Von Bertalanffy Parameters Research Articles

Age, growth and stock structure of the oceanic whitetip shark, Carcharhinus longimanus, from the southwestern equatorial Atlantic

Between November 1992 and November 1997, 258 specimens (71.0–250.0 cm-TL) of Carcharhinus longimanus were collected off northeastern Brazil (Brazilian EEZ). Vertebral sections from 110 individuals, 44 males (71.0–235.5 cm), 60 females (81.0–230.0 cm) and six of undetermined sex (120.5–187.2 cm) were analyzed. Mean MIR analysis showed that one band is formed annually starting in August. Male and female growth is similar, back-calculated von Bertalanffy parameters were L ∞ = 325.4 cm, K = 0.075 yr −1 and t 0 = −3.342 yr −1 for both sexes, whereas observed length-at-age parameters were L ∞ = 284.9 cm; K = 0.996 yr −1, and t 0 = −3.391 yr −1. Observed length-at-age described growth better than back-calculated lengths. Maturity is reached for both sexes at 180.0–190.0 cm, or 6–7 year-old individuals. The overall sample ranged from a recently born male from the 0 age-class (71.0 cm) to a 17 year-old female (250.0 cm). Growth rates are 25.2 cm yr −1 in the first free-living year, 13.6 cm yr −1 from ages 1 to 4, 9.7 cm yr −1 for adolescents of age 5 and 9.10 cm yr −1 for mature individuals. The size-range of the overall sample is similar to others collected in different locations worldwide. The species follows the K-selected pattern like most elasmobranchs.

Growth Curves for Graptemys, with a Comparison to Other Emydid Turtles

Abstract Von Bertalanffy growth-curve parameters were calculated from plastral annuli of specimens of Graptemys ouachitensis and G. pseudogeographica kohnii captured in western Kentucky, and museum specimens of G. ernsti from Alabama and G. caglei (males only) from Texas. Males had estimated values of k (intrinsic rate of growth toward asymptotic plastron length, PLA) ranging from 0.264 to 0.498. Values of k for females of three species (range 0.110–0.182) were significantly less than the corresponding values for males, whereas PLA values for females (range 175.3–220.2 mm) greatly exceeded PLA values of males (range 91.5–114.5 mm). There was a significant negative correlation of PLA with k within 13 emydid turtle populations for which von Bertalanffy parameter estimates were available, with a slope similar to those reported for fish taxa; however, this relationship was not evident for either male values or female values when data were analyzed by phylogenetically independent contrasts. Use of the Richards...

The biology of the skates Raja wallacei and R. pullopunctata (Batoidea: Rajidae) on the Agulhas Bank, South Africa

Aspects of the biology of Raja wallacei and R. pullopunctata were investigated using data collected in 1995 and 1996 from research and commercial trawls on the Agulhas Bank, South Africa. Age and growth parameters were investigated by examination of bands on the vertebral centrum. Estimates of Von Bertalanffy parameters for R. wallacei were L ∞ = 405.40 mm disc width (DW), K = 0.27 and t 0 = −0.08 years for males and L ∞ = 435.23 mm DW, K = 0.26 and t 0 = −0.21 years for females. For R. pullopunctata, the estimates were L ∞ = 770.50 mm DW, K = 0.10 and t 0 = −2.37 years for males and L ∞ = 1 326.75 mm DW, K = 0.05 and t 0 = −2.20 years for females. Growth was significantly different between sexes for both species. The oldest aged R. wallacei and R. pullopunctata were 15 and 18 years respectively. The length at first maturity was approximately 350 mm DW or 7 years of age for R. wallacei and 600 mm DW or 9 years of age for R. pullopunctata. The length-at-50% maturity for R. wallacei was 395 mm DW for males and 400 mm DW for females. R. wallacei fed primarily on benthic teleosts and crustaceans. There were significant differences (p < 0.05) in the diet between research- and commercially caught fish, in terms of percentage frequency of occurrence and volume of prey.

