# Comparison of Size Distribution of Fish Obtained from Gill Netting and the Distributions of Echoes from Hydroacoustics in Lake Dejguny (Poland)

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}, the mean absolute error (MAE), the Nash–Sutcliffe model efficiency coefficient (NSE), and root mean square error (RMSE). For the data from Lake Dejguny, the most similar distribution of fish echo proportions and the corresponding distribution of total length (TL) for fish larger than 62 mm were obtained using the TS–TL relation developed using fish from the Salmonidae, Percidae, and Cyprinidae families (2), and for fish larger than 74 mm, the relation was developed for the family Pericidae (4). No evidence was found to unambiguously verify the meanings of different sound frequencies (120 and 200 kHz) for which the TS–TL relationships used in the analysis were derived. The proposed procedure can be used to select the optimal regression equation.

## 1. Introduction

_{E}) according to the equation developed for perch (120 kHz) [2] is 264 mm, according to the equation (200 kHz) for the Percidae family [21] it is 318 mm, and according to the commonly used TS–TL conversion formula from Love [7], TL

_{E}= 559 mm (Figure 1). Additionally, for lower target strength values, these differences can be relatively large, e.g., for TS = −50 dB, TL

_{E}values can range from 35 to 68 mm (according to various equations developed by Frouzová et al. [2] for perch and carp). On the other hand, the differences in the target strengths for the same total length of fish according to different regression models can reach up to 3 dB [22]. It can therefore be assumed that the use of only one regression equation, without first checking its adequacy, may be one of the “specific methodological details” mentioned by Tušer et al. [15].

## 2. Materials and Methods

_{mean}= 12.0 m, Z

_{max}= 45.0 m), coregonid lake (length max. = 6.5 km, width max. = 2.4 km) located in northeastern Poland (54.0383° N, 21.6067° E). The contours of the lake and the survey design are shown in Figure 2.

^{−1}between 0 and 10 m in September and 0 and 15 m in October, decreasing to <2 mg L

^{−1}at a depth of 26/27 m.

#### 2.1. Gillnet Sampling

#### 2.2. Hydroacoustic

#### 2.2.1. Data Collection

^{−1}(Figure 2). The cutoff value for TS was set to −56 dB to avoid very small fish and other small, unwanted echoes from sources such as noise, air bubbles, and invertebrates [25,26].

#### 2.2.2. Data Post-Processing

_{E}in cm), two general multi-species regressions were used, i.e., one (adjusted to the different sound frequencies of 70, 120, and 200 kHz) from Love [7]:

_{E}) in the range of target strength (TS) from the ASCII files were determined in classes of 1.5 dB width created from −56 to −30.5 dB. For each equation, 6 distribution series were created, which contained data from gillnet catches arranged based on the designated TL

_{E}classes, i.e., the number of fish (N

_{E}) in the estimated length classes and the corresponding number of fish recorded acoustically (N

_{H}), giving a target-strength (TS) class.

_{n}(where n = 4, 5, …, 16) was calculated for n-pairs for N

_{H}and N

_{E}in the TS range of −30.5 to −51.5 dB of hydroacoustic and catch data, starting from the number of fish assigned to four classes, for TS −30.5 to −35 dB. It was assumed that a statistically significant change in the value of τ

_{n}against τ

_{n}

_{-1}determines the values for the discontinuity and indicates the limits of the range (TL

_{1}, TL

_{2}) in which the number of fish caught and recorded with hydroacoustic methods changed similarly. Further calculations were carried out only in these six ranges, separately for each equation. For each distribution series, the percentage share of acoustically identified fish (SFH) (identical in each distribution series) and the percentage share of fish caught (SF) were calculated (and vary depending on the equation being evaluated).

#### 2.2.3. Statistics

_{E}estimation methods on the consistency between the structure of caught fish and acoustically identified fish, the relative numbers of fish in the total length classes were compared using the same set of data. The class boundaries of the total length of the caught fish were determined using various TS–TL conversion equations in steps of 1.5 dB. It was assumed, following Białokoz and Chybowski [34], that the ichthyofauna structure expressed as a percentage provides a better picture of the lake’s ichthyofauna than the number or biomass of caught fish. A similar method of comparing hydroacoustic and catch data was used by Mehner et al. [10].

