Transactions of the American Fisheries Society 124:387-400. 1995© Copyright by the American Fisheries Society 1995

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

Environmental ConditionsHONGSHENG LlAO,1 CLAY L. FIERCE,2 AND DAVID H. WAHL

Kaskaskia Biological Station, Center for Aquatic EcologyIllinois Natural History Survey

Rural Route I. Box 157. Sullivan, Illinois 61951, USA, andZoology Department, Eastern Illinois University

Charleston, Illinois 61920, USA

JOSEPH B. RASMUSSEN AND WILLIAM C LEGGEir3

Department of Biology, McGill University1205 Avenue Dr. Penfield, Montreal. Quebec H3A IBl, Canada

Abstract.—We evaluated the relative weight (Wr) condition index as a field assessment tool withpumpkin seed Lepomis gibbosus and golden shiner Notemigonus crysoleucas, focusing on sourcesof variability and potential of Wr as a predictor of growth, prey availability, and environmentalconditions in 10 southern Quebec lakes over 2 years. To allow calculation of Wr, we developedstandard weight (Ws) equations for both species, using the regression-line-percentile (RLP) tech-nique. The proposed Wv equation in metric units (grams wet weight and millimeters total legnth,TL) for pumpkinseed is log|<)W;v = -5.179 + 3.237 log,0TL; for golden shiner it is Iog!0lV;v =—5.593 + 3.302 logioTL. Spatial and temporal variation in Wr was highly significant and largelyasynchronous in both species, although spring values were lowest in most lakes. The Wr indexfrequently varied with length, prompting us to examine relationships in stock and quality lengthfish separately. We found little evidence for a relationship between Wr and growth in either species.Pumpkinseed Wf& were positively correlated with total benthic invertebrate biomass: stock lengthWr was positively correlated with chironomid biomass, and quality length Wr was positivelycorrelated with gastropod biomass. The relative weight of quality length golden shiners waspositively correlated with chironomid biomass. Our results and those of other studies suggest thatthe common assumption of a relationship between Wr and growth in field populations should bereconsidered, but that Wr could be cautiously used as a working index of prey availability. Werecommend empirical or experimental verification when Wr is used as an assessment tool in fieldpopulations.

Condition indices are widely used in assessing prey availability (Anderson and Gutreuter 1983;freshwater fish populations (Nielsen and Johnson Busacker et al. 1990; Ney 1993).1983; Schreck and Moyle 1990; Murphy et al. There has been much debate concerning the use1991; Kohler and Hubert 1993). Condition indices of condition indices in recent literature, centeringmeasure the "plumpness" or "robustness1* offish, largely around methodological issues such as theand are easily calculated from routinely collected appropriateness of various indices (Bolger andlength-weight data. Condition is frequently as- Connolly 1989; Cone 1989; Springer et al. 1990).sumed to reflect not only characteristics of fish, Recently, the relative weight (Wr) condition indexsuch as health, "well-being," reproductive state, (Wege and Anderson 1978) has become popular,and growth, but also characteristics of the envi- prompting discussion regarding the various meth-ronment, such as habitat quality, water quality, and ods for generating the necessary standard weight———— (W(V) equations (Murphy et al. 1990, 1991). A more

1 Present address: Department of Animal Ecology, fundamental issue regarding the use of conditionScience II, Iowa State University, Ames, Iowa 50011, indices remains unresolved, however, and that isUSA. how to interpret condition of fish in natural pop-

2 Present address: National Biological Service, Iowa uiations. What does condition predict? EvidenceCooperative Fish and Wildlife Research Unit, Depart- for relationshi with th and olher character.ment of Animal Ecology, Science II, Iowa State Uni- . . , . .versity, Ames, Iowa 50011, USA. lstlcs mentioned earlier is scattered throughout the

3 Present address: Department of Biology, Queens literature on condition but is largely anecdotal. WeUniversity, Kingston, Ontario K7L 3N6, Canada. are aware of no previous uses of spatially and tem-

387

388 LIAO ET AL.

porally replicated sampling designs to evaluate Wras a tool for predicting growth, prey availability,and other factors in field populations.

The primary purpose of this study was to eval-uate Wr as a tool for assessing freshwater fish pop-ulations. To do this, we took advantage of a con-current study of littoral fish communities, inver-tebrate prey availability, limnological conditions,and growth of two fish species in 10 lakes in south-ern Quebec (Pierce et al. 1994). First, we devel-oped standard weight (Ws) equations for two ofthe dominant species in these lakes, pumpkinseedLepomis gibbosus and golden shiner Notemigonuscrysoleucas. Then, using these equations to cal-culate Wr, we analyzed sources and patterns ofvariation in Wr and explored relationships of Wrwith growth, fish biomass, prey biomass, and lim-nological variables. Results of this evaluation il-lustrate strengths and weaknesses of Wr as an as-sessment tool for fish populations in nature andwill help guide the use of Wr for other species.

MethodsStudy lakes and species.—Evaluation of Wr was

conducted in 10 lakes in the Eastern Townshipsregion of southern Quebec, Canada. Locations, lit-toral fish communities, and other characteristics ofthese lakes were recently described by Pierce etal. (1994). Pumpkinseeds and golden shiners arecommon and widely distributed littoral zone fishesin North America (Scott and Crossman 1973; Leeet al. 1980). Together, they account for 30% of thefish biomass of the littoral zone and are among themost abundant littoral species in these lakes(Pierce et al. 1994).