Spatial variation in mean growth rates at size of southern rock lobster, Jasus edwardsii, in South Australian waters

Size-specific growth rates of Jasus edwardsii were estimated from 16 000 recaptures of tagged lobsters during a 3-year mark–recapture study. The von Bertalanffy growth model was fitted to observed increases in carapace length. A normal likelihood of predicted length increment as a function of starting length and time-at-large was maximized. Estimated standard deviation of the likelihood, taken as an allometric function of predicted length increment, quantified individual growth variation. The distributions of residuals indicated satisfactory fits. von Bertalanffy parameters of growth were estimated at three levels of spatial resolution: 18 statistical reporting blocks, 6 growth subregions, and 2 fishery management zones. Among blocks, the mean annual growth of lobsters of 100 mm carapace length was 7–20 mm for males and 5–15 mm for females. Females grew more slowly after reaching sexual maturity. Growth rates declined by approximately 1 mm year –1 per 20 m increase in depth of habitat, at depths of 20 m and deeper. Density-dependent growth was indicated by spatial anti-correlation between male growth rates at 100 mm and fishery catches by number per unit effort. Regression implied that a 10% decrease in catch rate corresponded to increased growth by weight of 2–5%.

Population Structure and Growth of the Hermit Crab Diogenes pugilator (Decapoda: Anomura: Diogenidae) from the Northeastern Atlantic

ABSTRACT A population of the hermit crab Diogenes pugilator from the northeastern Atlantic (Barbate, Straits of Gilbraltar, Spain) was studied. The results show continuous recruitment throughout the year, within a size range from 0.4-1.02 mm in cephalothoracic shield length, as a consequence of the prevalence of ovigerous females throughout the year. The sex ratio was in favor of females. Results of size-frequency distributions from different locations show that there was no clear segregation of sizes by sexes or depths. Five cohorts can coexist, although a decrease in the number of specimens was observed in the second year studied, perhaps induced by human influences in the area (the building of a new harbor and the restoration of the beach). The values of the Von Bertalanffy parameters (K and Loo) showed slight differences between sexes and between years within sexes, as is shown in the φ' index analysis. The estimated maximum longevity of the individuals in the population studied was about 2 years, but normally the cohorts lived in the study area for approximately 1 year.

POPULATION STRUCTURE AND GROWTH OF THE HERMIT CRAB DIOGENES PUGILATOR (DECAPODA: ANOMURA: DIOGENIDAE) FROM THE NORTHEASTERN ATLANTIC

A population of the hermit crab Diogenes pugilator from the northeastern Atlantic (Barbate, Straits of Gilbraltar, Spain) was studied. The results show continuous recruitment throughout the year, within a size range from 0.4-1.02 mm in cephalothoracic shield length, as a consequence of the prevalence of ovigerous females throughout the year. The sex ratio was in favor of females. Results of size-frequency distributions from different locations show that there was no clear segregation of sizes by sexes or depths. Five cohorts can coexist, although a decrease in the number of specimens was observed in the second year studied, perhaps induced by human influences in the area (the building of a new harbor and the restoration of the beach). The values of the Von Bertalanffy parameters (K and Loo) showed slight differences between sexes and between years within sexes, as is shown in the φ' index analysis. The estimated maximum longevity of the individuals in the population studied was about 2 years, but normally the cohorts lived in the study area for approximately 1 year.

Age and growth of the blue stingray Dasyatis chrysonota chrysonota from the South-Eastern Cape coast of South Africa

The age and growth of blue stingray Dasyatis chrysonota chrysonota from the south-east coast of South Africa was investigated by examination of bands on the vertebral centra. The annual nature of band deposition was verified by centrum edge characteristics and supported by growth of known-age individuals kept in captivity. The derived Von Bertalanffy parameters from age and length data were L ∞ = 532 mm (disc width, DW), K = 0.175 and t 0 = −3.65 for males and L ∞ = 913 mm DW, K = 0.070 and t 0 = −4.48 for females. Growth of three captive specimens showed distinct seasonal differences, with a mean growth rate of 7.3 mm·month−1 during summer and 3.8 mm·month−1 during winter. The mean rate of growth in captivity for the first year after birth (66.7 mm·year−1) is similar to the value obtained from back-calculations (64.6 mm·year−1), but higher than the calculated value of 45.1 mm·year−1. The estimated age at first maturity is five years for males and seven years for females.

