Regression-line-percentile Research Articles

Proposed standard weight (W s) equation and standard length categories for Goldeye

Abstract Objective Goldeye Hiodon alosoides relative weight (Wr) and proportional size distribution (PSD) have not been able to be evaluated in populations across their range. The objective of this project was to develop and assess standard weight (Ws) equations with three different techniques along with developing standard length categories for Goldeye. Methods Length and weight data for 64,435 Goldeye Hiodon alosoides from 96 populations across Canada and the United States were collected to develop a Ws equation. We developed standard weight equations for Goldeye with the regression-line-percentile (RLP), empirical-percentile linear (EmP-L), and empirical-percentile quadratic (EmP-Q) techniques. Result We propose the RLP equation as log10W = 2.979 × log10L − 4.979, the EmP-L equation as log10W = 3.048 × log10L − 5.151, and the EmP-Q equation as log10W = 1.254 × log10L + 0.365 × (log10L)2 − 2.950, where W is weight (g) and L is total length (TL, mm). We also developed PSD length categories of 13, 20, 26, 33, and 40 cm TL representing stock, quality, preferred, memorable, and trophy categories, respectively. Conclusion These Ws equations and standard length categories will aid fisheries biologists in assessing Goldeye populations holistically across their range when developing management strategies.

Proposed Standard Weight (W s) Equations and Standard Length Categories for Redbreast Sunfish and Spotted Sunfish

Abstract We developed standard weight (Ws ) equations for Redbreast Sunfish Lepomis auritus and Spotted Sunfish L. punctatus using the traditional regression-line-percentile (RLP) technique and the empirical-percentile-linear (EmP-L), and the empirical-percentile quadratic (EmP-Q) method. Individual length and weight data for 175,541 Redbreast Sunfish from 8 to 31 cm TL across 315 populations and 66,851 Spotted Sunfish from 7 to 21 cm TL across 130 populations were used in the final analysis. These fish were collected from 1975 to 2021 by various agency and university personnel from most known populations across the species' native and introduced ranges in North America. We present the EmP-L-derived Ws equations for the Redbreast Sunfish as log10W = 3.1218 × log10L − 5.0018 and the Spotted Sunfish as log10W = 3.3343 × log10L − 5.3739, where W is weight (g) and L is total length (TL, mm). Equations from all methods exhibited length-related bias, but the EmP-L equations had a median bias of 0–0.6 for the length range that comprised 99.7% (for 8–24 cm TL) of Redbreast Sunfish and 99.0% (for 7–18 cm TL) of Spotted Sunfish in our data set. Regardless of the equation, the most bias was found at the upper end of the length spectrum, so we do not recommend these equations for Redbreast Sunfish ≥30 cm TL or Spotted Sunfish ≥20 cm TL. We also developed standard length categories for Redbreast Sunfish with minimum lengths for five standard length categories of 8, 13, 18, 20, and 25 cm TL for stock, quality, preferred, memorable, and trophy sizes and for Spotted sunfish 5, 10, 13, 15, and 18 cm TL, respectively. Development of a Ws equation and standard length categories will aid biologists in assessing condition and size structure of wild Redbreast Sunfish and Spotted Sunfish populations and those being propagated for supplemental stocking into areas with depressed native populations.

