Modelling individual variability in growth of bull trout in the Walla Walla River Basin using a hierarchical von Bertalanffy growth model

We examined growth in length of fluvial bull trout (Salvelinus confluentus) in the Walla Walla River Basin, Washington and Oregon. Our objectives were to quantify individual variability in growth; examine growth within and among years, life history forms, life stages and sexes; and estimate von Bertalanffy growth parameters. Individual variability was evaluated by modelling asymptotic length (L_∞) and the growth coefficient (k) as random variables. All models were fit with Bayesian methods and were evaluated for fit by the deviance information criterion. By incorporating individual variability, population‐level estimates of L_∞ and k appeared appropriate and estimated growth trajectories for specific bull trout fit individual observed patterns in growth. Growth trajectories and positive correlation between individual estimates of L_∞ and k suggest that some individuals grow at a faster rate and reach a larger maximum size than other individuals and those differences are maintained throughout life. Selected models suggest that fluvial migrants have higher estimates of L_∞ and k than residents, but there were only slight differences in parameter estimates among migrants from two adjacent spawning populations in the Walla Walla River Basin, as well as between males and females. Growth rates increased for fluvial migrants after subadult emigration. Individual variability in growth is consistent with the life history diversity assumed essential for bull trout population persistence. Quantifying this variability is important for modelling population dynamics and viability to conserve this threatened species.     

A temperature compensated von bertalanffy growth model for tagged red drum and black drum in Texas bays

Estimates of von Bertalanffy growth model (VBGM) parameters K and L_∞ were made for red drum (Sciaenops ocellatus), and black drum (Pogonias cromis), tagged and recaptured in Texas bays from November 1975 through June 1985. An annual temperature model was used to examine the growth model when periods of cold temperature were excluded. The best fit of the VBGM for red drum was based on time at large expressed in day-degrees with the coldest 60 days of the year excluded and yielded VBGM parameters estimates (± SE) of K = 0.422 (0.023) and L_∞ = 918 (21) mm. Black drum data were best fitted with time at large expressed in days with the coldest 120 days of the year excluded and yielded VBGM parameters of K = 0.219 (0.027) and L_∞ = 798 (42) mm. The exclusion of cold periods added to the body of evidence suggesting that scales and otoliths may be useful for ageing these species in the Gulf of Mexico. The source of the tag return (recreational fishermen, commercial fishermen, Texas Parks and Wildlife personnel) affected the parameter estimates. The pooled data, however, appeared to give the most reliable estimates.     

Age determination and growth of eel,Anguilla anguilla (L.), in lake Fertő Hungary

Ground and polished otolith sections, 0.2 mm thick, were produced from both sagittae of each fish, and repeated readings of the growth marks resulted in more accurate estimates of fish age. Supernumary zone formation in eel otoliths was a common phenomenon. The growth in length of the eels was accurately described by Bertalanffy's model using back-calculated lengths. Values of L_∞ = 1459 mm, K = 0.058 and t₀ = −0.869 years were determined. Mean incremental growth was calculated as 5–9 cm per year, showing that length increases rapidly with age. However, the growth of the eel population in Lake Fertő has become stunted, probably due to overstocking since 1975.     

Age,growth and demographic characteristics of <Emphasis Type="Italic">Sillago flindersi</Emphasis> exploited in a multi-species trawl fishery

This study investigated variability in the growth, length, and age compositions and the rates of mortality of Flinders’ sillago Sillago flindersi exploited in a demersal trawl fishery in eastern Australia. Sampling was done over 2 years across three depth strata at two locations approximately 400 km apart. Ageing of sectioned sagittal otoliths indicated that the observed maximum age of females was 6 years and that of males 5 years, that growth was variable and that the von Bertalanffy growth parameters significantly differed according to gender and location. Females attained a greater L _∞ than males, but males displayed greater k values. The L _∞ values of both sexes and the mean length-at-age for fish aged 3–5 years were greater at the location of highest latitude. Length and age compositions differed according to depth, with smaller (<15 cm FL) and younger (<2 years) fish generally more predominant in the shallow (<30 m) strata than in the deeper (>31 m) strata. S. flindersi appear to use the shallow strata as a juvenile habitat, moving to deeper waters as they grow. This depth stratification between cohorts may reduce intraspecific competition and could potentially be used as a spatial management tool to reduce any fishing-associated impacts on juveniles. Fish between 1 and 3 years old dominated the age compositions of populations combined across all depths, with estimated total mortality ranging between 2.24 and 2.40. Fishing mortality ranged between 1.54 and 1.70 and was more than twice the derived natural mortality. Exploitation rates were approximately 0.70, indicating that the species was heavily fished.     