Development of standard weight equations.—Weobtained weight-length data from 302 pumpkin-seed populations representing 11 states and prov-inces and 285 golden shiner populations repre-senting 9 states and provinces (Liao 1994) to de-velop standard weight (Ws) equations for each spe-cies. The data were of two general types: weightsand lengths of individual fish, or regressions de-scribing weight-length relationships of popula-tions. Individual weights and lengths were pro-vided by management and research personnel,along with site names, locations, and occasionallyadditional descriptive information. Most of thesedata sets contained no information regarding age,growth, or sex. Weight was either reported as orconverted to the nearest 0.1 g (wet) and total length(TL) to the nearest millimeter. Eight or more in-dividual fish and r2 > 0.80 for the regression ofweight (logjo) on length (logjo) were minimum

criteria for including populations in the develop-ment of Ws equations. Regressions describingweight-length relationships of many additionalpopulations were taken from published studies,agency reports, and data compilations. Whenknown, the same inclusion criteria as just de-scribed were used for these regressions. Regres-sions reported without sample size and r2 (5% ofpumpkinseed populations, <1% of golden shinerpopulations) were assumed to be valid and in-cluded.

Standard weight equations for pumpkinseedsand golden shiners were developed with the re-gression-line-percentile (RLP) technique (Murphyet al. 1990). The RLP technique is currently fa-vored for developing Ws equations because itweights each population equally and produces Wrestimates of low variance and free of length bias(Murphy et al. 1991). For each population, wecomputed a linear regression of weight (logio) onlength (logio) or used the existing one. We estab-lished 50 mm and 300 mm as minimum and max-imum points of the length range. At the midpointof each 1-cm length interval within this range (i.e.,55 mm, 65 mm, 75 mm, etc.), we calculated apredicted logio weight using the weight-length re-gression and then back-transformed these valuesto predicted arithmetic weights. For each lengthinterval, the 75th percentile was then calculatedfrom the predicted weights of all the populationsin the data set. Finally, the 75th percentile weightswere logio-transformed ar*d regressed against thecorresponding log IQ-transformed midpoint lengths,yielding the logio-logio version of the Ws equa-tion. Further details and rationale for the RLP tech-nique were given by Murphy et al. (1990).

Fish sampling for evaluating Wr—Using beachseines as described by Pierce et al. (1990), wesampled pumpkinseeds and golden shiners in eachof the 10 lakes once in early summer (hereafterreferred to as "early'*) and once in late summer(hereafter referred to as "late") during 1987 and1988. The early summer period was from 18 Juneto 26 June in 1987 and from 4 July to 15 July in1988. The late summer period was from 24 Augustto 17 September in 1987 and from 8 September to22 September in 1988. Details of the early and latesampling were presented by Pierce et al. (1994).Additional samples of both species were obtainedfrom 9 May to 20 May 1988 and are hereafterreferred to as "spring" samples.

Captured fish were anesthetized immediately in2-phenoxyethanol, put on ice, and frozen within afew hours. In the laboratory, a length-stratified

RELATIVE WEIGHT AS AN ASSESSMENT TOOL 389

random subsample of at least 50 fish (>50 mmTL) of each species from each combination of lakeand sampling date was weighed (wet) to the nearest0.01 g on an electronic balance and measured tothe nearest millimeter (TL). A few subsamplescontained fewer than 50 fish, reflecting low abun-dance on the corresponding sampling date. Scalesamples for age and growth analysis were collectedfrom each fish in spring and late 1988 subsamples.Pumpkinseed scales were taken at the tip of thedepressed left pectoral fin; golden shiner scaleswere taken above the lateral line dorsal to the tipof the depressed left pectoral fin. Sex was deter-mined for the spring subsamples only.

Determination of size-classes for test popula-tions.—We used the length categorization systemof Gabelhouse (1984) to establish meaningfullengths for comparisons of Wr and to examine re-lationships of Wr with growth and other variables.These descriptive categories were chosen becauseof their frequent use in fisheries studies and theirintuitive appeal. Minimum "stock" and "quality*1

lengths of 80 mm and 150 mm, respectively, wereused for pumpkinseeds (Gabelhouse 1984). Usingthe rationale of Gabelhouse (1984) and 305 mmas an estimate of maximum length (Becker 1983),we set minimum "stock" length as 70 mm (23%of maximum) and "quality" length as 120 mm(39% of maximum) for golden shiners. AlthoughGabelhouse's system includes three larger size-classes (preferred, memorable, trophy), very fewfish of these sizes were caught. Therefore, our size-specific analyses of Wr were restricted to stock andquality lengths.

Condition of test populations.—The Wr indexwas calculated for all fish with the equation

Wr = \QO-W/WS (1)

(Wege and Anderson 1978); W is the wet weightof the fish and Ws is the length-specific standardweight predicted from the appropriate Ws equationdescribed above. These individual Wr values wereused to explore sources of variation in Wr and therelationship with growth of individuals as de-scribed below.

For each subsample (i.e., for each combinationof species, lake, and sampling date), Wr was re-gressed against total length. If the regression wassignificant (slope significantly different from zeroat a = 0.05), it was used to generate size-specific(stock and quality) Wr estimates for that subsam-ple. If the regression was not significant, the sub-sample mean Wr was used to represent Wr for allsizes in that subsample. Neither regressions nor

subsample means were extrapolated beyond theranges of fish sizes in subsamples; this resulted inno Wr estimates for some size-classes on somesampling dates.