_{E}) would be the explanatory variable (O). The response variable (projected—P) was the distribution of the relative number of fish (%) caught and ordered within the limits of TL

_{E}classes determined according to the tested TS–TL regressions. The consistency of these distributions was tested by comparing the slope (coefficient a) of the equation y = ax + b and the coefficient of determination (r

^{2}). The coefficient of determination r

^{2}is a measure of the goodness of fit of the linear model, and it allowed us to assess the accuracy of the reconstruction of the relative number of fish caught based on the results obtained with hydroacoustic methods. R

^{2}ranges from 0 to 1, with larger values indicating a lower error variance. Values greater than 0.5 are considered acceptable [35]. This statistic is insensitive to additive and proportional differences between the model predictions and the measurement data [36], so when all predictions are wrong, r

^{2}may also obtain values close to 1.0 [37].

_{j}(j = 1, 2, …, n) is the share of the number of fish identified hydroacoustically and P

_{j}(j = 1, 2, …, n) is the share of the number of fish caught in the jth class determined by TL

_{E}limits.

_{E}based on hydroacoustic data can be considered higher when the values of NSE and r

^{2}are close to 1 and the lowest values of MAE and RMSE are close to 0 [44].

#### 2.2.4. Meta-Analysis

## 3. Results

#### 3.1. Gillnet Catches

#### 3.2. Hydroacoustics

_{H}) recorded in the 18 TS classes is presented in Table 2.

#### 3.3. Analysis

_{E}) in the TL

_{E}classes determined from the TS, according to various TS–TL relationships, is presented in Table 2. Different class boundaries of TL

_{E}classes at a given target strength (TS) caused the number of fish caught in individual classes to differ. The smallest relative differences (expressed as multiples of the arithmetic mean N

_{E}in a given class) were recorded in the class from −39.5 to >−38 dB (1.2), and the largest in the classes −50 to −51.5 dB (4.5) and −30.5 to −32 dB (4.2).

_{H}and N

_{E}data (in the same order) showed that changes in both variables (N

_{H}and N

_{E}) were similar in the range for n = 7(8) to n = 12 (τ

_{n}values ranged from 0.857 to 0.964, with p < 0.05) when TL

_{E}class boundaries were determined from Equation (2) and Equation (4) (Figure 5b,d). Therefore, the range (TL

_{1}, TL

_{2}) within which further calculations were carried out included fish with total body length ≥62.3 mm and ≥64.0 mm, respectively. According to the respective TS–TL relations, they correspond to a threshold of −47 dB. Therefore, the number of fish from catches in the subsets of data for further analysis for each relationship is 4365 and 4356, respectively, while the number recorded acoustically was 2591.

_{1}, TL

_{2}) was obtained for the multi-species TS–TL relation (Equation (1)), i.e., ≥63.8 mm, although the similarity of N

_{H}and N

_{E}pairs was observed in the range for n = 7 to n = 13, for which the values of τ

_{n}were from 0.837 to 0.917, with p < 0.05 (Figure 5a), and the relation for roach from Equation (5) was ≥62.0 mm, although pairwise similarity was observed in a narrower range n = 7–11 (Figure 5e). However, in this case, the values of τ

_{n}were also within a similar range of 0.867–0.944. According to the relevant TS–TL relationships, the lower limits of the range (TL

_{1}, TL

_{2}) corresponded to the thresholds of −48.5 dB and −45.5 dB, respectively. However, the number of fish from catches and acoustic recordings included in these subsets varied widely. For Equation (1), they were (N

_{L}=) 4356 and (N

_{H}=) 3387, and for Equation (5) they were (N

_{F-R}=) 3387 and (N

_{H}=) 1979.

_{E}using the other two equations, Equation (6) (for perch; Figure 5f) and Equation (3) (for the family Cyprinidae; Figure 5c) resulted in a narrowing of the range (TL

_{1}, TL

_{2}); the lower limits in the estimation of these equations were ≥93.0 mm and ≥90.5 mm, respectively. In these two cases, the values of τ

_{n}were slightly smaller at 0.697–0.818 and 0.786–0.905. Since, for these equations, the lower limits of the range (TL

_{1}, TL

_{2}) according to the TS–TL reports also corresponded to the TS threshold of −45.5 dB, the number of fish recorded acoustically N

_{H}included in the subsets was 1979, but the number of fish caught was lower than in the case of other equations, i.e., N

_{F-C}= 2621 and N

_{C}= 2691.

