(Ws) Equations and Standard Length Categories for 18 Warmwater Nongame and Riverine Fish Species

North American Journal of Fisheries Management 20:570±574, 2000 ᭧ Copyright by the American Fisheries Society 2000

Proposed Standard Weight (Ws) Equations and Standard Length Categories for 18 Warmwater Nongame and Riverine Fish Species

TIMOTHY J. BISTER,DAVID W. W ILLIS,* AND MICHAEL L. BROWN Department of Wildlife and Fisheries Sciences, Box 2140B, South Dakota State University, Brookings, South Dakota 57007, USA

STEPHEN M. JORDAN AND ROBERT M. NEUMANN Department of Natural Resources Management and Engineering, Box U-87, University of Connecticut, Storrs, Connecticut 06269, USA

MICHAEL C. QUIST AND CHRISTOPHER S. GUY Kansas Cooperative Fish and Wildlife Research Unit,1 205 Leasure Hall, Division of Biology, Kansas State University, Manhattan, Kansas 66506, USA

Abstract.ÐRelative weight (Wr) is one of several con- ®sh species, Ws equations must ®rst be available. dition indices used to assess the general health of ®shes. Anderson and Neumann (1996) reported accepted Standard weight (Ws) equations are required to calculate W equations for 33 ®sh species. Most of these W , but are unavailable for many nongame and riverine s r species are considered to be sport ®shes. To further ®sh species. Therefore, we developed Ws equations for the following taxa: longnose gar Lepisosteus osseus, assist biologists in ®shery assessments, we devel- spotted gar L. oculatus, common carp Cyprinus carpio, oped Ws equations for the following nongame and bigmouth buffalo Ictiobus cyprinellus, river carpsucker riverine ®sh species: longnose gar Lepisosteus os- Carpiodes carpio, shorthead redhorse Moxostoma ma- seus, spotted gar L. oculatus, common carp Cy- crolepidotum, smallmouth buffalo I. bubalus, white prinus carpio, bigmouth buffalo Ictiobus cyprinel- sucker Catostomus commersoni, black bullhead Ameiu- rus melas, brown bullhead A. nebulosus, ¯athead cat®sh lus, river carpsucker Carpiodes carpio, shorthead Pylodictis olivaris, white cat®sh A. catus, yellow bull- redhorse Moxostoma macrolepidotum, smallmouth head A. natalis, white perch Morone americana, yellow buffalo I. bubalus, white sucker Catostomus com- bass M. mississippiensis, green sun®sh Lepomis cyanel- mersoni, black bullhead Ameiurus melas, brown lus, rock bass Ambloplites rupestris, and warmouth L. bullhead A. nebulosus, ¯athead cat®sh Pylodictis gulosus. These Ws equations were evaluated with statis- olivaris, white cat®sh A. catus, yellow bullhead A. tical validation approaches similar to previously de®ned natalis, white perch Morone americana, yellow regression-line-percentile equations. Standard length categories were developed or revised for 10 of these 18 bass M. mississippiensis, green sun®sh Lepomis cy- species (longnose gar, spotted gar, bigmouth buffalo, anellus, rock bass Ambloplites rupestris, and war- river carpsucker, shorthead redhorse, smallmouth buf- mouth L. gulosus. falo, white sucker, brown bullhead, white cat®sh, and The objectives of this study were to develop or yellow bullhead) to allow for comparison of mean Wr revise W equations for these 18 species, which values within and among length categories instead of s would allow for expanded use of W in population assessing only population mean W . r r and community assessments for these nongame and riverine species. Standard length categories Introduction were also developed or revised for 10 of these species (longnose gar, spotted gar, bigmouth buf- Relative weight (Wr ϭ the ratio of a ®sh's weight, W, to the weight of a ``standard'' ®sh of falo, river carpsucker, shorthead redhorse, smallmouth buffalo, white sucker, brown bullhead, the same length, Ws) is a commonly used ®sh condition index (Blackwell et al. 2000). Before ®shery white cat®sh, and yellow bullhead) so that condition assessment could be evaluated for incre- biologists can assess the utility of Wr for various mental length-groups rather than population mean

Wr values (Murphy et al. 1991). * Corresponding author: david࿞[email protected] 1 The Unit is jointly supported by Kansas Department Methods of Wildlife and Parks, Kansas State University, the U.S. Geological Survey Biological Resource Division, and Letters soliciting contributions of weight±length the Wildlife Management Institute. data for 30 warmwater ®sh species were sent to Received July 26, 1999; accepted December 22, 1999 ®shery administrators of state and provincial con-