Life history traits of leopard coralgrouper Plectropomus leopardus in the Okinawa Islands, southwestern Japan

The life history of the leopard coralgrouper Plectropomus leopardus was examined for the purpose of stock evaluation and to help maintain populations in the Okinawa Islands, southwestern Japan. Age was estimated from cut and burnt otoliths, and gonads were observed histologically to reveal the growth, spawning period and relationships between age and both sexual development and sexual maturation for P. leopardus in waters north of Okinawa Island. The three parameters in the von Bertalanffy growth equation, L _∞ , k, and t ₀, were estimated at 61.2 cm fork length, 0.289, and 0.41, respectively. The oldest individual obtained among the specimens was 18.8 years. The spawning period started in May and lasted until July. During this period, 50 % of females reached maturity at 43.3 cm fork length and at 5 years of age. Due to the sexual transition from female to male, the sex ratio decreased to 50 % at 59.8 cm fork length and at 10.3 years of age.     

Gills,growth and activity across fishes

Life history theory suggests that maximum size and growth evolve to maximize fitness. In contrast, the Gill Oxygen Limitation Theory (GOLT) suggests that growth and maximum size in fishes and other aquatic, water-breathing organisms is constrained by the body mass-scaling of gill surface area. Here, we use new data and a novel phylogenetic Bayesian multilevel modelling framework to test this idea by asking the three questions posed by the GOLT regarding maximum size, growth and gills. Across fishes, we ask whether the body mass-scaling of gill surface area explains (1) variation in the von Bertalanffy growth coefficient (k) above and beyond that explained by asymptomatic size (W_∞), (2) variation in growth performance (a trait that integrates the tradeoff between k and W_∞) and (3) more variation in growth performance compared to activity (as approximated by caudal fin aspect ratio). Overall, we find that there is only a weak relationship among maximum size, growth and gill surface area across species. Indeed, the body mass-scaling of gill surface area does not explain much variation in k (especially for those species that reach the same W_∞) or growth performance. Activity explained three to five times more variation in growth performance compared to gill surface area. Our results suggest that in fishes, gill surface area is not the only factor that explains variation in maximum size and growth, and that other covariates (e.g. activity) are likely important in understanding how growth, maximum size and other life history traits vary across species.     

Changes in growth characteristics of the small abalone Haliotis diversicolor (Reeve, 1846) after one decade in a closed culture system: a comparison with wild populations

Small abalone Haliotis diversicolor (Reeve, 1846) is one of the smallest commercial abalone in the world. The successful application of artificial propagation and mass seed production techniques since the 1980s have resulted in the establishment of well-developed culture systems for small abalone in Taiwan. In the study reported here, we estimated the growth of a population of small abalone after a decade in a closed culture system and its growth characteristics with those of wild populations reported in previous studies. The von Bertalanffy growth equations of the shell length (L) and body weight (W) of cultured abalone were L _t  = 71.73 (1 ? e^{?0.84 (t?0.16)}) and W _t  = 47.70 (1 ? e^{?0.84 (t?0.16)})^3.180, respectively. The instantaneous rate of change for weight had an inflection point at the age of 1.54 years, indicating that cultured abalones reach their apex of body growth around this age. Compared with the wild populations, the cultured population exhibits a significantly smaller maximal shell length (L _∞) and a significantly larger growth coefficient (k). Based on our results, it appears that the artificial culture of generations of small albalone for one decade or more in a closed system could be one of the major factors causing the observed minimization of size in the cultured abalone; this may be an adaptation in which growth is traded off for the larger k.     

Movement patterns and growth estimates of big skate (Raja binoculata) based on tag-recapture data

From 2003 through 2006, 18,180 big skate (Raja binoculata) were tagged in three regions in British Columbia, Canada: northern Hecate Strait, Queen Charlotte Sound and the west coast of Vancouver Island. To date, this is the largest tagging program conducted for skates or rays worldwide. As of December 31, 2008, 7% of the tagged fish (n = 1238) have been recaptured through the commercial fisheries. Generally, 75% of the recaptured fish were recaptured within 21 km of the tagging location. Long-range movements (up to 2340 km) were undertaken by a small percentage (1.5%) of the recaptured fish. Tagged big skate were recaptured in waters off of Oregon, Washington, throughout the Gulf of Alaska and the Bering Sea. The majority of big skate recaptured outside of Canadian waters were female (83%, n = 15), of which 80% (n = 12) were likely immature at release. Three methods of estimating growth parameters were employed and produced varying results. The Gulland and Holt method was not able to produce growth parameter estimates. The GROTAG method for combined sexes produced von Bertalanffy growth curve parameters L_∞ (294.7 cm), K (0.05) and t₀ (?1.44) that were similar to published estimates for British Columbia big skates. The von Bertalanffy growth curve parameters produced by Fabens method for combined sexes were L_∞ = 168.6 cm, K = 0.16 and t₀ = ?0.81.     

