Volume 1
Issue 1
Fisheries
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES
Available Online: http://www.ejpau.media.pl/volume1/issue1/fisheries/art04.html
AGE AND GROWTH RATE OF PIKEPERCH IN THE POMERANIAN BAY IN 1998.
Jerzy Szypuła
A total of 150 pikeperch individuals caught in 1998 in the Pomeranian Bay were examined. The fish were picked out from 4 samples: 3 were obtained in March and 1 in April 1998. The standard methods of length and weight growth rate determination were used. When determining fish age, the verge coefficient was factored in (if Kr > 0.50, 1 was added to the scale annual ring count).
Key words: pikeperch, growth rate, mathematical growth models, condition coefficient.
Studies on age and growth of pikeperch (Stizostedion lucioperca L., 1758), carried out in the Pomeranian Bay in 1998, were aimed mainly at verification of earlier data obtained, with identical methodology, in 1995. The only methodological novelty introduced in 1998 involved using the verge coefficient alongside the scale annual ring count when determining fish age.
An additional aspect of the study concerned a possibility of relating differences in the pikeperch growth rate, if any, to environmental changes associated with the Pomeranian Bay water pollution caused by the River Oder discharge. The study forms a part of the project entitled "The fish growth rate in the unstable environment of the Oder estuary system", carried out by the Department of Fish Biology, Agricultural University of Szczecin.
The fish studied were caught in the Pomeranian Bay within MarchApril 1998; the catches were effected with a bottom trawl operated from SNB AR1, a research vessel owned by the Agricultural University in Szczecin. Three samples (36, 57, and 16 individuals) were obtained in March, the fourth sample (41 individuals) being obtained in April.
A total of 150 individuals measuring 21.465.5 cm l.c. (24.372.0 cm l.t.) and weighing 1054695 g (total weight) were examined. Additionally, the verge coefficient, Kr, was calculated using the generally known formula:
where:
R – total scale radius;
r_{n} – scale radius as measured from the centre to the last annual ring;
r_{n1} – scale radius as measured from the centre to the penultimate annual ring.
The length growth was determined with a number of methods, the back calculations being the principal one. To arrive at an optimal version of the method with respect to the materials on hand, the length (L = l.c.)  total scale radius (R) relationship was determined. The socalled standard length (the length at which scales appear) was considered; according to Heese (1992), the standard length is 2.5 cm. Eventually, the lengthscale radius relationship could be presented as the following equation:
L = 2.5000 + 11.8413 R^{0.8141}
Due to the nonlinearity of the equation, the Vovk's version was used to backcalculate the pikeperch length. Corrected values of the scale radius measured were inserted into the above equation in place of R and the corresponding L values were calculated.
Another method of the length growth rate determination involved calculation of mean lengths in individual age groups. When classifying the individuals examined into appropriate age groups, the scale annual ring counts and the verge coefficient (Kr) were used. The procedure used is described in detail in the RESULTS chapter. The backcalculated data were used to compute parameters of two mathematical length growth models: the von Bertalanffy equation and the modified power function.
The fish condition was determined by calculating the Fulton coefficient (K). The lengthweight relationship of the pikeperch studied was determined using the power function.
The weight growth rate was determined with three methods. The basic one involved converting lengths, backcalculated for each year of life, to weights using the LW relationship. The remaining two methods involved determining mean weights in age groups and the modified von Bertalanffy equation. In the last case, the equation parameters were determined with a simplified technique. The value of Wˇ was determined from the LW relationship in the following way:
Wˇ = kLˇ^{n} = 5126 g
where:
Lˇ – corresponds to the asymptotic length as determined when studying the length growth. The remaining parameters of the modified von Bertalanffy equation (K and t_{0}) are identical to those used in the length growth equation, n being the exponent in the LW relationship.
The verge coefficient distribution is shown in Fig. 1. Two clear peaks in Kr values are evident: a lower one (n = 16) at 0.21  0.30 and a higher one (n = 30) at 0.71  0.80. As the theoretical range of Kr should cover 0  1 (in practice, there are cases when Kr > 1; there were 10 such cases, i.e., 6.7% only, in the materials studied), the value of 0.50 was used as critical for differentiating between "low" and "high" Kr , the value falling approximately at the trough between the two Kr peaks. This division of Kr values was used when classifying the individuals examined into appropriate age groups. Those individuals with "low" Kr were classified to age groups exclusively on the basis of the scale annual ring count, while those with "high" values were grouped with age classes by 1 year older than accounted for by the annual ring count. This procedure of fish classification into to age group was used when determining the age distribution (Table 1) and when determinin g length and weight growth rates by calculating means in age groups. On the other hand, age group classification shown when presenting back readings (Table 2) was based exclusively on the annual ring count, hence differences in age distributions shown in Tables 1 and 2.
Fig. 1. Distribution of verge coefficient (Kr) values in examined fish
Distribution of the Kr values suggests that the pikeperch studied were just forming a new scale annual ring. Most (102, that is 68%) individuals showed "high" Kr values, which can be regarded as an evidence that a new annual ring for 1998 had not been formed yet. The remaining individuals (48, i.e., 32%) showed "low" Kr values, thus evidencing the presence of a newly formed 1998 annual ring. Mean Kr values for "low" and "high" groups were 0.29 and 0.77, respectively.
Table 1 presents length and age distributions of the pikeperch examined. Most numerous (48.7%) were the 4yrold fish; the 10% threshold was exceeded also by the 3 and 5yrolds (19.3 and 16.7%, respectively). Generally, the above three age groups included 84.7% of all the individuals examined. Among the 3cmwide length classes, three were prevailing: dominant (28.0%) was the 38.0  40.9 cm class, the 35.0  37.9 and 41.0  43.9 cm classes supplying 20.6 and 15.3% of all the individuals, respectively. The three classes combined accounted for 63.9% of all the individuals. As could be seen, dominance of the three most numerous age groups was much stronger than of the three most numerous length classes.
Table 1. Length and age composition of the fish examined 
Length class 
Age group 
n 
% 

