Age and growth of spiny dogfish (Squalus acanthias) in the Gulf of Alaska: analysis of alternative growth models

Ten growth models were fitted to age and growth data for spiny dogfish (Squalus acanthias) in the Gulf of Alaska. Previous studies of spiny dogfish growth have all fitted the t0 formulation of the von Bertalanffy model without examination of alternative models. Among the alternatives, we present a new two-phase von Bertalanffy growth model formulation with a logistically scaled k parameter and which estimates L0. A total of 1602 dogfish were aged from opportunistic collections with longline, rod and reel, set net, and trawling gear in the eastern and central Gulf of Alaska between 2004 and 2007. Ages were estimated from the median band count of three independent readings of the second dorsal spine plus the estimated number of worn bands for worn spines. Owing to a lack of small dogfish in the samples, lengths at age of small individuals were back-calculated from a subsample of 153 dogfish with unworn spines. The von Bertalanffy, two-parameter von Bertalanffy, two-phase von Bertalanffy, Gompertz, two-parameter Gompertz, and logistic models were fitted to length-at-age data for each sex separately, both with and without back-calculated lengths at age. The two-phase von Bertalanffy growth model produced the statistically best fit for both sexes of Gulf of Alaska spiny dogfish, resulting in L∞ = 87.2 and 102.5 cm and k= 0.106 and 0.058 for males and females, respectively.

Estimates of growth and comparisons of growth rates determined from length- and age-based models for populations of purple wrasse (Notolabrus fucicola)

Growth of a temperate reefa-ssociated fish, the purple wrasse (Notolabrus fucicola), was examined from two sites on the east coast of Tasmania by using age- and length-based models. Models based on the von Bertalanffy growth function, in the standard and a reparameterized form, were constructed by using otolith-derived age estimates. Growth trajectories from tag-recaptures were used to construct length-based growth models derived from the GROTAG model, in turn a reparameterization of the Fabens model. Likelihood ratio tests (LRTs) determined the optimal parameterization of the GROTAG model, including estimators of individual growth variability, seasonal growth, measurement error, and outliers for each data set. Growth models and parameter estimates were compared by bootstrap confidence intervals, LRTs, and randomization tests and plots of bootstrap parameter estimates. The relative merit of these methods for comparing models and parameters was evaluated; LRTs combined with bootstrapping and randomization tests provided the most insight into the relationships between parameter estimates. Significant differences in growth of purple wrasse were found between sites in both length- and age-based models. A significant difference in the peak growth season was found between sites, and a large difference in growth rate between sexes was found at one site with the use of length-based models.

Growth variation and stock structure in North Pacific albacore

Working paper NPALB/87/21 submitted to the 10th North Pacific Albacore Workshop. Paper reports the results of ongoing research on validated age and growth models and the elucidation of stock structure for the North Pacific albacore. (Document pdf contains 22 pages)

Using an inverse-logistic model to describe growth increments of blacklip abalone (Haliotis rubra) in Tasmania

A new description of growth in blacklip abalone (Haliotis rubra) with the use of an inverse-logistic model is introduced. The inverse-logistic model avoids the disadvantageous assumptions of either rapid or slow growth for small and juvenile individuals implied by the von Bertalanffy and Gompertz growth models, respectively, and allows for indeterminate growth where necessary. An inverse-logistic model was used to estimate the expected mean growth increment for different black-lip abalone populations around southern Tasmania, Australia. Estimates of the time needed for abalone to grow from settlement until recruitment (at 138 mm shell length) into the fishery varied from eight to nine years. The variability of the residuals about the predicted mean growth increments was described with either a second inverse-logistic relationship (standard deviation vs. initial length) or by a power relationship (standard deviation vs. predicted growth increment). The inverse-logistic model can describe linear growth of small and juvenile abalone (as observed in Tasmania), as well as a spectrum of growth possibilities, from determinate to indeterminate growth (a spectrum that would lead to a spread of maximum lengths).