570 MANAGEMENT BRIEFS 571

servation agencies and several U.S. Fish and Wild- the Ws equations, a test (Ho:ûϭ 0; P Ͻ 0.05) was life Service regional of®ces. Suf®cient data were conducted to determine if there was a consistent received to develop Ws equations for 18 warm- length-related bias in Wr values calculated with the water species. proposed Ws equation (Willis 1989; Neumann and These Ws equations were developed using the Murphy 1991). Regressions of Wr on ®sh TL were regression-line-percentile (RLP) technique pro- done for each population. We expected that some posed by Murphy et al. (1990). The validity of the populations would have slopes signi®cantly dif- solicited data was assessed by plotting the weight± ferent than zero (P Ͻ 0.05); however, if the num- total length (grams and millimeters, respectively) bers of negative and positive signi®cant slopes relationships for each population separately so that were not signi®cantly different, we accepted the individual outliers could be identi®ed. Outliers, Ws equation. which were probably a result of measurement er- Finally, we determined whether suf®cient pop- rors, were deleted from the data sets. Next, the ulations were available to reliably determine a Ws RLP technique required determination of the min- equation. Brown and Murphy (1996) reported that imum total length (TL) to be used in the Ws equa- a minimum of 50 populations would consistently tion development. Primarily, we sought to avoid provide reliable Ws equations. For data sets with inaccurate or imprecise weights for small ®sh. We fewer than 50 populations, they recommended us- calculated an error estimate (variance to mean ra- ing a bootstrap approach to determine whether the tio) for mean log10weight by centimeter TL group number of populations was suf®cient. Slopes from (SAS Institute 1996), which was then plotted as a each population log10weight±log10TL regression function of TL. The minimum TL was selected were randomly selected at sequential intervals of where variance: mean error was less than 0.02, three, with 100 iterations done to determine the which corresponded to the in¯ection point in the variance about the regression slope means. The plot for each species (Willis et al. 1991). We cal- sample variance for slopes decreased as sample culated a log10weight±log10TL regression equation size increased. We used the benchmark for a min- for each population in the data set using only ®sh imum level of precision (s2 Ͻ 0.002) that was rec- longer than the minimum TL selected in the pre- ommended by Brown and Murphy (1996). vious step. Populations were removed from the Length categories were developed or revised for database at this point if correlation coef®cients (r) 10 of the 18 ®sh species in this study. Gabelhouse were less than 0.90. Slopes were then plotted as a (1984) recommended that minimum stock, quality, function of intercepts (Pope et al. 1995) to identify preferred, memorable, and trophy lengths be set at and remove population outliers caused by insuf- 20±26, 36±41, 45±55, 59±64, and 74±80% of the ®cient sample size, narrow length range, or mis- world record length for each species, respectively. identi®ed length measurements other than TL (i.e., We compared world record lengths, obtained from body length, fork length, or standard length). the National Freshwater Fishing Hall of Fame and After the minimum TL was determined and the the International Game Fish Association, with the data set ®nalized, the Ws equation was developed longest ®sh in our database for each species. We using the RLP technique (Murphy et al. 1990). based the development of the length categories for First, we predicted mean ®sh weight in 1-cm in- a particular species on the longest ®sh in our da- tervals for each population. Then, we found the tabase if that length exceeded the world record 75th percentile of mean weights in each interval length. and regressed these means on TL to determine the Results and Discussion proposed Ws equation. Some previous RLP equations were developed after dividing data sets into The results from steps performed during the a development subset and a subset for testing po- RLP development of these Ws equations are tential length-related bias in Wr values (e.g., Pope lengthy and are therefore summarized in Bister et et al. 1995). This was in reality a test of the RLP al. (1999). These results include population sample method itself. Because the RLP method of Ws size, minimum length determination, population equation development has proven useful (i.e., no log10weight±log10TL regression parameters, boot- length-related bias) in many previous cases, we strap results, proportional stock density (PSD; An- did not believe it was necessary to test the RLP derson and Neumann 1996), and mean Wr by technique again. In addition, many data sets for length category for each population used in the Ws species in this study contained too few populations equation development. Parameters for log10weight to allow splitting into two data sets. To evaluate Ϫ log10length regression formulas for these 18 spe- 572 BISTER ET AL.

