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

Summary 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 ¼ 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 ¼ 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 ¼ 100aL b)3 . Relative weight Wrm ¼ 100W/ (amL b m ) 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.

[1]  C. Walters,et al.  Quantitative fisheries stock assessment: Choice, dynamics and uncertainty , 2004, Reviews in Fish Biology and Fisheries.

[2]  B. Zorica,et al.  Reproductive biology and length–weight relationship of painted comber, Serranus scriba (Linnaeus, 1758), in the Trogir Bay area (middle‐eastern Adriatic) , 2006 .

[3]  Brian R. Murphy,et al.  Evaluation of the Relative Weight (Wr ) Index, with New Applications to Walleye , 1990 .

[4]  D'arcy W. Thompson.  On Growth and Form , 1945 .

[5]  田口 喜三郎.  サケ成魚 (Oncorhynchus sp.) の自然死亡係数を推定する一つの試み,ならびにこれに基づく沖取漁業の合理性の検討-I , 1961 .

[6]  T. Borges,et al.  Weight–length relationships for eight species of the family Triglidae discarded on the south coast of Portugal , 2006 .

[7]  M. Srinath.  Empirical relationships to estimate the instantaneous rate of natural mortality , 1998 .

[8]  Mark Tatham,et al.  The General Approach , 2006 .

[9]  T. B. Bagenal.  Methods for assessment of fish production in fresh waters , 1979 .

[10]  Rainer Froese,et al.  Keep it simple: three indicators to deal with overfishing , 2004 .

[11]  A. Pallaoro,et al.  Co-variation of gonadosomatic index and parameters of length-weight relationships of Mediterranean horse mackerel, Trachurus mediterraneus (Steindachner, 1868), in the eastern Adriatic Sea , 2006 .

[12]  K. Stergiou,et al.  The Hellenic Seas : Physics, chemistry, biology and fisheries , 1997 .

[13]  San Pedro,et al.  The Weight-Length Relationship of the California Sardine ( Sardina cærulea ) at San Pedro Permalink , 2006 .

[14]  W. Martin.  The mechanics of environmental control of body form in fishes , 1949 .

[15]  R. Beverton,et al.  On the dynamics of exploited fish populations , 1993, Reviews in Fish Biology and Fisheries.

[16]  Kenneth G. Gerow,et al.  A New Method to Compute Standard-Weight Equations That Reduces Length-Related Bias , 2005 .

[17]  C. Kipling.  The Use of the Scales of the Brown Trout (Salmo trutta L.) for the Back-Calculation of Growth , 1962 .

[18]  F. N. Clark.  Fish Bulletin No. 12. The Weight-Length Relationship of the California Sardine (Sardina cærulea) at San Pedro , 1928 .

[19]  D. Weihs,et al.  Optimal Fish Cruising Speed , 1973, Nature.

[20]  D. Propst,et al.  Population dynamics of Gila trout in the Gila River drainage of the south-western United States. , 1997, Journal of fish biology.

[21]  William E. Ricker.  Handbook of computations for biological statistics of fish populations , 1960 .

[22]  A. Willer.  Die kleine Maräne (Coregonus albula L.) in Ostpreussen , 1924 .

[23]  W. Ricker.  Linear Regressions in Fishery Research , 1973 .

[24]  P. Safran.  Theoretical analysis of the weight-length relationship in fish juveniles , 1992 .

[25]  W. Ricker.  Computation and interpretation of biological statistics of fish populations , 1977 .

[26]  M. Kulbicki,et al.  A general approach to length-weight relationships for New Caledonian lagoon fishes , 2005 .

[27]  G. Mertz,et al.  THE LIMITS OF EXPLOITATION: A PRECAUTIONARY APPROACH , 1998 .

[28]  A. Keys,et al.  The Weight-Length Relation in Fishes. , 1928, Proceedings of the National Academy of Sciences of the United States of America.

[29]  R. Beverton.  Patterns of reproductive strategy parameters in some marine teleost fishes , 1992 .

[30]  K. Stergiou,et al.  Age, growth and mortality of red bandfish, Cepola macrophthalma (L.), in the western Aegean Sea (Greece) , 1992 .

[31]  E. K. Pikitch,et al.  Ecosystem-Based Fishery Management , 2004, Science.

[32]  Handbook of freshwater fishery biology , 1951 .

[33]  C. Walters,et al.  Quantitative Fisheries Stock Assessment , 1992, Springer US.

[34]  R. Froese,et al.  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 , 2000 .

[35]  K. Stergiou.  Abundance‐depth relationship, condition factor and adaptive value of zooplanktophagy for red bandfish, Cepola macrophthalma , 1993 .

[36]  F. W. Weymouth.  Fish Bulletin No. 7. The Life-History and Growth of the Pismo Clam (Tivela stultorum Mawe) , 1922 .

[37]  R. Hile.  Age and growth of the cisco, Leucichthys artedi (Le Sueur), in the lakes of the northeastern highlands, Wisconsin , 1936 .

[38]  K. Stergiou,et al.  Length-weight and length-length relationships of fish species from the Aegean Sea (Greece) , 2002 .

[39]  E. Cren,et al.  THE LENGTH-WEIGHT RELATIONSHIP AND SEASONAL CYCLE IN GONAD WEIGHT AND CONDITION IN THE PERCH , 2022 .

[40]  E. W. Shell,et al.  Tables for computing relative conditions of some common freshwater fishes , 1971 .

[41]  F. David,et al.  On the Dynamics of Exploited Fish Populations , 1959, Fish & Fisheries Series.