For comparing Wr with growth and food avail-ability across lakes, size-specific estimates fromthe early and late subsamples from both years wereaveraged by species and lake. This produced size-specific "average" estimates of Wr for each spe-cies in the 10 lakes and prevented unequal weight-ing of sampling periods due to variable numbersof fish in subsamples.

Growth of test populations.—We estimatedgrowth rates of individual fish by aging and back-calculating lengths at previous ages using scales(Busacker et al. 1990). Ten or more scales per fishwere cleaned and mounted between glass slides;large, opaque scales were impressed on acetateslides. All scales on slides were viewed when ageswere assigned to fish, and a single reader did allaging. Scales from 30 fish of both species wereviewed by a second reader, and age assignmentswere in 100% agreement. Ages assigned by read-ing scales corresponded well with length-frequen-cy distributions.

Radii and interannular distances on 10 scalesper fish were measured with a dissecting micro-scope (25x magnification), drawing tube, andcomputerized digitizing tablet as described by Frie(1982). Regenerated or otherwise distorted scaleswere not digitized, resulting in fewer than 10 rep-licate scales measured for some fish. Replicatemeasurements were then averaged for each fish,providing precise estimates of scale growth incre-ments for back-calculations (Newman and Weis-berg 1987).

We used the Fraser-Lee technique (Busacker etal. 1990) for back-calculation of lengths at pre-vious ages based on scale growth increments. In-tercepts (a) for back-calculation were generatedfrom regressions of fish length on scale radius from1,095 pumpkinseeds and 1,127 golden shiners dis-tributed approximately equally among all 10 studylakes. Whereas all fish from spring and late 1988subsamples were used in generating body-scalerelationships, fish older than 5 years were omittedfrom back-calculations to avoid potential errorsfrom incorrect aging of older fish. Pumpkinseedand golden shiner back-calculations were based onaverages of 81 and 104 fish per lake, respectively.

Using the back-calculated lengths at previousages and differences between successive lengthsas estimates of annual growth increments, we re-gressed annual growth increments against length

390 LIAO ET AL.

120

110-

100 150Total Length (mm)

200

FIGURE 1.—Example of variation in relative weight (Wr) among individual pumpkinseeds and relationships withfish length. Data points represent individual fish from Lake Brompton collected in (a) early 1988 and (b) late 1988.Vertical dashed lines indicate minimum stock (80 mm) and quality (150 mm) lengths. Shaded areas indicate Wrless than 100. Among-fish variation was similar in other lakes and for golden shiner. When no significant relationshipwith total length existed, as in panel a, Wr for both length-classes was represented by the mean Wr for that date(99.5 in this case). When a significant relationship with total length existed, as in panel b, Wr was estimated bysolving the H^-total length regression for stock and quality lengths (98.7 and 104.0, respectively, in this case).

at the start of the growing season for each speciesin each lake. All regressions had negative slopes,indicating decreasing annual growth with increas-ing size. Growth rates of young-of-year fish weresimply estimated as lengths at first annulus andwere not included in regressions, because initiallength was length at hatching and was essentiallythe same for all fish. Quadratic regressions wereused to improve fit when both linear and quadraticterms were significant (ot = 0.05). These size-spe-cific growth regressions explained averages of51% and 60% of the variation in annual growth ofpumpkinseed and golden shiner populations, re-spectively, and allowed estimation of "average"growth of a population at stock and quality lengths,

similar to the way in which size-specific Wr esti-mates were obtained, as described earlier. Express-ing growth as a function of fish size has severaladvantages over the more traditional age-specificapproach, especially when one is comparinggrowth among populations (Gutreuter 1987; Os-enberg et al. 1988).

Using fish from late 1988 subsamples only, weestimated recent growth of individual fish as thedifference between length at capture and back-cal-culated length at the last annulus. These recentgrowth increments were then regressed againstlength at last annulus for each species in each lake,similar to the procedure described earlier. Resid-uals from these regressions were used as length-

RELATIVE WEIGHT AS AN ASSESSMENT TOOL 391

corrected estimates of recent growth and were ex-amined for each species within each lake for cor-relation with Wr.

Fish biomass, prey biomass, and limnologicalvariables in study lakes.—Biomass of pumpkin-seeds, golden shiners, and the total littoral fishcommunity was estimated from the early and latesamples described earlier. Detailed descriptions ofthe procedures and analysis of these samples werepresented by Pierce et al. (1990, 1994).

Invertebrate prey and limnological variableswere sampled several times from May throughSeptember 1987 and 1988. Littoral sediment-dwelling and epiphytic macroinvertebrate preywere sampled as described by Rasmussen (1988).Organisms were identified, counted, and measuredfor conversion to biomass with length-mass re-gressions (Smock 1980; C. W. Osenberg, Univer-sity of California-Berkeley, unpublished data; J.B. Rasmussen, unpublished data).

Littoral zooplankton prey were sampled at 0700hours by triplicate bottom-to-surface vertical haulswith a 30.5-cm-diameter, 75-u.m-mesh net. Depthswere recorded to the nearest 0.1 m, and were gen-erally near 3 m. A filtering efficiency of 46%, es-timated by several calibrations with pooled Schin-dler-Patalas trap samples taken at 1-m intervals,was applied as a correction factor in biomass cal-culations. Samples were preserved in a sucrose-formalin solution (Haney and Hall 1973). Organ-isms in subsamples (usually 10% of sample) wereidentified and counted, and at least 30 individualsof each taxon were measured for conversion tobiomass with length-mass regressions (Dumont etal. 1975; Culver et al. 1985).

