Quantifying the Growth of Female Pacific Hake (Merluccius productus): An Example of Measuring Uncertainty and Bias in Non-linear Parameter Estimation

1990 ◽  
Vol 47 (4) ◽  
pp. 672-681 ◽  
Author(s):  
David W. Welch ◽  
Gordon A. McFarlane
Keyword(s):  
Growth Parameters ◽  
Growth Models ◽  
Nonlinear Models ◽  
Somatic Growth ◽  
Maximum Size ◽  
Diagnostic Methods ◽  
Parameter Estimates ◽  
Intrinsic Variability ◽  
Merluccius Productus ◽  
Size At Age

Estimates of size-at-age are commonly reported in fisheries studies, but statistical uncertainty and intrinsic variability in the growth parameters are less frequently examined. We examine these questions using recently-developed statistical methods for quantifying uncertainty and bias in parameter estimates for nonlinear models with independent and additive Gaussian errors. We also describe diagnostic methods to determine when the usual method for examining parameter uncertainty, linearization, is unacceptable. Both our review and our approach to uncertainty are generally applicable to nonlinear estimation, and not solely restricted to growth models. We illustrate our approach with length-at-age data for female Pacific hake (Merluccius productus) from Georgia Strait, British Columbia. Between-year variation in somatic growth seems to be restricted to the two von Bertalanffy growth parameters K and L∞. Mean asymptotic length declined by about 10% since the late 1970's while the parameter K nearly tripled in value. Closer examination showed that the decline in somatic growth was restricted to the maximum size attained. We argue that the changes are most consistent with selective removal of the largest individuals from the population by the fishery, rather than a response of growth rates to either environmental or density-dependent factors.

scholarly journals The Standard Deviation Structure as a New Approach to Growth Analysis in Weight and Length Data of Farmed Lutjanus guttatus

Fishes ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 60
Author(s):  
Sergio G. Castillo-Vargasmachuca ◽  
Eugenio Alberto Aragón-Noriega ◽  
Guillermo Rodríguez-Domínguez ◽  
Leonardo Martínez-Cárdenas ◽  
Eulalio Arámbul-Muñoz ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Growth Parameters ◽  
Growth Models ◽  
Growth Curves ◽  
Gompertz Model ◽  
Information Criterion ◽  
Weight Growth ◽  
Length Data ◽  
Size At Age ◽  
The Right

In the present study, size-at-age data (length and weight) of marine cage-reared spotted rose snapper Lutjanus guttatus were analyzed under four different variance assumptions (observed, constant, depensatory, and compensatory variances) to analyze the robustness of selecting the right standard deviation structure to parametrize the von Bertalanffy, Logistic, and Gompertz models. The selection of the best model and variance criteria was obtained based on the Bayesian information criterion (BIC). According to the BIC results, the observed variance in the present study was the best way to parametrize the three abovementioned growth models, and the Gompertz model best represented the length and weight growth curves. Based on these results, using the observed error structure to calculate the growth parameters in multi-model inference analyses is recommended.

scholarly journals Growth Parameters and Spawning Season Estimation of Four Important Flyingfishes in the Kuroshio Current Off Taiwan and Implications From Comparisons With Global Studies

2022 ◽  
Vol 8 ◽  
Author(s):  
Shui-Kai Chang ◽  
Tzu-Lun Yuan ◽  
Simon D. Hoyle ◽  
Jessica H. Farley ◽  
Jen-Chieh Shiao
Keyword(s):  
Growth Parameters ◽  
Growth Models ◽  
Growth Parameter ◽  
Optimal Growth ◽  
Kuroshio Current ◽  
Parameter Estimates ◽  
Special Importance ◽  
Von Bertalanffy ◽  
Multiple Model ◽  
The Kuroshio

Growth shapes the life history of fishes. Establishing appropriate aging procedures and selecting representative growth models are important steps in developing stock assessments. Flyingfishes (Exocoetidae) have ecological, economic, and cultural importance to many coastal countries including Taiwan. There are 29 species of flyingfishes found in the Kuroshio Current off Taiwan and adjacent waters, comprising 56% of the flyingfishes taxa recorded worldwide. Among the six dominant species in Taiwan, four are of special importance. This study reviews aging data of these four species, documents major points of the aging methods to address three aging issues identified in the literature, and applies multi-model inference to estimate sex-combined and sex-specific growth parameters for each species. The candidate growth models examined included von Bertalanffy, Gompertz, Logistic, and Richards models, and the resulting optimal model tended to be the von Bertalanffy model for sex-combined data and Gompertz and von Bertalanffy models for sex-specific cases. The study also estimates hatch dates from size data collected from 2008 to 2017; the results suggest that the four flyingfishes have two spawning seasons per year. Length-weight relationships are also estimated for each species. Finally, the study combines the optimal growth estimates from this study with estimates for all flyingfishes published globally, and statistically classifies the estimates into clusters by hierarchical clustering analysis of logged growth parameters. The results demonstrate that aging materials substantially affect growth parameter estimates. This is the first study to estimate growth parameters of flyingfishes with multiple model consideration. This study provides advice for aging flyingfishes based on the three aging issues and the classification analysis, including a recommendation of using the asterisci for aging flyingfishes to avoid complex otolith processing procedures, which could help researchers from coastal countries to obtain accurate growth parameters for many flyingfishes.

