# fishr Vignette - Fish Condition and Relative Weights

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1 fishr Vignette - Fish Condition and Relative Weights Dr. Derek Ogle, Northland College April 25, 2013 Condition is a measure of the physical health of a population of fish based on the fish s relative plumpness or fatness. Most often condition is computed by comparing the actual weight of a fish to some expectation of weight based on the length of the fish. In other words, measuring the condition of a particular fish is an exercise in determining if it weighs more or less than would be expected based on its length. An overall measure of condition for an entire population is obtained by averaging the condition of all fish in a sample. The utility of measuring fish conditions was summarized by Blackwell et al. (2000) in the following manner: Fish condition can be extremely important to fisheries managers. Plump fish may be indicators of favorable environmental conditions (e.g., habitat conditions, ample prey availability), whereas thin fish may indicate less favorable environmental conditions. Thus, being able to monitor fish well-being can be extremely useful for fisheries biologists who must make management recommendations concerning fish populations. There are at least eight metrics of condition (Bolger and Connolly 1989) of which three are commonly used by fisheries managers (Blackwell et al. 2000). These three measures are introduced in Section 1 and discussed within the context of four properties that should be evident in all condition metrics (Murphy et al. 1990). Those four properties are (1) consistency similar statistical properties and meaning regardless of species or length; (2) tractability analysis by standard statistical methods; (3) efficiency relative precision from small samples; and (4) robustness relative insensitivity to variations in the way the data was collected an analyzed. The relative weight metric will then be examined in more detail in Section 2. This vignette requires functions in the FSA and FSAdata package maintained by the author. These packages are loaded into R with > library(fsa) > library(fsadata) 1 Measures of Condition 1.1 Fulton s Condition Factor Fulton s condition factor is calculated with K = W L 3 constant where the constant is simply a scaling factor that is equal to if metric units are used (i.e., grams and millimeters) or if English units are used (i.e., pounds and inches) 1. Fulton s condition factor assumes isometric growth 2. If a fish stock does not exhibit isometric growth, which is often the case, then K tends to differ depending on the length of the fish, violating the consistency property. Furthermore, comparing K between species is problematic because both species would need to exhibit isometric growth for the comparison to be valid. Because of these limitations, Fulton s condition factor should be avoided. 1 These constants are used so that the values of K are not extremely small fractions. 2 See the length-weight vignette for a brief discussion of isometric and allometric growth. 1

2 1.2 LeCren s Relative Condition Factor The relative condition factor, introduced by Le Cren (1951), is calculated with Kn = W W where W is the predicted length-specific mean weight for the population under study (Blackwell et al. 2000). The average Kn across all lengths and species is 1.0 (Anderson and Neumann 1996). Thus, Kn is consistent across lengths. Bolger and Connolly (1989), however, show that Kn comparisons are restricted to species or regions that have the same slope (b) in the length-weight relationship. Thus, W is generally predicted from length-weight equations developed for a population (perhaps from several years of data) or for a region. 1.3 Relative Weight The relative weight, introduced by Wege and Anderson (1978), is calculated with W r = W 100 (1) W s where W s is a standard weight for fish of the same length. In simplistic terms, a standard weight equation for a particular species is a length-weight relationship designed to predict the 75th percentile 3 mean weight for a given value of length 4. Standard weight equations have been developed for a wide variety of species 5. It should be noted that the standard weight equations have been developed for either metric or English unit measurements but that the log 10 rather than the log e transformation is used 6. Blackwell et al. (2000) suggest that regional or population-specific W s equations should NOT be developed. If regional or populationspecific analysis is desired then Kn should be used. Recent trends, following the work of Gerow et al. (2005), have resulted in standard weight equations that are quadratic rather than linear. Examples of the use of quadratic standard weight equations can be found in Ogle and Winfield (2009) and Cooney and Kwak (2010). While use of these types of standard weight equations is not illustrated in this vignette, their use is a simple and straightforward modification of what is demonstrated here. The relative weight measure has become the most popular measure of condition (Blackwell et al. 2000). This popularity is partly due to the fact that relative weight summaries have been used as a surrogate measure of the general health of the fish (Brown and Murphy 1991; Neumann and Murphy 1992; Jonas et al. 1996; Brown and Murphy 2004; Kaufman et al. 2007; Rennie and Verdon 2008; but also see Copeland et al. 2008) as well as the environment (Liao et al. 1995; Blackwell et al. 2000; Rennie and Verdon 2008). Thus, relative weight summaries may be used as an indirect means for evaluating ecological relationships and the effects of management strategies (Murphy et al. 1991; Blackwell et al. 2000). In addition, Murphy et al. (1990) found the distributions of W r values to typically be symmetric (but not normal). Because t-tests and analysis of variance tests are relatively robust to departures from normality, as long as the distribution is symmetric, typical parametric inferential statistics can be used with W r values. It should be noted, though, that Gerow (Gerow et al. (2004), Gerow et al. (2005), and Gerow (2010)) has been critical of the idea that traditionally developed standard weight equations produce relative weight values that are not dependent on the length of the fish. 3 However, see Ogle and Winfield (2009) for an equation that uses the 50th percentile in addition to the 75th percentile. 4 Specific discussion of methods for computing the standard weight equations are discussed in detail in Murphy et al. (1990) and Blackwell et al. (2000) 5 In R, examine the data(wslit) data frame for all known equations 6 This is in contrast to what is shown in the length-weight vignette. 2