Modelling fish growth: Model selection,multi-model inference and model selection uncertainty

Model selection based on information theory is a relatively new paradigm in biological sciences with several advantages over the classical approaches. The aim of the present study was to apply information theory in the area of modelling fish growth and to show how model selection uncertainty may be taken into account when estimating growth parameters. The methodology was applied for length–age data of four species of fish, taken from the literature. Five-candidate models were fitted to each dataset: von Bertalanffy growth model (VBGM), generalized VBGM, Gompertz growth model, Schnute–Richards growth model, and logistic. In each case, the ‘best’ model was selected by minimizing the small-sample, bias-corrected form of the Akaike information criterion (AIC). To quantify the plausibility of each model, given the data and the set of five models, the ‘Akaike weight’ $w_i$ of each model was calculated. The average model was estimated for each case based on $w_i$. Following a multi-model inference (MMI) approach, the model-averaged asymptotic length ${\overline{L}}_{\infty }$ for each species was estimated, using all five models, by model-averaging estimations of L_∞ and weighting the prediction of each model by $w_i$. In the examples of this study, model selection uncertainty caused a magnification of the standard error of the asymptotic length of the best model (up to 3.9 times) and thus in all four cases estimating L_∞ from just the best model would have caused overestimation of precision of the asymptotic length. The VBGM, when used for inference, without being the best model, could cause biased point estimation and false evaluation of precision. Model selection uncertainty should not be ignored even if VBGM is the best model. Multi-model inference by model-averaging, based on Akaike weights, is recommended for making robust parameter estimations and for dealing with uncertainty in model selection.     

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, t₀, 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.     

Effects of exploitation on age, growth and mortality of the blackspot snapper, Lutjanus fulviflamma, at Mafia Island, Tanzania

Abstract Estimates of the growth parameters (L_∞ and K), mortality coefficients (Z, M and F) and exploitation rate (E) for the blackspot snapper, Lutjanus fulviflamma (Forsskål) from the Mafia Island Marine Park (MIMP) and adjacent intensively fished areas in Tanzania were determined. Sectioned otoliths showed that L. fulviflamma in the MIMP attained a maximum age of 18 years, with a high proportion of fish between 6 and 10 years old. The maximum age was 8 years in the intensively fished areas, with a preponderance of 2‐ and 4‐year‐old fish. The size structures of the populations in the MIMP and that in the intensively fished areas were markedly different, with the MIMP fish averaging (±SE) 211.4 ± 0.38 mm TL, but 154.6 ± 0.32 mm TL in the intensively fished areas. The von Bertalanffy growth parameters were L_∞ = 290.3 mm TL, K = 0.15 year^?1 and t₀ = ?2.7 years. There was no significant difference in growth between the four populations (L_∞: F‐stat = 0.14, P = 1.000, and K: F‐stat = 0.26, P = 0.992). Total mortality was 0.55 and 1.64 year^?1 in the MIMP and intensively fished areas, respectively, natural mortality 0.27 year^?1 and fishing mortality 0.18 and 1.37 year^?1 in the MIMP and intensively fished areas, respectively. The exploitation rate was 0.51 and 0.84 in the MIMP and intensively fished areas, respectively. The artisanal seine net fishery is directed mainly at younger fish in the intensively fished areas resulting in growth overfishing. The protracted life span, the slow growth and natural mortality rates imply that L. fulviflamma is vulnerable to overfishing and that the protection provided by the park, although limited, is vital for sustaining the fishery at Mafia Island.     