I 
II 
III 
IV 
V 
VI 
VII 
VIII 

20.0–22.9 
1 
– 
– 
– 
– 
– 
– 
– 
1 
0.7 
26.0–28.9 
– 
3 
3 
– 
– 
– 
– 
– 
6 
4.0 
29.0–31.9 
– 
5 
2 
1 
– 
– 
– 
– 
8 
5.3 
32.0–34.9 
– 
– 
12 
– 
– 
– 
– 
– 
12 
8.0 
35.0–37.9 
– 
– 
10 
21 
– 
– 
– 
– 
31 
20.6 
38.0–40.9 
– 
– 
2 
33 
7 
– 
– 
– 
42 
28.0 
41.0–43.9 
– 
– 
– 
17 
6 
– 
– 
– 
23 
15.3 
44.0–46.9 
– 
– 
– 
1 
8 
1 
– 
– 
10 
6.7 
47.0–49.9 
– 
– 
– 
– 
3 
4 
– 
– 
7 
4.7 
50.0–52.9 
– 
– 
– 
– 
1 
3 
1 
– 
5 
3.3 
53.0–55.9 
– 
– 
– 
– 
– 
1 
1 
– 
2 
1.3 
56.0–58.9 
– 
– 
– 
– 
– 
– 
– 
1 
1 
0.7 
59.0–61.9 
– 
– 
– 
– 
– 
– 
– 
1 
1 
0.7 
65.0–67.9 
– 
– 
– 
– 
– 
– 
– 
1 
1 
0.7 
n 
1 
8 
29 
73 
25 
9 
2 
3 
150 
100.0 
% 
0.7 
5.3 
19.3 
48.7 
16.7 
6.0 
1.3 
2.0 
Table 2 shows the pikeperch length growth, worked out with the back calculation method. It is only the l_{1} length of the first age group that is clearly lower than the corresponding l_{1 }values of the older age groups. Mean lengths of individual age groups in subsequent years of life differed slightly only, which, i.a., can be taken as an evidence that it was appropriate to use the Vovk’s technique of pikeperch length back calculation. Mean lengths () and their increments () in consecutive years of life point to a characteristic growth history: a very high increment in the first year of life, an almost half that in the second year, and gradually decreasing increments subsequently.
Table 2. Pikeperch length growth as determined with back calculations 
Age group 
n 
Length [l. c. cm] 

l_{1} 
l_{2} 
l_{3} 
l_{4} 
l_{5} 
l_{6} 
l_{7} 
l_{8} 

I 
1 
16.4 
– 
– 
– 
– 
– 
– 
– 
II 
22 
18.6 
27.0 
– 
– 
– 
– 
– 
– 
III 
72 
19.6 
27.6 
34.1 
– 
– 
– 
– 
– 
IV 
35 
19.2 
27.4 
34.0 
39.5 
– 
– 
– 
– 
V 
14 
20.0 
28.4 
35.3 
41.2 
46.2 
– 
– 
– 
VI 
3 
18.9 
27.6 
35.0 
41.7 
47.9 
52.5 
– 
– 
VII 
2 
19.5 
27.4 
35.8 
41.9 
46.7 
51.0 
54.6 
– 
VIII 
1 
19.7 
27.1 
34.9 
41.3 
45.3 
48.7 
52.5 
55.1 
19.4 
27.5 
34.3 
40.2 
46.5 
51.4 
53.9 
55.1 

