# Body Condition

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 below 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 and analyzed.

### Fulton’s Condition Factor

Fulton’s condition factor is calculated with

$K = \frac{W}{L^{3}}*constant$

where the constant is simply a scaling factor that is equal to $$100000$$ if metric units are used (i.e., grams and millimeters) or $$10000$$ if English units are used (i.e., pounds and inches).{^1] Fulton’s condition factor assumes isometric growth.1 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.

### LeCren’s Relative Condition Factor

The relative condition factor, introduced by Le Cren (1951), is calculated with

$Kn = \frac{W}{W'}$

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.

### Relative Weight

The relative weight, introduced by Wege and Anderson (1978), is calculated with

$Wr = \frac{W}{Ws}*100 \quad \quad \text{(1)}$

where $$Ws$$ 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 percentile2 mean weight for a given value of length.3 Standard weight equations have been developed for a wide variety of species.4 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. Blackwell et al. (2000) suggest that regional or population-specific $$Ws$$ equations should NOT be developed. If regional or population-specific 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 $$Wr$$ 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 $$Wr$$ 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.

### Comparisons Among Length Categories

A measure of overall condition using $$Wr$$ should not be computed without first determining if the $$Wr$$ values differ across fish lengths (Blackwell et al. 2000). In particular, Murphy et al. (1991) suggested that $$Wr$$ values should first be summarized within the usual five-cell length categories of Gabelhouse (1984).5 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 $$Wr$$ 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).

# Calculations in R

Methods for performing these calculations in R are described in Sections 7.1-7.3 and Chapter 8 of Ogle (2016).6

## Reproducibility Information

• Compiled Date: Tue Jan 02 2018
• Compiled Time: 1:44:59 PM
• R Version: R version 3.4.3 (2017-11-30)
• System: Windows, i386-w64-mingw32/i386 (32-bit)
• Base Packages: base, datasets, graphics, grDevices, methods, stats, utils
• Required Packages: FSA, FSAdata, captioner, knitr, dplyr, magrittr and their dependencies (assertthat, bindrcpp, car, digest, dunn.test, epitools, evaluate, glue, gplots, graphics, grDevices, highr, lmtest, markdown, methods, pkgconfig, plotrix, plyr, R6, Rcpp, rlang, sciplot, stats, stringr, tibble, tools, utils, yaml)
• Other Packages: bindrcpp_0.2, captioner_2.2.3, dplyr_0.7.4, FSA_0.8.18, FSAdata_0.3.6, knitr_1.17, magrittr_1.5
• Loaded-Only Packages: assertthat_0.2.0, backports_1.1.2, bindr_0.1, compiler_3.4.3, digest_0.6.13, evaluate_0.10.1, glue_1.2.0, htmltools_0.3.6, pkgconfig_2.0.1, plyr_1.8.4, R6_2.2.2, Rcpp_0.12.14, rlang_0.1.4, rmarkdown_1.8, rprojroot_1.3-1, stringi_1.1.6, stringr_1.2.0, tibble_1.3.4, tools_3.4.3, yaml_2.1.16
• Links: Script / RMarkdown

## References

Anderson, R., and R. Neumann. 1996. Length, weight, and associated structural indices. in, Murphy, B.R. and D.W. Willis, editors Fisheries Techniques, second edition, American Fisheries Society, Bethesda, Maryland:447–481.

Blackwell, B. G., M. L. Brown, and D. W. Willis. 2000. Relative weight (Wr) status and current use in fisheries assessment and management. Reviews in Fisheries Science 8:1–44.

Bolger, T., and P. L. Connolly. 1989. The selection of suitable indices for the measurement and analysis of fish condition. Journal of Fish Biology 34:171–182.

Brown, M. L., and B. R. Murphy. 1991. Relationship of relative weight (Wr) to proximate composition of juvenile Striped Bass and hybrid Striped Bass. Transactions of the American Fisheries Society 120:509–518.

Brown, M. L., and B. R. Murphy. 2004. Seasonal dynamics of direct and indirect condition indices in relation to energy allocation in Largemouth Bass micropterus salmoides (Lacepede). Ecology of Freshwater Fish 13:23–36.

Cooney, P. B., and T. J. Kwak. 2010. Development of standard weight equations for Caribbean and Gulf of Mexico amphidromous fishes. North American Journal of Fisheries Management 30:1203–1209.

Copeland, T., B. R. Murphy, and J. J. Ney. 2008. Interpretation of relative weight in three populations of wild Bluegills: A cautionary tale. North American Journal of Fisheries Management 28:386–377.

Gabelhouse, D. W. 1984. A length-categorization system to assess fish stocks. North American Journal of Fisheries Management 4:273–285.

Gerow, K. G. 2010. Biases with the regression line percentile method and the fallacy of a single standard weight. North American Journal of Fisheries Management 30:679–690.

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 length-related biases in standard weight equations. North American Journal of Fisheries Management 24:903–910.

Jonas, J. L., C. E. Kraft, and T. L. Margenau. 1996. Assessment of seasonal changes in energy density and condition in age-0 and age-1 Muskellunge. Transactions of the American Fisheries Society 125:203–210.

Kaufman, S. D., T. A. Johnston, W. C. Leggett, M. D. Moles, J. M. Casselman, and A. I. Schulte-Hostedde. 2007. Relationships between body condition indices and proximate composition in adult Walleyes. Transactions of the American Fisheries Society 136:1566–1576.

Le Cren, E. D. 1951. The length-weight relationship and seasonal cycle in gonad weight and condition in the Perch (Perca flavescens). Journal of Animal Ecology 20:201–219.

Liao, H., C.L. Pierce, D. H. Wahl, J. B. Rasmussen, and W. C. Leggett. 1995. Relative weight (Wr) as a field assessment tool: Relationships with growth, prey biomass, and environmental conditions. Transactions of the American Fisheries Society 124:387–400.

Murphy, B. R., M. L. Brown, and T. A. Springer. 1990. Evaluation of the relative weight (Wr) index, with new applications to Walleye. North American Journal of Fisheries Management 10:85–97.

Murphy, B. R., D. W. Willis, and T. A. Springer. 1991. The relative weight index in fisheries management: Status and needs. Fisheries (Bethesda) 16(2):30–38.

Neumann, R. M., and B. R. Murphy. 1992. Seasonal relationships of relative weight to body composition in White Crappie Pomoxis annularis Rafinesque. Aquaculture Research 23:243–251.

Ogle, D. H. 2016. Introductory fisheries analyses with R. Chapman & Hall/CRC, Boca Raton, FL.

Ogle, D. H., and I. J. Winfield. 2009. Ruffe length-weight relationships with a proposed standard weight equation. North American Journal of Fisheries Management 29:850–858.

Rennie, M. D., and R. Verdon. 2008. Development and evaluation of condition indices for the Lake Whitefish. North American Journal of Fisheries Management 28:1270–1293.

Wege, G. W., and R. O. Anderson. 1978. Relative weight (Wr): A new index of condition for Largemouth Bass. Pages 79–91 in G. D. Novinger and J. G. Dillard, editors. New approaches to the management of small impoundments. American Fisheries Society.

1. See the length-weight vignette for a brief discussion of isometric and allometric growth.

2. However, see Ogle and Winfield (2009) for an equation that uses the 50th percentile in addition to the 75th percentile.

3. Specific discussion of methods for computing the standard weight equations are discussed in detail in Murphy et al. (1990) and Blackwell et al. (2000).

4. In R, examine the data frame for all known equations

5. The five-cell length categorization scheme of Gabelhouse (1984) was defined in the size structure module.

6. Scripts for these calculations are here.