Growth dynamics of the spinner shark (Carcharhinus brevipinna) off the United States southeast and Gulf of Mexico coasts: a comparison of methods

The age and growth dynamics of the spinner shark (Carcharhinus brevipinna) in the northwest Atlantic Ocean off the southeast United States and in the Gulf of Mexico were examined and four growth models were used to examine variation in the ability to fit size-at-age data. The von Bertalanffy growth model, an alternative equation of the von Bertalanffy growth model with a size-at-birth intercept, the Gompertz growth model, and a logistic model were fitted to sex-specific observed size-at-age data. Considering the statistical criteria (e.g., lowest mean square error [MSE], high coefficient-of-determination, and greatest level of significance) we desired for this study, the logistic model provided the best overall fit to the size-at-age data, whereas the von Bertalanffy growth model gave the worst. For “biological validity,” the von Bertalanffy model for female sharks provided estimates similar to those reported in other studies. However, the von Bertalanffy model was deemed inappropriate for describing the growth of male spinner sharks because estimates of theoretical maximum size (L∞) indicated a size much larger than that observed in the field. However, the growth coefficient (k= 0.14/yr) from the Gompertz model provided an estimate most similar to that reported for other large coastal species. The analysis of growth for spinner shark in the present study demonstrates the importance of fitting alternative models when standard models fit the data poorly or when growth estimates do not appear to be realistic.

Age, growth, mortality, and radiometric age validation of gray snapper (Lutjanus griseus) from Louisiana

The gray snapper (Lutjanus griseus) is a temperate and tropical reef fish that is found along the Gulf of Mexico and Atlantic coasts of the southeastern United States. The recreational fishery for gray snapper has developed rapidly in south Louisiana with the advent of harvest and seasonal restrictions on the established red snapper (L. campechanus) fishery. We examined the age and growth of gray snapper in Louisiana with the use of cross-sectioned sagittae. A total of 833 specimens, (441 males, 387 females, and 5 of unknown sex) were opportunistically sampled from the recreational fishery from August 1998 to August 2002. Males ranged in size from 222 to 732 mm total length (TL) and from 280 g to 5700 g total weight (TW) and females ranged from 254 to 756 mm TL and from 340 g to 5800 g TW. Both edge analysis and bomb radiocarbon analyses were used to validate otolith-based age estimates. Ages were estimated for 718 individuals; both males and females ranged from 1 to 28 years. The von Bertalanffy growth models derived from TL at age were Lt = 655.4{1–e[–0.23(t)]} for males, Lt = 657.3{1–e[– 0.21(t)]} for females, and L t = 656.4{1–e[– 0.22 (t)]} for all specimens of known sex. Catch curves were used to produce a total mortality (Z) estimate of 0.17. Estimates of M calculated with various methods ranged from 0.15 to 0.50; however we felt that M= 0.15 was the most appropriate estimate based on our estimate of Z. Full recruitment to the gray snapper recreational fishery began at age 4, was completed by age 8, and there was no discernible peak in the catch curve dome.

Red snapper (Lutjanus campechanus) demographic structure in the northern Gulf of Mexico based on spatial patterns in growth rates and morphometrics

Red snapper (Lutjanus campechanus) in the United States waters of the Gulf of Mexico (GOM) has been considered a single unit stock since management of the species began in 1991. The validity of this assumption is essential to management decisions because measures of growth can differ for nonmixing populations. We examined growth rates, size-at-age, and length and weight information of red snapper collected from the recreational harvests of Alabama (n=2010), Louisiana (n=1905), and Texas (n =1277) from 1999 to 2001. Ages were obtained from 5035 otolith sections and ranged from one to 45 years. Fork length, total weight, and age-frequency distributions differed significantly among all states; Texas, however, had a much higher proportion of smaller, younger fish. All red snapper showed rapid growth until about age 10 years, after which growth slowed considerably. Von Bertalanffy growth models of both mean fork length and mean total weight-at-age predicted significantly smaller fish at age from Texas, whereas no differences were found between Alabama and Louisiana models. Texas red snapper were also shown to differ significantly from both Alabama and Louisiana red snapper in regressions of mean weight at age. Demographic variation in growth rates may indicate the existence of separate management units of red snapper in the GOM. Our data indicate that the red snapper inhabiting the waters off Texas are reaching smaller maximum sizes at a faster rate and have a consistently smaller total weight at age than those collected from Louisiana and Alabama waters. Whether these differences are environmentally induced or are the result of genetic divergence remains to be determined, but they should be considered for future management regulations.

