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Juraj Holčík and Karel Pivnička

Laboratory of Fishery Research and Hydrobiology
Slovak Academy of Agriculture
Bratislava and Department of Systematic Zoology
Charles University, Prague


The use of multiple-sample mark-recapture methods for fish population estimations in large reservoirs and lakes is described. The methods can be used also when unfavourable shore and bottom conditions only allow the use of passive fishing gear for sampling. Under such circumstances, however, multiple estimations are required which allow corrections to be made of previous estimates and models of the whole population to be constructed. Increase of estimated values in the course of long-term experiments is due to higher mortality or less vulnerability of marked fish and also to changes in fish activity. Examples and the method for population reconstruction are introduced.


L'utilisation de méthodes multiples d'échantillonnage avec récupération des marques pour évaluer les populations de poissons dans les grands réservoirs et les lacs est décrite. Ces méthodes peuvent également être utilisées lorsque des conditions défavorables de rivage et de fond ne permettent d'utiliser que des engins de pêche passifs. Dans ces cas, il convient toutefois de réaliser des évaluations multiples, qui permettent de corriger les évaluations précédentes et d'établir des modèles pour l'ensemble de la population. L'augmentation des valeurs estimées à l'occasion d'expériences à long terme est due à une mortalité croissante ou au fait que les poissons marqués deviennent moins vulnérables ou encore à des modifications de l'activité des poissons. On cite des exemples et on décrit la méthode de repeuplement.









When estimating fish populations in larger reservoirs and lakes by multiple-sample mark-recapture methods the researcher usually meets a number of problems. The most relevant ones arise in connexion with experiments of longer duration which are influenced by sampling conditions including the size of lake or reservoir. Steep shores and/or bottoms covered by impediments exclude the use of the active fishing gear, i.e., haul seines, and allow only the use of passive methods, i.e., gillnets, trammel nets and traps. Here the impossibility of capturing and marking a large number of fish excludes the use of Petersen's method and it is necessary to use the method of Schnabel. Whilst the advantage of the first method is the reduced possibility of changes in population abundance during the period of the experiment and a good knowledge of conditions claimed for selected reliability levels of estimation (Robson and Regier, 1968), the advantage of Schnabel's method is the cumulation of individual estimations and thus a balancing of possible chance variations in the proportion of recapture in the catch. This contribution deals with experience obtained during the fish population estimations in the Klíčava Reservoir (67 ha, maximal depth 37 m, volume 9.5 × 106 m3, elevation 294 m) and in the Morské Oko Lake (13.8 ha, maximal depth 25 m, volume 1.24 × 106 m3, elevation 619 m). For more details concerning the Klíčava reservoir see papers of Oliva and Holčík (1965), Holčík (1970), Pivnička (1971), Holčíkkand Pivnička (1972) and černý and Pivnička (1973). The Morské Oko Lake is situated in the Vihorlat mountains (Carpathian arch), eastern Slovakia. In both water bodies only gillnets, trammel nets and traps could be used due to shore and bottom conditions unfavourable to other types of gear. Due to this limitation only the most abundant, big- and medium-sized species, were estimated. In the Klíčava Reservoir there were roach (Rutilus rutilus), perch (Perca fluviatilis), tench (Tinca tinca), rudd (Scardinius erythrophthalmus), pike (Esox lucius), chub (Leuciscus cephalus), carp (Cyprinus carpio) and pike-perch (Stizostedion lucioperca) out of the total 16 species and, in the Morské Oko Lake, rainbow trout (Salmo gairdneri) and brown trout (Salmo trutta m. fario) out of the total four species. The duration of experiments was 28–31 weekly periods in the Klíčava Reservoir and 5–17 daily periods in the Morské Oko Lake.

Three particular problems will be discussed:

  1. the problem of increase of estimated values during consecutive periods;

  2. changes of fish activity and their influence on estimations; and

  3. utilization of successive estimations for construction of models of the population.


