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Kj. W. Jensen

Freshwater Fishery Laboratory, P.O. Box 63, Vollebekk


In a Norwegian mountain lake harbouring brown trout yearly experiments in tagging- recapture have been done in the period 1958–73. The fishery has been completely controlled during the period. Population estimates for the years 1958–66 have been obtained by correcting the virtual populations for natural mortality. The resulting population estimates were compared with corresponding Petersen estimates corrected for recruitment. In another mountain lake with similar conditions Petersen estimates based on tagged trout were compared with population estimates obtained from independent calculations of yield-recruitment- mortality.

The Petersen estimates are in good agreement with the other estimates. It is therefore concluded that eventual changes in vulnerability to gillnets caused by Carlin tagging are too small to give serious bias to Petersen estimates of brown trout.


Dans un lac de montagne norvégien ayant une population de truite (Salmo trutta L.) des expériences de marquage-recapture furent effectuées pendant la période 1958–73. La pêche fut entièrement contrôlée durant cette période. Des estimations de la population pour les années 1958–66 furent obtenues par la rectification de ces populations pour la mortalité naturelle. Les estimations furent comparées aux estimations Petersen rectifiées pour le recrutement. Dans un autre lac de montagne ayant des conditions similaires des estimations Petersen, basées sur des truites marquées, furent comparées à d'autres estimations de population obtenues au moyen de calculs indépendants du rendement, du recrutement et de la mortalité.

Les estimations Petersen se comparent favorablement aux autres estimations. On en conclut que des changements de vulnérabilité aux filets maillants provoqués par le marquage Carlin sont trop faibles pour influer sérieusement sur les estimations Petersen de la truite.

Lake ∅vre Heimdalsvatn is a small lake (77.5 ha) situated in the central mountains of southern Norway at an altitude of 1 090 metres. The lake harbours only brown trout and a very small population of minnow (Phoxinus phoxinus L.). Since 1958 the fishery in the lake has been completely controlled. In 1958 the lake was very densely populated with small, slow-growing trout. More intensive fishing in the following years reduced the trout population significantly.

The ice usually breaks up in the first half of June; the fishing season begins in the beginning of July and usually ends in the beginning of October. A number of trout were tagged in August, 1958. In the years 1959–73 the tagging was always done in June-July at the beginning of the fishing season. Numbered Carlin tags with double steel thread were used, and the tags were attached below the front of the dorsal fin in the way commonly used in smolt tagging and described by Carlin (1955). Trout for tagging were caught on a chase- net or on hook, and kept under observation in small natural ponds for 12 h or more before being released.

As the number of trout caught and the age composition of the catch is known for the years 1958–71 (scale analysis of the 1972 material not yet completed) virtual populations (Fry, 1949) can be constructed for a sequence of years. These are shown in Table I. The yearly rate of survival, S, in each of the years 1961–64 and 1966–68 was estimated from the tagging data. As the yearly survival and the number of tagged trout caught in each month was known the natural mortality coefficient, M, could be estimated by a method described by Regier (1962). On average the estimated natural mortality was M = 0.31.

From the virtual populations the true abundance of the different year-classes can be estimated by monthly addition of the estimated number of fish killed by natural mortality. The detailed procedure will be published elsewhere; the results are shown in Table II. The author believes these estimates (the v.p. estimates) to be sufficiently correct to serve as a basis for checking population estimates obtained by means of the Petersen mark-recapture method for the same years.

Ricker (1958 p. 86) mentions six conditions that must be met if valid Petersen estimates shall be obtained. In our case no tags were lost during the first fishing season after tagging; tagging and fishing was done all over the lake; all recaptured tages were recognized and reported. A condition that may have been violated was that the tagged specimens could have suffered a higher natural mortality than the untagged fish, but this is always difficult to control. The resulting Petersen estimates would then be too high. As the fishing season corresponds with the growth season, recruitment (growth into vulnerable size) took place, so we must correct the estimates for recruitment. Further, immigration of small trout from the nursery streams was going on during the fishing season. The v.p. estimates include all trout in a year-class which are alive at a certain time regardless of whether they at that time are living in the lake itself or in a nursery stream. For small trout the Petersen estimates can therefore be expected to be lower than the v.p. estimates. Of gravest concern is the possibility of increased vulnerability caused by the tags. Most of the fishing in the lake was done with gillnets, and the tags can be entangled in the nets. Especially for tagged trout smaller than the model length corresponding to a certain mesh size the vulnerability could be increased, and the resulting Petersen estimates tend to be too small.

We shall use the Petersen estimate for 1961 to illustrate the method used to correct for recruitment. The tagging in 1961 took place in the period 28 June-3 July. The length distribution of the tagged fish and the recaptures in 1961 are shown in Table III. Fish smaller than 20 cm when tagged were not recaptured. Apparently the probability of recapture is highest for trout bigger than about 26 centimetres. Because of this we shall exclude all trout that were smaller than 20 cm at the time of tagging and we shall make separate estimates of the length group 20–25 cm and the group 26 cm and more.

The growth season had already begun when the tagging took place. Too few scale samples from July were available to calculate the length increment between annulus completion and tagging, so 10 mm was chosen as a reasonable average value. This means that our estimate shall exclude all trout with back-calculated length smaller than 19 cm, and we shall estimate separately the group 19–24 cm and the group 25 cm or more when the annulus was completed in 1961.

Table IV shows for different age groups the back-calculated lengths when the last annulus was laid down in 1961. These figures were used to divide the total catch in 1961 after 3 July on the two length groups 19–24 cm and 25 cm and bigger. The results are shown in Table V.

