Information-theory approach to allometric growth of marine organisms

Allometric growth investigations are usually conducted by fitting the allometric model (L) y = axb ⇔ log y = log a + b log x (y, x are morphometric characters and b the allometric exponent), which is quite simple both conceptually and mathematically, and its parameters are easy to estimate by linear regression. However b is not necessarily constant and it may change either continuously or abruptly at specific breakpoints; thus, the simple L model quite often fails to describe allometric growth successfully. In the current context, a better alternative is proposed, based on Kullback-Leibler (K-L) information theory and multi-model inference (MMI). Allometric growth was investigated in eight marine species: the bivalves Pecten jacobaeus and Pinna nobilis, the squids Todarodes sagittatus and Todaropsis eblanae, the crab Pachygrapsus marmoratus (females), the ghost shrimp Pestarella tyrrhena (males), and the fishes Trachurus trachurus and Sparus aurata. In each of the eight species, a pair of body parts was measured and the allometric growth of one body part in relation to the other (reference dimension) was studied, by fitting five different candidate models including: the simple allometric model, two models assuming that b changed continuously and two other assuming that b had a breakpoint. For each species, the 'best' model was selected by minimizing the small-sample, bias-corrected form of the Akaike Information Criterion. To quantify the plausibility of each model, given the data and the set of five models, the 'Akaike weight' wi of each model was calculated; based on wi the average model was estimated for each case. MMI is beneficial, more robust, and may reveal more information than the classical approach. As demonstrated with the given examples, estimation of b from the linear model, when it was not supported by the data, revealed some characteristic pitfalls, such as concluding positive allometry when there is actually negative or vice versa, or reporting allometry when the data in reality support isometric growth or vice versa. © 2006 Springer-Verlag

Information-theory approach to allometric growth of marine organisms

Allometric growth investigations are usually conducted by fitting the allometric model (L) y = axb ⇔ log y = log a + b log x (y, x are morphometric characters and b the allometric exponent), which is quite simple both conceptually and mathematically, and its parameters are easy to estimate by linear regression. However b is not necessarily constant and it may change either continuously or abruptly at specific breakpoints; thus, the simple L model quite often fails to describe allometric growth successfully. In the current context, a better alternative is proposed, based on Kullback-Leibler (K-L) information theory and multi-model inference (MMI). Allometric growth was investigated in eight marine species: the bivalves Pecten jacobaeus and Pinna nobilis, the squids Todarodes sagittatus and Todaropsis eblanae, the crab Pachygrapsus marmoratus (females), the ghost shrimp Pestarella tyrrhena (males), and the fishes Trachurus trachurus and Sparus aurata. In each of the eight species, a pair of body parts was measured and the allometric growth of one body part in relation to the other (reference dimension) was studied, by fitting five different candidate models including: the simple allometric model, two models assuming that b changed continuously and two other assuming that b had a breakpoint. For each species, the 'best' model was selected by minimizing the small-sample, bias-corrected form of the Akaike Information Criterion. To quantify the plausibility of each model, given the data and the set of five models, the 'Akaike weight' wi of each model was calculated; based on wi the average model was estimated for each case. MMI is beneficial, more robust, and may reveal more information than the classical approach. As demonstrated with the given examples, estimation of b from the linear model, when it was not supported by the data, revealed some characteristic pitfalls, such as concluding positive allometry when there is actually negative or vice versa, or reporting allometry when the data in reality support isometric growth or vice versa. © 2006 Springer-Verlag

Growth and reproduction of horse mackerel, Trachurus trachurus (carangidae)

There is a broad knowledge of the growth and reproduction of Trachurus trachurus, although important gaps still exist. Horse mackerel are a long-lived species, reaching up to 40 years of age. They have isometric growth, although the alometric parameter b may vary throughout the year and in relation to latitude. Growth to age 3 is rapid compared to slower growth later in life. Phenomena of density dependent growth have been observed in the northeast Atlantic. Horse mackerel are an asynchronous species. The following stages of atresia have been validated in horse mackerel: alpha, beta, and delta. The transition in females from the spawning state to post spawning is very fast. The spawning fraction in horse mackerel is estimated to be between 8.3 nd 20.9&Eth;Horse mackerel have a long spawning season (up to 8 months), which varies according to geography. Length at first maturity is between 16 and 25 cm, most commonly around 21 cm. Males mature at a slightly smaller length than females. The age at first maturity for females has been estimated to range from 2 to 4 years, depending on the geography. Batch fecundity has been estimated to range between 172¿209 oocytes per gram-female-weight. Female spawning lasts between 65 and 94 days. An individual female can release from 5 to 16 batches during the spawning period. The estimated potential annual relative fecundity ranges from 1040 to 3280 oocytes per gram-female-weigh

Growth and reproduction of horse mackerel, Trachurus trachurus (Carangidae)

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