Most estimations of numbers of individual species in the Klíčava Reservoir, made in 1957 and 1963–72 respectively, showed increasing value of during consecutive weekly periods from April to October. This mainly applied to the most numerically abundant populations, such as roach and perch (Figures 1 and 2). Estimations of less abundant fish, such as chub in 1967 and tench remained relatively stable in all years. The reasons for such increases may be as follows:

  1. the small number of “c” (number of fish in sample) and “m” (number of marked fish in the population) in particular periods relative to the population number in the reservoir. Thus the product (“mc”) does not even attain the supposed abundan abundance of species;

  2. mortality of marked fish. With regard to the use of gillnets and trammel nets one should consider a higher mortality of marked fish and/or a lower probability of catching them again. In this case the “mc” product increases too and the probability of catching the marked fish (“r”) decreases. Thus, the value of shows an increasing trend. As an example a hypothetical population is proposed where = 10 000; m = 600; c = 100 and r = 6. If “m” decreases to half, due to mortality, then also the probability of catching the marked fish decreases to approximately half in a sample of the same size, thus i.e., the estimate is doubled. Theoretically it is possible here to make corrections for mortality as made by Holčík (1970a); however, two difficulties arise: (a) the mortality calculated from successive age groups often differs from the true value; and (b) obviously the mortality rate varies within the period of the estimation experiment.

Estimates are not influenced by natality, i.e., by the number of fish which gradually enters into the experiment. This can be demonstrated by the same example as above but where suddenly increases by 100 percent then the probability of catching the marked fish decreases to half, thus i.e., the estimate corresponds with reality. Therefore, the remarks of Robson and Regier (1971) on the equilibrium of mortality and natality (of unmarked fish) should be understood in this way.

Changes in the age composition of the population, i.e., the input or output of prevailing age groups, operate in fact in the same way as natality and mortality and thus bias the estimated .

With respect to the mortality of marked fish the size of the sample should be considered. This depends on the size of the population under estimation. From this point of view estimations in any water body can be divided into two groups:

  1. estimations of numerically very abundant species (i.e., roach and perch in the Klíčava Reservoir, rainbow trout in the Morské Oko Lake);

  2. estimations of less numerous species (chub, rudd, pike, tench, pike-perch and carp in the former and the brown trout in the latter).

In the first group an estimate can be made within a relatively short period when sampling and marking are performed at the time of the highest activity of the fish, e.g., at spawning. Since spawning grounds are usually limited to a few places only where the fish are concentrated, one can sample and mark sufficient numbers of them within a relatively short time. This happened in 1969 and 1971 in the case of roach and in all years in the case of perch in the Klíčava Reservoir where most of the first-handled fish were caught and marked during the prespawning and spawning activity; estimates of both species were considered to be finished at the end of the spawning period. In the case of rainbow trout from the Morské Oko Lake the estimation performed during the summer of 1967 failed completely due to no recoveries within three weeks. At the beginning of the next year, when the experiments were carried out in the spring months, the estimations were performed during 5–17 days. In this case, even the values obtained in the course of the first third of the experiment can be considered to be sufficiently accurate because of their stability during subsequent periods; the confidence limits however became more narrow with time (Figure 3). Besides the spawning period one can exploit increased activity of at least some species of fish before the onset of winter. It was again the rainbow trout in the Morské Oko Lake whose population number has been estimated during the late autumn at the time of surface freezing, and almost the same results were obtained as with the spring experiments (Table I).

When estimating the population number of less numerous species it is not usually possible to utilize heightened activity and a lengthening of the estimation period becomes necessary, as in all species mentioned from the Klíčava Reservoir where the experiments lasted up to the end of the vegetation period.

In connexion with the first group, there were differences in estimates of numbers of perch and roach. The estimated of perch rapidly reached a high level and then increased very slowly (Figure 2), whilst the of roach increased throughout the experiment (Figure 1).

