ,Y 0  X.,Y.  0  6  = V*i = V o • V i • o- i • o" i N  w  l  p  R X  R y R  =  x  x  removal (catch) from class X  Y  y  removal (catch) from class Y  R + R x y  =  t o t a l removal (catch)  i  = '  size of random samples taken at times t ^  o  '=  size of random samples of o r i g i n a l population  n  l  • -  size o f random samples of escapement  x  I' i  = -  the numbers i n classes X and Y respectively i n sample i  n  n  y  Vo y  =  =  the numbers in classes X and Y respectively i n the o r i g i n a l population  x  l ' l y  =  ^  e  n u m  ^  ^n classes X and Y respectively i n the escapement  e r s  The maximum l i k e l i h o o d estimators, then, are:  X. =  u  0  *  x  x  n i  0  —  - n  n (n,R  =  __  -  Q  = 1^000,000  io "oi  n x  Y  o X l  - x.R)  0  NQ  = 500,000  n  = N -X Q  x  = 500,000  Q  X.1 = X0 - Rx = 200,000 ' Y  x  = Y -R Q  y  = 300,000  i f the following parameters are used: CLASSES SEX SAMPLE  MALES (Y) % y  FEMALES (X) % x  ±  ±  TOTAL SAMPLE SIZE  ORIGINAL POPULATION  50 1250 ( y ) 5*0 1250 ( x ) 2500 ( n )  ESCAPEMENT (N - R)  60 1500 (y^ kO 2000 (m )  CATCH (R)  SIZE OF CATCH (R)  0  y  200,000 (R ) y  Q  Q  1000 (a^) 2500 (x^) 60 3000 (m ) 5000 (m)  kO  x  300,000 (R ) x  An asymptotic variance-covariance matrix computation provides an equation with which to estimate the variance of each individual estimate of the original population size.  This estimate permits weighting of the.mean  of a group of population estimates, which improves the accuracy of the mean since the effects of strongly divergent estimates (large variance) are reduced.  2(x ) .  -2°  0  S  "1  1  <p -  V  0  ,2,„  >  n  r(B„) =  " l  0  For the preceding numerical example, the estimate of variance of X^ i s 1,600,000,000 and N  i s 12,400,000,000.  Q  A necessary extension of this variance estimate is to account for variance caused hy use of sub-samples of the commercial catch rather than total samples.  This is accounted for by Chapman (1955) by some additions  to the basic variance equation. X  q  S  2  r w  ( M  ,  0 0 , 11 , Y  n  0  X  n  "*x  Y  l  r 2  y  ( 0 - l) P  P  /  R  2  ,  3  \  P  0 n  ( l  0  - V  ,  3  F  n  l  (  l  -  V  l  ;  ( o- i> p  p  The variance estimate for the preceding numerical example is S (N ) 2  Q  =  12,401,200,000.  Chapman (1955) presents an equation for the estimation of NQ which includes two correction factors for unreported losses (or gains): the f i r s t (K) is for loss proportional to catch (net-induced mortality);  the second  (E) is for loss which is not proportional to removal (natural mortality).  8 I f a large sample size i s assumed (n^*-> N^),  then the sample  statistics  can be replaced by the population parameters (x^ becomes X^, y^ becomes Y^, etc.)  and the estimate of N  Q  converges i n p r o b a b i l i t y to  (N R  - X.R) - ER  A  0  0 ( N ^  - X Q R K I + K) - E X  where unreported removals are:  and actual removals are:  Q  f o r X,  KR^  f o r N,  KR + E  f o r X, R . x f o r N,  + KR  + E x  R + KR + E  Using previous data, assume K = .01 and E = 1000.  The estimate of N  Q  from  these previous data i s 99^*000• There are a number of assumptions upon which the change of composition population estimate i s based: (1)  A closed population i n which i t i s assumed that n e g l i g i b l e emigration, immigration, recruitment, natural or any other unaccounted mortality i s occurring at the time of removal (exploitation) i s necessary.  (2)  The population must be composed of at l e a s t two distinguishable classes of individuals which are unequally vulnerable as a r e s u l t of the method of removal ( g i l l n e t selection f o r medium sized f i s h ) or of l o c a l laws regarding removal (hunting regulations which l i m i t k i l l to males).  (3)  Population samples taken before and a f t e r the removal proeess are random with respect to the s p e c i f i e d classes of i n d i v i d u a l s .  Rivers Inlet Survey In sampling at the mouth of the i n l e t f o r the pre-exploitation population and at the head of the i n l e t f o r the post-exploitation population, a 36-foot chartered commercial drum seiner was used.  A seiner was chosen  because i t causes minimal physical damage to f i s h (Hartt, 19^3)> and because  9 of i t s e f f i c i e n c y and r e l a t i v e n o n - s e l e c t i v i t y . The seine was 250 fathoms in t o t a l length hy 16 fathoms i n t o t a l depth, i t s body was made of 3-inch tarred cotton web and there were kO fathoms of 1^-inch herring web on the bunt.  (The web size and the bunt mesh were s p e c i a l l y chosen f o r juvenile  salmon studies, therefore a l l adults should have been caught.) A seine s k i f f was used t o maneuver the outer end of the seine. Early i n the f i s h i n g season, t e s t f i s h i n g was conducted at various locations at the mouth of the i n l e t .  The only s i t e found to be  suitable was near the mouth of Goose Bay (see Figure l ) .  Sites i n Darby  Channel were strongly influenced by t i d e s , s i t e s near Sharbau Island, Major Brown Rock, Dimsby Point and Addenbroke Point were open t o the sea wind, which made f i s h i n g i n these areas possible at only certain times.  The distances involved i n t r a v e l l i n g between these s i t e s , the  speed o f the seiner (8 m.p.h.) and the r e l a t i v e size of the catch l e d f i n a l l y to the s e l e c t i o n of an area around Cow Island (mouth of Goose Bay) as the major f i s h i n g s i t e . A l l f i s h caught i n the mouth of the i n l e t were measured (nose t o fork length, accurate t o .5 cm.) and sampled f o r sex (estimated from external c h a r a c t e r i s t i c s ) ; determinations).  a scale sample was taken (to be used i n age  Also, the f i s h were tagged with a "spaghetti"-type tag,  t h i s type having been chosen because o f i t s n o n - s e l e c t i v i t y t o g i I I nets (Davis, 1959). The tags used i n t h i s experiment were made of l/l6-inch tubing ( r e s i n i t e tubing, Borden Co. Chemical Division) with a legend printed on the tubing;  no transparent covering tube was used.  Tags were  applied with a s t a i n l e s s s t e e l rod with one end t h i n enough to f i t inside of the tag end the other end sharpened i n a three-sided point (so that i t would cut i t s way through instead of r i p p i n g ) . The tag was slipped over the t h i n end of t h i s rod, sewed through the f i s h , and held in; place by  10  FIGURE 1.  Map showing location, of various landmarks mentioned i n the text.  an over-hand knot.  The f i s h were tagged i n order to provide an i n d i c a t i o n  of timing, and a stock of f i s h upon which to t r y a "change of composition" estimate. Fishing at the head of the i n l e t f o r a post-exploitation (escapement) sample was concentrated at the extreme head of the i n l e t i n the hope that sampled f i s h would not d r i f t back across the commercial boundary.  Spaghetti-  tagged f i s h caught i n the sample were to be used i n making a population estimate.  Length measurements (nose-fork), scale samples and estimates of  sex were taken;  f i s h were tagged with large (22  mm.)  Petersen disc tags,  the purpose of which was to provide an i n d i c a t i o n of the d r i f t of f i s h back across the commercial boundary, and a means of estimating population size (by recovery i n the l a k e ) . Sampling near the outlet of Owikeno Lake was c a r r i e d out to provide a second sample of the exploited population, as well as to recover the Petersen disc tags and spaghetti tags applied e a r l i e r .  Sampling  was  o r i g i n a l l y to be by beach seine, but high water conditions d i d not permit t h i s , so the beach seine was modified to a small purse seine.  Nose-fork  and orbital-hypural lengths were measured, scales taken and sexes estimated. The commercial catch was packers.  sampled as i t was being delivered to f i s h  Samples were taken mainly at Wadhams and Sampson IV (near Dawson's  Landing), but also at Good Hope (see Figure l ) , and on c o l l e c t i n g boats. Both nose-fork and orbital-hypural lengths were measured.  Since nose-fork  lengths were taken i n the tagging operations, because of the ease of measuring l i v e f i s h , and since p r e v i o u s l y - c o l l e c t e d data are predominantly i n orbital-hypural lengths, because they were taken i n spawning ground surveys, both measurements were taken i n t h i s experiment  i n order to provide  data from which a conversion f a c t o r could be calculated.  Scale samples were  taken to provide an estimate of the age composition.  Estimates of sex were  recorded f i r s t (based on external c h a r a c t e r i s t i c s ) and then, i f the captain of the packer would permit i t , f i s h were dissected and the actual sex recorded.  Comparison between estimated and actual sex provided a means of  quantifying the accuracy of the sex estimates. 1965  operated from 6:30 p.m.  through July 2 1 .  The commercial f i s h e r y i n  Sunday u n t i l 6:30 p.m.  Thursday and from June 2k  On July 2 0 , a 3-day f i s h i n g week was declared (Thursday-  July 22 was omitted). week;  was  A t o t a l closure of 18 days was declared the following  the f i s h e r y reopened August 8 . The major tag returns were of the spaghetti tags<*  A reward of  50 cents f o r each tag was offered to stimulate return of tags.  A canvas  of a l l the major f i s h camps on two days of each closed period was  conducted  to recover tags found by the fishermen and to d i s t r i b u t e tag return  envelopes.  A l l the c o l l e c t i n g boats operating i n the i n l e t were provided with tag return instructions and given a supply of tag return envelopes to d i s t r i b u t e to fishermen.  When the f l e e t moved to the Fraser River, a canvas of boats  f i s h i n g that r i v e r was  conducted i n a further e f f o r t to recover tags.  RESULTS Rivers Inlet F i e l d Study As the change i n composition method of population estimation requires samples of the pre-exploitation population, f i s h removed by exploitation, and the p o s t - e x p l o i t a t i o n population, analysis by t h i s method was l i m i t e d to a c e n t r a l l+-week period of the migration by the l a c k of one or more of these samples (see Appendices 2 to k).  