Estimating long-term growth-rate changes of southern bluefin tuna (Thunnus maccoyii) from two periods of tag-return data

Southern bluefin tuna (SBT) (Thunnus maccoyii) growth rates are estimated from tag-return data associated with two time periods, the 1960s and 1980s. The traditional von Bertalanffy growth model (VBG) and a two-phase VBG model were fitted to the data by maximum likelihood. The traditional VBG model did not provide an adequate representation of growth in SBT, and the two-phase VBG yielded a significantly better fit. The results indicated that significant change occurs in the pattern of growth in relation to a VBG curve during the juvenile stages of the SBT life cycle, which may be related to the transition from a tightly schooling fish that spends substantial time in near and surface shore waters to one that is found primarily in more offshore and deeper waters. The results suggest that more complex growth models should be considered for other tunas and for other species that show a marked change in habitat use with age. The likelihood surface for the two-phase VBG model was found to be bimodal and some implications of this are investigated. Significant and substantial differences were found in the growth for fish spawned in the 1960s and in the 1980s, such that after age four there is a difference of about one year in the expected age of a fish of similar length which persists over the size range for which meaningful recapture data are available. This difference may be a density-dependent response as a consequence of the marked reduction in the SBT population. Given the key role that estimates of growth have in most stock assessments, the results indicate that there is a need both for the regular monitoring of growth rates and for provisions for changes in growth over time (possibly related to changes in abundance) in the stock assessment models used for SBT and other species.

Age and growth of blue rockfish (Sebastes mystinus) from central and northern California

Otoliths from blue rockfish (Sebastes mystinus), were aged by using a combination of surface and break-and-burn methods. The samples were collected between 1978 and 1998 off central and northern California. Annual growth increments in the otoliths were validated by using edge analysis for females up to age 23 and for males to age 25.The first annual growth increment was identified by comparing the diameter of the otolith from fish known to be one year old collected in May (when translucent zone formation was completed) to the mean diameter of the first translucent zone in the otoliths from older fish. Our estimated maxi-mum ages of 44 years for males and 41 years for females were much older than those reported in previous studies. Von Bertalanffy growth models were developed for each sex. Females grew faster and reached larger maximum length than males. The growth models were similar to those generated in other studies of this species in southern and central California. Fish from northern and central California had similar maximum sizes, maximum ages, and growth model parameters.

Age and growth of the bastard grunt (Pomadasys incisus: Haemulidae) inhabiting the Canarian archipelago, Northwest Africa

The bastard grunt (Pomadasys incisus) is one of the most abundant coastal demersal fishes inhabiting the Canary Islands. Age and growth were studied from samples collected between October 2000 and September 2001. Growth analysis revealed that this species is a fast growing and moderately short-lived species (ages up to seven years recorded). Length-at-age was described by the von Bertalanffy growth model (L∞=309.58 mm; k=0.220/year; t0=–1.865 year), the Schnute growth model (y1=126.66 mm; y2=293.50 mm; a=–0.426; b= 5.963), and the seasonalized von Bertalanffy growth model (L∞=309.93 mm; k=0.218/ year; t0= –1.896 year; C=0.555; ts=0.652). Individuals grow quickly in their first year, attaining approximately 60% of their maximum length; after the first year, their growth rate drops rapidly as energy is probably diverted to reproduction. The parameters of the von Bertalanffy weight growth curve were W∞=788.22 mm; k=0.1567/year; t0= –1.984 year. Fish total length and otolith radius were closely correlated, r2=0.912. A power relationship was estimated between the total length and the otolith radius (a=49.93; ν=0.851). A year’s growth was represented by an opaque and hyaline (translucent) zone—an annulus. Backcalculated lengths were similar to those predicted by the growth models. Growth parameters estimated from the backcalculated sizes at age were L∞=315.23 mm; k=0.217/year; and t0= –1.73 year.