3 2 Relative Weights in R Throughout this vignette, the total length (in) and weight (g) data from Bluegill (Lepomis macrochirus) sampled in two years from a small catch-and-release lake in northern Wisconsin will be examined. These data (along with other data) can be found in the InchLake2 data frame in the FSAdata package. The entire data frame is loaded into R and the structure and the first six rows of data are viewed with > data(inchlake2) > str(inchlake2) 'data.frame': 516 obs. of 8 variables: \$ netid : int \$ fishid : int \$ species: Factor w/ 9 levels "Black Crappie",..: \$ length : num \$ weight : num \$ sex : Factor w/ 2 levels "m","u": \$ mat : Factor w/ 2 levels "r","u": \$ year : int > head(inchlake2) netid fishid species length weight sex mat year Bluegill u u Bluegill u u Bluegill u u Bluegill u u Bluegill u u Bluegill u u 2008 As the types of units for the length and weight measurements do not match, either the lengths need to be converted to mm or the weights converted to pounds. Below the length measurements are converted to the nearest whole mm and stored into a new variable > InchLake2\$lenmm <- round(inchlake2\$length*25.4,0) > head(inchlake2) netid fishid species length weight sex mat year lenmm Bluegill u u Bluegill u u Bluegill u u Bluegill u u Bluegill u u Bluegill u u The Bluegill data from 2007 are isolated with > bg <- Subset(InchLake2,year==2007 & species=="bluegill") > str(bg) 'data.frame': 109 obs. of 9 variables: \$ netid : int \$ fishid : int \$ species: Factor w/ 1 level "Bluegill": \$ length : num \$ weight : num \$ sex : Factor w/ 1 level "u": \$ mat : Factor w/ 1 level "u":

4 \$ year : int \$ lenmm : num Note, from the data frame structure, that the number of observations in bg is reduced from the original data frame and that the species variable has only one level the level of the species of interest. 2.1 Manually Computing W r Computing relative weights is a two-step process. First, a variable containing the standard weight for each fish s observed length is created by substituting each fish s observed length into the species-specific standard weight equation. Second, a variable of relative weights is computed by dividing the fish s observed weight by the fish s calculated standard weight. The coefficients for any known standard weight equation can be efficently found with wsval(). This function requires the desired species name, in quotes and spelled correctly 7, as the first argument and the desired units of measurement in units= (either "metric" for use with mm and grams or "English" for use with inches and pounds). Some standard weight equations have been developed for other than the 75th percentile (usually the 50th or, occasionally, also the 25th percentile). The default is to return values for the 75th percentile but this can be altered by including a value for another percentile in ref=. It should be noted that equations have not been developed for all species in both types of units and for other than 75th percentile reference points. If you ask for a species in a situation (units and reference combination) in which the standard weight equation does not exist, then an error will be produced by wsval(). The standard weight equation information for Bluegill is found and stored into an object called bg.eqn with 8 > ( bg.eqn <- wsval("bluegill",units="metric") ) species units type ref int slope quad min.len max.len measure method 20 Bluegill metric linear NA 80 NA TL Other comment source 20 none Hillman, 1982 Note that the results will indicate if the standard weight equation is of the linear or quadratic form (in type ), what the minimum (and occasionally maximum) length (in min.len as mm) over which the equation should be applied, and which length measurement is applicable (in measure and nearly always total length (TL)). As the standard weight equation is only valid for Bluegill of at least 80 mm, the bg data frame was reduced to only those fish larger than 80 mm with > bg80 <- Subset(bg,lenmm>=bg.eqn\$min.len) A column of standard weights for each fish in the data frame is then constructed by predicting the log 10 (W s) from the observed log 10 (L) with the provided equation coefficients and then back-transforming these to the observed scale by raising the result to the power of 10. This is accomplished for this example with > bg80\$ws <- 10^(bg.eqn\$int+bg.eqn\$slope*log10(bg80\$lenmm)) The relative weight was then calculated and appended to the data frame using (1) with 7 Note that part of spelling correctly here means that only the first word in compound named species is capitalized. 8 The extra parentheses around the second line simply forces R to print the results of the object at the time of assigning. 4