The f i r s t week of f i s h i n g lacks a post-  e x p l o i t a t i o n sample, which i s to be expected as f i s h have not yet reached the head of the i n l e t .  The second week has the necessary samples but the  size of the p o s t - e x p l o i t a t i o n sample i s questionably small (l8).  The  t h i r d , fourth and f i f t h weeks have complete sets of data with s u f f i c i e n t sample s i z e s . for  At the end of the f i f t h week, the commercial f i s h e r y closed  18 days, thereby removing the selective process.  Sampling i n Owikeno  Lake to provide a secondary p o s t - e x p l o i t a t i o n sample provided no data usable i n population estimation because the samples d i d not span the necessary time period and were taken with a d i f f e r e n t type of gear, therefore under a d i f f e r e n t selective regime. The weekly periods have been divided so that the p r e - e x p l o i t a t i o n sample i s taken at the f i r s t of the week and the commercial catch and post-exploitation samples are taken l a t e r i n the week.  Based on the modal  rate of migration, the three samples should a l l be from the same stock of  fish. The data c o l l e c t e d permitted population estimation based on age  length c h a r a c t e r i s t i c s .  Using age as estimated from scale analysis, N  and Q  ( o r i g i n a l population size) was estimated using three age groups (see Appendix 5)«  Analysis of length data f o r an estimate of  out with three d i f f e r e n t length groupings: Appendices 6, 7 and  8).  3 cm.,  was  carried  8 cm. and 13 cm.  (see  The estimates r e s u l t i n g from the age and length analyses were grouped i n a number of d i f f e r e n t manners.  Each estimate was weighted  with the r e c i p r o c a l of i t s variance. A graphical analysis i n which i n d i v i d u a l estimates of N  Q  were p l o t t e d against t h e i r variances  permitted a v i s u a l estimate of the c e n t r a l or most l i k e l y estimates (see Appendix 9) • Corrections f o r periods not sampled, catch outside the sampling s i t e and unaccounted mortality are applied i n c a l c u l a t i o n of f i n a l estimates (see Appendix  10).  DISCUSSION The Dichotomous Method In a l l population estimation techniques the d i f f i c u l t y of meeting the basic assumptions l i m i t s the accuracy of estimates. assumptions, the more d i f f i c u l t they are t o meet.  The grosser the  The assumptions of  the dichotomous population estimation method are r e l a t i v e l y easy to meet. I f the time between the "before" and " a f t e r " samples i s minimized, the e f f e c t s of emigration, immigration, recruitment, and natural mortality should also be minimal.  In many cases populations tend to overlap, such that  animals removed from these areas of overlap cannot be c l a s s i f i e d as belonging to one population or the other; immigration.  t h i s s i t u a t i o n may be considered a form of  A l t e r n a t i v e l y , a p o r t i o n of the population's range may  inaccessible to the form of e x p l o i t a t i o n ;  be  i f there i s l i t t l e mixing within  the population, the inaccessible p o r t i o n may be treated as a separate population. The assumption of s e l e c t i v i t y of removal appears to be quite secure as most forms of e x p l o i t a t i o n tend to show some s e l e c t i v i t y , u s u a l l y by size.  "A s e l e c t i v e process i n f i s h i n g may be defined as any process which  gives r i s e to differences i n the p r o b a b i l i t y of capture among members of the exploitable f i s h " (Parrish, 1963)*  "From general inspection of the size  frequency d i s t r i b u t i o n i n catches taken by g i l l n e t s of d i f f e r e n t mesh sizes, i t has long been believed that the t y p i c a l selection curve i s s i m i l a r to the normal d i s t r i b u t i o n .  The f r a c t i o n of the number of f i s h of a c e r t a i n  length which encounter the net and are retained by i t i s thus highest at a c e r t a i n length, and decreases symmetrically to zero both above and below that length" (Holt, 1963). Peterson (195*0 demonstrated g i l l n e t s e l e c t i v i t y by s i z e ;  also g i l l n e t s e l e c t i o n by sex i n P a c i f i c salmon as'ra r e s u l t of  secondary  sexual c h a r a c t e r i s t i c s ( i . e . , male pink salmon, Oncorhynchus  gorbuscha, selected f o r more highly than females).  Sport f i s h i n g and  hunting tend to be selective by regulations applied to them, usually a minimum s i z e , sex, or both.  Behaviour of animals may  change at d i f f e r e n t  ages or states of sexual maturity, r e s u l t i n g i n responses which make the animal more or l e s s susceptible to the form of removal. true i n sport f i s h i n g and  This i s e s p e c i a l l y  hunting.  Qualitative c h a r a c t e r i s t i c s , such as age or sex, have the advantage over quantitative c h a r a c t e r i s t i c s , such as weight, i n that boundaries of the classes of c h a r a c t e r i s t i c s are n a t u r a l l y defined.  Any changes i n the  d i s t r i b u t i o n of i n d i v i d u a l s of an age c l a s s r e l a t i v e to length r e s u l t s i n no change i n the population estimate provided the proportion of the class to the t o t a l population does not change.  age  Generally, q u a l i t a t i v e  c h a r a c t e r i s t i c s are r e a d i l y grouped, therefore they lead to a l i m i t e d amount of sampling b i a s . Quantitative c h a r a c t e r i s t i c s form an i n f i n i t e array of sub-groups. The necessity of measuring these sub-groups permits i n f i l t r a t i o n of considerable amounts of b i a s .  To use the data i n a change of  composition  type of population estimation, the data must be grouped i n t o a usable number of groups.  This necessitates using e i t h e r a number of groups of  random size or a series of groups of equal size defined by e i t h e r the numbers i n the group or a f i x e d span of the measured character ( i . e . , 3 groupings).  cm.  Both of these forms of grouping o f f e r much p o t e n t i a l b i a s .  There i s a l i n e a r r e l a t i o n s h i p between the sitse of catch (R) and estimate of the o r i g i n a l population s i z e . estimated N  Q  i n Figure 2.  The rate of change of the  as a r e s u l t of changes i n R i s equal to the slope of the l i n e I f the center of s e l e c t i o n remains constant the more marked :  the s e l e c t i o n i s (smaller m /m), smaller the slope w i l l be.  the smaller the catch w i l l be, and the  As a r e s u l t , the smaller the slope gets, the  17  (OOO'OOI *) ON  FIGURE 2.  0.3±VWI±S3  Changes in the estimated pre-exploitatlon population size as a result of changes ' in the size of catch. Composition data remaining constant. Based on data from previous example calculation on page 6. Catch and estimated N i n numbers of fish. 1  n  18 l e s s e f f e c t catch, regardless of i t s size, has on the estimate o f N^, therefore the more accurate the estimation of N . Q  I f the fate o f s e l e c t i v i t y  i s within the c o n t r o l of a f i s h e r y manager wanting to use a dichotomous population estimation method, i t would he very advantageous t o maximize the selection. size  In any case, the r e l a t i o n s h i p between the o r i g i n a l population and the catch (R) makes i t v i t a l that accurate estimates of the  size of catch be used i n computations i f accuracy of resultant estimations of N  Q  i s t o be achieved. Changes i n the aforementioned "slope f a c t o r " due t o sampling bias  can cause a gross bias i n the estimate of N^. I f length i s the selected character, a constant measuring bias can cause marked e f f e c t s on the estimate of N . Q  In Table I, the r e s u l t o f reducing f i s h lengths by one  centimeter i s shown i n the column headed "Commercial catch, biased". This type of e r r o r could r e s u l t because o f untrained personnel o r f a u l t y equipment and could occur i n a l l the samples, r e s u l t i n g i n a t o t a l average bias of 1 cm. Using 6 cm. length groupings of the three stocks, estimates o f the o r i g i n a l population size were calculated using a c t u a l and biased lengths.  The estimates were a l l made using a Model I I type of computation.  The marked differences between the biased and actual estimates o f the o r i g i n a l population emphasize the importance of the assumption o f unbiased samples of the selected character. When the proportion o f class X i n the p r e - e x p l o i t a t i o n population exceeds the proportion o f Glass X i n the post-exploitation population, an increased value f o r the catch of c l a s s X r e s u l t s i n an increased estimate of N  Q  ( P Q - > P-^ J  common occurrence  ^> m  x  = ^>NQ).  i n my data.  This s i t u a t i o n i s probably the most  I t occurs three times i n Table I .  19 TABLE I .  Demonstration of the e f f e c t of sampling bias using hypothetical data. COMMERCIAL  PREEXPLOITATION LENGTH  35 36 37  38 39 40 1+1 1+2 1*3 1+1+  1+5 1+6 1+7  1+8  k9 50 51 52 53 51+ 55 56 57  58  59  60 61 62 63  61+  65 66 67 68 69  Actual  0  1+  1 2 1  \  12 .025  POSTEXPLOITATION  1  (  1 1  .002  1  .002  X l  )(  P l  )  N, Actual  Biased  •  20 .080 181,712  181,712  8 .032; 328,002  305,9^6  5 5 9,  1  1+  2  .001+  3 •006  I  2 2  1 s  3 3 M .093 8 120 9 17 17 35 16. 56. 1+1 77 50 61 53 298 .616 50 261+ 26 53 72 23 27, 29. 21" 18 19 19 ll+ 81 .167 21+ 111 ll+ 12 1+ 20 18. 9. 8" 5" 1+ 5 11 27 .056 1+ 25 1+ 5 l 3 2. * l+81+(  Biased  (n^Hmx/m) (m^On^/m)  (x )(Po) 1 1 21 .01+3 5 6 8 3'  CATCH  523 (m)  •  .229 196 , -375  1 3  17 .068  559,762 1,061+,3H  1+.  .505 205  .392  9, 19 3*+ 1+6 180 .723 h3 2l+  I7l+,661+  264,998  19 .076  128,088  110,090  5 .020  66,303  29,539  Hi  .212 101  .01+8  17  .193  .oi+o  6" 3 3 2 5 3 2  21+9(3^)  20 When the proportion of class X in the pre-exploitation population is less than the proportion of class X in the post-exploitation population, increased values for the catch of class X results in a decreased estimate of N  Q  (P < P 0  1  : > m  x  =<N ). Q  These conditions occur relatively frequently  and can he expected to occur in length data analysis, in an area of displacement of the escapement curve as a result of selectivity (i.e., i f escapement is displaced two units to the right of the pre-exploitation population curve, the use of the data in the area of displacement may result in the abovementioned condition (PQ<£P^).).' If the proportion of class X in the post-exploitation population exceeds the proportion of class X in the catch but not in the pre-exploitation population, negative values for the estimate of N  Q  result.  This w i l l occur  when using data from an area of a frequency distribution with moderate numbers of individuals but with very low rate of removal. This situation does not occur commonly. If the proportion of class X in the post-exploitation population exceeds the proportion of class X in the pre-exploitation population but not in the catch, negative values of the estimate of\N result. Q  These  conditions are found when using data from an area of a frequency distribution which is not heavily selected for, in a population with a low rate of exploitation. When the proportion of class X in the pre-exploitation population equals this same proportion in the catch and also in the post-exploitation population, no selection has occurred;  the 'dichotomous methods of population  estimation do not function and the value of  equals zero. This situation  could occur almost anywhere in a frequency distribution, but Is most likely to occur in the area of selective displacement of the escapement curve. This situation could also occur i f the range of sampling for the frequency 0.'-•••  . •'. ••;  . •  ' • '-'v  -;):•'.•  :v.  ctiiA  and  mtern.ct  . .on ;  d i s t r i b u t i o n was such that i t encompassed a l l selection and interaction within the sample and n u l l i f i e d the s e l e c t i o n . A l l o f the above-mentioned situations can, and do, occur i n data, e s p e c i a l l y with small samples.  Many of the "undesirable" situations can  be avoided or eliminated by the choice of a sample range i n the frequency d i s t r i b u t i o n which provides the "desirable" s i t u a t i o n s .  The a r b i t r a r i n e s s  of t h i s choice o f sample range could lead to a conscious or unconscious biasing of the N  Q  estimate.  I t seems probable that the best way t o  eliminate t h i s bias i s t o use a f i x e d sample range (e.g., each range i s defined as containing the number o f s e r i a l length groupings which contains as near to 100 individuals as p o s s i b l e ) , or sample range (e.g., every range covers 6 cm.).  I f a large number .of independent estimates are  desired, a running mean of a sample range  (1st range = 50-55; 2nd =  51-56; etc.) may be used. In general, catch could be expected t o be under-evaluated because o f unaccounted m o r t a l i t y i n the form of unknown natural mortality (not proportional to catch) and net-induced m o r t a l i t y (proportional t o catch).  The e f f e c t s o f these two forms o f unaccounted m o r t a l i t y on the  estimated size of the o r i g i n a l population ( N ) are shown i n Figure 3» Q  With K (net-induced mortality) acting by i t s e l f (E = 0), the lower rates of K cause more change per percentage of m o r t a l i t y i n the estimated than do the higher rates.  The rate of decrease i n estimated N  Q  decreases  with an increase i n the rate of net-induced mortality (Figure 3). When E (natural m o r t a l i t y ~ a number and not a rate) acts alone, the rate of decrease i n estimated NQ decreases with increased n a t u r a l m o r t a l i t y (Figure 3). At low values o f K, the E t o N b a s i c a l l y the same as when K equals zero.  Q  r e l a t i o n s h i p remains  At a K value of j u s t below .2,  changes i n E cause no changes i n the estimated N , that i s , the isopleth N  450  400  500 ESTIMATED  550 N  600  650  0  Isopleths of rate of net-induced mortality (K) plotted against natural mortality (E) and resultant estimated  K . Data based on B = 605,000,  K  = 301,000,  = 695,000, X = 35^,000, variable K and E. n  of K at t h i s rate of net-induced mortality i s a straight l i n e .  With K  l a r g e r than t h i s value, increased E tends to increase estimated N i t s actual value.  At low values of E, the e f f e c t s of K are r a p i d l y diminished,  hut at an ever decreasing r a t e . small;  towards  Q  When E i s very large, the e f f e c t of K i s very  the converse i s also t r u e i I f the f i s h e r y manager has the a b i l i t y to control the amount of net-  induced mortality, the e f f e c t s of n a t u r a l m o r t a l i t y could be eliminated by f i x i n g K at the value which produced the straight l i n e v e r t i c a l isopleth and then making an adjustment f o r K. The biasing e f f e c t s r e s u l t i n g from unaccounted net-induced mortality (K) can be minimized by s e l e c t i o n of the l o c a t i o n at which the pre-exploltation population sample i s taken.  Net-induced m o r t a l i t y  occurring between the pre- and post-exploitation sampling s i t e s tends to bias the estimated N  Q  such that an i n f l a t e d N  Q  estimate r e s u l t s .  Net-  induced m o r t a l i t y as a r e s u l t of another f i s h e r y operating before f i s h reach the pre-exploitation sampling s i t e tends t o bias the estimate of N  Q  such that a deflated value r e s u l t s .  The rate of net-induced m o r t a l i t y  can be assumed to be proportional t o catch and constant over the entire f i s h i n g area.  I f the catch d i s t r i b u t i o n over the f i s h i n g area i s known,  then sampling so that one-half of the catch occurred inside and the other outside of the pre-exploitatibn sampling s i t e would r e s u l t i n an i n t e r action between the net-induced m o r t a l i t y i n these two halves which should r e s u l t i n mutual cancellation, thereby eliminating the bias due t o unaccounted net-induced m o r t a l i t y . The presence of net-induced m o r t a l i t y (K) and n a t u r a l m o r t a l i t y (E) must be accepted as f a c t .  The problem of quantifying e i t h e r K or E i s  extremely d i f f i c u l t and i n most cases must be s a t i s f i e d by hardly more than a poorly informed guess.  The value of K should be easier to estimate than E, because i t i s proportional to catch and proportional to the number of f i s h escaping the nets and l i v i n g .  To arrive at a value of K i t i s necessary, as with  E, to estimate i t , but with K there are some guide l i n e s .  With knowledge  of the incidence of g i l l n e t marked f i s h i n the escapement, the rate of migration of the f i s h , the d i s t r i b u t i o n of e f f o r t over the migration route and the calculated rates of exploitation, i t should be possible to back-calculate an approximate rate at which f i s h escape g i l l n e t s and l i v e . Significant  estimates of f i s h escaping g i l l n e t s have ranged from  0 to 30 per cent of the t o t a l number of f i s h entering the net.  This value  w i l l vary considerably with weather conditions, f i s h s i z e , type of twine of net, e t c .  I t seems reasonable that the value of K should remain  proportional to the t o t a l number of f i s h f a l l i n g out of the net provided the set i s of reasonable length. Dasmann (1952) points out that "Small errors i n determining the sex r a t i o may be magnified many times when t h i s r a t i o i s used to compute t o t a l numbers.  Such magnification i s most marked i n l i g h t l y hunted herds  where the sex r a t i o approaches u n i t y " . As the r e l a t i v e c a t c h a b i l i t y  of  X to Y approaches 1, (E /X )/(R /Y ) = 1, the sample size must approach W  Q  to remain representative.  The more marked the selectivity,, the more  accurate the population estimate;  also, the smaller the necessary sample  size required. The d e s i r a b i l i t y of minimal variance of  such that i t provides  the most r e l i a b l e population estimate leads one to t r y to adjust factors, such as sample size, to achieve t h i s end.  Chapman (1955) demonstrates  that through elementary calculus the equation f o r the r a t i o i s n^/n^ = (X^Y^/XQYQ) and n.. + n  n  2  of n^ to n  Q  when NQ i s t o be found with variance minimized  f i x e d ( i . e . , f i x e d t o t a l sample s i z e ) .  From t h i s equation i t  can be seen that the l e s s s e l e c t i v i t y exhibited, the l a r g e r the n^ sample required t o minimize the variance. demonstration data (page 6 ) are n  Q  The optimum sample sizes f o r the = 3355.7 and n  1  = 1644.3.  Rivers Inlet Sockeye Salmon F i e l d Evaluation The assumption o f s e l e c t i o n of sockeye salmon by the g i l l n e t f i s h e r y i n Rivers Inlet i s met (see Figure 4 ) .  The main portion of the  catch i s from the l e f t of the peak frequency of the p r e - e x p l o i t a t i o n stocks.  Removing f i s h from the left-hand side of the peak tends t o  move the peak to the r i g h t ;  as a r e s u l t , the post-exploitation peak  i s displaced t o the r i g h t of that of the o r i g i n a l population.  The  distance that t h i s peak i s displaced i s a function o f the rate of e x p l o i t a t i o n and the l o c a t i o n of maximum selection;  even though the catch  i n Figure 4 i s only s l i g h t l y displaced t o the l e f t o f the pre-exploitation population, a high rate of e x p l o i t a t i o n can move the escapement curve r e l a t i v e l y f a r t o the r i g h t .  S e l e c t i v i t y centered near the peak o f the  o r i g i n a l population curve with a high e x p l o i t a t i o n rate w i l l cause the escapement curve t o move f a r t h e s t and also may r e s u l t i n the formation of another mode on the escapement curve i f the range of s e l e c t i v i t y i s narrow enough. As the f i s h smaller than 45 cm. are r e l a t i v e l y unexploited, t h e i r actual numbers do not change but t h e i r contribution t o the t o t a l population increases.  