Investigation of an iterative method for fitting von Bertalanffy growth equation using data on the halfbeak fish Hemirhamphus sajori (T et S)

Fitting growth data to the von Bertalanffy growth function usually involves the traditional Ford-Walford plot method and the statistical maximum likelihood method. The former uses only the growth data with equal time intervals; the latter requires a large amount of computation. The iterative method presented in this paper demands less computation and it can use any growth data. The paper demonstrates a method to fit growth data to the linearized version of the von Bertalanffy growth formula by a group of simulated data. Results show that the correct solution can be obtained from an R 2 matrix, and that the maximum R 2 value corresponds to the correct von Bertalanffy parameters. Real data on halfbeak fish ( Hemirhamphus sajori (T et S)), a recently emerged pelagic fish species in the Yellow and Bohai seas, are also used to test the method.

A preliminary estimate of age and growth of the dusky sharkCarcharhinus obscurusfrom the South-West Indian Ocean, with comparisons to the western North Atlantic population

Age and growth of the dusky shark Carcarhinus obscurus from the South-West Indian Ocean was determined from bands in the vertebrae of 42 individuals. Age to maturity was estimated at 20,5 years for males and between 17 and 24 years for females. The oldest fish examined was a 34-year-old female. The Von Bertalanffy parameters calculated for the sexes combined were: L ∞ = 334, K = 0,047 and t 0 = −5,18. The growth rate of dusky sharks from the South-West Indian Ocean was similar to that of the western North Atlantic population.

Variation in fish growth characteristics along a river course

Variation in the growth patterns of roach, Rutilus rutilus (L.), pike, Esox lucius L., and chub, Leuciscus cephalus (L.) was examined along the upper Warta River, where human impact (mostly pollution) has influenced the longitudinal zonation on the fish assemblage. Significant differences were found in the exponent of weight-length relationships for roach and chub populations occupying different zones of the river, but no such variation was observed in pike. Moreover, pike growth was isometric, whereas roach and chub grew allometrically, with regression coefficients (slope) above 3. Although the length-at-age data were similar for each zone, the von Bertalanffy parameters (L inf, K and t 0) suggest that there may exist some inter-zone variation in the overall growth patterns of these species. All the species grew better in the zone where the index of relative abundance (relating dominance of a particular species to its maximum abundance in river system) achieved its highest value. The results suggest that a relative abundance index expressed in this way can be a good index of ‘habitat quality’.

Growth rates of five species of subtidal clam on a beach in the South Island, New Zealand

Growth rates of five species of New Zealand surf clams were estimated at Cloudy Bay, Marlborough, from analyses of sequential length-frequency samples with the computer program MULTIFAN and analyses of incremental growth of marked individuals with the computer program GROTAG. The von Bertalanffy parameters k and L∞ estimated by MULTIFAN were: Paphies donacina, 0.33 and 94.1; Spisula aequilatera, 1.01 and 60.3; Mactra murchisoni, 0.57 and 88; M. discors, 0.41 and 68; data for Dosinia anus could not be analysed reliably. These parameters estimated by GROTAG were: P. donacina, 0.35 and 84.8; S. aequilatera, 1.74 and 57.6; M. murchisoni, 0.58 and 80.6; M. discors, 0.54 and 61.5; D. anus, 0.36 and 61.6. The age-based growth estimated by MULTIFAN is not strictly comparable with the length-based growth estimated by GROTAG, but graphical comparisons show that both programs estimate similar growth rates for each species of surf clam. Interspecies differences in growth rates are hypothesized to be related to differences in species depth distribution within the surf zone. S. aequilatera, with the highest growth rate, is found just inshore of the primary wave break, where surf diatom abundance is postulated to be highest. An extension to the linear growth model of GROTAG that allows the predicted growth of larger animals to decline asymptotically to zero and never be negative is presented.

Growth of the Pacific pomfret, Brama japonica: a comparison between otolith and length–frequency (MULTIFAN) analysis

Age and growth of the Pacific pomfret, Brama japonica, were independently estimated with presumed daily increments within otolith microstructure and MULTIFAN analysis of length–frequency distributions obtained from drift net fisheries. Likelihood ratio tests detected significant differences between sexes and geographic areas in von Bertalanffy parameter estimates from otolith analysis. Otolith interpretations indicated that the species is short lived (age 3+), fast growing (growth coefficient (K) &gt; 1.1), and fully recruited to the North Pacific squid drift net fishery at &lt; 1 yr old. Back-calculated hatching dates indicate a protracted spawning period. MULTIFAN models fit the length–frequency data with an assumption of both annual and biannual recruitment. Growth parameter estimates were asymptotic fork length (FL∞) = 49.9 cm, K = 0.57 for an annual cohort model, and FL∞ = 49.4 cm, K = 1.0 for a biannual cohort model. The growth model derived from otolith increment counts is closer to the MULTIFAN model that assumes biannual length–frequency modes, rather than annual modes.