^{2}= 0.91). Among the TS–TL relations, the use of which allowed a slope close to unity to be obtained, the highest accuracy of the estimation of the percentage of fish caught based on acoustic data was provided by Equations (2) (r

^{2}= 0.90) and (5) (r

^{2}= 0.85).

_{E}classes that the regression, describing the relationship between the percentage share of caught and acoustically recorded fish, had the smallest error (Figure 6). The mean absolute error (MAE) based on these relationships was almost identical and amounted to 1.7% (share of fish abundance). The MAE in the case of using Equation (5) was greater than 2.2%, and for other equations it was less than 3%. The RMSE, which allows us to assess the importance of large errors, for Equations (2) and (4) (2.5 and 2.3, respectively) was at least twice as low as it was for Equations (1) and (6) (4.9 to 6.4).

_{E}classes determined using Equation (3). This value indicated that this equation should not be used to predict the TL structure of fish based on acoustic data. The NSE in the case of Equations (1) and (6) was <0.75, which indicated that the prediction based on them can only bring satisfactory results. The NSE in the case of Equations (2) and (4) reached a value close to 0.9, which indicated a good agreement between hydroacoustic and fishing data.

#### 3.4. Meta-Analysis

^{2}ranged from 0.97 to 0.94. The same was true for the estimation according to Equation (4); there were two subset boundaries ≥ 74.0 mm and ≥85.6 mm, for which a was 1.0135 and 0.9805 and r

^{2}was 0.948 and 0.925, respectively.

## 4. Discussion

^{2}= 0.94 (Figure S2). Therefore, it was not possible to show the fish caught in the two classes with the highest TL, corresponding to TS > −33.4 dB, although such individuals were present in the hydroacoustic data (Table 2). On the other hand, only one fish was assigned to three classes, limited by TS in the range of −34.9 to −30.5 dB, while in the case of total length estimation using Equations (2), (3), and (5), it was 25 to 39 fish (Table 3). Similar observations (“the contribution of large individuals (usually predators) to the size structure was greatly underestimated”), were also made by Tušer et al. [15], who used the TS regression based on Love [7]. Similar results were obtained for fish with a TL > 120 mm using Equations (2) and (4)–(6) (Figure S2). The coefficient a of the regression was between 0.52 and 0.79. Only the TS–TL relationship according to Borysenko et al. [21] for the Cyprinidae family allowed us to obtain a coefficient a close to unity (0.96) with the coefficient of determination r

^{2}= 0.99.

^{2}, as well as NSE, MAE, and RSME, made it possible to assess the dispersion of the compared values of the percentage share of fish from catches and those identified acoustically.

^{2}= 0.9, NSE = 0.9). The estimation of size class boundaries also generated the smallest errors (RSME > 2.5%, MAE > 1.7%). However, by restricting the test to fish larger than 74 mm, greater accuracy can be obtained by using the relationship of Borysenko et al. [21].

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Location map of hydroacoustic survey transects (solid light blue line) in Lake Dejguny (Poland) during September/October 2021. The solid orange line marks the initial fragments of 1000 pings, from which the catch and hydroacoustics data were used in the cross-compliance analysis; detailed explanations can be found in the text (Section 2.2.1).

**Figure 3.**Water depth along selected fragments of transects (marked in orange in Figure 2) from the subset of acoustic data adopted for the analysis (Dejguny Lake, 7/8 October 2021).

**Figure 4.**Fish body length (TL) distribution in Lake Dejguny (<0.1% in the range of 330–390 mm), based on catches made with Nordic multimesh gillnets on 27–30 September 2021.