This can be seen i n the difference between the pre- and post-  e x p l o i t a t i o n curves i n the smaller than 45 cm. range. (10$)  I f the 5z= 45 cm. = 10  and the > 4 5 cm. = 90 (90$) and these undergo 50 per cent e x p l o i t a t i o n ,  the r e s u l t s are:  ^ 4 5 cm. = 10 ( 2 0 $ ) ;  > 45 cm. = 40 ( 8 0 $ ) .  The smaller  than 45 cm. range contained only 10 per cent of the population before e x p l o i t a t i o n , but as a r e s u l t of s e l e c t i o n contained 20 per cent a f t e r exploitation.  FISH  FIGURE U.  LENGTH  (CMS)  G i l l n e t s e l e c t i v i t y as demonstrated i n Rivers Inlet commercial f i s h e r y f o r sockeye salmon (0, nerka).  27 The r e l a t i v e l y heavy removal of the greater than 58 cm. f i s h resulted i n a major reduction i n t h e i r percentage contribution t o the, post-exploitation population. The sampling schedule used i n the f i e l d study was poor because i t was not representative of p o s t - e x p l o i t a t i o n or p r e - e x p l o i t a t i o n populations.  E a r l y i n the f i s h i n g period, the pre-exploitation samples  were taken during f i s h e r y closures i n an area i n which f i s h had already undergone considerable s e l e c t i o n i n the outer f i s h e r y .  As a r e s u l t , during  t h i s period the amount of s e l e c t i o n applied t o these stocks previous to sampling was over-estimated such that true value.  i s estimated at a lower than i t s  Sampling only during the f i s h i n g period each week at the post-  e x p l o i t a t i o n sampling s i t e should tend t o under-evaluate these stocks.  the s e l e c t i o n of  The pooling e f f e c t at the head of the i n l e t should cause a  damping e f f e c t on s e l e c t i o n which I would expect to cause an underestimation of NQ, e s p e c i a l l y on weekly estimates. As a r e s u l t o f the sampling and escapement pooling, the sum of the weekly estimates o f N  Q  schedule  should be  lower than the r e a l value. The catch s t a t i s t i c s are based on a whole s t a t i s t i c a l area;  there-  fore, they had t o be adjusted t o be used i n these computations. The adjustment used was e f f o r t , i n the form o f boat d i s t r i b u t i o n ( i . e . , proportion o f boats inside and outside sampling s i t e ) .  A comparison of  expected catch calculated i n t h i s manner with estimated catch d i s t r i b u t i o n s made independently by a f i s h e r i e s o f f i c e r showed good c o r r e l a t i o n . I t was proposed t o use sex as a selected character but evaluation of the v a l i d i t y o f the sex estimations i n the immature sockeye showed that the data were u n r e l i a b l e .  The sources o f e r r o r i n sex estimation arise from  the immature condition of the f i s h sampled and the necessity of returning f i s h t o the water unharmed ( i . e . , actual sex could not be ascertained by  28 dissection).  In samples i n which actual and estimated sex could he taken,  the accuracy of sex estimation was found to he 76.51 per cent. of inaccuracy would cause large biases i n the estimated N^;  This degree  therefore, sex  was not used as a selected character. Using ages as estimated from scale analyses, N each age group.  Q  was estimated using  The data f o r 3-year-old f i s h have the advantage o f being  representative at low sample sizes because of the very low removal, but they have a major disadvantage i n that estimates of N  Q  are extremely  sensitive t o bias of catch as a r e s u l t of the large slope f a c t o r that occurs i n t h i s age group. The 4-year-old f i s h comprise the major part o f the stock (60-80$) and i t might be expected that t h i s age group would be the most representative because of large samples, but t h i s abundance may contribute t o the damping e f f e c t between areas o f high and low selection within the sample.  This  i n t e r n a l i n t e r a c t i o n as a r e s u l t of sample sizes i s probably what affeeted the estimate o f N  Q  based on o v e r a l l 4-year-old data (see Appendix 5). The  r e l a t i v e l y large slope factor r e s u l t i n g from t h i s age group comprising a large part o f the catch makes the estimate o f N  Q  sensitive t o bias o f  catch (R). Five-year-old data may have the same problems as the other two age groups.  A large slope f a c t o r can make t h i s group very susceptible  to bias i n catch.  Sample size can cause problems;  i f i t i s small i t may be  poorly representative, i f i t i s large i t may hide s e l e c t i o n within i t s range. The choice of the "best" estimate of N  Q  based on age i s d i f f i c u l t .  The aberrancy o f the 4-year-old estimate eliminates i t as a p o t e n t i a l best estimate unless a sum of weekly estimates i s used instead of the o v e r a l l estimate.  The higher variance of the 3-year-old estimate might lead to  r e j e c t i o n of i t i n favour of the 5-year-old estimate.  The 3-year-old  o v e r a l l estimate (89^,363) and the summed weekly 5-year-old estimate  (722,385) are probably the best estimates of  N  Q  based on age (Appendix 5).  A l l of the other estimates are too small i n r e l a t i o n to the catch (1+76,890) and the d i s t r i b u t i o n and i n t e n s i t y of e f f o r t . Analysis of length data f o r an estimate of NQ was c a r r i e d out with three d i f f e r e n t length groupings;  3 cm.,  8 cm. and 13 cm.  The 3 cm. length  grouping analysis provided t h i r t e e n estimates (12 independent, 1 dependent) of K . f o r the four weekly periods and the o v e r a l l time period (see Appendix Q  6).  A l l of the estimates based on the 32-3*+ cm. length grouping are aberrant.  The July 2-8  estimate i s zero because of l a c k of data i n the post-exploitation  sample i n the length range at t h i s time period. and the o v e r a l l estimate are a l l negative.  The other weekly estimates  The sample size i n t h i s size  range i s so small that random chance capture of one of these individuals can greatly bias these estimates.  The low variance of the July 16-22.  estimate i s a r e s u l t of no f i s h of that length i n the commercial sample i n that time p e r i o d (see variance equation). July 2-8  The N  Q  » G estimates of the  sample are a r e s u l t of l a c k of data i n that length grouping. The NQ estimates f o r July 23-29 appear to be quite divergent.  This condition i s probably a r e s u l t of the r e l a t i v e l y small size of the pre-exploitation sample. as w e l l as sporadicj the most aberrant. the J u l y 2-29  Sampling of f i s h l e s s than 52 cm. was  sparse  correspondingly, estimates based on small f i s h are  The negative values of W  (overall) and July 16-22  Q  f o r the 68-70 cm. group f o r  periods are probably a r e s u l t of  the small sample sizes i n t h i s length grouping.  The negative  value i n  the 56-58 cm. length grouping on July 2-29 i s a r e s u l t of using data from the area of escapement curve displacement.  In t h i s area, small changes i n  the length groupings used can make major differences i n N  N  estimates.  The weighted means of N presented i n Appendix 6.  Q  f o r the f i v e time periods are also  The means axe weighted by the use o f the  r e c i p r o c a l of t h e i r variance.  The July 2-29 estimates range from  -2,289,751 t o 6,267,544. The best estimates appear to be those i n the 38-40 cm. group;  the sum o f the weekly estimates (716,622) i s good, as i s  the o v e r a l l (July 2-29) estimate (8l2,54l).  The extreme estimates can be  rejected on the grounds of being smaller than the commercial catch or being so large as t o have received an extremely low rate of e x p l o i t a t i o n . Five estimates of N  f o r f i v e time periods were provided by the 8 cm.  Q  length grouping analysis (see Appendix 7). The i n d i v i d u a l estimates f o r each time period appear t o be better grouped i n the 8 cm. grouping analysis than i n the 3 cm. grouping.  This could be a r e f l e c t i o n o f the increased  sample size and the probable decrease i n the e f f e c t o f random v a r i a t i o n . The range of estimates of  f o r the July 2-8 period could be p a r t i a l l y  a t t r i b u t e d t o the small sample sizes i n t h i s period.  The 40-47, cm. length  grouping i s made up of individuals from the area between the main body o f the 3-year-olds and 4-year-olds.  As a r e s u l t , the sample i s small and  subject t o composition changes as a r e s u l t of changes i n i t s s i z e .  Any  deviation from the mean of the time period by estimates i n t h i s length grouping may be a t t r i b u t e d to t h i s p o s s i b i l i t y .  S i m i l a r l y , the 56*»63 cm.  length grouping encompasses the area between the peak numbers o f 4- and 5-year-olds and i s therefore subject t o t h i s same possible source of b i a s . The most l i k e l y estimates o f o r i g i n a l population size are the  32-39 cm. o v e r a l l estimate and the sum of the weekly 48-55 cm. estimates. A l l other estimates are highly divergent and can be disregarded on the basis 1  of size o f catch and i n t e n s i t y o f e f f o r t . Three estimates o f N  Q  ( o r i g i n a l population size) were provided by  the 13 cm. length grouping analysis (see Appendix 8). The boundaries of  these three groups are r e l a t i v e l y s i m i l a r t o those of the age grouping analysis and one would expect comparable estimates. the case.  This, however, i s not  A l l the estimates i n t h i s analysis were widely divergent from the  estimates of the other three analyses.  I t seems probable that one of the  main causes of t h i s divergence i s within-sample  i n t e r a c t i o n between areas  of high and low s e l e c t i o n covering or creating s e l e c t i o n . The estimates of N  Q  are generally l a r g e r than would be expected.  The most reasonable estimates are the summed weekly 32-kk cm. and weekly weighted mean  (962,915)  (983,173) estimates.  The choice of a "one best, estimate" f o r each o f the f i v e time periods i s very d i f f i c u l t .  