SD 
1.46 
1.70 
1.63 
1.92 
1.62 
2.53 
2.27 
– 

v 
7.5 
6.2 
4.8 
4.8 
3.5 
4.9 
4.2 
– 

19.4 
8.1 
6.8 
5.9 
6.3 
4.9 
2.5 
1.2 

n 
150 
149 
127 
55 
20 
6 
3 
1 
The relatively limited scatter of length data should be emphasised. The highest coefficient of variation (v), recorded in the first year of life, was 7.5% only; the scatter of length data in the subsequent years was still more confined, the coefficient of variation ranging from 3.5% for l_{5} to 6.2% for l_{2}.
The backcalculated results served as a basis for calculating two mathematical growth models: the von Bertalanffy equation and the modified power function. The respective models can be formulated as:
L_{t} = 68.7[1 – e^{0.1958(t+0.6573)}]
L_{t} = 41.2692t^{0.3148} – 22.8845
The results are summarised in Table 3; for comparative purposes, the table contains also the backcalculated length data (treated as a basis on which to compare other results) and the data determined with means in age groups.
Table 3. Pikeperch length growth as calculated with different methods (l. c. cm) 
Age group 
Method 

back calculations 
mean length in age group 
von Bertalanffy equation 
modified power function 

I 
19.4 
21.4 
19.0 
18.4 
II 
27.5 
29.0 
27.9 
28.4 
III 
34.3 
34.2 
35.1 
35.4 
IV 
40.2 
39.1 
41.1 
41.0 
V 
46.5 
43.3 
46.0 
45.6 
VI 
51.4 
49.7 
50.0 
49.7 
VII 
53.9 
53.9 
53.4 
53.9 
VIII 
55.1 
60.5 
56.1 
56.5 
The two models allow to fairly accurately characterise the pikeperch length growth, the von Bertalanffy model proving to be most precise. The results obtained with that model differed from the backcalculated data by 0.74, on the average, while the lengths calculated with the modified power function differed slightly more (by 0.97 cm). Clearly larger differences (by 1.87 on the average) appeared when the backcalculated data were compared with means in age groups.
Fig. 2 illustrates the lengthweight relationship for the pikeperch studied. The relationship was described with the following power function:
W = 0.0040 L^{3.3249}
where W is fish weight (g) and L is fish length (l.c.; cm). As can be seen in the plot, the curve illustrating the relationship runs very close to the data points corresponding to mean weights in consecutive length classes.
Fig. 2. Lengthweight relationship in pikeperch
Results of weight growth determination, obtained with all the three methods described in detail in MATERIALS AND METHODS, are summarised in Table 4.
Table 4. Pikeperch weight growth as calculated with different methods (g) 
Age group 
Method 

length to weight conversion 
mean weight in age group 
modified von Bertalanffy equation 