Cohort analysis on a freshwater fish Osteochilus hasselti C. & V. (Cyprinidae) at Bukit Merah Reservoir,Malaysia

An earlier cohort analysis using catch-at-length data (for the period May 1979–April 1980) on the stock of Osteochilus hasselti C. & V. computes statistics on: (1) the total stock at the start of the cohort (N = 22.7 × 10⁵) (these stock numbers decrease progressively at successive lengths, in a steady state and assuming constant natural mortality rate, M = 2.1); (2) catch numbers in a cohort totalling 780 940 individuals; (3) the exploitation rate of the cohort of E = 0.34, suggesting moderate exploitation of the species at Bukit Merah Reservoir, Malaysia.However, the validity of cohort analysis on a species exploited at a very early age depends on the input value of the variables natural mortality rate (M), fishing mortality rate of terminal largest fish (F_ter), and growth parameters (L_∞, K). Because of the methodological difficulties in estimation and verification of M, F_ter and K values of O. hasselti, a range of values of input variables is adopted for comparison. The effect of the variability of M values (0.5, 1.0, 1.5 and 2.5) on the computation results of smaller size-class fishes N_L is significantly different from that based on M = 2.1, showing a much lower population size.The variability of input values of F_ter (range 0.5–2.5) and K (0.28–2.62) is tested on their effects on the population size of recruits. The combined effect of M and K in the relationship of $\text{M}\text{K}$ ranging from 0.8 to 2.5 is varied to decide the possible values of K. In general, the different input values of M, F_ter and K result in lower estimates of the population size of recruits, N_r This is about 28% lower than N_r = 22.7 × 10⁵ when M = F_ter = 2.1 and K = 1.15. With an inherent computational bias, the population size of N_r = 22.7 × 10⁵ is probably an under-estimate, but it is both reasonable and biologically possible for O. hasselti at Bukit Merah Reservoir, Malaysia, since the input variables are generated from representative length composition data of commercial catches and tagging data.     

Fitting growth with the von Bertalanffy growth function: a comparison of three approaches of multivariate analysis of fish growth in aquaculture experiments

Three approaches for multivariate analysis of fish growth in aquaculture experiments with Nile tilapia (Oreochromis niloticus niloticus L.) based on the von Bertalanffy growth curve are presented and compared. The approaches are: an extended Gulland‐and‐Holt (GH) plot, a forced extended GH plot and a multilinear regression analysis for the growth parameter K. All three models provide valuable insight into the major environmental factors influencing the daily growth rate and explain 28–46% of the variance of the observed daily growth rate of the used data set. For all three methods, the modelled parameter is significantly related to the net yield of Nile tilapia and can, therefore, be used for the predictive modelling of management scenarios. The extended GH plot loads the influence of environmental parameters upon L_∞, while the forced extended GH plot and Direct fitting of K load the influence on the growth parameter K. The latter is more in the tradition of aquaculture research. But the forced extended GH plot and Direct fitting of K can only be applied if L_∞ of the cultured species is known, as the selected L_∞ influences the variance in the regression variables.     

Use of stochastic models to estimate the growth of the Port Jackson shark,Heterodontus portusjacksoni,off eastern Victoria,Australia

Three stochastic models were used to describe the growth of Heterodontus portusjacksoni off eastern Victoria, Australia. The models are based on a reparametrization of the von Bertalanffy growth model to take account of length-at-age heterogeneity, and incorporate random variation of the von Bertalanffy growth coefficient (k), using three different probability distribution functions (pdfs): Weibull, gamma and log-normal. They were fitted to the lengths of 179 specimens (79 females and 100 males), and associated age estimates obtained by counting growth bands in the inner trunk dentine layer of the dorsal-fin spines. The species is relatively long-lived (maximum estimated age of 35 years for females and 28 years for males) and slow growing, but has rapid growth during the early stages of life. All the models provided similar growth parameters and length-at-age quantiles. However, Kullbac?s information mean indicated that the stochastic model assuming a log-normal distribution fitted the length-at-age data better for both females (L∞ = 1337, E(k) = 0.059, t₀ = 5.294) and males (L∞ = 1125, E(k) = 0.075, t₀ = 4.944) than the models assuming other distributions. The χ² likelihood ratio test indicated that females and males grow differently.     