The weighted means of the age, 3 can., and  8 cm. analyses showed some agreement f o r the July 2-8, 9-15 and 23-29 time periods.  There i s no i n d i c a t i o n of agreement i n the July 16-22 time period.  The weighted means of the 13 cm,, analysis.are a l l markedly divergent from the weighted means of the other analyses.  The variances of the results of  the 13 cm. analysis are very much lower than those o f the other analyses; as a r e s u l t , an o v e r a l l weighted mean may be p u l l e d strongly toward the  13 cm. estimates (July 16-22 and 23-29, o v e r a l l weighted mean; see Appendix 9)« A weighted mean of the age, 3 cm. and 8 cm. estimates brings the July  16-22 and 23-29 estimates back into l i n e , but a l l the estimates are  small i n r e l a t i o n t o adjusted catch (Appendix 9). This same weighted mean, with negative values omitted, gave l a r g e r estimates, but these were s t i l l small i n r e l a t i o n t o catch. A graphical analysis of the estimated  was attempted by p l o t t i n g  the i n d i v i d u a l estimates and t h e i r variances on a graph with variance and N  axes (see Figures 5, 6 and 7).  The purpose o f t h i s analysis i s to get  32  IO'V ui  < EE <  >  IO  °  IO  < 2  10  8  10"  10  10  200  400  600  800  N„  1000  In July  • °  Positive Negative  +  All numbers  = 810,000 ; '05x10  O  No extremes  - 765,000  S  Omitting neg.  A  Absolute values = 920,000 ;  1200  1400  s  1600  thousands  -9 x IO  10  915,000 •, -6 x IO  10  isoo  2-29 — • Exceeds and negative — o Exceeds and positive  FIGURE 5. Graphical a n a l y s i s f o r J u l y 2-29 ( o v e r a l l ) . Estimates of N derived from use o f a l l numbers, no extremes, o m i t t i n g negatives, and absolute values estimates. Q  ;  I x IO  11  2000  33 O  12 |0  <t E < S A • o I0  e  tu l - 10" <  2  All numbers  = 31,000 •, 2 x 10  •  No extremes  = 28,500 •, 3 x IO  S  Omitting  neg. = 33,000 ;  6 x 10*  A  Absolute values = 36,500 ;  7 x IO  4  W  w  +  10  10  10  20  30  40  N  0  50 60 in thousands July  70  80  90  9  9  100  2-8  10 UJ  g io'  2  <  > IOV 10  5 UJ  10' -  10  50  100  150  200  FIGURE 6.  Positive Negative  All numbers  = 210,000  10  D  No extremes  = 275,000  9,x IO  S  Omitting neg.  = 250,000  4 x 10  A  Absolute values = 257,000  250 300 in thousands July  • °  +  350  _L_  400  450  9-15 —• Exceeds and negative —o Exceeds •• and positive  Graphical analysis f o r July 2-8 and July 9-15. Estimates o f N derived from use of a l l numbers, no extremes, omitting negatives, and absolute value s est imates.  8  9 9  I x 10  500  3h  10" UJ  2  IO  12  or > 10'° u. O  10  LU  5 10  s  s  h- • CO  UJ  ,  0  75,000t 4 x 1 0  +  All numbers  a  No extremes  S  Omitting neg. = 480,000;  = 174,000; 6 x 10  A Absolute values = 3 6 6 , 0 0 0  4  100  200  300  400  "8tX  500 600 700 N In thousands  900  0  July 1 6 - 2 2  s  14  10  ce < X  I0  K  I0  C  A°S.  + £ IO  6  I-  UJ  |  0  All numbers  =  4,000  a No extremes  = I 7,000  S Omitting  = 33,000  neg.  A Absolute values = 3 0 , 0 0 0  «  10'  20  40  60  80  100 120 140 N in thousands  160  180  0  July • ° FIGURE 7.  Positive Negative  23-29 — • Exceeds and negative — o Exceeds and positive  Graphical analysis f o r July 16-22 and July 23-29. Estimates o f derived from use o f a l l numbers, no extremes, omitting negatives, and absolute values estimates.  10" 4 x10  a v i s u a l estimate of a central, or most l i k e l y , estimate of the o r i g i n a l population s i z e .  The use o f t h i s analysis i s j u s t i f i e d i n that other  methods of combining data t o a single estimate only take into account the variance inherent i n the mathematics of the estimation. Allowance  i s made  f o r other sources of variance i n the graphical analysis, e s p e c i a l l y i n the "no extremes" estimate.  Using an o v e r a l l two-dimensional mode, the " a l l  data" estimates o f Appendix 9 r e s u l t e d . 9) produced not much better estimates.  Omitting a l l negatives  (Appendix  On a s i m i l a r p l o t the center of  a clumped area was used as an estimate (see "no extremes" i n Appendix 9)« (  These estimates appear to be reasonable, r e l a t i v e t o catch, but probably are s t i l l small (except July 2-29 estimates). Of the eleven July 2-29 estimates, that based on age appears to be the best  (601,400). There are two groups of estimates i n t h i s time  period, the 400,000-500,000 and the  800,000-900,000 groups.  The l a r g e r  groups might be the best estimate i f unaccounted mortality i s r e l a t i v e l y high;  i f i t i s not, the middle numbers are most l i k e l y . An estimation o f the numbers of f i s h entering before and a f t e r  the period i n which-complete samples were taken must be based on same method other than a dichotomous technique.  An i n d i c a t i o n o f r e l a t i v e  abundance may be calculated from the catch per u n i t e f f o r t of the commercial f i s h e r y or the tagging boat.  The commercial f i s h e r y should  be the better estimator early i n the season;  a f t e r the closure o f the  commercial f i s h e r y , the tagging boat i s the only i n d i c a t o r .  The catch per  u n i t e f f o r t f o r the period before July 10 should be a function of the t o t a l numbers o f f i s h available to the f i s h e r y . r e l a t i v e l y low; gear i n t e r a c t i o n .  The e f f o r t during t h i s period i s  therefore, i t should be reasonable t o assume l i t t l e or no Correlation between catch per u n i t e f f o r t and estimated  NQ is poor;  there axe too few points to establish any relationship.  If i t  is assumed that fish entering the inlet axe normally distributed through time, a symmetrical curve can be drawn over estimated weekly Q ' S . Graphical N  analysis can be used on this curve to approximate the number of fish entering the inlet in the time periods before and after the dichotomous estimates were possible.  The relatively small proportion of the ran contri-  buted by these " t a i l " portions of the curve should make the assumptions of their shape and size relatively insignificant. A graphical plot of average daily catch with a smoothed curve interconnecting the points results i n an asymmetrical curve (Figure 8). By superimposing on the catch curve a-symmetrical curve with parameters the same as the left-hand portion of the catch curve, Figure 8 results. In over half of the groups of estimates i n Appendix 9, the above-described graph of N  Q  closely parallels the symmetrical catch curve.  Close parallels  between these two curves give weight to the r e l i a b i l i t y of the W  Q  bution.  distri-  The divergence of the catch curve from the symmetrical could  be a function of secondary catch and of change of effort.  If the  symmetrical catch curve i s taken to represent the actual migration into the fishing area from the ocean and i s representative of incoming stocks then the numbers of fish entering the inlet could also be estimated. As the fishery in Rivers Inlet i s solely a gillnet fishery, rough water conditions could be expected to result i n a relatively high loss of fish from the nets. If f i s h are dead in the net and f a l l out they are lost.  Of the l i v e f i s h escaping the nets, some die shortly after;  the  number dying could be affected by the depth to which the fish sink before recovering.  The mortality of f i s h lost from the nets should be directly,  proportional to the number of gillnet marked fish i n the escapement. It should also be direct,ly proportional to the catch, i f environmental  37 90,000  80,000  Adjusted catch Estimated N Catch curves  0  70,000  60,000 X  li.  50,000  Ii.  o  40,000  m 5  Z  30,000  X  20,000  10,000-  I  26  28 30 JUNE  2  8  10  12  14 16 JULY  18  20  '  22  I  I  24  "V  L  26  28  J_l_l  L.  30  DATE i  FIGURE 8.  D i s t r i b u t i o n of estimated W  Q  and catch through time.  Estimated N i s based on the no extremes data from Appendix 9 . Dotted l i n e represents an hypothetical catch curve. The symmetrical curve i s hypothesized as approximating N ; divergence of t h i s curve from the actual catch curve i s a r e s u l t of secondary catch.  conditions (mainly weather) are constant. However, nothing more than arbitrary estimation i s possible i n putting a value to K (net-induced mortality);  therefore, K must be disregarded in computations but remembered  in the f i n a l interpretation in.that i t w i l l bias estimates  upwards i f not  taken into account. Unaccounted natural mortality may cause a bias to the estimate of W. Q  In the last three years, an increase in the value of hair seal hides  has resulted i n a decrease in the numbers of this natural predator.  Seals  were observed only i n Owikeno Lake and the upper Wannock. River. Observar  tions of sea lions were limited to outside the inlet;  numbers observed  were small. K i l l e r whales were observed irregularly i n the area;  a pod  of 25 was the largest observed. The main body of fish appear to migrate through the inlet rapidly (3 to k days) (see Figures 9 and 10) and then m i l l at the head of the inlet. This rapid migration coupled with the apparent high rates of exploitation and low incidence of natural predators, leads me to believe that natural mortality i s relatively insignificant i n this ease. of estimated H  Q  A l l my calculations  disregard the effects of natural mortality.  Rivers Inlet sockeye typically mili about in the head of the inlet for variable lengths; of time before migrating upstream. Often, there appears to be a build-up of f i s h i n the head of the inlet, after .which almost a l l the f i s h migrate upstream within a 12-day period. In the period of build-up, f i s h tend to move in and out with the tides.  When the build-  up has reached certain proportions, t i d a l movements take the f i s h back and forth across the commercial boundary, thereby making them susceptible to the fishery a second time.  The fishery tends to show an increasing con-  centration along the boundary as the season progresses, such that up to  39  FIGURE 9 .  