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 = aLb 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 Kmean = 100aLb−3. Relative weight Wrm = 100W/(amLbm) can be used for comparing the condition of individuals across populations, where am is the geometric mean of a and bm 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

Empirical relationships to estimate asymptotic length, length at first maturity and length at maximum yield per recruit in fishes, with a simple method to evaluate length frequency data

Empirical relationships are presented to estimate in fishes, asymptotic length (L∞) from maximum observed length (Lmax), length at first maturity (Lm) from L∞, life span (tmax) from age at first maturity (tm), and length at maximum possible yield per recruit (Lopt) from L∞ and from Lm, respectively. The age at Lopt is found to be a good indicator of generation time in fishes. A spreadsheet containing the various equations can be downloaded from the Internet at http://www.fishbase.org/download as popdynJFB.zip. A simple method is presented for evaluation of length–frequency data in their relationship to L∞, Lm and Lopt. This can be used to evaluate the quality of the length–frequency sample and the status of the population. Three examples demonstrate the usefulness of this method. 2000 The Fisheries Society of the British Isle

Simple methods to obtain preliminary growth estimates for fishes

Explored were methods to derive preliminary information on growth from other known life history parameters such as maximum size and size and age at first maturity. Use was made of the fact that with asymptotic length known, only one point is needed to determine the general shape of a von Bertalanffy growth curve. An empirical relationship was used to predict asymptotic length from maximum observed length. We used mean size reached at age 1 or 2 or mean age and size at first maturity, as is often provided in the literature, to derive preliminary von Bertalanffy growth curves. Results of this approach were then compared with published growth estimates. We used an empirical relationship to predict length at first maturity from asymptotic length when only the age at first maturity was given in the literature. Temperate fishes usually have restricted spawning periods lasting a few months per year and maturity is typically reached in the first, second, third, or later year, i.e. in steps of 12 months, with larger species maturing later. We used data in FishBase (http://www.fishbase.org) to establish typical ranges for age at first maturity and growth performance of temperate fishes as a function of maximum size. We present an approach that uses this framework to derive preliminary growth estimates for species of which only the maximum size is known