Water temperatures were estimated with a com-bination of littoral and pelagic temperature profilesat 1-m depth intervals. Littoral temperature pro-files were recorded near fish sampling areas fromthe surface to the bottom (—3 m). Pelagic profileswere recorded at offshore locations from the sur-face to a depth of 3 m. Temperatures from indi-vidual profiles were averaged across depths, andthese values were then averaged over the 2 yearsof sampling for each lake. Chlorophyll-^ concen-trations were determined from integrated epilim-netic water samples obtained from offshore loca-tions with a tube sampler; triplicate 500-mL sub-samples were vacuum-filtered (65-jxm pores), fro-zen in the field, and extracted in the laboratory(Strickland and Parsons 1968). We sampled sub-merged littoral macrophyte biomass and fish con-currently as described by Pierce et al. (1990).

Statistical analyses.—We analyzed data using

TABLE 1.—Summary of ANOVAs testing the effects oflake, year, and season on Wr of pumpkinseeds and goldenshiners in 10 southern Quebec lakes. Data are from theearly and late summer samples, 1987 and 1988. Sums ofsquares are type III (SAS Institute 1985).

Source ofvariation

Lake(L)Year (Y)Season (S)L x YL X SY X SL X Y X SError

LakeYearSeasonL X YL X SY X SL X Y X SError

df

9119919

2,495

9I19919

2,565

Sum ofsquares

Pumpkinseed16,837.6

21.8767.2

5,797.98,047.13,606.22,351.9

163,421.1Golden shiner

19.215.61,854.8

724.35.021.1

10,444.711,060.812.154.5

186.241.8

F

28.560.33

11.719.84

13.6555.063.99

29.4125.549.987.68

15.98152.3320.92

P

0.00010.560.00060.00010.00010.00010.0001

0.00010.00010.00160.00010.00010.00010.0001

linear regression, quadratic regression, analysis ofvariance (ANOVA), and correlation analysis. Lin-ear regressions of logiQ-transformed length andweight data were performed to generate Ws equa-tions with the RLP method as described earlier.Lake, yearly, and seasonal variation in Wr of bothspecies was evaluated with 3-way ANOVAs withinteractions, and sex and lake variation was eval-uated with 2-way ANOVAs with interactions. Datafor relative weight were analyzed untransformed.Relationships of Wr with growth and other vari-ables were examined by regression and correlationanalysis. Growth data were analyzed untransfor-med; other variables were transformed as de-scribed by Pierce et al. (1994). All analyses wereperformed with the CORK, GLM, REG, and UNI-VARIATE procedures of SAS (SAS Institute1988).

ResultsStandard Weight Equations

The proposed standard weight (Ws) equation forpumpkinseed is

logioW, = -5.179 + 3.237.|og,oTL; (2)

for golden shiner it is

= -5.593 + 3.302.1og1()TL; (3)

Ws is standard weight in grams and TL is totallength in millimeters. These Ws equations were

392 LIAO ET AL.

Brompton Magog

Early Late1987

Spring Early Late Early Late1988 1987

Spring Early Late1988

FIGURE 2.—Temporal changes in relative weight (Wr) of stock length (80 mm, solid lines) and quality length(150 mm, dashed lines) pumpkinseeds in southern Quebec lakes. Overlapping data points indicate a nonsignificantregression of Wr on fish length and are represented by the mean Wr for that date. Nonoverlapping data pointsrepresent size-specific Wr estimates from a significant regression of Wr on fish length for that date. Missing datapoints indicate that no fish of that size were sampled on that date. Shaded areas indicated Wr less than 100.

used to calculate Wr of individual fish from testpopulations.

Influence of Fish Length on Wr

Plots of Wr of individual fish showed variablerelationships with fish length, depending on spe-cies, lake, and sampling date (e.g., Figure 1). Re-gressions of Wr on length were significant (a =0.05) in 40% of the pumpkinseed subsamples and33% of the golden shiner subsamples (early andlate subsamples only). In both species, 31 % of thesignificant regressions had positive slopes, and69% had negative slopes. Significant regressionsfor a given species and lake were usually all eitherpositive or negative, although there were both pos-itive and negative regressions for golden shiner intwo lakes (Brompton and d'Argent). There was nocase of significant regressions occurring in all sub-

samples of a given species and lake, but it wascommon for at least one subsample to have a sig-nificant regression. The examples in Figure 1 arerepresentative of the overall pattern of relation-ships of Wr with length; correlations were ephem-eral, perhaps reflecting changing relative ecolog-ical conditions for fish of different sizes over time.