A criterion for terminating the estimation for both species is to transform proportionally the real estimate into a label model where is known (for instance 1 000 as in the case of roach - Figure 4; or 500 in the case of perch - Figure 5). This model shows that the estimation of roach in 1968 reached the chosen after 6–7 periods in contrast to 1967 when this level was not reached at all due to a low number of marked fish. The 1967 estimates were therefore rejected. The estimates of perch in 1967 and 1968 respectively attained the required level after 4–5 periods (for more details see Pivnička, 1971). The continuing increase of roach estimates in natural conditions when compared with label model in 1968 can be explained merely due to changes in activity of particular age classes, as will be mentioned in the next chapter, or due to a considerable mortality of fish after spawning.

A criterion for showing the correctness of an estimate consists in its repetition and in a comparison of abundance of corresponding age classes in successive years.

Observations of several years duration show that during periods of spawning activity a number of species, including such sensitive ones as trout and pike-perch, are very resistant to handling and wounding and thus the hazard of higher mortality due to gillnets and trammel nets decreases. This indicates the advantage of estimation at times of spawning. It should be noted that, at this time, immature fish and nonspawning fish are also active.


In the course of a long-term experiment one should consider also changes in ecological characteristics of the fish under estimation. This can be recognized by the change in the frequency of age groups in the sample and, in connexion with passive fishing gear, it will be convenient to call these changes “activity changes”.

Table II shows age composition of roach samples in the Klíčava Reservoir in 1967 and 1968 respectively. In particular months the proportion of different age groups varied significantly according to the chi-square values. From analysis of partial data the highest values are from spring and autumn months when the activity of fish increased (spawning, feeding migrations).

These changes, which can be observed also in other species, significantly bias population estimates. Age groups which are active at the beginning of the experiment can be sampled and marked in a larger amount than later when their activity decreases and their share in the catch is substituted by other groups not previously active. It also follows from Table I that in different years the activity of the same age group may be completely different (fifth age group of roach in 1967 and 1968 respectively). Leaving aside spawning by part of the same age group, as observed both in rainbow trout and roach, also results in it having a lower number in the sample thus misrepresenting its real proportion in the population and decreasing the correctness of the estimate. Likewise, the transition to other types of diet, which is typical of roach and perch, displays a similar bias. Younger and smaller fish feed on plankton while older and larger individuals feed on benthos or become predators. In all cases some segregation in space can be found due to the departure of older fish for deeper and more distant parts of the reservoir. Thus, the vulnerability of the same age group can change during the year. Anyway, the changing activity of fish has a similar influence on estimates to mortality and natality, i.e., estimated shows continuously increasing value.


Because of selectivity of the fishing gear and changes in ecology, estimates performed in a single year may give an idea of the density of only a part of the population. Estimates repeated in successive years permit the recognition of that part of the population which cannot be estimated directly and allows for adjustments of previous estimates which may not be correct. For this purpose three conditions should be fulfilled.

  1. methods should be standard concerning the period of estimation, type of fishing gear, release of fish and other field operations;

  2. the age composition of samples of fish under estimation should be determined; and

  3. the survival and/or mortality rates of the year classes in successive years should be calculated.

The starting point for the reconstruction is a portion of the population consisting of that age group whose share in the sample is assumed to be proportional to its share in the whole population. As an example we will quote the reconstruction of the roach population in the Klíčava Reservoir (Table III) and of the rainbow trout population in the Morské Oko Lake (Tables IV-VI).