Proposed Standard Weight (Ws) Equation and Length Categories for Utah Chub

Abstract Condition indices, such as relative weight (Wr), provide a simple method for comparing length–weight relationships among populations. However, no standard weight (Ws) equation has been developed for Utah Chub Gila atraria, a species of important management focus in the Intermountain West. We obtained length–weight data for 30,541 Utah Chub from 24 populations in Idaho, Montana, Utah, and Wyoming. We used the regression line percentile (RLP), linear empirical percentile (EmP), and quadratic EmP methods to develop average (50th percentile) and above average (75th percentile) Ws equations. Additionally, Froese’s method was used to develop another Ws equation for Utah Chub. Length-related biases were detected in Ws equations developed using the RLP, 50th percentile quadratic EmP, and Froese methods. The linear EmP Ws equations did not exhibit length-related biases for the 50th and 75th percentiles. We propose using the 75th percentile linear EmP Ws equation for Utah Chub between 90 and 410 mm TL. The EmP 75th percentile equation was log10(Ws) = −4.938 + 3.031·log10(TL), where Ws is weight in grams and TL is in millimeters. The English equivalent of this equation is log10(Ws) = −3.335 + 3.031·log10(TL), where Ws is weight in pounds and TL is in inches for 4–16-in Utah Chub. Additionally, we propose that minimum TLs of 100 mm (4 in; stock), 200 mm (8 in; quality), 250 mm (10 in; preferred), 300 mm (12 in; memorable), and 380 mm (15 in; trophy) be used to calculate proportional size distribution (PSD) indices. Better understanding Utah Chub populations using Wr and PSDs will aid managers in assessing management strategies (e.g., biological controls) focused on Utah Chub.

Proposed Standard Weight (Ws) Equations for Arctic Grayling

AbstractRelative weight (Wr) is an index that is commonly used by fisheries managers to evaluate the condition within and among fish populations. Managers also use Wr comparisons to assess condition dynamics among species. Rather than using population‐level mean Wr for comparisons, standard length categories are frequently used to evaluate mean Wr differences among length categories. To establish Wr values for a species, a species‐specific standard weight (Ws) equation is required. Regression‐line‐percentile (RLP) and empirical‐percentile (EmP) methods were used with length–weight data that were collected from 50 Arctic Grayling Thymallus arcticus populations in the United States and Canada. The RLP method yielded a Ws equation of log10Ws(g) = −5.241 + 3.083 log10TL(mm) and the EmP method of log10Ws(g) = −5.279 + 3.096 log10TL(mm). These equations were developed to calculate relative weights (Wr) for fish measuring 150 mm total length (TL) and greater. Subsequent analysis did not reveal significant systematic length‐related bias in the application of either Ws equation. Furthermore, differences in Ws calculations between the methods were at most 2.2% over the lengths that we observed. Our findings highlight the relative importance of using a robust data set when calculating Ws equations over the method used to calculate Ws. We suggest that both equations are valid and managers should report which Ws equation was used.

Proposed Standard Weight (W s) Equation and Standard Length Categories for Shoal Bass

Abstract Standard weight (Ws) equations have been proposed for a variety of fishes, including many of the black basses Micropterus spp. We developed Ws equations for Shoal Bass M. cataractae by using the traditional regression-line-percentile (RLP) technique and the relatively new empirical-percentile (EmP) method. Length and weight data for 9,058 Shoal Bass from 15 populations were used in this analysis. These fish were collected from 1978 to 2017 by various agency and university personnel from most of the known populations across the species’ range in Alabama, Florida, and Georgia. The resulting Ws equations were log10W = 3.243·log10L − 5.490 for the RLP technique and log10W = 1.225·log10L + 0.415·(log10L)2 – 3.052 for the quadratic EmP technique, where W is weight (g) and L is TL (mm). Unlike the quadratic EmP equation, the RLP equation exhibited a slight length-related bias on each end of the length spectrum, so we recommend the EmP technique as the preferred equation for this species. To assess fish population size structure, we also propose minimum lengths for five standard TL categories of 18, 28, 35, 43, and 51 cm for stock, quality, preferred, memorable, and trophy sizes, respectively. Development of a Ws equation and standard TL categories will aid biologists in evaluating and monitoring Shoal Bass populations as part of continuing conservation efforts.

Proposed standard mass equations for European chub Leuciscus cephalus in Italy

Total length (L(T)) and mass measurements of 28,596 specimens of European chub Leuciscus cephalus, collected from a variety of waterways across Italy, were used to compute standard mass (W(s)) equations by both empirical percentile (EmP) and regression line percentile (RLP) methods. The use of the EmP W(s) equation [log(10) W(s) = -4·79 + 2·68log(10) L(T) + 0·10(log(10) L(T))(2)] to compute relative mass (W(r)) of L. cephalus in Italy is suggested, as it was not influenced by length-related bias (L(T) range of application = 70-470 mm).