Spatial and Temporal Variation in Wr

The Wr of both species varied significantly andasynchronously among lakes, years, and seasons(Table 1; Figures 2, 3). Interactions of all vari-ables were highly significant (ANOVA) for bothspecies (Table 1), making interpretations diffi-cult. These tests of the effects of lake, year, andseason can be considered conservative, becausevariation due to length was contained in the errorsums of squares. Figures 2 and 3 illustrate this,

RELATIVE WEIGHT AS AN ASSESSMENT TOOL 393

Brompton Magog

120

110-

100

00

Hertel

80 «V.MV.VM»ni»VWr---———

Early Late1987

Waterloo

Spring Early Late Early Late1988 1987

Spring Early Late1988

FIGURE 3.—Temporal changes in relative weight (Wr) of stock length (70 mm, solid lines) and quality length(120 mm, dashed lines) golden shiners in southern Quebec lakes. Details are the same as those for Figure 2.

showing that although Wr tended to be higher insome lakes and lower in others, the temporal pat-terns differed considerably among lakes. Early Wrwas higher than late Wr in some lakes, whereasthe reverse was true in others. In some lakes, earlyWr was higher than late Wr in one year but lowerin the other year. The only consistent pattern wasthat the lowest Wrs occurred in spring in mostlakes.

Influence of Sex on Wr

There were no significant differences in Wr be-tween males and females of either species in thespring subsamples (Table 2). The spring sampleswere collected from all lakes just before the be-ginning of the spawning seasons of both species,and thus at a time when sexual differences in Wr,if any, would likely be most evident. The highlysignificant lake effects (Table 2), here in the ab-sence of interacting temporal effects, further sup-

port the previous inference of significant differ-ences in Wr among lakes.

Intra- and Interspecific Relationships inWr Among Lakes

Intraspecific correlations of Wr of stock andquality length fish among lakes showed mixed re-sults. The Wr estimates of stock length pumpkin-seeds were not significantly correlated with Wr es-timates of quality length pumpkinseeds among the10 lakes (r = 0.65, P = 0.059). In contrast, thecorresponding correlation for golden shiners wassignificant (r = 0.83, P = 0.003). These resultssuggest greater among-lake independence of fac-tors related to pumpkinseed Wr across length thanof those related to golden shiner Wr.

Interspecific correlations of Wr estimates of bothstock and quality length fish among lakes werenonsignificant (stock length: r = 0.42, P = 0.227;quality length: r = 0.50, P = 0.167), suggesting

394 LIAO ET AL.

TABLE 2.—Summary of ANOVAs testing the effects oflake and sex on Wr of pumpkinseeds and golden shinersin 10 southern Quebec lakes. Data are from the springsamples, 1988. Sums of squares are type III (SAS Institute1988).

Source ofvariation

Lake(L)Sex (S)L X SError

LakeSexL X SError

df

919

461

919

413

Sum ofsquares

Pumpkinseed13,769.4

13.8355.3

25,510.7Golden shiner

6,191.013.6

422.117,690.7

F

27.650.250.71

18.100.321.41

P

0.00010.620.70

0.00010.570.20

that Wr responses of the two species to environ-mental conditions in lakes differed.

Relationship of Wr with GrowthWe found little evidence for a relationship be-

tween Wr and growth. There were no significantcorrelations of size-specific Wr estimates with cor-responding size-specific growth estimates amonglakes (Table 3). Although these results suggest ageneral lack of relationship, they are based on lakemeans of seasonally and annually varying Wr es-timates and therefore could potentially containconfounding individual and temporal variation. Asa test of the relationship of Wr and growth amongindividual fish, we examined correlations ofgrowth residuals (length-corrected estimates of re-cent growth) with Wr in each subsample (e.g., Fig-ure 4). These correlations compared late summerWfS with growth during that summer among in-dividual fish in subsamples. Eighty percent ofthese correlations for both species were nonsig-nificant (P > 0.05; e.g., Figure 4c). Three of thefour significant (P < 0.05) correlations were neg-ative (e.g., Figure 4d), contrary to the a priori ex-pectation of a positive relationship.

Relationships of Wr with Fish Biomass, PreyBiomass, and Limnological Variables

We found no evidence of density dependence inWr estimates among lakes for either species (Table3). Neither total fish biomass nor conspecific bio-mass were significantly correlated with Wr.

The strongest relationships in our data set werebetween Wr estimates and biomass estimates ofbenthic prey among lakes, especially for pump-kinseeds (Table 3). The Wr of both stock and qual-

TABLE 3.—Correlations of relative weight (Wr) ofpumpkinseeds and golden shiners with growth, fish bio-mass, and prey biomass in 10 southern Quebec lakes; Pvalues are given in parentheses. All data used in correla-tions are lake averages; fish and prey biomass data arefrom Pierce et al. (1994). Spring 1988 Wr data were notincluded in calculation of lake averages.

Pumpkinseed

Variable

Growth8

Littoral fish biomassTotal

Conspecific

Littoral benthos biomassTotal

Gastropods

Chironomids

Littoral zooplanktonbiomass

Stocklength

0.41(0.242)

0.38(0.283)0.28

(0.440)

0.69(0.027)0.53

(0.115)0.72

(0.018)

0.22(0.538)

Qualitylength

-0.24(0.539)

0.07(0.864)0.28

(0.461)

0.90(0.001)0.84

(0.004)0.58

(0.098)

0.19(0.626)

Golden

Stocklength

0.37(0.291)

0.51(0.133)

-0.31(0.389)

0.12(0.739)

-0.03(0.929)0.61

(0.063)

0.44(0.202)

shiner

Qualitylength

0.51(0.129)

0.59(0.072)

-0.01(0.989)

0.41(0.244)0.26

(0.467)0.72

(0.019)

0.41(0.242)

a Appropriate size-specific growth estimates were used for com-parison with Wr (i.e.. growth of stock length fish compared withWr of stock length fish, growth of quality length fish comparedwith Wr of quality length fish).

ity length pumpkinseeds was positively correlatedwith total benthos biomass; the quality length re-lationship was particularly strong (Table 3). TheWr of stock length pumpkinseeds was positivelycorrelated with chironomid biomass (Figure 5a),and Wr of quality length pumpkinseeds was pos-itively correlated with gastropod biomass (Figure5b). The Wr of quality length golden shiners waspositively correlated with chironomid biomass(Table 3). We found no significant correlations be-tween Wr of either species and littoral zooplanktonbiomass (Table 3).