In the case of roach it was assumed that the fourth age group was present in samples at the same proportion as in the whole population. For this year class the total annual survival rate was calculated from the number of the fourth age group in 1968 and of the fifth age group in 1969 estimates respectively which is:

While it is true that in some later samples the fourth age group was present in a lower proportion than its actual share in the population we accepted this value because there is no significant difference between it and other values found later. The estimates performed in 1964–71 allow four other survival rates to be calculated:

Together with the abovementioned S = 0.645 the mean is 0.608, s = 0.053 and sx = 0.027. The variability is low, thus the first value can also be used. The reconstruction path in Table III is shown by arrows. Besides the survival rate the age composition of the samples used for growth studies was also utilized in years when no estimation experiments were performed. Thus, between the year 1971 (with estimation) and 1972 (without estimation) the number of the fourth age group in 1971 was converted to that of the fifth age group in the following year using the mentioned value of S. In 1972 this age group formed 65 percent of the investigated sample. The numbers of other age groups were determined according to their percentage in scalimetrically analysed sample. An alternative method of reconstruction was used in 1970. The number of fish in age groups 5–7 from 1969 was recalculated to that of the age groups 6–8 in 1970 and then divided according to the age composition of the sample analysed.

An attempt was also made to find the number of fish in the first age group using the annual survival rate S = 0.3. The first age group of the perch population has been reconstructed using this value and it was found to correspond well with mortality rate of yearlings (černy and Pivnička, 1973).

Another type of reconstruction was used for the rainbow trout population in the Morské Oko Lake. Here the data on reproduction characteristics were also utilized (fecundity, number of spawning nests, sex composition). The mean constant instantaneous mortality rate (Z), derived from the estimated number of age groups 3–4, 4–5 and 5–6 according to spring estimations 1968–69 and 1969–70 respectively, was used for this calculation. These age groups were supposed to be proportional both in the sample and in the whole population. For the calculation, the following formula was utilized (Holčík, 1970 and 1973):

where N =estimated number of fish in age group
Z =instantaneous mortality rate
t =number of days elapsed between two estimations.

For reconstruction of age groups 1–3, the value Z = 1.23 is used. The numbers of fish in the first age group in the spring of 1969 and 1970 and the second age group in the spring of 1970 were found using the converted formula . To find the number of fish in the first age group the value of instantaneous mortality rate Z = 2.88 is used. This has been calculated from the hypothetical number of the age group 1 in 1965 (i.e., derived from the number of fish in the age group 3 in 1968) and the observed number of eggs laid in spring of 1968. The method for the calculation is shown in Table IV. To prove the correctness of the reconstruction the calculation of each age group has been performed for particular seasons and years beginning with the autumn 1968 when the number of days elapsed between the separate estimations was substituted for “t” (Table V). As seen, there is a remarkable coincidence between the calculated and observed values. For the final reconstruction (Table V) the values from the spring estimations were considered to be valid with the exception of those for the fifth age group in spring 1969 and 1970 respectively where observed figures were substituted by the calculated ones because the former were considered to be too low or high respectively with regard to their relation with the previous or following year. For the number of fish in autumn only the calculated values were used because the autumn estimation was considered to be less accurate than the spring one.


We are of the opinion that the multiple-sample mark-recapture method can be successfully used in large reservoirs even in cases when only passive fishing gear can be used. Under these circumstances, however, the single estimation method gives only a rough and approximate idea of the density of population and it can also be considered biased. Information on the true population status can be obtained only by multiple estimations providing that identical sampling methods as well as the age composition of samples are determined. Knowledge of details of the ecology of the fish under estimation, including their behaviour and its application to sampling, increases the validity of experiment and shortens its duration. Thus, the use of passive fishing gear may not be a limiting factor in the accuracy of estimation and some advantage could be seen in this respect since sampling by gillnets and traps requires only a minimum number of workers in the field and experimental expenses can thus be lowered (in the Klíčava Reservoir all estimations were performed by one specialist and two to three technicians, and in the Morské Oko Lake by one specialist and one technician). The possibility of making corrections of previous estimates, and also in optimal cases of finding the true number of the whole population, makes the results of multiple-sample mark- recapture methods equivalent to those reached by direct enumeration.