Growth, age structure, and productivity of ling,Genypterus blacodes(Ophidiidae), in New Zealand waters

Abstract Growth of ling, Genypterus blacodes, from four areas around southern New Zealand (West Coast South Island, Chatham Rise, Southern Plateau, Bounty Platform) was determined by counting rings in otoliths. This aging method was validated by using the progression of modal peaks in length frequencies and by analysing the changing state of otolith margins over 1 year. Calculated von Bertalanffy parameters showed that females grew significantly faster than males in all areas, and that growth rates were significantly different between areas. Ling grew fastest off the West Coast and slowest on the Southern Plateau. Instantaneous natural mortality is in the range 0.17–0.20, and instantaneous fishing mortality is < 0.1 in all areas. Differences in growth rates, length‐frequency distributions, sex ratios, and ages at recruitment indicate that gene flow between areas is probably slight, so there is justification for managing ling as several stocks.

Growth, age structure, and productivity of jack mackerels (Trachurus spp.) in New Zealand waters

Abstract Growth of jack mackerels, Trachurus novaezelandiae and Trachurus declivis, off the central west coast and in the Bay of Plenty, New Zealand, was determined by counting growth check rings in otoliths. One growth check ring appeared to be laid down each year. Peaks in length‐frequencies corresponded to calculated mean lengths at age, and strong or weak age classes progressed through the population at a rate concurrent with the annual deposition of rings. No significant sexual differences in growth were apparent for either species but geographical differences are indicated. The von Bertalanffy parameters l 8, k, and t 0 that are considered to describe growth best are 37.7 cm, 0.23 yr−1, ‐2.12 yr for T. novaezelandiae in the Bay of Plenty, 35.3 cm, 0.31 yr−1, ‐0.59 yr for T. novaezelandiae off the central west coast, and 45.8 cm, 0.28 yr−1, ‐0.74 yr for T. declivis off the central west coast, respectively. The best estimate of instantaneous natural mortality is 0.18 for both species. Instantaneous fi...

Revised Estimates of Age and Growth of the Sandbar Shark (Carcharhinus plumbeus) from the Western North Atlantic

Age and growth of the sandbar shark (Carcharhinus plumbeus) were determined from tag and recapture data covering a 26-yr period (1964–90). Results were compared with previously published age and growth estimates based primarily on rings in vertebrae. Recent long-term tag returns suggest that the sandbar shark grows much slower than previously proposed and may take nearly 30 yr to reach maturity. Revised von Bertalanffy parameters (sexes combined) are L∞ = 186, k = 0.046, and t0 = −6.45. The limitations of ageing elasmobranchs solely from rings in vertebrae and the need for validating rings in hardparts of fishes are discussed.

Interpretable Statistical Tests for Growth Comparisons using Parameters in the von Bertalanffy Equation

Likelihood ratio, t-, univariate χ2-, and T2-tests have been proposed to compare von Bertalanffy parameters among stocks. As commonly applied, all of these tests are approximate, with the accuracy of each dependent on the nonlinearity of the von Bertalanffy equation, sample size, and if present, the degree of heterogeneity in the error variances. An empirical comparison of these procedures shows that the likelihood ratio test often differs in outcome from the others. Analysis of the conflicting cases by confidence region comparisons and Monte Carlo simulations almost always resolved the outcome in favor of the likelihood ratio test. The parameter effects component of nonlinearity was found to be the principal factor biasing the t-, univariate χ2-, and T2-tests. Reparameterizations of the von Bertalanffy equation substantially reduced, but did not completely eliminate, conflicting outcomes. It is concluded that the likelihood ratio test is the most accurate of the procedures considered in this study, and whenever possible, it should be the approach of choice.