I 
77 
105 
72 
II 
244 
296 
255 
III 
509 
523 
551 
IV 
863 
812 
929 
V 
1400 
1126 
1351 
VI 
1954 
1807 
1787 
VII 
2288 
2277 
2213 
VIII 
2462 
3463 
2612 
Comparison of length to weight conversion with data obtained with the other two methods showed that the modified von Bertalanffy equation produced lower differences (71 g on the average), while differences between mean weights in age groups data and those yielded by the basic method were almost three times as high (198 g on the average). It should be emphasised that such a pronounced difference was caused by a large discrepancy (more than 1000 g) between weights in the eighth year of life.
The average condition coefficient, K, calculated from the Fulton formula, was 1.33. Changes in the condition coefficient, observed in individual length classes and age groups showed a clear tendency to increase with fish length and age. Fig. 3 illustrates relationships between K and the fish length and weight as described by linear regression equations. Both cases produced high correlation coefficients (0.9346 and 0.9735) which, together with the number of degrees of freedom, evidence statistical significance of both regressions (Parker, 1978).
Fig. 3. Changes in condition coefficient (K) with length (A) and age (B) of pikeperch  
When the verge coefficient is taken into account during classification of fish individuals into age groups, a better fit of mean lengths determined for consecutive age groups to the results of back calculations is obtained. A comparison of the relevant data in Table 3 (first and second column) allows to note that the data oscillate in a way: larger mean lengths in age groups are alternated by higher backcalculated data. Although the average difference between mean lengths in age groups and backcalculated data is almost twice that when the mathematical growth models are applied, that difference is only 4.6% of the average pikeperch length calculated from backcalculated data for the first 8 years of life. It should be borne in mind that this situation could occur because the samples were collected when a new annual ring was just forming on the scales. Most probably, differences between mean lengths in age groups and backcalculated lengths would still have been reduced, if the number of individuals without a new annual ring ("high" Kr) had been more or less equal to that of individuals showing the already formed new ring ("low" Kr). Unfortunately, the materials on hand were dominated (68% of all fish) by those individuals with "high" Kr.
A comparison of data of this study with the results obtained, with identical methodology, from the Pomeranian Bay in 1995 (Szypuła, 1996) shows some differences between length and age distributions yielded by both studies. The fish studied in 1995 were dominated by the 3234.5 cm class, the 3840.9 cm class dominating in this study. The age distributions were less different, the 3yrold individuals predominating in both cases. It should be remembered that when classifying fish into age groups in 1995, the verge coefficient was not taken into account, the scale annual ring count being used only; for this reason, the 1995 data on age distribution should be compared with Table 2 of this study. In the 1995 materials, fewer age groups were recorded (groups IIVI vs. groups IVIII in 1998).
In the two studies, the lengths (l.c.) in consecutive years of life were most similar in the second and third year of life. In the remaining years, slightly longer fish were recorded in 1995 (the maximum difference of 2.3 cm was observed in the sixth year of life). The scatted of data in 1995 was quite pronounced (11.2% coefficient of variation in the first year of life vs. 7.5% in 1998).
Earlier (19741977) studies on age and growth of the pikeperch in Lake D±bie and River Regalica (Krzykawski, Szypuła 1982) showed a high similarity in the age composition of the fish examined. The 3yrold individuals predominated among the Lake D±bie fish, the Regalica materials being dominated by the 3yrolds as well, with a slightly lower contribution of the 4yrolds. The number of age groups in Lake D±bie was higher (from group 0+ to X), that in Regalica (from group II to VIII) being similar to the number in the present study.
Characteristic were differences in the length growth rate. The Lake D±bie and Regalica pikeperch grew at a clearly slower rate during the first 2 years of life. A reverse situation was observed in subsequent years, the length differences (in favour of the Lake D±bie and Regalica individuals) increasing gradually to reach 14.2 and 12.3 cm, respectively, in the eighth year of life. It is possible that the length data for the Pomeranian Bay pikeperch are not fully representative due to the very low number of individuals examined. A similar situation (a clearly lower growth rate in the first year of life, the rate picking up and differences gradually increasing as of the third year) is observed when the results of this study are compared with data reported by Korycki (1976) and Nagięć (1961); however, the length differences, particularly those in the eighth year of life, were not as great. The present data and the results published by the authors referred to above show similar trends with respect to the weight gr owth rate.
The lengthgrowth relationships for the Pomeranian Bay pikeperch in 1995 and 1998 were very similar. Mean values of the condition coefficients were identical in the two years (K = 1.33). Changes in the condition coefficient relative to the fish length and age, too, proceeded in a similar manner (values of K increased in both years with fish size and age).
 The growth of length and weight of the Pomeranian Bay pikeperch in 1998 was very similar to corresponding results obtained in 1995. Very similar were also the lengthweight relationship and condition, as well as the relationship of the latter with the fish length and age.
 Earlier data on growth of pikeperch in other areas (Lake D±bie, River Regalica, lakes near Węgorzewo) pointed to a slower growth in the first two years of life and a faster growth later on. Particularly large differences (with respect to the Pomeranian Bay pikeperch) were recorded in older fish.
 Using the verge coefficient when classifying individuals into age groups allows a better fit of data on mean lengths in age groups to backcalculated results. An additional prerequisite calls for collecting materials for the analyses when a new annual ring is being formed on scales.
 Heese T., 1992: Optimalisation of methods based on back calculations in fish growth rate determination, Monograph, of Faculty of Overland and Sanitary Engineering No. 42 Koszalin. [In Polish].
 Korycki A., 1976: Pikeperch, PWRiL Warszawa. [In Polish].
 Krzykawski S., Szypuła J., 1982: Growth and feeding of pikeperch in the Lake D±bie and Regalica River in 19741977, Zesz. Nauk. AR Szczec. 93: 326. [In Polish].
 Nagięć M., 1961: The growth of pikeperch (Lucioperca lucioperca (L.) in North Polish lakes, Rocz. Nauk Rol. Ser. B 77 (2): 549580. [In Polish].
 Parker R. E., 1978:, Introductory statistics for biology, PWN, Warszawa. [In Polish].
 Szypuła J., 1996: The age and growth rate of pikeperch in Pomeranian Bay, Zesz. Nauk. AR Szczec. 171: 3543. [In Polish].
Submited: October 1998
Jerzy Szypuła
Department of Fish Biology,
Agricultural University of Szczecin
4 Kazimierza Królewicza St., 71550 Szczecin, Poland
Responses to this article, comments are invited and should be submitted within three months of the publication of the article. If accepted for publication, they will be published in the chapter headed ‘Discussions’ in each series and hyperlinked to the article.