6 illustrated in the recodespecies() help. A simple conversion for the InchLake2 data frame is completed with > InchLake2 <- recodespecies(~species,data=inchlake2) > levels(inchlake2\$species1) [1] "Black crappie" "Bluegill" "Bluntnose minnow" "Fathead minnow" [5] "Iowa darter" "Largemouth bass" "Pumpkinseed" "Tadpole madtom" [9] "Yellow perch" The wrdataprep() requires three arguments a formula of the form weight~length+species in the first argument, the data frame in data=, and the units of measurement in units=. Species for which no standard weight equation is known can be eliminated from the resulting data frame with remove.other=true. Individuals that are below the minimum length for which the standard weight quation does not apply can be removed with remove.submin=true. Removing the species without a known standard weight equation or those individual below the minimum length is not a requirement but it will speed-up the process and make the resulting tables less cluttered. The InchLake2 data frame can be appended with the length categorization variable with > InchLake2 <- wrdataprep(weight~lenmm+species1,data=inchlake2,units="metric", remove.other=true,remove.submin=true) Warning: The following species do not have known standard weight equations: Bluntnose minnow, Fathead minnow, Iowa darter, Tadpole madtom > head(inchlake2) netid fishid species length weight sex mat year lenmm species1 ws Black Crappie u u Black crappie Black Crappie u u Black crappie Black Crappie u u Black crappie Black Crappie u u Black crappie Black Crappie u u Black crappie Black Crappie u u Black crappie wr The data could then be subsetted and summarized as described more thoroughly in Section 3. For example, the following illustrates how to compute the mean W r for each species and year combination > Summarize(wr~year*species,data=InchLake2,digits=1) Warning: To continue, variable(s) on RHS of formula were converted to a factor. year species n Mean St. Dev. Min. 1st Qu. Median 3rd Qu. Max Black Crappie Black Crappie Bluegill Bluegill Largemouth Bass NA Largemouth Bass Pumpkinseed Pumpkinseed NA Yellow Perch Yellow Perch