**Figure 5.**Changes in the value of the Kendall coefficient (τ) for the series of n data pairs (n = 4 to 16) of the number of fish caught using Nordic multimesh gillnets (N

_{E}) in TL

_{E}classes determined based on various TS–TL relationships and the corresponding number of fish determined hydroacoustically (N

_{H}). The change in the value of the Kendall coefficient (Δτ) is marked in red, indicating the incompatibility of pairs within the observed data. (

**a**) Equation (1), (

**b**) Equation (2), (

**c**) Equation (3), (

**d**) Equation (4), (

**e**) Equation (5), and (

**f**) Equation (6); *—p < 0.1; **—p < 0.05; ***—p < 0.01.

**Figure 6.**Regression between the relative proportion of fish caught with Nordic multimesh gillnets (SF) assigned to total length (TL) classes (marked with an orange line) according to various TS–TL regressions from the literature, and the relative proportion of hydroacoustically identified fish (SFH). (

**a**–

**f**) as in Figure 4.

**Figure 7.**Opportunities to optimize the regression (marked with a green line) between the relative proportion of fish caught with Nordic multimesh gillnets (SF) that have been assigned to overall length (TL) classes according to various TS–TL relationships and the relative proportion of hydroacoustically identified fish (SFH). The optimization consisted in narrowing down the data subsets by removing classes based on the stepwise NSE analysis (search for the maximum NSE; cf. Table 3). (

**a**–

**e**) as in Figure 4.

**Table 1.**List of species and abundance of fish in benthic gillnet fisheries on 27–30 September 2021, in Lake Dejguny.

Species | Abundance (%) |
---|---|

perch (Perca fluviatilus L.) | 36.0 |

European smelt (Osmerus eperlanus L.) | 21.1 |

roach (Rutilus rutilus L.) | 17.7 |

bream (Blicca bjoerkna L.) | 10.4 |

freshwater bream (Abramis brama L.) | 4.6 |

ruffe (Gymnocephalus cernuus L.) | 4.5 |

vendance (Coregonus albula L.) | 4.1 |

bleak (Alburnus alburnus L.) | 1.1 |

rudd (Scardinius erythrophthalmus L.) | 0.2 |

pike (Esox lucius L.) | 0.2 |

tench (Tinca tinca L.) | <0.1 |

bitterling (Rhodeus amarus L.) | <0.1 |

spined loach (Cobitis taenia L.) | <0.1 |

burbot (Lota lota L.) | <0.1 |

**Table 2.**Size structure of registered echoes (number of fish—N

_{H}), by target strength (TS in dB) on 7/8 October 2021, and the number of fish caught with gillnets on 27–30 September 2021, in TS classes (with a spread of 1.5 dB) based on various TS–TL relationships (Equations (1)–(6)). Subsets of data after removal of fish smaller than the TS for the small fish threshold (defined for each TS–TL relationship) are marked in plain font, and deleted data are in italics (explanations in the text).

TS [dB] | −56.0 | −54.5 | −53.0 | −51.5 | −50.0 | −48.5 | −47.0 | −45.5 | −44.0 | −42.5 | −41.0 | −39.5 | −38.0 | −36.5 | −35.0 | −33.5 | −32.0 | −30.5 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

N_{H} | 1718 | 1723 | 1623 | 1385 | 1146 | 796 | 612 | 479 | 424 | 364 | 263 | 196 | 126 | 60 | 22 | 30 | 12 | 3 |

N_{L} | 5 | 84 | 18 | 18 | 63 | 1362 | 352 | 1125 | 631 | 298 | 228 | 239 | 82 | 26 | 12 | 1 | 0 | 0 |

N_{F} | 1 | 39 | 57 | 10 | 17 | 55 | 739 | 919 | 832 | 715 | 430 | 228 | 225 | 170 | 68 | 23 | 14 | 2 |

N_{C} | 89 | 16 | 7 | 32 | 137 | 1436 | 133 | 481 | 1076 | 442 | 152 | 250 | 156 | 87 | 25 | 17 | 8 | 0 |

N_{P} | 5 | 42 | 58 | 7 | 25 | 51 | 771 | 872 | 730 | 715 | 394 | 250 | 168 | 247 | 129 | 42 | 21 | 17 |

N_{F-R} | 0 | 0 | 1 | 46 | 58 | 17 | 49 | 1158 | 574 | 1127 | 640 | 302 | 293 | 193 | 57 | 20 | 9 | 0 |

N_{F-P} | 112 | 25 | 26 | 191 | 1012 | 408 | 149 | 896 | 457 | 247 | 293 | 133 | 127 | 183 | 115 | 90 | 37 | 43 |

**Table 3.**Nash–Sutcliffe efficiency coefficient (NSE) for n-pairs of the relative share of fish caught with multi-mesh Nordic gillnets and hydroacoustic data in TS classes (with a range of 1.5 dB) determined on the basis of the TS–TL relationship according to Equations (1)–(6). Values in bold with an underline indicate the TS (and TL

_{E}) threshold for which a best-fit linear regression can be created.