Age, growth, and reproduction of permit (Trachinotus falcatus) in Florida waters

We examined 536 permit (Trachinotus falcatus, 65–916 mm FL) collected from the waters of Florida Keys and from the Tampa Bay area on Florida’s Gulf coast to describe their growth and reproduction.Among permit that we sexed, females ranged from 266 to 916 mm in length (mean=617) and males ranged from 274 to 855 mm (mean=601). Ages of 297 permit ranging from 102 to 900 mm FL were estimated from thin-sectioned otoliths (sagittae). The large proportion of otoliths with an annulus on the margin and an otolith from an OTC-injected fish suggested that a single annulus was formed each year during late spring or early summer.Permit reach a maximum age of at least 23 years.Permit grew rapidly until an age of about five years, and then growth slowed considerably. Male and female von Bertalanffy growth models were not significantly different, and the sexes-combined growth model was FL=753.1(1–e –0.348(Age+0.585)). Gonad development was seasonal, and spawning occurred during late spring and summer over artificial and natural reefs at depths of 10–30 m. Ovaries that contained oocytes in the final stages of oocyte maturation or postovulatory follicles were found during May–July. We estimated that 50% of the females in the population had reached sexual maturity by 547 mm and an age of 3.1 years and that 50% of the males in the population had reached sexual maturity by 486 mm and an age of 2.3 years. Because Florida regulations restrict the maximum size of permit caught in recreational and commercial fisheries to 20-inch (508-mm), most fish harvested are sexually immature. With the current size selectivity of the fishery, the spawning stock biomass of permit could decrease quickly in response to moderate levels of fishing mortality; thus, the regulations in place in Florida to restrict harvest levels appear to be justified.

Age, growth, mortality, and distribution of pinfish (Lagodon rhomboides) in Tampa Bay and adjacent Gulf of Mexico waters

Life-history dynamics of pinfish (Lagodon rhomboides) were examined from data derived from random station surveys conducted in Tampa Bay and adjacent Gulf of Mexico waters during 1993–97. In addition, patterns in spatial distribution and abundance in Gulf of Mexico waters were investigated. Ages determined from whole otoliths ranged from 0 to 7 years, and von Bertalanffy growth models for males and females were not significantly different. Von Bertalanffy growth model parameters were L∞=219.9 mm SL, k =0.33/yr, and t0 =–1.10 years for all fish combined. High gonadosomatic indices during October–December indicated that some spawning may occur in Tampa Bay. Estimated lengths at 50% maturity were 132 mm SL for males and 131 mm SL for females. Total instantaneous mortality rates derived from the Chapman-Robson estimator ranged from 0.88 to 1.08/yr, and natural mortality was estimated to be 0.78/yr. In Gulf of Mexico waters, pinfish catch rates declined with increasing depth, and most pinfish were caught in <17 m of water. Length distributions showed that pinfish segregate by size with increasing depth.

Morphometrics, length-weight relationship and condition of Rastrineobola argentea (Pellegrin 1904) in the Winam Gulf of Lake Victoria (Kenya)

Correlation between total length (TL), fork length (FL) and standard length (SL) of Raslrineobola argentea (pellegrin 1904) in the Winam Gulf of Lake Victoria indicate that FL = 0.92 TL - 0.74 and SL = 0.90 TL - 1.74. Length-weight relationship of log-transformed data shows that the slopes of the regression lines were 3.06 to 3.22 for juveniles, 2.70 to 3.05 for males and 3.24 to 3.71 for females. The slopes were significantly different between groups at at a =0.05. The Fulton's condition factor (K) was highest in December (1.019-1.073) and March/April (1.015-1.030) but lowest in June (1:00-1.025) for all stations. Significant differences between groups demands for the use of different growth models for juveniles, males and females especially for the von Bertalanffy growth equation which uses length-weight relationship. Observed cyclic viations in condition factor suggests two peak breeding seasons for this species in the Winam Gulf. The practical lmplications of these results in stock assessment using length-based fish stock assessment methods is briefly discussed.