7 3 Follow-up Analyses and Interpretation 3.1 Comparisons Among Length Categories A measure of overall condition using W r should not be computed without first determining if the W r values differ across fish lengths (Blackwell et al. 2000). In particular, Murphy et al. (1991) suggested that W r values should first be summarized within the usual five-cell length categories of Gabelhouse (1984) 10. Use of the five-cell model can be problematic at times because of small sample sizes in the larger length categories. Thus, other authors have summarized by 25- or 50-mm length categories. The mean W r values in the length categories are then tested with analysis of variance methods to determine if differences exist among the length categories. Adjacent length categories that are statistically equal can then be pooled together. If no statistical differences among categories exist, then all length categories can be pooled and an overall measure of condition for the population can be computed. Relative weights should be reported as whole numbers (Blackwell et al. 2000). A new variable containing the five-cell length categories is appended to the InchLake2 data frame using pssdataprep() which has largely the same arguments as wsdataprep() with the exception that the formula is of the form length~species and the units= is set to "mm", "cm", or in, respectively. For example, > InchLake2 <- pssdataprep(lenmm~species1,data=inchlake2,units="mm") > head(inchlake2) netid fishid species length weight sex mat year lenmm species1 ws Black Crappie u u Black crappie Black Crappie u u Black crappie Black Crappie u u Black crappie Black Crappie u u Black crappie Black Crappie u u Black crappie Black Crappie u u Black crappie wr PSScat memorable memorable memorable preferred preferred preferred As an illustration, the differences among length categories for Bluegill captured in 2007 were examined by first extracting this group of fish > bg07 <- Subset(InchLake2, species=="bluegill" & year==2007) One-way analysis of variance is then used to determine if significant differences in mean W r exist among the length categories. The fitplot() function gives a visual (Figure 2) of the results. > lm1 <- lm(wr~psscat,data=bg07) > anova(lm1) Analysis of Variance Table Response: wr Df Sum Sq Mean Sq F value Pr(>F) PSScat e-05 Residuals > fitplot(lm1,main="",xlab="length Category (mm)") 7

8 wr stock quality preferred Length Category (mm) Figure 1. Mean relative weight of Inch Lake Bluegill captured in 2007 by length category. These results show that there is a significant difference in mean W r value among the length categories (p < 0.005). The relatively small values of W r (i.e., less than 100), especially for stock-sized fish, suggests that Bluegill in Inch Lake in 2007 were relatively skinny fish. 3.2 Comparisons Among Years The relative weight of Bluegill in Inch Lake was compared between years (2007 and 2008) to determine if the condition of Bluegill had changed between those two years. Analysis for 2007 (see above) suggested that relative weight differed significantly among lenght categories. Thus, these data are best analyzed with a two-way ANOVA. The Bluegills were isolated and a factored year variable created with > bg <- Subset(InchLake2,species=="Bluegill") > bg\$fyear <- factor(bg\$year) > str(bg) 'data.frame': 160 obs. of 14 variables: \$ netid : int \$ fishid : int \$ species : Factor w/ 1 level "Bluegill": \$ length : num \$ weight : num \$ sex : Factor w/ 1 level "u": \$ mat : Factor w/ 1 level "u": \$ year : int \$ lenmm : num \$ species1: Factor w/ 1 level "Bluegill": \$ ws : num \$ wr : num \$ PSScat : Factor w/ 3 levels "stock","quality",..: \$ fyear : Factor w/ 2 levels "2007","2008": The five-cell length categorization scheme of Gabelhouse (1984) was defined in the size structure vignette 8

9 A two-way ANOVA to compare the mean relative weight between the two years and among the length categories is conducted with > lm2 <- lm(wr~fyear*psscat,data=bg) > anova(lm2) Analysis of Variance Table Response: wr Df Sum Sq Mean Sq F value Pr(>F) fyear PSScat e-11 fyear:psscat Residuals > fitplot(lm2,main="",xlab="year",ylab="mean Relative Weight",ylim=c(65,100),cex.leg=0.75) Mean Relative Weight stock quality preferred Year Figure 2. Mean relative weight of Inch Lake Bluegill captured in 2007 and 2008 by length category. These results suggest that the mean W r value for Bluegill captured in 2008 is lower than for Bluegill captured in 2007 across all length categories and that mean W r generally increased with size category in both year. NEED TO ADD MULTIPLE COMPARISONS HERE. 9