Chlorophyll a was the only limnological vari-able significantly correlated with Wrt and only forpumpkinseeds. Correlations of pumpkinseed Wrwith chlorophyll a were positive (stock length: r= 0.67, P = 0.035; quality length: r = 0.75, P =0.019). All correlations of Wr with temperature andmacrophyte biomass were nonsignificant (P >0.05).

DiscussionOur Ws equations are the first formally proposed

standard weight equations for pumpkinseed andgolden shiner, thus allowing calculation of Wr forthese species. Standard weight equations have

RELATIVE WEIGHT AS AN ASSESSMENT TOOL 395

10-Roxtonr*»0.83P - 0.0001

50

40H

30

20

10-P - 0.0001

30 60 90 120 150 180 20 40 60 80 100 120 140 160

Length at Last Annulus (mm)

12-

8-

4 -

o --4-

-8-

Roxton m c

F--0.13 "P - 04260 " v̂" .

'..: :* "fml • •

" •". "V

128 -

4 -

0 -

-4-

-8-

.19

d• *

• *•'" •9 -• *v -. •

d'Argent • .r - -0.43 • \P m 0.002 . \ •

50 60 70 80 90 100 110 120 130 50 60 70 80 90 100 110 120 130Relative Weight (Wr)

FIGURE 4.—Example of relationships of recent growth increments with length (a, b) and of growth residualswith relative weight (W,.) (c, d) for individual golden shiners collected in 1988 from Roxton Pond and Lac d'Argent,Quebec. Lengths at last annuli and recent growth increments since last annuli were estimated by back-calculation.Growth residuals are residual variation in growth not explained by regressions of growth increments on length(panels a and b). and thus represent length-corrected estimates of growth of individual fish since the last annulus.These length-corrected growth estimates of individual fish were then examined for correlation with Wr (panels cand d) for each species in each lake.

been proposed for over 30 species and are used byat least 19 state fisheries management agencies forcalculating Wr (Murphy et al. 199I). Although Wrhas become the favored index for expressing con-dition in fish, it still must be used and interpretedwith care. We agree with Springer and Murphy(Springer et al. 1990) that Ws more properly rep-resents a benchmark for comparison than a goalfor management. Furthermore, we believe that itis important to clearly distinguish between the is-sue of how best to calculate condition, and oncean appropriate condition index is selected, whatinformation it provides about fish and their envi-ronment. Our intention was neither to contributeto the debate (Bolger and Connolly 1989; Cone1989; Springer et al. 1990) over Wx methodology,nor to give explicit support for the RLP technique;thus, we have not provided exhaustive documen-

tation of the performance of our Ws equations. Sev-eral recent studies (Murphy et al. 1990; Brown andMurphy 1991; Neumann and Murphy 1991; Williset al. 1991) with other species demonstrate thatthe RLP technique produces acceptable equations.In particular, this technique produces Wr estimatesfree of length bias, allowing changes in Wr withlength in a population to be interpreted as realphenomena rather than methodological artifacts.We believe that our proposed Ws equations willprovide useful standards for calculating and com-paring Wr for pumpkinseeds and golden shinersand have been valuable in enabling us to evaluatethe predictive utility of Wr with data from thesespecies.

We found significant relationships of Wr withlength, both positive and negative, in many of oursubsamples of each species. Roughly similar pat-

396 LIAO ET AL.

115

110

105-

~z 100-

95

PumpkinseedStock Length

r = 0.72P =0.018

0 0.2 0.4 0.6 0.8 1 1.2 1.4Chironomid Biomass (log^g -m*2+ 1))

115

110

105-

100-

95

PumpkinseedQuality Length

r = 0.84P =0.004

0.4 0.6 0.8 1 1.2 1.4Gastropod Biomass (log^g.nrr2* 1))

FIGURE 5.—Relationships of relative weight (Wr) of(a) stock length (80 mm) pumpkinseeds with chironomidbiomass and (b) quality length (150 mm) pumpkinseedswith gastropod biomass in southern Quebec lakes. Datapoints represent lake averages; prey data are from Pierceet al. (1994). Spring 1988 Wrdata were not included incalculation of lake averages. Shaded areas indicate Wrless than 100.

