Empirical Percentile Standard Weight Equation ... - Wiley Online Library

North American Journal of Fisheries Management 28:1843–1846, 2008 Ó Copyright by the American Fisheries Society 2008 DOI: 10.1577/M07-193.1

[Management Brief]

Empirical Percentile Standard Weight Equation for the Blacktail Redhorse ANDREW L. RYPEL* Department of Biological Sciences, University of Alabama, Box 870206, Tuscaloosa, Alabama 35487-0206, USA

TRACY J. RICHTER Idaho Power Company, Environmental Affairs Department, 1221 West Idaho Street, Boise, Idaho 83703, USA Abstract.—We generated a standard weight (Ws) equation for the blacktail redhorse Moxostoma poecilurum by use of the empirical percentile (EmP) method. Length and weight data were compiled from 3,098 individuals representing 60 populations across five states in the southeastern USA. These data were subsequently used to create the Ws equation. The species’ total length (TL) constraints (130–450 mm) were used to produce the final Ws equation: log10Ws ¼ 5.182 þ 3.087 log10TL. No length-related bias could be detected from the equation, indicating that it is a strong Ws equation. A separate data set from 42 populations and 179 individuals was used to validate the Ws equation. We recommend use of this equation for assessment of blacktail redhorse population dynamics, and we contend that creation of EmP Ws equations for other nongame fishes would be useful in management of fish communities as a whole.

Fishery managers regularly calculate condition factors to assess the overall health and productivity of freshwater fish populations (Gutreuter and Childress 1990; Miranda 1993; DiCenzo et al. 1995; Didenko et al. 2004). Condition factors reflect important fish physiological characteristics, such as lipid storage, body morphology, and growth rate (Liao et al. 1995; Anderson and Neumann 1996; Bister et al. 2000; Froese 2006; Rypel et al. 2006; Stevenson and Woods 2006). Over the last 20 years in the USA, relative weight (Wr) has emerged as the most popular index for assessing condition of freshwater fish (Wege and Anderson 1978; Murphy and Willis 1991; Guy et al. 2002; Gerow et al. 2004). Values of Wr that are far below 100 for an individual, size-group, or population suggest problems such as low prey availability or high predator density, whereas values well above 100 indicate a prey surplus or low predator density (Anderson and Neumann 1996). The Wr is calculated by the equation: * Corresponding author: [email protected] Received October 29, 2007; accepted June 24, 2008 Published online December 18, 2008

Wr ¼ ðW=Ws Þ 3 100; where W is the weight of a particular fish and Ws is the predicted standard weight for that same fish as calculated from a composite of length–weight regressions throughout the range of the species. Until recently, Ws equations were developed by use of the regression line percentile (RLP) method. However, Gerow et al. (2004) described significant length-related biases for Ws equations developed with the RLP method. Biases originate from a statistical phenomenon referred to as the bow-tie effect, which is characterized by grossly over- or underestimated weight predictions (i.e., Ws) at the extremes of the fish size continuum (Gerow et al. 2004). Managers were encouraged to develop future Ws equations by using the empirical percentile (EmP) method (Gerow et al. 2005). Blacktail redhorses Moxostoma poecilurum are distributed in the southeastern USA and occur naturally in Gulf-slope drainages from the Choctawhatchee River west to Galveston Bay, including the Mobile and Lower Mississippi River drainages (Boschung and Mayden 2004). The species is purportedly stable (Boschung and Mayden 2004), but virtually nothing in known about its population trends or general characteristics. Because populations of many other southeastern sucker species are known to have exhibited widespread declines in recent times (Hand and Jackson 2003; Cooke et al. 2005; Grabowski and Isely 2006), any management tools that can assist in conserving southeastern suckers would be advantageous. In this study, we used the EmP method to develop a Ws equation for the blacktail redhorse. Methods Length and weight data for blacktail redhorses were solicited and field collected across the entire range of the species. Population samples with fewer than 10 individuals were excluded from further analysis. Data from each population were examined graphically for

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between the two methodologies are presented. All statistical analyses were performed with the Statistical Analysis System (SAS). Results and Discussion

FIGURE 1.—Blacktail redhorse relative weights produced by the empirical percentile (EmP) equation (black circles) or the EmP quadratic (EmP-Q) equation (white circles) and plotted in relation to total length. Because of the high degree of similarity in results, symbols representing the two equations are superimposed such that the black circles are concealed by the white circles.