Comparative study of growth of flatfishes on the west coast of Brittany

Lusitanian and boreal flatfish species live in the Bay of Douarnenez (Brittany, France); ten are abundant enough to be the subject of this growth investigation. In all species, females attain greater ultimate size than males, and oldest specimens are frequently female. Species are segre‐gated to their longevity: those rapidly reaching their asymptotic length have the shortest life spans and also the highest values of the Von Bertalanffy parameter K.In the bay, species of the boreal fish fauna (plaice, dab) find suitable environmental conditions for rapid growth; fish of the Lusitanian fauna (sand soles) grow slower than those living in southern areas.In the Atlantic Ocean, the growth of the sole is better than in the North Sea and the Mediterranean.

Age and growth of angler-fish ( Lophius piscatorius L.) in the north Irish Sea

Age analysis was carried out on 3739 angler-fish taken from the north Irish Sea between May 1983 and June 1985. A variety of ossified structures were examined, including fin rays, teeth, vertebrae and otoliths; the latter proving suitable for routine ageing. Validation of ageing was obtained from the observation of seasonal changes in otolith marginal growth, growth of young fish and following of an identified year class through the fishery. Derived growth rates agreed well with the temporal progression of length/frequency modes through time. Growth rates were calculated from length-at-age data and von Bertalanffy parameters fitted yielding the equation; L = 105.555 [1-exp (−0.1759 ( t−0.380))]. Growth in weight and weight/length relationships were also examined. The complex growth patterns of the otoliths are discussed in relation to feeding behaviour and difficulties in interpretation outlined. The results obtained are compared with other studies of Lophiid growth.

Inferring the Distribution of the Parameters of the von Bertalanffy Growth Model from Length Moments

A theoretical approach is described for determining the joint distribution of the parameters of the von Bertalanffy growth model from statistical moments of length. The approach extends the work of K. J. Sainsbury, who had demonstrated that different mean parameter estimates are obtained by assuming that the von Bertalanffy equation applies to individual fish rather than to groups of fish. Sainsbury articulated the goal of studying the joint probability distributions of K and L∞ in animal populations and developed a maximum likelihood procedure for estimating the parameters of particular distributional forms describing K and L∞, which were assumed for mathematical convenience to be statistically independent. The primary goal of the present paper is to provide a framework for future research in generalizing Sainsbury's approach by considering (K, L∞) to be a random vector described by a joint probability density function and by allowing broader classes of distributions to be considered. Minimum cross-entropy (MCE) inversion, an information–theoretic methodology for approximating probability distributions, is shown to be effective in selecting a reasonable and unique joint distribution corresponding to observable length moments. Appealing features of the MCE methodology include the ability to include prior knowledge of uncertain applicability and the capacity of the resulting approximate distribution to represent potential stochastic dependencies between the von Bertalanffy parameters. Several numerical examples, using simulated and historical data, are presented to illustrate how information about the variation and covariation of L∞ and K can be inferred from a minimal set of length moments. The directions developed in this paper are far from a practical and useful methodology. The MCE inversion procedure is a "method of moments," with no statistical assessment of reliability. Further research is needed to make this promising pdf approximation scheme better suited for real fisheries problems.

Age determination, growth, mortality and age of first reproduction in adult Queen Conch, Strombus gigas L., off Puerto Rico

Growth and mortality of adult Strombus gigas L. was studied in a population offshore of La Parguera, Puerto Rico. Adult queen conchs do not grow in shell length, but only in shell thickness. Growth in thickness of the flared shell-lip was measured during a 2-year mark-recapture study and modelled using the von Bertalanffy growth function. Model parameters were K=0.3706 year −1 and L ∞ (asymptotic lip-thickness) =54.9 mm; the third von Bertalanffy parameter, t 0, cannot be obtained from mark-recapture data alone. Growth in tissue, meat and shell weights of adults were determined using the von Bertalanffy growth function in conjunction with regression equations for weights versus shell length and/or lip thickness. Total instantaneous mortality in adults, determined using von Bertalanffy parameters and lip-thickness frequency analysis, was 1.66 year −1. Subtracting a previous estimate of fishing mortality ( F=1.14 year −1) yielded a natural mortality ( M) of 0.52 year −1. Given an average age at maturation, defined by the formation of the flared shell-lip, of 3.2 years, the age of first reproduction was estimated at 3.6 years, but could be as much as 4 years.