terns have been shown for walleye Stizostedionvitreum (Murphy et al. 1990), yellow perch Percaflavescens (Willis et al. 1991), white crappie Po-moxis annularis and black crappie P. nigromacu-latus (Neumann and Murphy 1991), and stripedbass M or one saxatilis and palmetto bass M. chry-sops $ X M. saxatilis <£ (Brown and Murphy1991). A significant change in Wr with lengthmight be expected in cases in which species un-dergo size-related changes in resource needs, andresources required or preferred by different size-classes vary. Size-related (or ontogenetic) preyand habitat switching is well known for many fishspecies (Zaret 1980; Mittelbach 1981; Keast1985), including the species mentioned above.Pumpkinseeds, for example, undergo pronounceddietary shifts from zooplankton to small littoralinvertebrates to gastropods as they grow (Sadzi-kowski and Wallace 1976; Keast 1978; Mittelbach1984; Osenberg and Mittelbach 1989). Prey abun-

dance varies widely among lakes and other aquaticsystems (Hanson and Peters 1984; Rasmussen1988), and it is reasonable to assume that differentprey types will often vary independently. There-fore, we believe that the general agreement of ourresults with those of previous work showing a mix-ture of positive, negative, and nonsignificant re-lationships of Wr with length is consistent withpresent knowledge of the resource ecology of fish-es. Because of the variable nature of this relation-ship, use of mean Wr for summarizing conditionof fish populations should be avoided unless a lackof relationship with length is demonstrated. Again,pumpkinseeds provide a good example. The Wr ofstock and quality length pumpkinseeds was notsignificantly correlated across our set of 10 lakes,reflecting different JVr-length relationships amonglakes. Comparing these populations by mean Wrwould obscure potentially important size-relatedphenomena.

The Wr of pumpkinseeds and golden shiners var-ied both spatially (across 10 lakes) and temporally(between early and late summer and over 2 yearsof sampling). Furthermore, spatial and temporalpatterns of variation in Wr among lakes were in-consistent over time and vice versa. Temporal vari-ation in condition has been reported in previousstudies of yellow perch (Le Cren 1951; Guy andWillis 1991), burbot Lota lota (Pulliainen and Kor-honen 1990), black crappie (Gabelhouse 1991;Guy and Willis 1991), and northern pike Esox lu-cius and walleye (Guy and Willis 1991), but thesestudies were all limited to single systems. With theexception of the study of Gutreuter and Childress(1990), we are aware of no previous studies de-signed to simultaneously quantify and compareboth temporal and spatial variation. The previousstudies of temporal variation in condition (andprobably many unpublished data) have resulted inthe common practice of sampling during "stan-dard" seasons for assessing condition and otherparameters (Gabelhouse 1991). The temporalasynchrony of our results suggest that so-called"standard" time periods might not be as compa-rable among lakes as previously believed.

In contrast to the pattern of temporal asynchronywe observed in summer, the spring subsamples hadthe lowest Wr values in most of our lakes, a patternsimilar to that documented by Le Cren (1951) foryellow perch. Our spring subsamples were takenbefore the fish spawned and presumably reflectcoincident declines in condition due to overwin-tering in cold Canadian lakes rather than directspawning activities.

RELATIVE WEIGHT AS AN ASSESSMENT TOOL 397

Contrary to results of some previous studies andcommon expectations, we found scant evidence fora relationship of Wr with growth. The first paperproposing Wr as a condition index reported a pos-itive correlation between Wr and growth of large-mouth bass Micropterus salmoides (Wege and An-derson 1978). Likewise, positive relationshipshave been shown for northern pike (Willis 1989),yellow perch (Willis et al. 1991), and juvenilestriped and palmetto basses (Brown and Murphy1991). These empirical results have apparently ledto the common notion that Wr and other conditionindices can be used as indicators of growth; poorcondition indicates poor growth and vice versa.Despite recent contradictory evidence (Gutreuterand Childress 1990; Gabelhouse 1991), this notionnow appears in the general methodological liter-ature (e.g., Busacker et al. 1990; Ney 1993). Wedo not dispute previous results showing positiverelationships between Wr (or other condition in-dices) and growth. Rather, we believe that the col-lective evidence to date suggests that the assump-tion of condition mirroring growth should not bemade uncritically. Perhaps cautious use of Wr asan indicator of growth could be justified in limitedsituations in which an appropriate empirical or ex-perimental basis exists.

Another factor commonly linked with Wr in themethodological literature is prey availability (An-derson and Gutreuter 1983; Busacker et al. 1990;Flickinger and Bulow 1993; Ney 1993). Low Wrvalues are assumed to reflect prey scarcity, where-as high values are assumed to reflect an abundanceof prey. Our results provide some support for thisrelationship. Benthic invertebrates are known tobe very important in the diets of pumpkinseeds(Scott and Crossman 1973; Sadzikowski and Wal-lace 1976; Keast 1978), and Wr of both stock andquality length pumpkinseeds was positively cor-related with benthos biomass in our study lakes.Our results also corresponded well with the knowndietary shift by pumpkinseeds; Wr of stock lengthfish was positively correlated with chironomid bio-mass, and Wr of quality length fish was positivelycorrelated with gastropod biomass. These two preytaxa accounted for averages of 24% and 41 % ofthe total littoral invertebrate biomass in theselakes, respectively (Pierce et al. 1994).

Relationships of golden shiner Wr with preywere less evident; the only statistically significantcorrelation was between Wr of quality length fishand chironomid biomass. Perhaps the lack of clearrelationships between body condition of goldenshiners and prey availability reflects their appar-

ently flexible and omnivorous diet. Golden shinershave been reported to use varying foraging be-haviors (Ehlinger 1989) and to feed on zooplank-ton, soft-bodied macroinvertebrates, phytoplank-ton, and periphyton (Keast and Webb 1966; Scottand Crossman 1973; Hall et al. 1979). Alterna-tively, the lack of strong Wr-prey relationships forgolden shiners could have other explanations, in-cluding failure to adequately quantify an importantprey taxon, lack of food limitation, or existenceof other controlling factors that mask potentialfood effects. Although our data provide better sup-port for the use of Wr as an index of prey avail-ability than of growth, the somewhat equivocalgolden shiner results suggest that this relationshipshould be inferred cautiously for other species un-less diets are known precisely and the relationshipis empirically or experimentally verified.