Proposed Standard Weight (Ws) Equation and Standard Length Categories for Suwannee Bass

Abstract We developed standard weight (Ws) equations for Suwannee bass Micropterus notius using the traditional regression-line-percentile (RLP) technique and the newer empirical-percentile (EmP) method. Length and weight data for 2,137 Suwannee bass at least 11 cm total length (TL) collected from all 10 populations within the species' narrow geographic range were used to develop the equations. The resulting Ws equations were log10 W = −5.548 + 3.303 × log10 L and log10 W = −1.014 − 0.583 × log10 L + 0.828 × (log10 L)2 (where W is weight in grams and L is TL in millimeters) for the RLP and quadratic EmP techniques, respectively. The RLP-derived Ws equation exhibited a small (<4%) bias that varied by length-group but that was insignificant for management purposes. To assess fish population size structure, we also propose minimum lengths for five standard length categories of 15, 25, 30, 35, and 40 cm TL for stock, quality, preferred, memorable, and trophy sizes, respectively. Urban development and the recent introduction of nonnative species into some of these systems pose threats to the conservation of this rare black bass. Thus, the development of a Ws equation and standard length categories will aid biologists in evaluating and monitoring Suwannee bass populations as part of continuing conservation efforts.

Assessing Length-Related Bias and the Need for Data Standardization in the Development of Standard Weight Equations

Abstract The recently developed empirical percentile (EmP) method, a technique for deriving standard weight (Ws) equations, putatively reduces the length-related biases that often plague such equations. To determine whether the EmP method is superior to the regression line–percentile (RLP) method in reducing length-related biases, we developed new Ws equations by applying both methods to two morphologically distinct species, walleye Sander vitreus and black crappie Pomoxis nigromaculatus. We also investigated diagnostic approaches to provide quality control for weight–length data. We evaluated the new Ws equations with filtered independent data to determine which equation reduced length bias the most. We suggest a protocol for evaluating length-related bias using an independent data set. Our results showed that for randomly selected walleye populations, the RLP method did not have any length-related biases when relative weight (Wr) was plotted as a function of length. However, the Wr values calculated from the EmP Ws equations were length biased when the latter were applied to those same populations. Both methods generated Ws equations that were length biased when Wr was plotted as a function of length for black crappies. Further, the absolute difference in Wr between the RLP and EmP methods indicates that there is little difference between the methods as far as their relevance to management is concerned. Based on these results, we believe that revising existing Ws equations using the EmP method is unnecessary and that the RLP technique should remain the standard for developing Ws equations pending the development of an approach that clearly eliminates methodological length bias.

Biases with the Regression Line Percentile Method and the Fallacy of a Single Standard Weight

AbstractThe regression line percentile (RLP) method for computing standard weight (Ws) equations produces third‐quartile estimates that tend to be biased downward for long fish as a result of extrapolation acting in concert with systematic variation in the distribution of length–weight relationships among fish populations. Parameter mismatch in the development and use of Ws equations (i.e., third quartile for development of Ws equations and use of mean relative weight Wr for application and testing) induces artifactual biases when testing equations and leads to the appearance of reduced fish condition when applied to longer fish. Consistent interpretation of mean Wr against a single standard (e.g., third quartile, median, or any other) is not usually possible due to nonconstant variation in the distributions of mean Wr among species and among length‐classes for a given species. I recommend that future computations of Ws use quadratic equations for all three quartiles to enable consistent and more informative interpretation of mean Wr.