Reproductive biology of pink dentex Dentex gibbosus (Rafinesque) from the Adriatic Sea, Croatia

A 4‐year study (May 1997–December 2000) of the reproductive biology of pink dentex Dentex gibbosus (Rafinesque) from the Adriatic Sea revealed that this species is a rudimentary hermaphrodite. The smallest mature males and females captured were 38.70 cm in total length (T_L) and 39.80 cm in total length (T_L) respectively. The von Bertalanffy growth parameters estimated for the entire population were: L_∞=107.24, K=0.12 and t₀=−0.90. Fifty per cent of the population were sexually mature at 41.50 cm T_L, while 100% of the specimens were sexually mature at 57.00 cm T_L. Both monthly gonadosomatic index and macroscopically determined gonad stages strongly indicate that the pink dentex from the Adriatic Sea spawn partially in August, September and October. The mean value of absolute fecundity (F) was 1672 × 10⁶ eggs. The results of great fertility of the pink dentex, partial spawning and relatively late sexual maturation suggest that the pink dentex has a high potential for commercial culture.     

Is the fast growth of an equatorial Micropterus salmoides population explained by high water temperature?

Britton JR, Harper DM, Oyugi DO. Is the fast growth of an equatorial Micropterus salmoides population explained by high water temperature? Ecology of Freshwater Fish 2010: 19: 228–238. © 2010 John Wiley & Sons A/S Abstract – Marginal increment analysis of scales collected from the introduced Micropterus salmoides population of Lake Naivasha, Kenya revealed the formation of an annual growth check, validating their use to age individual fish. Subsequent analysis of scales from 372 fish collected between 2002 and 2009 revealed individuals were very fast growing compared with native populations in North America and other introduced populations in Europe, South America, Africa and Asia. This was likely to be as a result of the water temperatures in Lake Naivasha exceeding 20 °C throughout the year. This was corroborated by a meta‐analysis of the growth parameters asymptotic length L_∞ and growth coefficient K from across their geographical range that revealed variance was explained by differences in mean annual air temperatures. At a break point of approximately 10 °C, there was a shift to reduced L_∞ and increased K, suggesting a temperature driven trade‐off between growth rate and ultimate length. When adjusted for temperature and weighted for sample size, there were significant differences between the growth parameters of the North American and introduced populations, suggesting that other abiotic and biotic variables were also important determinants of the growth of individuals between the two ranges.     

Identifying mangrove areas for fisheries enhancement; population assessment in a patchy habitat

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Spatial variability in the somatic growth of pikeperch Sander lucioperca,an invasive piscivorous fish

Introduced fishes can develop invasive populations that impact native species and ecosystems. Understanding the population ecology of introduced species in their extended ranges and how this compares to their native ranges is therefore important for informing their management. Here, the age and somatic growth rates of the piscivorous freshwater fish pikeperch Sander lucioperca were analysed across their invasive and native ranges to determine their spatial patterns and drivers. Analyses were initially completed in their invaded range in central and western England. Populations varied spatially in their growth rates; being slowest for a population in a narrow and shallow canal and fastest in a large, impounded lowland river. A meta‐analysis of parameters of the von Bertalanffy growth model then revealed that across their native and invasive ranges, their theoretical ultimate lengths (L_∞) and growth coefficients (K) were significantly related to latitude, but not longitude. Their relationships with latitude were nonlinear, with higher values of L_∞ and lower values of K being evident towards their northerly and southerly range limits. Faster growth rates were evident in the middle of their range (45 to 55°N), suggesting temperatures here were most optimal for growth, but were in a trade‐off with reduced ultimate lengths. These spatial patterns suggest that whilst introduced S. lucioperca can colonise new waters across a wide area, the expression of their life‐history traits will vary spatially, with potential implications for how invasive populations establish and integrate into native fish communities.     

Age estimation of Antarctic minke whales <Emphasis Type="Italic">Balaenoptera bonaerensis</Emphasis> based on aspartic acid racemization technique

Counting of the growth layers in the earplugs is the most accepted technique for determining chronological age of Antarctic minke whales; however, unreadable growth layers form in some individuals, especially in young animals. In this study, aspartic acid racemization (AAR) technique was developed for estimating ages in this species with the aim of complementing the age estimated using earplugs. To validate the technique and to determine the specific coefficients for age estimation, the ratio of d and l-enantiomers of aspartic acid (Asp D/L) in lens of 18 whales and 20 fetuses were analyzed and compared with earplug-based age estimates. The equation for age estimation by AAR in this species was as follows: Log_e{[1 + (Asp D/L)_act]/[1 ? (Asp D/L)_act]} = 2.30 × 10^?3 × earplug age (year) + 0.0201 (p < 0.001, r ²  = 0.918). There is a strong correlation between the age estimates by AAR and earplugs. This study was successful in developing the AAR technique for the Antarctic minke whale, and the application of this technique can complement the age estimation of this species based on earplug readings, especially for young animals with unreadable earplugs.