Table I

Comparison between estimates of rainbow trout number obtained during spring and autumn samplings in Morské Oko Lake

  1–5 May 19688116151 007
31 October–11 November 19689823532 285
16 April– 5 May 1969700513977
  2–12 November 19697314001 217

Table II

Age frequency of roach samples by months in 1967 and 1968 respectively compared by chi-square
Expected values in brackets

 Age group 19671968
April and May JuneJulyAugustSeptember and OctoberTotal April and MayJune JulyAugustSeptember and OctoberTotal 
327 (17.7)19 (16.1)8 (17.7)34 (35.3)3 (4.3)91------
496 (100.7)82 (91.7)99 (100.7)218 (201.5)24 (24.3)51929 (43.9)6 (9.2)14 (19.1)23 (21.0)54 (32.8)126
513 (19.6)24 (17.8)30 (19.6)32 (39.2)2 (4.7)101133 (125.9)27 (26.3)62 (54.6)60 (60.2)79 (94.1)361
69 (7.0)7 (6.4)8 (7.0)6 (14.0)6 (1.7)3620 (12.2)5 (2.5)3 (5.3)4 (5.8)3 (9.1)35
p (%)3.629.< 10.818.921.368.9< 1< 1

Table III
Age composition (%) of sample and abundance () of the roach population in the Klíčava Reservoir in 1964–72 Underlined figures represent estimated values

Age group1964196719681969197019711972
1-435 870-6 143-165 933-1 653-2 367-?-?
2-43 416-7 533-1 843-49 780-496-719-?
313.213 9589.730 6322.24 8595.01 18941.332 1080.83201.9464
431.02 93069.554 30022.919 758a3.03 1311.976762.024 6000.8195
543.44 11014.911 65064.833 50036.012 7445.02 0201.975565.015 867
67.36905.14 0006.73 46653.018 67221.78 7673.51 4908.22 002
74.13870.76361.99823.01 05729.011 71616.06 3607.41 806
810.0950.11781.5570--1.148515.86 21816.74 076

a Original estimation 11 800 fish

Table IV
Reconstruction of the rainbow trout population from the Morské Oko Lake I. Determination of abundance of age groups 1 and 2 Underlined figures represent observed data found at spring estimation, arrows show direction of reconstruction Instantaneous mortality rate Z = 1.23 between age groups 1–3 and Z = 2.88 between eggs and age group one

Age group196819691970
0 (eggs)96 48059 496-
12 8315 4393 249
21 3038281 563

Table V
Reconstruction of the rainbow trout population II. Determination of age group abundance starting with 1968 spring estimation Observed figures in brackets, “X” denotes significant chi-square

 Age group196819691970
0–0 +(96 480)21 842---
1–1 +  2 831 1 4975 4392 835-
2–2 + 1 303   689  825   4301 563
3–3 + (   244)(  381)   (   102) X(   239)
(   454)   241  380  198   234
4–4 + (   101)(  146)   (     25) X   (  134) X
(   182)    96  13369   108
5–5 +     (     34) X    (    39)  X   (       4) X   (    72) X
(     36)     19    5328    38
6–6 + -    (      3)  X- (    13)
(      8)      4    105     15

Table VI
Reconstruction of the rainbow trout population III. Final status at each season Last derivations shown by arrows

Age group196819691970
0–0 +
96 480
21 842
59 496
13 048
1–1 +
2 831
1 497
5 439
2 835
3 249
2–2 +
1 303
1 563
3–3 +
4–4 +
5–5 +
6–6 +

Figure 1

Figure 1 Course of estimation of the roach population in 1967 and 1968 respectively Abscissa = weekly periods; ordinate = estimated

Figure 2

Figure 2 Course of estimation of the perch population in 1967 and 1968 respectively Abscissa = weekly periods; ordinate = estimated

Figure 3

Figure 3 Estimation of the rainbow trout population in spring of 1968, 1969 and 1970 respectively Heavy central lines represent estimated , weaker upper and lower lines are relevant confidence limits Abscissa = daily periods

Figure 4

Figure 4 Estimations of the roach population in 1967 and 1968 respectively transformed into a label model at = 1 000

Figure 5

Figure 5 Estimations of the perch population in 1967 and 1968 respectively transformed into a label model at = 500

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