TABLE 1.ÐParameters for log10weight Ϫ log10length regression formulas for 18 warmwater ®sh species. Values for metric equations were in millimeters and grams; values for English equations were in inches and pounds. Political units are the number of states or provinces that contributed data for each species. Equations were previously unavailable for all species, except those marked with an asterisk, which are revised.

Intercept (a) Minimum Number of total length Number of political Species Metric English Slope (b) (mm) populations units Longnose gar Ϫ6.811 Ϫ4.623 3.449 200 32 13 Spotted gar Ϫ6.551 Ϫ4.388 3.431 250 47 8 Common carp* Ϫ4.639 Ϫ3.194 2.920 200 167 22 Bigmouth buffalo* Ϫ5.069 Ϫ3.346 3.118 150 39 9 River carpsucker* Ϫ4.839 Ϫ3.293 2.992 130 61 13 Shorthead redhorse Ϫ4.841 Ϫ3.337 2.962 100 45 13 Smallmouth buffalo* Ϫ5.298 Ϫ3.448 3.208 200 66 13 White sucker Ϫ4.755 Ϫ3.282 2.940 100 172 6 Black bullhead Ϫ4.974 Ϫ3.297 3.085 130 87 11 Brown bullhead Ϫ5.076 Ϫ3.371 3.105 130 74 12 Flathead cat®sh Ϫ5.542 Ϫ3.661 3.230 130 74 14 White cat®sh Ϫ5.851 Ϫ3.739 3.395 100 21 6 Yellow bullhead Ϫ5.374 Ϫ3.491 3.232 60 62 12 White perch Ϫ5.122 Ϫ3.373 3.136 80 43 10 Yellow bass Ϫ5.142 Ϫ3.398 3.133 70 22 7 Green sun®sh* Ϫ4.915 Ϫ3.216 3.101 60 43 9 Rock bass* Ϫ4.827 Ϫ3.166 3.074 80 129 12 Warmouth Ϫ5.180 Ϫ3.284 3.241 80 66 12 cies are listed in Table 1. We are proposing revised slopes, 25 were positive and 33 were negative. The

Ws equations for common carp, bigmouth buffalo, occurrence of positive and negative slopes was not river carpsucker, smallmouth buffalo, rock bass, signi®cantly different (␹2 ϭ 0.55, P ϭ 0.46). and green sun®sh. Of these previously available Nuances in length-related condition anomalies

Ws equations, rock bass was the only species for can go undetected if population mean Wr is the which Anderson and Neumann (1996) reported a only aspect of condition assessment. Population

Ws equation. However, while this previous rock mean Wr values should not be calculated unless bass Ws equation was developed using a technique the in¯uence of length has been quanti®ed. Mur- similar to the RLP method, it was based on mean phy et al. (1991) suggested that biologists either weights rather than the 75th percentile (Blackwell plot Wr as a function of ®sh length to look for et al. 2000). Thus, Wr values calculated with the length-related trends or calculate mean Wr values previous equation would be higher than expected within the ®ve-cell length categories proposed by using the proposed 75th percentile RLP equation. Gabelhouse (1984). World record lengths for ®shes

We recommend the use of our revised Ws equation not normally targeted by anglers may not be rep- for rock bass to allow Wr comparisons among spe- resentative of actual growth potential. Therefore, cies (i.e., all based on 75th-percentile standards). we developed minimum lengths for each category

Additionally, the previous Ws equations for com- (stock, quality, preferred, memorable, and trophy) mon carp, bigmouth buffalo, smallmouth buffalo, based on either the world record length or the lon- and green sun®sh were developed with methods gest ®sh in each data set (Table 2), whichever was now considered to be invalid (Murphy et al. 1991; longer. We revised the length ranges proposed by Blackwell et al. 2000). Consequently, we recom- Gabelhouse (1984) for shorthead redhorse because mend the use of our revised Ws equations for these our database contained a ®sh substantially longer species. than the world record length on which original

All Ws equations reported here were tested for length categories were based (Table 2). Although length-related bias in the data sets (Bister et al. these length categories may not seem applicable 1999). For example, the common carp data set to nongame species, this is an accepted method of contained 167 population samples; 109 samples subdividing sampling data for many species and had slopes for the Wr±TL regression that were not should be a useful tool in population condition and signi®cantly different from zero, and 58 samples size structure analyses. had slopes that were signi®cantly different from We had two primary goals when we initiated zero. Of the 58 relationships with signi®cant this study. First, we anticipated that development MANAGEMENT BRIEFS 573

TABLE 2.ÐLength categories (in inches and centimeters) that should be used to calculate mean relative weight (Wr) values and stock density indices (Gabelhouse 1984) for the 18 ®sh species included in this study.

