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

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

2006 | R. Froese
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 development of these concepts, while the meta-analysis explores 3929 weight–length relationships of the type $ W = aL^{b} $ for 1773 fish species. It shows that 82% of the variance in $ \log a $ over b can be explained by allometric versus isometric growth patterns and different body shapes. Median b = 3.03 is significantly larger than 3.0, indicating a tendency towards slightly positive-allometric growth in most fish. 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. True cases of strong allometric growth exist, with three examples given. Within species, a plot of $ \log a $ vs b can detect outliers in weight–length relationships. An equation to calculate mean condition factors from weight–length relationships is $ K_{mean} = 100aL^{b-3} $. Relative weight $ W_{rm} = 100W/(a_{m}L^{b_{m}}) $ can compare the condition of individuals across populations. Twelve recommendations for proper use and presentation of weight–length relationships, condition factors, and relative weight are given. The study highlights the historical development of weight–length relationships and condition factors, starting with the cube law of Galileo, followed by Fulton's condition factor and its evolution. It discusses the use of logarithmic transformations and the importance of considering allometric and isometric growth. The meta-analysis confirms that the mean exponent b is around 3.03, slightly above 3.0, indicating a tendency towards positive-allometric growth. The study also identifies that extreme values of b are often based on few weight–length relationships and that true allometric growth is rare. The study provides guidelines for interpreting and using weight–length relationships, condition factors, and relative weight in fisheries research.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 development of these concepts, while the meta-analysis explores 3929 weight–length relationships of the type $ W = aL^{b} $ for 1773 fish species. It shows that 82% of the variance in $ \log a $ over b can be explained by allometric versus isometric growth patterns and different body shapes. Median b = 3.03 is significantly larger than 3.0, indicating a tendency towards slightly positive-allometric growth in most fish. 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. True cases of strong allometric growth exist, with three examples given. Within species, a plot of $ \log a $ vs b can detect outliers in weight–length relationships. An equation to calculate mean condition factors from weight–length relationships is $ K_{mean} = 100aL^{b-3} $. Relative weight $ W_{rm} = 100W/(a_{m}L^{b_{m}}) $ can compare the condition of individuals across populations. Twelve recommendations for proper use and presentation of weight–length relationships, condition factors, and relative weight are given. The study highlights the historical development of weight–length relationships and condition factors, starting with the cube law of Galileo, followed by Fulton's condition factor and its evolution. It discusses the use of logarithmic transformations and the importance of considering allometric and isometric growth. The meta-analysis confirms that the mean exponent b is around 3.03, slightly above 3.0, indicating a tendency towards positive-allometric growth. The study also identifies that extreme values of b are often based on few weight–length relationships and that true allometric growth is rare. The study provides guidelines for interpreting and using weight–length relationships, condition factors, and relative weight in fisheries research.
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