Mean number of days to recovery site of fish tagged at the mouth of Goose Bay (x). Interconnecting lines represent possible migration pattern of sockeye salmon through the inlet.  1+0  FIGURE 10.  Modal number o f days t o recovery s i t e of f i s h tagged at the mouth o f Goose Bay ( x ) . Figure i s representative o f the rate of migration of the bulk o f the f i s h .  one-half of the f l e e t i s f i s h i n g as close t o the boundary as possible i n the l a s t week of f i s h i n g .  This high i n t e n s i t y of boundary f i s h i n g i s  usually coordinated t o some extent with the maximum build-up of sockeye i n the head o f the i n l e t ;  as a r e s u l t , secondary catch of these f i s h can be  very high. Catch data are assumed to be l i m i t e d t o primary catch;  secondary  catch tends t o i n f l a t e catch data and thereby i n f l a t e the estimated o r i g i n a l population size  The secondary s e l e c t i o n r e s u l t i n g from secondary catch  w i l l tend to deflate estimated N . Q  When secondary catch i s small i n r e l a t i o n  to t o t a l catch, the sampling regime w i l l tend t o cause an under-estimation of W Q .  Conversely, when secondary catch i s large i n r e l a t i o n t o t o t a l catch,  the sampling regime w i l l tend t o cause over-estimation o f N . Q  The over-  estimation i s reduced o r reversed by the action o f secondary s e l e c t i o n which accompanies high rates of secondary catch.  Seasonal increase i n secondary  catch i s expected t o cause a progressive biasing o f the estimated K^. I f , over the season, i n f l a t i o n o f WQ by secondary-catch and d e f l a t i o n of N  Q  by secondary selection do not cancel each other, there i s bias of N  from these sources which cannot r e a d i l y be quantified.  Q  Some i n d i c a t i o n of  secondary catch was derived from return o f tags applied to f i s h i n the extreme head o f the i n l e t . secondary catch o f 10.7  From t h i s source, an estimated minimum rate of  per cent was calculated.  There i s a p o t e n t i a l bias r e s u l t i n g from differences i n the rates of migration throughout the season.  The main bulk of the f i s h appear t o  t r a v e l at approximately the same rate o f speed.  The mode o f the rate o f  migration from the tagging s i t e to the commercial boundary was approximately three days.  Using the mean, the rate o f migration appeared to- accelerate  throughout the season (early season, 5*1 days;  mid-season, k.3 days;  lat  season, 3.7  days).  The e f f e c t s of the d i f f e r e n t rates of speed would he  that faster-moving f i s h would he available f o r e x p l o i t a t i o n f o r a shorter time than slower-moving f i s h .  I f a l l the f i s h at the end of the run are  moving slowly, they w i l l show a very high rate of e x p l o i t a t i o n .  Conversely,  the f i s h from e a r l y i n the run may be predominantly fast-moving f i s h , and therefore w i l l show l i t t l e e x p l o i t a t i o n .  This f a c t o r , coupled with the  progressive increase of e f f o r t throughout the season, could r e s u l t i n marked e f f e c t s i n the estimated  i f f i s h size or the selected character  is not randomly d i s t r i b u t e d over the t o t a l time period as i t appears to be i n my data. The various estimates of be corrected f o r the aforementioned  i n Appendix 10 should, where possible, sources of e r r o r .  Using the graphical  technique described above, values f o r the l e f t - and right-hand t a i l s of the curves can be estimated.  Calculations of escapement (N^) using data from  the left-hand t a i l have the adjusted catch f o r the time period removed. A l l estimates of N  Q  are based on adjusted values of catch.  This  adjustment was necessary to account f o r f i s h caught outside the pree x p l o i t a t i o n sampling s i t e . sampling s i t e ;  There were 162,910 f i s h caught outside the  t h i s number should be added t o the estimated  to get  a true pre-exploitation population s i z e . Unaccounted m o r t a l i t y cannot be quantified with the data a v a i l a b l e . Assuming that no n a t u r a l mortality occurs, variations i n the rate of netinduced m o r t a l i t y can be applied to the estimated of WQ to demonstrate the possible r e s u l t s .  In Appendix 9, K (net-induced mortality) values of 0,  10 and 20 per cent are presented. It appears to be impossible to correct f o r any bias r e s u l t i n g from secondary catch or secondary s e l e c t i o n .  The use of the o v e r a l l (July  2-29)  data may eliminate t h i s e f f e c t .  The secondary catch s e l e c t i o n may be one  of the reasons that the July 2-29 estimate i s almost always l a r g e r than the sum of i t s component estimates. Bias due to d i f f e r e n t rates o f migration throughout the season, i f i t e x i s t s , may be minimized by the use o f o v e r a l l data rather than weekly data.  One problem with using o v e r a l l data i s that the size o f  the sample, although more representative, may permit interactions between parts o f a sample t o damp strong s e l e c t i o n ; I have assumed no natural mortality and a rate o f net-induced mortality o f approximately .10. With an allowance f o r net-induced mortality which occurred between the sampling s i t e and spawning grounds, the escapement estimates are further lowered.  I think that the "excluding  extreme values" estimates (clumped) from Appendix 9 axe probably the single best estimates.  When the assumed rates o f unaccounted mortality are applied  to these estimates, a probable spawning ground escapement o f approximately 175,000 sockeye i s achieved. population o f 900,000 sockeye.  This escapement i s from an estimated o r i g i n a l Applying the assumed rates of unaccounted  mortality t o the other estimates r e s u l t s i n estimations o f spawning ground escapements of from -194,971 t o 952,961 sockeye.  I f negative escapements  are regarded as impossible, the remaining escapement estimates form a c e n t r a l clump ranging from about 100,000 to 350,000 sockeye.  The estimated  o r i g i n a l population size from which these escapements are achieved ranges from  820,000 t o 1,120,000. The approximate center o f t h i s clump o f estimates  i s at about 250,000 sockeye, considerably higher than the "excluding extreme values" estimate.  1* Comparison of Dichotomous and Mark-Re capture Techniques Disregarding relative cost, "The tag sample procedure is under a l l circumstances more efficient than the change of composition estimation method" (Chapman, 1955).  The mark-recapture estimation procedure yields  more information for the same amount of effort hut i t operates on broader assumptions than the change of composition method. The following i s a tabulation of the assumptions of the dichotomous and mark^recapttire methods of population estimation: DICHOTOMOUS METHOD closed population  MARK-RE CAPTURE METHOD recruitment is insignificant during study period Marks do not affect natural mortality  *  selective removal of at least one of the population classes  marks are not lost  *  removal data are correct  a l l marks are recognized and returned  *  samples before and after removal are random  marks randomly mix with non marks marks do not affect vulnerability * to gear  Of the mark-re capture technique assumptions, four in particular (asterisked in the foregoing tabulation) are extremely d i f f i c u l t to warrant in many studies, especially those dealing with commercial fisheries. The condition that a l l marks are recognized and returned i s often not met because commercial fishermen often fear that stricter regulations w i l l result from a high return of tags.  The reward offered for the return of  tags often is so small as not to stimulate any effort toward return of tags.  Both of these problems could be remedied by a public relations  campaign coordinated with higher tag return rewards.  In some species the  assumptions of no tag loss or tag-induced mortality are justified for only  extremely short time periods.  Combined with this, the assumption of no gear  selectivity relative to the marks adds a major potential bias.  The signi-  ficance of these assumptions makes the use of the mark-recapture technique more susceptable to bias than the dichotomous technique in a l l but ideal situations. If the assumptions of both methods can be met, the mark-recapture procedure provides data from which rate of recruitment, survival rate over a time period, rate of exploitation and population size can be calculated. Individual and group migrations and distributions can be followed through use of the mark-recapture procedure.  The change of composition procedure  can provide rate of recruitment ( i f i t approaches "knife-edge recruitment"), survival, rate of exploitation and population size, but estimates from this procedure have much larger variances than those from the mark-re capture procedure.  The major advantage of the change in composition procedure i s  that the assumptions upon which i t i s based are considerably more diminutive than those of the mark-re capture procedure.  One advantage of the mark-  recapture estimation method i s that the estimates are not affected by secondary catch, secondary selection, time lag, etc. The relative cost of the two types of procedure may affect the choice of procedure.  "The  change of composition method must always be better i f tagging i s prohibitively costly",  but " i f tagging i s no more costly than classification,  from the large sample point of view, the tag sample procedure i s under a l l circumstances more efficient than the change of composition estimation method" (Chapman, 1 9 5 5 ) . Two different estimates of population size can be obtained for the purposes of comparison by conducting both markrrecapture and change of composition studies.  It i s possible to combine the two procedures and  get what is probably the best single estimate.  If the number of individuals  tagged is of such size that at least a moderate number of tags are recovered, the tagged population can be treated as a "population" upon which to apply the change of composition method. This approach can be used provided the tags are not selected for by the method of removal.  