Ruffe Length–Weight Relationships with a Proposed Standard Weight Equation

AbstractRuffe Gymnocephalus cernuus length–weight data from 141 data sets were obtained from a variety of waters across Europe and the Laurentian Great Lakes for summarization and development of standard weight (Ws) equations. The mean slopes of the length–weight relationships from all populations and for all percentiles except the 95th percentile were not different from 3.0, suggesting that ruffe growth is generally isometric. The Ws equations developed using the regression line percentile, linear empirical percentile (EmP), and Froese's methods exhibited length‐related biases. The quadratic EmP Ws equations for the 75th and 50th percentiles did not exhibit length‐related biases and thus can be used to compute the relative weight of ruffe. The EmP 75th percentile Ws equation was log10(Ws75) = −2.5800 + 0.6210·log10(total length, TL) + 0.6073·[log10(TL)]2, and the 50th percentile Ws equation was log10(Ws50) = −3.3524 + 1.3969·log10(TL) + 0.4054·[log10(TL)]2 when constrained to ruffe between 55 and 205 mm TL. We propose that the minimum TL for a five‐cell length categorization system used to compute stock indices for ruffe be 55, 90, 120, 140, and 175 mm TL. These results provide a method for computing relative weight indices for typical (50th percentile) and above‐average (75th percentile) ruffe; this method will allow comparisons of body condition across time, among habitats, among bodies of water, and among length categories.

Development and Evaluation of Standard Weight Equations for Bridgelip Suckers and Largescale Suckers

AbstractFisheries assessment tools originally created for use with game fish populations are now helping to assess individual nongame species and to evaluate fish communities. Length and weight measurements of individuals within a species can be summarized into condition indices that give insight into the health and condition of the individual and the aquatic community. Such data (weight (g) and total length (TL, mm)) were obtained for 105 populations of bridgelip suckers Catostomus columbianus and 135 populations of largescale suckers C. macrocheilus from three northwestern states. These data were used to develop standard weight (Ws) equations via the regression‐line percentile (RLP) and empirical percentile (EmP) methods. Length constraints were 130–460 mm TL for bridgelip suckers and 170–640 mm TL for largescale suckers. The data set was limited by TL constraints and split into development and validation sets. The RLP method yielded the following Ws equations: log10Ws = −5.01699 + 3.02648·log10TL for bridgelip suckers and log10Ws = −4.94684 + 2.99720·log10TL for largescale suckers. Equations based on the EmP method were log10Ws = −5.09721 + 3.04947·log10TL for bridgelip suckers and log10Ws = −5.2586 + 3.12136·log10TL for largescale suckers. For both species, the relative weights produced from RLP and EmP equations differed by less than 10%. However, differences were inconsistent over the length range, indicating a length‐related bias. Based on this assessment, use of EmP Ws equations for bridgelip suckers and largescale suckers is recommended. Further, the EmP method should be used to establish new Ws equations.

A New Method to Compute Standard-Weight Equations That Reduces Length-Related Bias

Abstract We propose a new method for developing standard-weight (Ws) equations for use in the computation of relative weight (Wr) because the regression line–percentile (RLP) method often leads to length-related biases in Ws equations. We studied the structural properties of Ws equations developed by the RLP method through simulations, identified reasons for biases, and compared Ws equations computed by the RLP method and the new method. The new method is similar to the RLP method but is based on means of measured weights rather than on means of weights predicted from regression models. The new method also models curvilinear Ws relationships not accounted for by the RLP method. For some length-classes in some species, the relative weights computed from Ws equations developed by the new method were more than 20 Wr units different from those using Ws equations developed by the RLP method. We recommend assessment of published Ws equations developed by the RLP method for length-related bias and use of the new method for computing new Ws equations when bias is identified.