Density-dependent interactions, both intra- andinterspecific, have been well documented for a va-riety of species (Hanson and Leggett 1985; Mit-telbach 1988; Persson and Greenberg 1990), typ-ically resulting in reduced feeding success,growth, or altered habitat use. These effects aregenerally interpreted as exploitative competitionfor some limiting resource or possibly interferencecompetition via behavioral interactions. Althoughnot a direct test for their existence, we hypothe-sized that Wr might reflect such interactions, vary-ing inversely with biomass of either conspecificsor the entire littoral community. Despite large vari-ation of fish biomass across our lakes (Pierce etal. 1994), we found no evidence that Wr variedwith biomass. These results may indicate a lack ofcompetitive interactions involving these species(but see Hanson and Leggett 1985), but experi-ments would be required to test this interpretation.We speculate that Wr may have potential in as-sessing extremely intense competition, such as oc-curs in situations involving exotic species.

Of the limnological variables that we examined,only chlorophyll a was significantly correlatedwith Wr and only for pumpkinseeds. As a generalindex of water quality and lake productivity (Carl-son 1977; Oglesby 1977), chlorophyll-^ data arewidely available and could also potentially belinked with fish condition. The positive correla-tions of Wr with chlorophyll a for both stock andquality length pumpkinseeds are consistent withthe relationships of pumpkinseed Wr and benthos,assuming "bottom-up" control among trophic lev-els (McQueen et al. 1986). The lack of relationshipof golden shiner WfS with chlorophyll a is alsoconsistent with the weaker Wr-prey relationships

398 LIAO ET AL.

for this species. We hesitate in making this inter-pretation, however, and believe that because of thenecessary intermediate linkages required, inferringrelationships between fish condition and limno-logical indices of lake productivity should prob-ably be avoided.

Implications for Wr as an Assessment ToolRelative weight will vary with fish length in

some populations but not in others. Furthermore,the existence and even the sign of this relationshipin a population might change over time. Use ofmean Wr to characterize these populations will sys-tematically overestimate condition of fish at oneend of the length range and underestimate it at theother end. We urge biologists to test for lengthrelationships before using mean population Wr. Inaddition to more accurately expressing condition,discovery of length-related changes in Wr mayprovide important additional information about thepopulation and system, such as availability of dif-ferent resources, size-structured interactions, andlife-history phenomena.

Relative weight will generally vary temporally,but temporal variation may be asynchronousamong populations. Thus, assessing Wr at one"standard" period (e.g., by fall electrofishing) forcomparison among populations may not provide atrue comparison; Wr of one population might beat its maximum, while others could be increasingor decreasing. We suggest that biologists measureWr at different times in a coordinated fashionamong populations to examine the pattern of tem-poral variation. If temporal variation is negligibleor the pattern is consistent among populations,comparisons based on a standard sampling periodare justified. Otherwise, comparisons of Wr amongpopulations should probably be based on temporalaverages.

The common assumption of a positive relation-ship between Wr and growth should be reconsid-ered. Relative weight may reflect growth of somespecies under certain circumstances, but thisshould be empirically or experimentally demon-strated before Wr is used as a predictor of growth.Uncritical use of Wr as a growth indicator couldlead to substantial errors in field assessment offishpopulations, and probably already has.

Relative weight may be a good predictor of preyavailability, especially for species with relativelynarrow or well-defined diets. We suggest that Wrcould be used as a working index of prey avail-ability but recommend verifying this relationshipif possible.

Aquatic and fisheries ecology are rapidly de-veloping and progressively intertwining fields(Kerfoot and Sih 1987; Carpenter 1988; Northcote1988), and much of the excitement in these areasis sustained by new studies proposing opposingmechanisms, indirect effects, alternative path-ways, and other ideas that complicate our modelsof how these systems work. Accordingly, we feelthat the simplicity and historical inertia of fieldassessment tools such as Wr must be weighedagainst a healthy dose of caution regarding theirinterpretation. As a practical matter, we advocatetesting for relationships before assuming their ex-istence. With proper care and foresight, Wr andother field assessment indices can be importanttools in both research and management.

AcknowledgmentsWe thank numerous research and management

personnel for providing length-weight data, es-pecially Doug Austen, Neil Cunningham, Jim Gal-lagher, and David Green. Brian Walker, LesleyPope, and Michel Simard provided assistance inboth the field and laboratory, and Carolyn Hunt,John Kalas, and Barb Thomas helped with digi-tizing scales. Comments from John Ballenot, EricBollinger, David Clappf Kipp Kruse, Robert Mauk,Brian Murphy, and the Kaskaskia Biological Sta-tion Aquatic Ecology Discussion Group improvedthe quality of this paper. Support was provided bythe Natural Sciences and Engineering ResearchCouncil of Canada (NSERC), the Fonds pour laFormation de Chercheurs et FAide a la Recherche(FCAR), the Donner Foundation, the Illinois Nat-ural History Survey, and the Council for FacultyResearch and International Student Service ofEastern Illinois University.

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Received June 2, 1994Accepted December 20, 1994