Cube law, condition factor and weight-length relationships: history, meta-analysis and recommendations

This study presents a historical review, a meta-analysis, and recommendations for users about weight-length relationships, condition factors and relative weight equations. The historical review traces the developments of the respective concepts. The meta-analysis explores 3929 weight-length relationships of the type W = aL(b) for 1773 species of fishes. It shows that 82% of the variance in a plot of log a over b can be explained by allometric versus isometric growth patterns and by different body shapes of the respective species. Across species median b = 3.03 is significantly larger than 3.0, thus indicating a tendency towards slightly positive-allometric growth (increase in relative body thickness or plumpness) in most fishes. The expected range of 2.5 < b < 3.5 is confirmed. Mean estimates of b outside this range are often based on only one or two weight-length relationships per species. However, true cases of strong allometric growth do exist and three examples are given. Within species, a plot of log a vs b can be used to detect outliers in weight-length relationships. An equation to calculate mean condition factors from weight-length relationships is given as K-mean = 100aL(b-3). Relative weight W-rm = 100W/(a(m)L(m)(b)) can be used for comparing the condition of individuals across populations, where a(m) is the geometric mean of a and b(m) is the mean of b across all available weight-length relationships for a given species. Twelve recommendations for proper use and presentation of weight-length relationships, condition factors and relative weight are given.