It has the advantage  that the parameters of the tagged population are known and not estimated. If there i s reasonable agreement between the mark-recapture  and  change of composition estimates, the results of both tests may be combined to form a single test. The many sources of error inherent i n both the indirect count and the mark-recpature methods of population estimation may tend to make the use of these estimates for management purposes questionable. "However, management w i l l always be faced with the necessity of making population estimates, a good guess must be rated higher than none at a l l . If estimates are guided evidence"  they w i l l be better than estimates made without such (Dasmann, 1 9 5 2 ) .  hi SUMMARY A primary estimate of pre-exploitation population size can be made with knowledge of the compositions and the harvested catch. simultaneous  of the o r i g i n a l and f i n a l populations,  The estimate can be made through the use of  equations or a maximum l i k e l i h o o d estimator formulation.  Using a d e r i v a t i o n o f the formula f o r the inverse o f the  asymptotic  variance-covariance matrix, an estimate of the asymptotic variance can be made. Allowance f o r a d d i t i o n a l variance r e s u l t i n g from the use of subsamples of catch can be made by some additions to the basic variance equation. Estimated o r i g i n a l population size i s a function of the size of the catch.  The rate o f change of the estimated o r i g i n a l population size  r e l a t i v e to catch i s determined by a slope f a c t o r which i s composed of the proportions o f the selected character i n the pre- and post-exploitation populations and the catch samples;  i t i s therefore a representation of  selective removal. Biased data can greatly a f f e c t the estimates of o r i g i n a l population size.  The amount and d i r e c t i o n o f bias are determined by the slope f a c t o r . Unaccounted mortality i n the form o f net-induced mortality and  natural m o r t a l i t y cause a d e f i n i t e bias i n the estimation of the o r i g i n a l population s i z e . I f the rate of net-induced mortality can be held at a r e l a t i v e l y low l e v e l (through f i s h e r y regulation), changes i n the number of f i s h l o s t to natural mortality do not r e s u l t i n any changes i n the estimated population size.  In t h i s manner, e f f e c t s of n a t u r a l mortality can be  eliminated. I f the catch d i s t r i b u t i o n over the f i s h i n g area o f a f i s h e r y f o r migrant species i s known, and the rate of net-induced mortality can be  assumed to be constant and proportional to catch over the entire fishing area, then taking the pre-exploitation sample from the middle of the fleet (so that half the catch occurs on each side of the sampling site) causes an interaction between the net-induced mortality inside and outside the sampling site such that one cancels the other. In this manner, effects of net-induced mortality can be eliminated. In most cases, the two samples are of approximately equal size, but the accuracy of the estimate can be improved and its variance reduced by adjusting the sizes of the pre- and post-exploitation samples relative to the intensity of selection occurring in the fishery. Assuming no natural mortality, a net-induced mortality in Rivers Inlet of 10 per cent and a latent net-induced mortality which occurs in fresh water of 10 to 20 per cent, approximately 175,000 sockeye escaped to the spawning grounds from an original population of approximately 900,000. The assumptions upon which the change of composition population estimation procedure i s based are considerably more diminutive than those of the markrecapture procedure.  The change of composition procedure i s less efficient,  relative to the f i n a l data available, than the mark-recapture procedure. The mark-recapture procedure i s not affected by factors which affect the change of composition procedure, such as secondary catch, secondary selection, or time lag.  49 LITERA.TURE CITED Allen, D. L. 1942. A pheasant inventory method based upon k i l l records and sex ratios. Trans. N. A. Wildl. Conf. 7 : 3 2 9 - 3 3 3 . Chapman, D. G. 1 9 5 4 . The estimation of biological populations. Ann. Math. Statist. 2 5 : 1-15. 1955. Population estimation based on change of composition caused by a selective removal. Biometrika 42: 279-290. Dasmann, R. P. 1 9 5 2 . Methods for estimating deer populations from k i l l data. Calif. Fish and Game.- 3 8 : 225-233. . Davis, W. S. 1 9 5 9 . Field test of Petersen, streamer, and spaghetti tags on striped bass, Roccus saxatilis. Calif. Fish and Game 8 8 : 319-329. Hartt, A. C. 1 9 6 3 . Problems in tagging salmon at sea. Spec. Pub. 4: 144-155.  I. C. N. A. F.  Holt, S. J . 1 9 6 3 . A method for determining gear selectivity and i t s applications. I. C. N. A. F. Spec. Pub. 5 : I O 6 - H 5 . Kelker, G. H. 1 9 4 0 . Estimating deer populations by a differential hunting loss in the sexes. Proc. Utah Acad. Sci. A. L. 1 7 : 65-69. Kelker, G. H. 1 9 4 2 . Sex-ratio equations and formulas for determining hunting loss in the sexes. Proc. Utah Acad. Sci. A. L. 1 9 : I89-I98. L i , J . C. R. 1 9 6 4 . Statistical Inference.  Vol. I.  Edwards Bros. Inc. '  Mottley, C i McC. 1 9 4 2 . Modern methods of studying fish population. Trans. N. A. Wildl. Conf. 7 : 356-368. Parrish, B. B. 1 9 6 3 . Some remarks on selection processes in fishing operations. I. C. N. A. F. Spec. Pub. 5 : 166-170. Peterson, A. E. 1 9 5 4 . The selective action of gillnets on Fraser River sockeye salmon. I. P. S. F. C. Bull. 5 , 1 0 1 p . Petrides, G. A. 1949. Viewpoints on the analysis of open season sex and age ratios. Trans. ,N. A. Wildl..Conf; 1 4 : . 3 9 1 - 4 1 0 . Rasmussen, D. I., and E. R. Daman. 1 9 4 3 . Census methods and their application in the management of mule deer. Trans. N. A. Wildl. Conf. 8 : 369-38O. Ricker, W. E. 1 9 5 8 . Handbook of computations for biological statistics of f i s h populations. Fish. Res. Bd-i Can. Bull. 1 1 9 , 300p. Riordan, L. E. 1 9 4 8 . The sexing of deer and elk by airplane in Colorado. Trans. W. A. Wildl. Conf. 1 3 : 4 0 9 - 4 3 0 . Vaughn, A. E. 1955* Estimation of a biological population which is subject to biased mortality. PhD. Thesis,.Stanford University, 44p.  50 APPENDIX 1. Vaughn for N  Q  DERIVATION OP N  ESTIMATION EQUATION  Q  (1955) demonstrated the derivation of an estimation equation  using only simple algebra.  I have transformed her symbols to Chapman's  (1955) equivalents t o provide continuity.  o/o  x  n  =  proportion of c l a s s X individuals i n pre-exploitation population.  ^(XQ/HQ)  =  expected number of i n d i v i d u a l s i n class X i n the pre-exploit a t i o n population,  m /m  =  proportion o f class X individuals i n the commercial catch.  R(m /m)  =  R  X  N  Q  =  expected number of individuals i n class X i n the catch.  X  - R  =  N^  =  number of f i s h i n the post-exploitation population.  N ( x / n ) - R(m /m) = Q  0  0  number of f i s h i n class X i n the post-exploitation  x  population. ( N ^ x ^ n ^ ) - R(m /m))/(NQ - R)  =  x  proportion of class X i n the escapement.  n ( x / n )(N ) - (m /m)(R) 1  x-  Q  =  solving f o r N. t h i s becomes:  1  0  NQ - R  i o - i = YoV o " V V m ) R . 1 0 " i oV o 1 * T » ^ ^ o " i o^ " ( / )) o^ i " i( / ) ) ofci - i ^ " oi io " Vi " io x K  x  X  n w  N  R  n  n  =  n x  n  0  R  n  =  x R  n  X  n  n m 1 x  m x  n  x  )  m R  n  R  m R R  n R  x  n x  x  This formulation i s b a s i c a l l y the same as Chapman's i n that the sign r e v e r s a l i s negated by sign c a n c e l l a t i o n t o provide the same answer as Chapman's equation.  Vaughn  (1955) also demonstrates that t h i s equation i s  the maximum l i k e l i h o o d estimator of N , Q  manner r e s u l t s i n  Deriving the equation i n t h i s  / „ N  _  - 1 X  R )  0 x nx which i s i d e n t i c a l t o the aforementioned equations. n ; L  0  0  ±  51 APPENDIX 2.  PRE-EXPLOITATION POPULATION DATA  The d a i l y sample size (outer sample) and the number of sets necessary to catch t h i s sample ( e f f o r t ) are presented. Rate of tag return from t h i s sample i s given as a percentage (percent return) and the calculated mean and modal rates of migration (mi./day) and time between tagging and capture (days out) are presented.  DATE  26/6 27 28 29 30 1/7 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 2k  25 26 27 28 29 30 31 1/8  OUTER SAMPLE  2 1 1 0 7 3 1 11 2 9 33  EFFORT (SETS)  2 3 3 1 2 4 3 2 3 1 2  MEAN mi./day  MODAL  days out  mi./day  days out  PER CENT RETURN  7.4  2.5  7  3  18.2  4.4 4.7  5.5 3.6  8 5  3 2  22.2 36.4  121 413 460  5 1 3  5.1 5.8 5.7  3.9 3.2 2.6  7 12 21  3 2 1  33.9 38.5 45.9  41 272 270 487  1 4 3 2  3.6 5.9 6.9 7.4  4.8 3.2 2.6 1.8  5 7 11 9  4 3 2 1  30.0 31.3 31.5 35.5  156 11 97 1  3 3 4 1  4.6 7.5 9.1  3.8 3.0 2.1  5 7 21  4 3 1.5  6.4 36.4 18.6  54 0 19  3 3 3  2,472  65  APPENDIX 3 .  COMMERCIAL CATCH DATA  The d a i l y commercial catch ( t o t a l comm. catch), e f f o r t (comm. e f f o r t ) and catch per u n i t e f f o r t (c/f) are presented. The sample size (comm. sample size) and the size of the catch adjusted f o r the number of f i s h caught outside the outer sample s i t e (adjusted comm. catch) are also presented.  DATE  COMM. EFFORT  TOTAL COMM. CATCH  c/f  ADJUSTED COMM. CATCH  COMM. SAMPLE SIZE  28/6 29 30 1/7 2 Q J  188 208 200 348  874 1,319 1,748 2 968  4.7 6.3 8.7 6.9  219 330 438 624  71 196 5 296  5 6 7 8 Q y 10 ii 12 13 14 15 16 17 18 19 20 21 22 23  333 409 419 814  14,757 14,305 12,844 28,888  41.3 26.7 30.7 34.3  6,093 5,722 5,138 10,958  246 535 187 495  921 879 827 1,503  122,053 70,383 64,238 72,077  132.5 80.1 77.7 47.9  86,481 49,268 44,967 50,099  499 501 513 499  1,119 1,114 1,586  85,770 42,402 44,277  50.0 38.1 28.0  77,648 38,162 39,927  525 500 500  749 620 664  31,171 17,864 13,262  40.8 28.1 20.0  31,171 17,864 13,392  421 224 281  12,901  641,200  478,501  6,494  2k  25 26 27 28  APPENDIX k.  