the presence of outliers; two populations were excluded for this reason. To minimize inconsistency associated with spawning, data collected during March and April (the known spawning months for the species; Boschung and Mayden 2004) were also excluded. A minimum total length (TL) was calculated to account for variability associated with polymorphism and weighing accuracies in small fish. Minimum TL was calculated as the inflection point of the variance : mean ratio of log10(weight) for 10-mm length-classes (Murphy et al. 1990). Biases associated with larger fish were accounted for by establishing a maximum TL. Using the methods of Gerow et al. (2005), we plotted the number of fish populations per 10-mm length-class and calculated the maximum TL as the value at which the number of fish populations per length-class fell to three. After TL constraints were established, the initial data were parsed into two sets: a large development data set and a small validation data set. The Ws equation was developed by applying the EmP method to the development data set. Mean log10TL and log10(weight) were calculated for each 10-mm length-group. The third quartile of mean weight was regressed against TL to develop the EmP equation. We used the validation data set to validate the proposed Ws equations. After calculating Wr values from the EmP Ws equation, we plotted the residuals against log10TL to visually determine whether any linear or quadratic trends were present. To further illustrate the importance of using the EmP methodology, we also developed a Ws equation with the RLP method using the same data sets described above. Comparisons

The development data set consisted of 3,098 individual fish from 60 populations across Florida, Alabama, Mississippi, Louisiana, and Texas. Only populations with more than 10 individuals were included. The length range established for blacktail redhorses was 130–450 mm TL. Nine fish exceeding 450 mm were excluded from the development data set (the longest of these fish was 585 mm TL). The validation data set was limited to 179 fish from 42 populations. The EmP equation for blacktail redhorses is log10 Ws ¼ 5:182 þ 3:087 log10 TL: Based on this equation, variation in log10TL explained 99% of the variation in log10(weight) (i.e., R2 ¼ 0.99, P , 0.0001). The EmP methodology also calls for fitting a quadratic component to the data. The EmP quadratic equation (EmP-Q) for the blacktail redhorse is log10 Ws ¼ 5:451 þ 3:312 log10 TL 0:0468 ðlog10 TLÞ2 : The EmP-Q equation was significant overall (R2 ¼ 0.99, P , 0.0001); however, the quadratic portion did not add to the significance of the linear equation (P ¼ 0.63). We calculated Wr for the validation data set using both the EmP and the EmP-Q equations; plots of Wr against TL based on the two equations were indistinguishable (Figure 1). For this reason, we recommend that managers use the simpler, linear version of the EmP equation. When EmP Wr was plotted against TL for the validation data set, no sizerelated bias was detected (slope ¼ 0.007, R2 ¼ 0.0002). A Ws equation was also developed using the RLP method. The RLP equation for the blacktail redhorse is log10 Ws ¼ 4:989 þ 3:017 log10 TL: A plot of RLP residuals against TL showed a pattern (Figure 2) that suggested a dependency between the residuals and TL. However, no pattern was apparent in the plot of EmP residuals against TL (Figure 2). Consistent with previous research comparing RLP and EmP equations (e.g., Richter 2007), the magnitude of RLP residuals was smaller than that of EmP residuals. However, this difference was caused by a loss in variability when transitioning from actual means (EmP) to modeled means (RLP); therefore, the magnitude of


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FIGURE 2.—Residuals of relative weight plotted in relation to log10(total length) of blacktail redhorses sampled throughout the southeastern USA; relative weights were calculated by the empirical percentile (EmP) method (white circles) or the regression line percentile (RLP) method (black circles).

residuals should not be viewed as representing whether an equation is ‘‘better’’ or ‘‘worse,’’ because the two equations are based on fundamentally different types of data. However, any directional bias observed (such as that for the RLP equation) is critical and should be noted. In the validation data set, Ws values based on the EmP method were higher than those based on the RLP method. To summarize differences between Ws equations, we plotted RLP and EmP values of Wr against TL (Gerow et al. 2005); in some cases, the Wr values differed by as much as 16%, but the difference was not consistent and decreased with increasing length (Figure 3). These results further confirm that managers should use EmP equations in preference to RLP equations whenever possible and that future equations should be developed with the EmP methodology alone. Several recent studies have espoused the use of Wr for assisting in the management and conservation of nongame fishes, particularly those that are threatened or endangered (Bister et al. 2000; Didenko et al. 2004; Richter 2007). This is based on known positive relationships between fish relative condition, fish growth rate, and quality of aquatic ecosystems (Bister et al. 2000; Didenko et al. 2004; Rypel et al. 2006; Rypel and Layman 2008). As managers begin the arduous task of developing management policy geared toward conservation of both game and nongame fishes, rapid acquisition of population-level metrics for nongame fishes is inherently necessary (Minckley et al. 2003; Cooke et al. 2005; Grabowski and Isely 2006). In the past, Wr has provided basic information on the ecology of game fishes that has shaped sound game fish management policy; analogous approaches hold promise for aiding in conservation of countless