Reference-growth rate – a simple and handy parameter summarizing the influence of environmental conditions

Abstract Environmental changes may have an impact on life conditions of the fish, e.g. food supply for the fish. The prevailing environmental conditions apply evenly to all age groups of one stock. Small fish have high growth rates, whereas large fish grow with low rates. But, it can be shown on the basis of the von Bertalanffy-growth model that it is sufficient to know only the growth rate of one single age group to compute the growth rates of all other age groups. The growth rate of a reference fish GRF (e.g. a fish with a body mass of 1 kg) was introduced as a reference growth describing the current food condition of all age groups of the stock. As an example a time series of the reference-growth rate of the northern cod stock (NAFO, 3K) was computed for the time span 1979 to 1999. For the northern cod stock it can be observed that environmental conditions caused growth rates below the long-term mean for seven years in a row. After a prolonged hunger period the fish stock collapsed in 1992 also by the impact of fisheries - and this was probably not a coincidence. Now, with the reference-growth rate GRF a simple and handy parameter was found to summarize the influence of the environmental conditions on growth and other derived models and therefore makes it easier to compute the influence of environmental changes within stock assessment. Zusammenfassung Veränderungen der Umwelt können Auswirkungen auf die Lebensbedingungen der Fische haben, z. B. auf das Nahrungsangebot der Fische. Die vorherrschenden Umgebungsbedingungen wirken gleichmäßig auf alle Altersgruppen eines Bestandes, wobei typischer Weise kleineFische hohe Wachstumsraten haben, während die großen Fische mit niedrigen Raten wachsen. Auf der Grundlage des von Bertalanffy-Wachstumsmodells kann gezeigt werden, dass es ausreicht, nur die Wachstumsrate von einer einzigen Altersgruppe zu kennen, um die Wachstumsraten von allen anderen Altersgruppen berechnen zu können. Die Wachstumsrate eines Referenz-Fisches (z.B. eines Fisches mit einer Körpermasse von 1 kg) wurde als Referenz-Wachstum GRF eingeführt, die den aktuellen Zustand des Nahrungsangebots füralle Altersgruppen des Bestandes beschreibt. Als Beispiel wurde einer Zeitreihe der Referenz-Wachstumsraten des nördlichen Kabeljaubestandes (NAFO, 3K) für die Zeitsraum 1979 bis 1999 berechnet. Für diesen Kabeljaubestand war zu beobachten, dass Umgebungsbedingungen für sieben Jahre in Folge Wachstumsraten unter dem langjährigen Mittelwert verursachten. Nach einer längeren Hungerperiode kollabierte dieser Fischbestand im Jahr 1992 auch durch den Einfluß der Fischerei - und dies war sicher kein Zufall. Jetzt, mit der Referenz-Wachstumsrate GRF, ist ein einfacher und handlicher Parameter gefunden, der es gestattet den Einfluss der Umweltbedingungen auf die Wachstumsbedingungen und andere davon abgeleitete Modelle zusammenzufassen. Dies macht es einfach, den Einfluss von Umweltveränderungen innerhalb der Bestandsabschätzungen zu berechnen.

Structural dynamic eutrophication models

This article discusses problems of modelling the seasonal succession of algal species in lakes and reservoirs, and the adaptive selection of certain groups of algae in response to changes in the inputs and relative concentrations of nutrients and other environmental variables. A new generation of quantitative models is being developed which attempts to translate some important biological properties of species (survival, variation, inheritance, reproductive rates and population growth) into predictions about the survival of the fittest, where ”fitness” is measured or estimated in thermodynamic terms. The concept of ”exergy” and its calculation is explored to examine maximal exergy as a measure of fitness in ecosystems, and its use for calculating changes in species composition by means of structural dynamic models. These models accomodate short-term changes in parameters that affect the adaptive responses (species selection) of algae.