Relative Weight as a Body Condition Index for Chain Pickerel

ABSTRACT Weight-length data from 115 chain pickerel Esox niger populations from 13 states and one Canadian province were used to develop a standard weight (Ws) equation that would allow calculation of relative weight (Wr) values. We developed the 75th-percentile Ws equation using the regression-line-percentile (RLP) method. The proposed Ws equation is log10 Ws(g) = −5.824 + 3.243 log10total length (TL; mm). The English equivalent of this equation is log10 Ws(lb) = −3.293 + 3.243 log10TL(in). The equation is useful for 150 mm and longer chain pickerel. We found no evidence of consistent trends of increasing or decreasing Wr values calculated with the proposed RLP Ws equation. We recommend the use of the proposed RLP Ws equation for assessment of chain pickerel body condition. The proposed Ws equation should serve as a basis for further evaluation of Wr as an index to growth and other physiological trends for chain pickerel.

Proposed Revision of the Standard-Weight Equation for Rainbow Trout

ABSTRACT We developed standard-weight equations for rainbow trout by applying the regression-line-percentile (RLP) technique to samples from 81 lotic and 50 lentic populations from across North America. Because the length-weight relationship differed between lotic and lentic fish populations, we developed separate equations for those populations. They are log10Ws= −5.023 + 3.024log10TL (lotic) and log10Ws= −4.898 + 2.990log10TL (lentic), where Ws is the standard weight in grams and TL is the total length in millimeters. The equivalent English-unit lotic and lentic RLP equations are log10Ws= −3.432 + 3.024log10TL and log10Ws = −3.354 + 2.990log10TL, respectively, where Ws is the standard weight in pounds and TL is the total length in inches. Computed Wr values using the RLP equations did not systematically change with increasing fish length. Significant differences in Wr were not observed between samples from lotic and lentic populations or among length categories when our RLP equations were used.

Management: Briefs Selection of a Minimum Sample Size for Application of the Regression-Line–Percentile Technique

Abstract Proper application of the relative weight (Wr ) index depends on development of a standard weight (Ws ) equation for the target species. Development of Ws equations has been facilitated by the regression-line–percentile (RLP) technique, but the minimum data needed to develop a Ws equation with the RLP technique has not been investigated. We applied the bootstrap technique to data sets containing slope values from population log10 weight–log10 total length regressions for nine fish species (50–292 populations each). We randomly selected regression slopes at sequential intervals of five, and each iteration was repeated 100 times to determine the variance about the regression slope means. The sample variance for slopes was observed to decline in an exponential fashion. A minimum level of precision based on the sample variance (<0.002) provided a conservative estimate of necessary sample size (N ≥ 50). This variance benchmark is sufficient for the current level of precision required in the developmen...

A Revised Standard Weight (Ws) Equation for Channel Catfish

ABSTRACT Weight and length data were obtained from state, regional, and provincial biologists for 241 channel catfish (Ictalurus punctatus) populations, representative of the species geographic range. We randomly selected 60% of the populations to develop a new standard weight (Ws) equation and used the remainder as an independent test set. The regression-line-percentile (RLP) technique was applied to the development data set providing a 75th percentile-based metric Ws equation of log10 Ws (g) = −5.800 + 3.294 log10 total length (TL, mm). The English equivalent is log10 Ws (lb) = −3.829 + 3.294 log10 TL (in). The remaining 98 populations were used to test both current and new Ws equations for length-related changes in relative weight (Wr) values. Regression of Wr values on TL by population showed that the current equation produced 15% more slopes that were significant (H0: β = 0) than did the new equation. An analysis of significant slopes produced from the RLP-generated equation showed a ratio of 31 positive to 20 negative slopes. The current equation yielded a ratio of 58 positive to 7 negative slopes. Because of the length-related trends in Wr values associated with the current equation we recommend that researchers apply the new RLP equation to field data for further testing and validation. The new RLP Ws equation is valid for application to channel catfish having a TL of 70 mm or greater, as opposed to a minimum TL of 280 mm recommended for the current equation.