Category Stock Quality Preferred Memorable Trophy Species (in) (cm) (in) (cm) (in) (cm) (in) (cm) (in) (cm) Longnose gara 16 41 27 69 36 91 45 114 55 140 Spotted gara 12 30 19 48 25 64 31 79 39 99 Common carpb 11 28 16 41 21 53 26 66 33 84 Bigmouth buffaloa 11 28 18 46 24 61 30 76 37 94 River carpsuckera 7 18 11 28 14 36 18 46 22 56 Shorthead redhorsec 6 15 10 25 13 33 16 41 20 51 Smallmouth buffaloa 11 28 18 46 24 61 30 76 37 94 White suckera 6 15 10 25 13 33 16 41 20 51 Black bullheadb 6 15 9 23 12 30 15 38 18 46 Brown bullheada 5 13 8 20 11 28 14 36 17 43 Flathead cat®shd 14 35 20 51 28 71 34 86 40 102 White cat®sha 8 20 13 33 17 43 21 53 26 66 Yellow bullheada 4 10 7 18 9 23 11 28 14 36 White perchb 5 13 8 20 10 25 12 30 15 38 Yellow basse 4 10 7 18 9 23 11 28 13 33 Green sun®shb 3 8 6 15 8 20 10 25 12 30 Rock bassb 4 10 7 18 9 23 11 28 13 33 Warmouthb 3 8 6 15 8 20 10 25 12 30 a Developed during current study. b Proposed by Gabelhouse (1984). c Maximum total length in data set (651 mm) was substantially longer than the world record (521 mm); thus, we revised the length ranges proposed by Gabelhouse (1984). d Proposed by Quinn (1991). e Proposed by Anderson and Gutreuter (1983).

of Ws equations for nongame and riverine ®shes Department of Wildlife and Fisheries, Maine De- would allow expanded use of Wr. Secondly, we partment of Inland Fisheries and Wildlife, Mary- hoped that this expansion would lead to continued land DNR, Minnesota DNR, Mississippi State Uni- evaluation of the usefulness of Wr as a ®shery versity, Missouri DOC, Missouri River Benthic assessment tool. For example, Wr can serve as an Fishes Group, Nebraska Game and Parks Com- indicator of prey availability (Wege and Anderson mission, New Brunswick Department of Natural 1978; Liao et al. 1995; Marwitz and Hubert 1997; Resources and Energy, New York Department of Porath and Peters 1997). With current interest in Environmental Conservation, North Carolina ecosystem-level approaches to management, we Wildlife Resources Commission, North Dakota also hope that these Ws standards will facilitate Game and Fish Department, Nova Scotia Depart- assessment at the community level. ment of Fisheries and Aquaculture, Oklahoma De- partment of Wildlife Conservation, Oregon De- Acknowledgments partment of Fish and Wildlife, Saskatchewan En- This project was sponsored by the Fisheries vironment and Resource Management, South Da- Management Section and Fisheries Administrators kota Department of Game, Fish and Parks, Section of the American Fisheries Society. We Tennessee Valley Authority, Tennessee Wildlife would like to thank the following agencies for con- Resources Agency, Texas Parks and Wildlife De- tributing information for this project: Alabama De- partment, U.S. Fish and Wildlife Service, U.S. partment of Conservation (DOC), Arkansas Game Geological Survey, Utah DNR, Vermont Depart- and Fish Commission, Colorado Department of ment of Fish and Wildlife, Virginia Department of Natural Resources (DNR), Connecticut Depart- Game and Inland Fisheries, Washington Depart- ment of Environmental Protection, Delaware De- ment of Fish and Wildlife, Wisconsin DNR, and partment of Natural Resources and Environmental the Wyoming Game and Fish Department. We Control, East Carolina University, Florida Game would also like to thank the following individuals and Freshwater Fish Commission, The Hudson whose efforts in contributing data made this pro- River Foundation, Indiana DNR, Iowa DNR, Kan- ject possible: M. Baird, C. Batsavage, D. Benson, sas Department of Wildlife and Parks, Louisiana J. Benton, M. Bivin, B. Blackwell, M. Boone, M. 574 BISTER ET AL.

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