FIGURE 3.—Blacktail redhorse relative weights produced by the empirical percentile (EmP) equation (black circles) or the regression line percentile (RLP) equation (white circles) and plotted in relation to total length.

nongame fishes. Many sucker populations have suffered regrettable population declines over the last 30 years, such that swift yet sound conservation measures are currently sought to arrest these trends (Hand and Jackson 2003; Cooke et al. 2005; Kennedy and Vinyard 2006). Whereas little data or guidance exists on the age and growth of many sucker species, Wr provides a rapid, accessible, and noninvasive metric for identifying potentially at-risk sucker populations (e.g., those with a low mean Wr). Moreover, many agencies currently have long-term data sets describing sucker lengths and weights; this information would allow for immediate detection of any long-term declines in condition that may have occurred, possibly as a result of environmental change. Because relative condition integrates key physiological components of fish life history (e.g., lipid storage and growth), it offers a strong, accessible metric that managers can use to assess the overall health and fitness of sucker populations as well as population-level responses to ecosystem disturbance (Propst and Gido 2004; Mueller 2005; Quist et al. 2005; Rypel et al. 2006; Rypel and Layman 2008). We recommend use of the EmP Ws equation for calculation of blacktail redhorse Wr, which can be employed in conjunction with other population metrics (e.g., age and growth) to aid in developing future management plans and obtaining a basic knowledge of blacktail redhorse population ecology. Acknowledgments We thank the following persons and agencies who graciously contributed length and weight data used in this study: W. Garrett, Jr. and J. Mitchell (Alabama Power Company); S. Rider, K. Floyd, P. Ekema, R. Andress, J. Moss, J. Haffner, G. Lovell, D. Armstrong,


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and K. Weathers (Alabama Department of Conservation and Natural Resources); D. Bayne, W. Seesock, and E. Reutebuch (Auburn University); T. Kennedy, A. Benke, and R. Findlay (University of Alabama); K. Meals (University of Mississippi); D. Riecke (Mississippi Department of Wildlife, Fisheries, and Parks); T. Hall (National Council for Air and Stream Improvement); S. Miranda (Mississippi State University); W. Kelso (Louisiana State University); and D. Terre (Texas Parks and Wildlife Department). This research was supported by a University of Alabama Graduate Student Fellowship, the University of Alabama Department of Biological Sciences, and the David R. Bayne Scholarship of the Alabama Fisheries Association. References Anderson, R. O., and R. M. Neumann. 1996. Length, weight and associated structural indices. Pages 447–482 in B. R. Murphy and D. W. Willis, editors. Fisheries techniques, 2nd edition. American Fisheries Society, Bethesda, Maryland. Bister, T. J., D. W. Willis, M. L. Brown, S. M. Jordan, R. M. Neumann, M. C. Quist, and C. S. Guy. 2000. Proposed standard weight (Ws) equations and standard length categories for 18 warmwater nongame and riverine fish species. North American Journal of Fisheries Management 20:570–574. Boschung, H. T., and R. L. Mayden. 2004. Fishes of Alabama. Smithsonian Books, Washington, D.C. Cooke, S. J., C. M. Bunt, S. J. Hamilton, C. A. Jennings, M. P. Pearson, M. S. Cooperman, and D. F. Markle. 2005. Threats, conservation strategies, and prognosis for suckers (Catostomidae) in North America: insights from regional case studies of a diverse family of non-game fishes. Biological Conservation 121:317–331. DiCenzo, V. J., M. J. Maceina, and W. C. Reeves. 1995. Factors related to growth and condition of the Alabama subspecies of spotted bass in reservoirs. North American Journal of Fisheries Management 15:794–798. Didenko, A. V., S. A. Bonar, and W. J. Matter. 2004. Standard weight (Ws) equations for four rare desert fishes. North American Journal of Fisheries Management 24:697–703. Froese, R. 2006. Cube law, condition factor and weight-length relationships: history, meta-analysis and recommendations. Journal of Applied Ichthyology 22:241–253. Gerow, K. G., R. C. Anderson-Sprecher, and W. A. Hubert. 2005. A new method to compute standard-weight equations that reduces length-related bias. North American Journal of Fisheries Management 25:1288–1300. Gerow, K. G., W. A. Hubert, and R. C. Anderson-Sprecher. 2004. An alternative approach to detection of lengthrelated biases in standard weight equations. North American Journal of Fisheries Management 24:903–910. Grabowski, T. B., and J. J. Isely. 2006. Seasonal and diel movements and habitat use of robust redhorses in the lower Savannah River, Georgia and South Carolina. Transactions of the American Fisheries Society 135:1145–1155. Gutreuter, S., and W. M. Childress. 1990. Evaluation of condition indices for estimation of growth of largemouth

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