Proposed Revision of the Standard Weight (Ws) Equation for Redear Sunfish

ABSTRACT Weight-length data were compiled from 289 redear sunfish Lepomis microlophus populations. We applied the regression-line-percentile (RLP) technique to weight-length data for 150 redear sunfish populations to develop a new 75th-percentile standard weight (Ws) equation. The proposed RLP Ws equation, log10 Ws = −4.968 + 3.119log10TL where Ws is the standard weight in grams and TL is the total length in millimeters, is valid for fish >70 mm TL. The English-unit equivalent, log10Wg = −3.263 + 3.119log10TL where Ws is the standard weight in pounds and TL is the total length in inches, is valid for fish >3 in TL. We used the remaining 139 independent populations to evaluate the current [log10 Ws = −5.164 + 3.227(log10TL)] and RLP Ws equations for any length-related biases. We confirmed that the current Ws equation is length-biased. That is, relative weight (Wr) values significantly decreased with increasing fish length for far more populations (N=45) than they increased (N=7). We tested the proposed RLP...

Relative Weight (Wr) as a Field Assessment Tool: Relationships with Growth, Prey Biomass, and Environmental Conditions

We evaluated the relative weight (Wr) condition index as a field assessment tool with pumpkinseed Lepomis gibbosus and golden shiner Notemigonus crysoleucas, focusing on sources of variability and potential of Wr as a predictor of growth, prey availability, and environmental conditions in 10 southern Quebec lakes over 2 years. To allow calculation of Wr, we developed standard weight (Ws) equations for both species, using the regression-line-percentile (RLP) technique. The proposed Ws equation in metric units (grams wet weight and millimeters total legnth, TL) for pumpkinseed is log10Ws = –5.179 + 3.237 log10TL; for golden shiner it is log10Ws = –5.593 + 3.302 log10TL. Spatial and temporal variation in Wr was highly significant and largely asynchronous in both species, although spring values were lowest in most lakes. The Wr index frequently varied with length, prompting us to examine relationships in stock and quality length fish separately. We found little evidence for a relationship between Wr and growth in either species. Pumpkinseed Ws were positively correlated with total benthic invertebrate biomass: stock length Wr was positively correlated with chironomid biomass, and quality length Wr was positively correlated with gastropod biomass. The relative weight of quality length golden shiners was positively correlated with chironomid biomass. Our results and those of other studies suggest that the common assumption of a relationship between Wr and growth in field populations should be reconsidered, but that Wr could be cautiously used as a working index of prey availability. We recommend empirical or experimental verification when Wr is used as an assessment tool in field populations.

Proposed Revision of the Standard Weight (WS) Equation for Smallmouth Bass

Abstract Weight-length data from 50 populations of smallmouth bass Micropterus dolomieu (N = 6,731) in 19 states were used to develop a revised standard weight (WS ) equation for smallmouth bass. The regression-line–percentile (RLP) technique was used to develop the proposed 75th-percentile WS equation from length-weight regressions for individual smallmouth bass populations. The proposed Ws equation, log10 WS (weight, g) = –5.329 + 3.200 log10 L(total length, mm), is valid for fish 150 mm long and longer. The English-unit equivalent, log10 WS (lb) = –3.491 + 3.200 log10 L(total length, in), is valid for fish 6 in long and longer.

Evaluation of the Relative Weight (Wr) Index for Assessment of White Crappie and Black Crappie Populations

Abstract We evaluated a large data set and confirmed that current standard weight (Ws ) equations for white crappies Pomoxis annularis and black crappies P. nigromaculatus are length-biased. We applied the regression-line-percentile (RLP) technique to length-weight data for 27,002 white crappies (175 populations) and 21,709 black crappies (80 populations) to develop new 75th-percentile Ws relationships. The proposed Ws equations are log10 Ws (g) = –5.642 + 3.332 log10TL(mm) for white crappies and log10 Ws (g) = –5.618+ 3.345 log10TL(mm) for black crappies; TL is total length. There was no systematic bias evident in Wr values (Wr = 100· W /Ws ; W is individual fish weight) calculated with the RLP-generated equations. Frequency distributions of population-mean Wr values were consistent with those from studies of other fish species. No regional trends in Wr were observed. Moderate correlations were found between Wr and population structure. Relative weight was generally highest in the spring, decreased after...