In the same way the figures in Table IV were used to divide the v.p. estimate for 1 July 1961 on the two length groups (Table VI).

For the Petersen estimates we shall use the common formula (with Bailey's correction):

The figures are given in Table VII. For (r + 1) smaller than 51 the approximate 95 percent confidence intervals were obtained by treating (r + 1) as a variable in a Poisson distribution. For (r + 1) bigger than 50 the binomial confidence intervals for the ratio were used.

The same methods were used for all the years 1958–66 and the results are shown in Table VIII. As seen from the last column in the table, five of the Petersen estimates (the Np values) are smaller than the estimates from the virtual population (the Nv values) and eight are bigger. This indicates that in the involved length groups there is no serious increase in the vulnerability of the trout carrying the Carlin tags. In seven of the comparisons the difference between the two kinds of estimates is 10 percent or smaller. The greatest difference is only 26 percent, but the broad confidence intervals warn us that much greater differences could easily have appeared.

In another trout lake in the same district (Lake Olavatn, 2.72 km2, altitude 967 m) where the fishery was completely controlled in 1969 and 1970, tagging data were combined with catch figures, data on growth and gillnet selectivity to estimate the equilibrium yield. The estimated yield was in good agreement with the observed catch (Jensen 1972). The model used showed a population of 3 890 trout of age five years or more on 1 July 1969. The corresponding (independent) Petersen estimate based on tagging and recapture was 3 877 with 95 percent confidence interval 2 942–4 812. Again there is good agreement between a Petersen estimate of trout carrying Carlin tags and another independent estimate.

The conclusion that can be drawn from these experiments is that although the vulnerability to gillnets for brown trout may be increased by Carlin-tagging, the change in vulnerability is usually too small to give serious bias to population estimates based on tagging- recapture.

Table I
Æ. Heimdalsvatn - Virtual populations of trout
195815161538831 3151 4961 4391 5502 086      
195911222094468731 2081 5051 9381 756     
1960  4962204027711 1631 7371 6801 174    
1961  311821332664881 0221 3271 0391 794   
1962  363124631253335966771 4381 136  
1963    87934861543159091 0302 648 
1964    12111551903076352 0452 834
1965     1  26311182181 0312 328
1966         11824704581 687
1967         14833205830
1968         1 1743265
1969         1   434
1970             210
1971              3

Table II
Æ. Heimdalsvatn - Estimated year-class abundance on 1 July
195815161711 0461 7412 1962 5813 2534 921       15 940
195911272606231 1441 7232 3573 5053 759      13 400
1960  61062794839341 4732 4232 7052 326     10 735
1961  4131001513045711 2391 7201 6073 220    8 929
1962  363528681423847059052 0942 151   6 521
1963    88935951843911 1391 5014 583  7 953
1964    121116571163798022 9095 698 9 982
1965     1  28401352721 3663 7923 9839 599
1966         22028885692 2302 735 

Table III
Æ. Heimdalsvatn - Length distribution at tagging and recaptures in 1961 of trout tagged in 1961
 Length (cm)Total
No. tagged1349910192030182917209741121214  
No. recaptured  232474910151394341011 92  
% recapture005033224037203056527645444310010005010043.0

Table IV
Back-calculated length at last annulus in 1961
AgeLength (cm)Total
3 years
151      16  
4       "
611375    86  
5       "
6       "
7       "
8       "
9       "
     2 4749  
10     "
11     "
12     "

Table V
Estimated age distribution in the catch in 1961 after 3 July
Total catch after tagging613343406866473411901024852 754
19 cm and bigger at last annulus4972746746473411901024852 382
19–24 cm at last annulus497270572181218   1 153
25 cm and bigger at last annulus  41024663201821024851 229

Table VI
Æ. Heimdalsvatn - Trout population on 1 July 1961. (V.p. estimates)
 AGE (years)Total
 345678910 and more 
Number alive2 9953 2201 6071 7201 239571304268     
19 cm and bigger at annulus1879361 2931 6911 239571304268    6 489
19–24 cm at annulus1879361 2731 4353483512 4 226
25 cm and bigger at annulus  20256891536292268    2 263

Table VII
Æ. Heimdalsvatn - Petersen estimates of trout population on 3 July 1961
 mrcp95% conf. int. for p
19–24 cm at annulus71221 1533 5622 374–5 620     
25 cm and bigger at annulus139701 2292 4081 904–3 233     

Table VIII
Æ. Heimdalsvatn- Petersen and v.p. estimates of trout populations
DateLength at last annulusmrcp95% conf. int. for pvp:v
8.8.195824 cm and bigger68181 1494 1162 636–6 836     5 0010.82     
9.7.195925 cm and bigger3171 0313 9992 030–9 273     3 9171.02     
6.7.196025 cm and bigger1861 3823 5561 726–8 859     3 4521.03     
3.7.196119–24 cm71221 1533 5622 374–5 620     4 2260.84     
3.7.196125 cm and bigger139701 2292 4081 904–3 233     2 2631.06     
3.7.196225 cm and bigger70358291 6141 166–2 304     1 5251.06     
8.7.196321–24 cm33117021 9331 107–3 742     1 8821.03     
8.7.196325 cm and bigger76344601 001720–1 437     7931.26     
1.7.196421–24 cm51128533 3501 959–6 294     3 3031.01     
1.7.196425 cm and bigger54225101 200800–1 893     1 0951.10     
14.7.196525 cm and bigger123617051 4011 088–1 746     1 8760.75     
14.7.196520–24 cm57106633 4411 923–6 894     4 1040.84     
14.7.196625 cm and bigger160628062 0501 594–2 552     2 2930.89     

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