POST-EXPLOITATION POPULATION DATA  The size of the d a i l y escapement samples and lake samples are tabulated, as are the rates o f tag return and the e f f o r t .  DATE  7/7 8 9 10 11 12 13 Ik  15 16 17 18 19 20 21 22 23  ESCAPEMENT SAMPLE SIZE  EFFORT (SETS)  PER CENT RETURN  3 15  2 2  93 308  3 1  6.1+ 3.6  399  1 1  3.8 2.1+  If12  311 99 93  1 1 2 3  8.3 2.6  93 127 83  3 3 3  2,285  26  2*4-9  2k  25 26 27 28 29 30 31 1/8 2 3 5 6 7 8  LAKE SAMPLE SIZE  17 13 10 115 58 69 11 1 12l+ 85 *+7 79 97 69 23 6o 38 27 12 60 25 1,01+0  APPENDIX 5.  ESTIMATED N  Q  AND ITS VARIANCE CALCULATED FROM AGE GROUPINGS  Calculations are broken down into four weekly periods and one o v e r a l l p e r i o d .  JULY 2-8  JULY 9-15  1+8,077  269,11+9  .38761+9660xl0  .68622131+xlO  JULY 16-22  JULY 2-29 (overall)  JULY 2 3 - 2 9  3-YEAR-OLD N  o  Variance  9  -1+15,672 8  89^,363  -5^,H9  .111+89722X10  12  .3290993xl0  .653P911xl0  9  1 0  ^-YEAR-OLD N  o  Variance  100,1+35  -135,610  301,591  .23902088X10  11  .72551900xl0  9  .25365288xl0  - 2 , 37*+, 550  18,159 .30296l7l+xl0  9  .21306238X10 *  8  11  5-YEAR-OLD N  o  Variance WEIGHTED MEAiT  6,678 .36028930xl0 27,192  210,91+3 9  .800596l7xl0 267,522  262,21+7  21+2,517 9  .98285315xl0 156,536  1 0  587,595  .I+223398OXIO  11  12,229  .33503990xl0 691,1+00  10  APPENDIX 6 .  ESTIMATED N  Q  AND ITS VARIANCE CALCULATED FROM 3 CM. LENGTH GROUPINGS  weighted means of the four weekly and the o v e r a l l periods are weighted with the r e c i p r o c a l of variance.  32-34 CM. N  0  Variance 35-37 CM. 0 N  Variance 38-40 CM. N  0  JULY 2-8  JULY 9-15  00000  -1,250,253  . 00000000x10'35  -JULY 16-22  -15,152  14  .54368676x10' 274,998  46,273 .78242633xl0  9  .30055725x10^  .12 .63092627x10'  ,138l888xl0  N  Variance  44-46 CM. N  o  Variance 47-49 CM. 0  0000000  .84259212x10-  9  .22262354x10 30,996  8 .50088713x10' 54,427  N  Variance 50-52 CM. 0 Variance  N  249,284 11  .19935244x10'  10  242,927 13 .33385263x10'  9  11  .11582154x10-  .14 .l6233225xl0' 731,052  10  .23396358xlO"  626,706 .25873307x10'.11  -25,889  -169,667  10  .61855844x10  .47313858xlO-10  .178l3249xl0  .12 .20342368x10" 683,608  12 .12924835x10-  ,94708354x10 23,505 .10275891x10'  11 .12306127X10'  836,430 .12005855X10  11  812,541  -32,713 9  -265,422 12  24,450  156,624  307,790  10  -266,235  ,l46ll664xl0  .46501329x10'  1 3  337,271  Variance 41-43 CM. 0  .8842159xl0  JULY 2-29 (overall)  -82,442  1,294,885  265,411  146,653  .28833903xl0  9  JULY 2 3 - 2 9  12  .74454587X10  10  786,890 11 .20652878xl02,663,664  .10  -689,244 .296607x10',13  .33550728xl0  15  1,421,400  ,51183145x10-.11  -23,697 Q .68380692X10  0  2,564,123 .10330664xl0  x:5  Continued  VJ1  -4-  CVJ  ON  OJ  I  o ir\ co H  3  CVJ . ^  H IfN t•v ON CO CM •* CM  •» ON  r«  CM ON •» H CVJ ON CO  o  co  c--  CO NO  I  CO OJ  H  a  NO CM ITN  CM CM  O NO CO  I  O  .*  C - NO •\ IfN rH CO  0 H  -3CVJ  O  ITN H I ON  -=r X CO ON t -=T rH NO  o- o  ON CO NO CM CO CVJ  CO •  ON  CO I CVJ  CO  o  CO  3  s  NO CO CO CO NO  . i r v a  LTN I  CO ITN  ti  I  NO 00 NO -3" CO CVJ  tl  >  •  00 IfN 1 NO IfN  o  CO ITN  s  ti  ^ &  a  3  °.  -=r  t>- X •\ ON ITN CO rH CO H CO 1 0-  NOn  <i H  rH  CO  1  •x  CO CO  8  d> o  •rl  o j3  8  o S  NO NO  ^  I  IA NO  >  3  0  NO  XH  rH  H  ON ITN CM  3  ON CO ON H •  2L  ON  O  cvi  CVJ  CVJ CO •  00 CVJ  9  t-  H  CO  oS O JS H a > a > o NO I ON IfN  *  NO  0  CO  CO  o o NO o ON o o 3N  O NO -=J" t ITN 00  •V  NO  NO  H  CO ON  Cl) O  •\  o  ON O  H O  NO ON  NO CO IT N 1 BN  CO rH 0 X * CVJ CO IA CVJ ON CO -=tCO ON ON H •  -* ITN ITN  O  ti  H  q  t-  cvi  ^  H  « 3  q CO rH 0 0- X 00 CVJ CO ITN ON CO  rH  O  0 CO ON CO •\ -=f- t H OJ NO 0 CVJ co CO CM •  H  O  NO  IfN  O H  3  O  5?  I  3  ON  CO ON ON CVJ CO ITN «  O  CO IfN -* CM  CVJ  TT  H  ITN ON NO «\ ON  3  ITN ON  co  3  CO  I  » ti  H  X  OJ  3 •$ CVJ  El ro NO  3  CO  H NO NO  ON  CVJ CO  CO  CVJ  co  ON 0 H r-j  ITN ON  lo  °2  IA CVJ C - l>00 H CO ITN CO  CM  o  ti C-  •\ ITN ON CM r>. N§  H  3•> NO S  o  CVJ NO O NO  CO  ITN  CO CO  IA H  £ H  2o  ON  SI  O  ON CH NO NO CVJ O •» H NO CO CO  e»  I  o  ON CVJ  tfN  IA X * VO ON CO 0- CO ro IA H  CM CO ON  a  CO  o  o o o o o o  i  CO cb~  ITN  81  H  CVJ  o  •S  CVJ  NO  CO o  a O S CI  00 NO  -rt  o S !>  Q  3  H a  APPENDIX 7 .  ESTIMATED N  Q  AND ITS VARIANCE CALCULATED FROM 8 CM. LENGTH GROUPINGS  Weighted means of the four weekly and the o v e r a l l periods are weighted with the r e c i p r o c a l o f variance.  32-39 CM. w  o  Variance k0-k7 N  JULY 2-8  JULY 9-15  59,478  283,901  .22157298xl0  10  CM.  Variance  .27275895xl0  9  48-55 CM. w  Variance  .13544779xl0  12  9  14,249  o  10  Variance  •35979525x10  131,593 s  64-71 CM. N  Variance WEIGHTED MEAN N  Q  .67082272XIO  9  17,063  .12870993xl0  10  117,508  19,855  o  .10665773xl0  270,997  .4l096400xl0  -887,688  -27,631 111  909,156  .13313050xl0  12  1,046,991  .2O78l046xl0  .13394448X10  9  56-63 CM. N  -50,744 lif  344,208  -95,980  o  .20584026xl0  .4l421321xl0  JULY 23-29  2,048,207  267,712  32,263  o  JULY 16-22  JULY 2-29 (overall)  .33380785xl0  1 2  .11951154x10  Q  .15315108x10  .34383358xl0  1,979,018  29,472  1,400,495  .23592095xl0  12,139  11  249,127  H3,56l  .32174338xl0  .12717505X10  9  -1,455,880  1 2  11  553,597  .72001123xl0 13,397  .19110152X10  9  .338i7901xl0  1 3  26,435 1 0  .77210101xl0  10  3,180,897 9  .64735048xlo 406,869  1 2  APPENDIX 8 . ESTIMATED N AND ITS VARIANCE CALCULATED FROM 13 CM. LENGTH GROUPINGS Q  Weighted means of the four weekly and the overall periods are weighted with the reciprocal of variance.  JULY 2-8  JULY 9-15  JULY 16-22  48,044  659  JULY 2-29 (overall)  JULY 2 3 - 2 9  32-1+4 CM. K  9H,759  o  Variance  .37217814X10  .25203254xl0  11  10  1,243,704  2,453 1  .42l24784xl0  4  .21205644xl0  .82495980xl0  6  9  45-57 CM. N  1,060,618  0  Variance  .22498213xl0  2,166  43,165 .259l4459xl0  12  1 2  1,991,404  2,701  .26028221X10  .60984239x10  7  .85837483xl0  1 0  58-70 CM.  o u Variance N  WEIGHTED MEAN N  Q  47,210  -.0000  -.OOOOOOOOxlO"  .I4l01525xl010  932,889  47,494  38  991 .29501120x10 284  4  -.0000  2,523 .1024O694X10 2,506  6  -.0000000x10'  3 8  1,309,263  VJI  CO  59 APPENDIX 9 .  DIFFERENT ESTIMATES OF N  Q  RESULTING FROM  A NUMBER OF TREATMENTS OF THE DATA  SOURCE  JULY 2 - 8  JULY 9-15  JULY 1 6 - 2 2  JULY 23-29  JULY 2-29 (overall)  ADJUSTED CATCH  27,9H  230,814  155,737  62,427  476,890  AGE WEIGHTED MEAN  27,192  267,522  156,536  12,229  691,400  3 CM. WEIGHTED MEAN  21,878  259,146  36,061  -6,743  466,618  8 CM. WEIGHTED MEAN  17,063  270,997  1,400,495  12,139  406,869  13 CM. WEIGHTED MEAN  932,889  47,494  284  2,506  1,309,263  OVERALL WEIGHTED MEAN  20,295  311,471  285  2,544  947,556  OVERALL-13 CM. WEIGHTED MEAN  20,393  272,359  101,011  13,390  527,175  OVERALL-13 CM. NO NEGATIVES WEIGHTED MEAN  20,479  272,452  141,573  16,513  538,002  GRAPHICAL MODE ALL DATA  32,500  157,000  225,000  4,000  810,000  ABSOLUTE #'S GRAPHICAL MODE  36,500  250,000  240,000  30,000  920,000  NO EXTREMES GRAPHICAL MODE  28,500  255,000  174,000  17,000  765,000  OMITTING NEGATIVES GRAPHICAL MODE  31,000  238,000  245,000  23,000  915,000  APPENDIX 10.  ESTIMATED N FROM APP. 9 AGE  w  os  N  is 0T  N  1T  N  3 CM.  N  os  N  is 0T  N  1T  N  8 CM.  N  os  N  is  INCLUDING TAILS OF CURVE  ALLOWANCE FOR ADJUSTMENT OF R  710,400  873,310  214,510  231,899  231,899  167,319  113,499  310,342  318,342  481,252  -166,548  -160,159 637,528  460,777 -213,216  466,618  -160,159 474,618  468,601 -189,101 610,671  -10,272  -3,883  -3,883  -47,031  591,007 -82,986  1,700,694  1,717,754  1,880,664  1,223,804 406,869  1,239,253  1,239,253  1,740,791 1,083,089  586,839 -54,572  564,591  952,961 548,766  -93,111  -125,227  1,119,611 461,909  1,057,540  l,4l6,06l  1,329,292  758,359  655,299  983,173  1,034,457  N  is  506,283  555,956  1,197,367 555,956  1,309,263  1,360,547 882,046  1,523,457 882,046  1T  -76,435 787,492  691,400  os  W  597,558  -39,883 825,021  N  0T  617,819  645,389 3,978  -70,021  K  K = .20  482,479 3,978  1T  N  K = .10  463,479 -13,411  423,929 -54,572  0T  N  13 CM.  OVERALL RESULTS  832,373  1,626,954  383,547  Continued  APPENDIX 1 0 . Continued. ESTIMATED N FROM APP. 9 OVERALL WEIGHTED MEAN  WEIGHTED MEAN  3^0,59^  503,501+  1+88,805  1+79,322  N  is  -1^2,291  -137,902  -137,902  -168,879  -194,971  "oT  9^7,556  953,556  1,116,1+66  1,01+6,071  990,122  lr70,066  V7M55  l+7l+,l+55  388,369  316,129  N  os  1+07,153  1+23,653  586,563  56l+,3l+l  5j+8,537  N  is  -69,737  -5»+, 81+8  -5l+,8l+7  -93,361  -125,1+56  0T  527,175  5^3,675  706,585  673,1+51  61+8,555  50,285  65,171+  65,171+  15,71+9  -25,1+38  "os  1+51,017  1+69,267  598,899  605,807  586,51+8  "is  -25,873  -9,23!+  -9,23l+  -51,895  -87,1+1+5  538,002  556,252  719,162  68l+,89l  659,01+2  61,112  77,751  77,751  27,187  -1^,951  418,500  1+36,500  599,^10  576,021  559,292  -58,390  -1+2,001  -1+2,001  -81,681  -n.1+,701  810,000  828,250  991,160  932,151  885,692  333,110  3^9,^99  31+9,1+99  27I+, 1+1+9  211,699  "OT "IT ALL DATA GRAPHICAL MODE  K = .20  33*+,595  "IT  OMITTING NEGATIVES  K = .10  os  N  OVERALL-13 CM.  ALLOWANCE FOR ADJUSTMENT OF R  N  "IT OVERALL-13 CM.  INCLUDING TAILS: OF CURVE  "os "is N  0T  "IT  Continued  APPENDIX 10.  ESTIMATED N FROM APP. 9 ABSOLUTE VALUES OF ALL DATA  EXCLUDING EXTREME VALUES  OMITTING NEGATIVES  N  0S  N  1S  N  0T  W  1T  N  os  N  1S  N  0T  H  N  N  N  os 1S  OT 1T  Q  Continued  INCLUDING TAILS OF CURVE  ALLOWANCE FOR ADJUSTMENT OF R  K = .10  K = .20  556,500  584,750  747,660  710,791  682,792  79,610  106,249  106,249  53,089  8,799  920,000  948,250  1,111,160  l,o4l,246  985,692  443,110  469,749  469,749  383,544  311,699  474,500  497,500  660,410  631,481  609,992  -2,390  18,999  18,999  -26,221  •64,001  765,000  788,000  950,910  895,565  852,162  288,110  309,499  309,499  237,863  178,169  537,000  561,000  723,910  689,201  662,992  60,110  82,499  82,499  31,499  -11,001  915,000  939,000  1,101,910  1,032,838  977,992  438,110  460,499  460,499  375A36  303,999  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0302525/manifest

Comment

Related Items