10 References Anderson, R. and R. Neumann Length, weight, and associated structural indices. in, Murphy, B.R. and D.W. Willis, editors Fisheries Techniques, second edition, American Fisheries Society, Bethesda, Maryland pp Blackwell, B. G., M. L. Brown, and D. W. Willis Relative weight (Wr) status and current use in fisheries assessment and management. Reviews in Fisheries Science 8: , 2, 7 Bolger, T. and P. L. Connolly The selection of suitable indices for the measurement and analysis of fish condition. Journal of Fish Biology 34: , 2 Brown, M. L. and B. R. Murphy Relationship of relative weight (Wr) to proximate composition of juvenile striped bass and hybrid striped bass. Transactions of the American Fisheries Society 120: Brown, M. L. and B. R. Murphy Seasonal dynamics of direct and indirect condition indices in relation to energy allocation in largemouth bass Micropterus salmoides (Lacepede). Ecology of Freshwater Fish 13: Cooney, P. B. and T. J. Kwak Development of standard weight equations for caribbean and gulf of mexico amphidromous fishes. North American Journal of Fishe 30: Copeland, T., B. R. Murphy, and J. J. Ney Interpretation of relative weight in three populations of wild bluegills: A cautionary tale. North American Journal of Fisheries Management 28: Gabelhouse, J., D. W A length-categorization system to assess fish stocks. North American Journal of Fisheries Management 4: , 8 Gerow, K. G Biases with the regression line percentile method and the fallacy of a single standard weight. North American Journal of Fisheries Management 30: Gerow, K. G., R. C. Anderson-Sprecher, and W. A. Hubert A new method to compute standard-weight equations that reduces length-related bias. North American Journal of Fisheries Management 25: Gerow, K. G., W. A. Hubert, and R. C. Anderson-Sprecher An alternative approach to detection of length-related biases in standard weight equations. North American Journal of Fisheries Management 24: Jonas, J. L., C. E. Kraft, and T. L. Margenau Assessment of seasonal changes in energy density and condition in age-0 and age-1 muskellunge. Transactions of the American Fisheries Society 125: Kaufman, S. D., T. A. Johnston, W. C. Leggett, M. D. Moles, J. M. Casselman, and A. I. Schulte-Hostedde Relationships between body condition indices and proximate composition in adult walleyes. Transactions of the American Fisheries Society 136: Le Cren, E. D The length-weight relationship and seasonal cycle in gonad weight and condition in the perch (Perca flavescens). Journal of Animal Ecology. 20: Liao, H., C. L. Pierce, D. H. Wahl, J. B. Rasmussen, and W. C. Leggett Relative weight (Wr) as a field assessment tool: Relationships with growth, prey biomass, and environmental conditions. Transactions of the American Fisheries Society 124: Murphy, B. R., M. L. Brown, and T. A. Springer Evaluation of the relative weight (Wr) index, with new applications to walleye. North American Journal of Fisheries Management 10: , 2 Murphy, B. R., D. W. Willis, and T. A. Springer The relative weight index in fisheries management: Status and needs. Fisheries (Bethesda) 16(2): , 7 Neumann, R. M. and B. R. Murphy Seasonal relationships of relative weight to body composition in white crappie Pomoxis annularis Rafinesque. Aquaculture Research 23:

11 Ogle, D. H. and I. J. Winfield Ruffe length-weight relationships with a proposed standard weight equation. North American Journal of Fisheries Management Rennie, M. D. and R. Verdon Development and evaluation of condition indices for the lake whitefish. North American Journal of Fisheries Management 28: Wege, G. W. and R. O. Anderson Relative weight (Wr): A new index of condition for largemouth bass. In G. D. Novinger and J. G. Dillard (editors), New Approaches to the Management of Small Impoundments, Special Publication, volume 5, pp , American Fisheries Society. 2 11

12 Reproducibility Information Version Information ˆ Compiled Date: Thu Apr ˆ Compiled Time: 10:21:13 AM ˆ Code Execution Time: 2.15 s R Information ˆ R Version: R version ( ) ˆ System: Windows, i386-w64-mingw32/i386 (32-bit) ˆ Base Packages: base, datasets, graphics, grdevices, methods, stats, tcltk, utils ˆ Other Packages: FSA 0.3.5, FSAdata 0.1.3, gdata , knitr 1.2, plyr 1.8, reshape ˆ Loaded-Only Packages: car , cluster , digest 0.6.3, evaluate 0.4.3, formatr 0.7, gplots , grid 3.0.0, gtools 2.7.1, Hmisc , lattice , multcomp , nlme , plotrix 3.4-7, quantreg 4.97, relax , sciplot 1.1-0, SparseM 0.97, stringr 0.6.2, TeachingDemos 2.9, tools ˆ Required Packages: FSA, FSAdata and their dependencies (car, gdata, gplots, Hmisc, knitr, multcomp, nlme, plotrix, quantreg, relax, reshape, sciplot, tcltk, TeachingDemos) 12

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