Equation (1) | Equation (2) | Equation (3) for Family Cyprinidae | Equation (4) for Family Percidae | Equation (5) for Roach | Equation (6) for Perch | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

TS (dB) | TL_{E} (mm) | NSE | TL_{E} (mm) | NSE | TL_{E} (mm) | NSE | TL_{E} (mm) | NSE | TL_{E} (mm) | NSE | TL_{E} (mm) | NSE |

−48.5 | 63.8 | 0.527 | ||||||||||

−47.0 | 76.4 | 0.367 | 62.3 | 0.899 | 64.0 | 0.911 | 62.0 | 0.822 | 93.0 | 0.677 | ||

−45.5 | 91.6 | 0.387 | 73.3 | 0.939 | 74.0 | 0.443 | 74.0 | 0.937 | 75.0 | 0.751 | 103.3 | 0.711 |

−44.0 | 109.7 | 0.833 | 86.3 | 0.932 | 85.6 | 0.262 | 85.6 | 0.916 | 90.8 | 0.797 | 114.6 | 0.576 |

−42.5 | 131.5 | 0.762 | 101.6 | 0.926 | 99.0 | 0.810 | 99.0 | 0.863 | 109.9 | 0.915 | 127.2 | 0.622 |

−41.0 | 157.6 | 0.784 | 119.7 | 0.907 | 114.6 | 0.639 | 114.6 | 0.780 | 133.0 | 0.842 | 141.2 | 0.252 |

−39.5 | 188.8 | 0.780 | 140.9 | 0.803 | 132.5 | 0.978 | 132.5 | 0.558 | 160.9 | 0.873 | 159.7 | −0.332 |

−38.0 | 226.2 | 0.359 | 165.9 | 0.773 | 153.3 | 0.951 | 153.3 | −0.092 | 194.7 | 0.334 | ||

−36.5 | 271.1 | −0.440 | 195.3 | −0.201 | 177.4 | 0.800 | 235.6 | −0.266 | ||||

−35.0 | 205.2 | 0.116 | ||||||||||

−33.5 | 237.4 | 0.065 | ||||||||||

−32.0 | 274.7 | −0.151 |

**Table 4.**Ranges of total length (TL), number of fish, number of investigated species, and their environment in the study of the relationship between target strength (TS) and total length (TL) of fish.

Citation | Equation in This Study | Number of Fish | Length Range (mm) | Number of Species | Environment |
---|---|---|---|---|---|

[7] | 1 | 36 | 48–224 | 8 | Marine-brackish—44% Marine-brackish-Freshwater—25% Freshwater—31% |

[2] | 2 | 40 | 72–710 | 6 | Freshwater (from the Rimov reservoir and local fish farms) |

[20] | 3 | 39 | 60–360 | 4 | Freshwater (from Irtysh River) |

[20] | 4 | 19 | 120–390 | 2 | Freshwater (from Irtysh River) |

[2] | 5 | 8 | 117–305 | 1 (Roach) | Freshwater |

[2] | 6 | 5 | 101–290 | 1 (Perch) | Freshwater |

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## Share and Cite

**MDPI and ACS Style**

Hutorowicz, A.; Ulikowski, D.; Tunowski, J.
Comparison of Size Distribution of Fish Obtained from Gill Netting and the Distributions of Echoes from Hydroacoustics in Lake Dejguny (Poland). *Water* **2023**, *15*, 1117.
https://doi.org/10.3390/w15061117

**AMA Style**

Hutorowicz A, Ulikowski D, Tunowski J.
Comparison of Size Distribution of Fish Obtained from Gill Netting and the Distributions of Echoes from Hydroacoustics in Lake Dejguny (Poland). *Water*. 2023; 15(6):1117.
https://doi.org/10.3390/w15061117

**Chicago/Turabian Style**

Hutorowicz, Andrzej, Dariusz Ulikowski, and Jacek Tunowski.
2023. "Comparison of Size Distribution of Fish Obtained from Gill Netting and the Distributions of Echoes from Hydroacoustics in Lake Dejguny (Poland)" *Water* 15, no. 6: 1117.
https://doi.org/10.3390/w15061117