scholarly journals Harbour porpoises (Phocoena phocoena) in the North Atlantic: Biological parameters

2003 ◽  
Vol 5 ◽  
pp. 71 ◽  
Author(s):  
Christina Lockyer
Keyword(s):  
North Atlantic ◽  
Growth Parameters ◽  
Growth Models ◽  
Maximum Size ◽  
Biological Information ◽  
Biological Parameters ◽  
Structure Information ◽  
The North ◽  
Age Related ◽  
The North Atlantic

Biological parameters for harbour porpoises are reviewed throughout their range in the North Atlantic. Most information is based on studies of a combination of directed catches, bycatches and strandings. All these sources are valuable for providing biological information, but each carries some bias when it comes to interpretation of parameters, especially those involving age structure. Information on age-related parameters, reproduction and growth is presented and assessed by region and/or population, of which there may be 14 throughout the North Atlantic. Among age related parameters, maximum longevity recorded is 24 years; maximal rate of population growth is probably 9.4% but in the range 5-10%; mortality is highest in year 1, and <5% of the population live beyond 12 years; an estimate of 0.867 with a maximum age of 23 years has been given for survival. Among reproductive parameters, age at sexual maturation falls between 3-4 years for both sexes; age at first parturition is probably 4-5 years; age at first ovulation is >3 years; ovulation rates fall in the range 0.64 - 0.988 corpus per year, and reproductive interval is 1.01-1.57 years; pregnancy rates are generally in the range 0.74 - 0.986 per year, meaning that not all females produce a calf every year; there is seasonal breeding/mating in the period June–August; gestation lasts 10-11 months; parturition generally occurs between mid-May to mid-July; duration of lactation is uncertain, but is probably at least 8 months; size at birth is usually in the range 65-75 cm with a maximum size of about 80 cm. Sex ratio is biased to males throughout life: 1.1-1.2 males : 1.0 females in the foetal stage, and 1.1-1.7 males : 1.0 females post-natal. Growth parameters indicate an asymptotic length and weight that varies with population, but usually falls in the range 153-163 cm and 55-65 kg for females and 141-149 cm and 46-51 kg for males. Growth models used for length and weight are typically based on von Bertalanffy and Gompertz models. Length at sexual maturity also varies with population, but is usually in the range 138-147 cm for females and 127-135 cm for males. There is no information based on vertebral epiphyseal fusion to indicate age at physical maturity. Foetal growth appears normal, but there is uncertainty about the existence of embryonic diapause. Size/age at weaning are uncertain, but size may be <115 cm and at an age >8 months; however, entirely independent feeding may not occur until about 10 months.

scholarly journals Individual, spatial and inter-sex variation in somatic growth: a study of Piaractus mesopotamicus (Characiformes: Serrasalmidae), a long-distance freshwater Neotropical migratory fish

2017 ◽  
Vol 15 (2) ◽  
Author(s):  
Luzia da S. Lourenço ◽  
Rosa Maria R. da Costa ◽  
Patrícia L. Rondon ◽  
Lúcia A. F. Mateus
Keyword(s):  
River Basin ◽  
Growth Parameters ◽  
Growth Models ◽  
Average Length ◽  
Somatic Growth ◽  
Information Criterion ◽  
Individual Variability ◽  
Fish Growth ◽  
Long Distance ◽  
Piaractus Mesopotamicus

ABSTRACT Growth is a fundamental biological process, driven by multiple endogenous (intra-individual) and exogenous (environmental) factors that maintain individual fitness and population stability. The current study aims to assess whether individual, spatial (headwaters and floodplains) and inter-sex variation occurs in the growth of Piaractus mesopotamicus in the Cuiabá River basin. Samples were collected monthly from July 2006 to July 2007, at two areas in the Cuiabá River basin (headwaters and floodplain). Three growth models (individuals; individuals and sex factors; individuals and areas factors) were developed and compared the fish growth parameters using Akaike information criterion (AIC). The best fit to the length-at-age data was obtained by a model that considered individual variation and sex. The theoretical maximum average length ( L∞ ) was 64.99 cm for females, and 63.23 cm for males. Females showed a growth rate (k) of 0.230 yr-1and males of 0.196 yr-1. Thus, could be concluded that individual variability and sex were the main sources of variation in P. mesopotamicus somatic growth parameters.

scholarly journals Modeling the Lag Time of Listeria monocytogenes from Viable Count Enumeration and Optical Density Data

2002 ◽  
Vol 68 (12) ◽  
pp. 5816-5825 ◽  
Author(s):  
F. Baty ◽  
J. P. Flandrois ◽  
M. L. Delignette-Muller
Keyword(s):  
Listeria Monocytogenes ◽  
Optical Density ◽  
Growth Parameters ◽  
Growth Models ◽  
Growth Parameter ◽  
Viable Count ◽  
Linear Increase ◽  
Lag Phase ◽  
Parameter Estimates ◽  
Phase Duration

ABSTRACT The following two factors significantly influence estimates of the maximum specific growth rate (μmax) and the lag-phase duration (λ): (i) the technique used to monitor bacterial growth and (ii) the model fitted to estimate parameters. In this study, nine strains of Listeria monocytogenes were monitored simultaneously by optical density (OD) analysis and by viable count enumeration (VCE) analysis. Four usual growth models were fitted to our data, and estimates of growth parameters were compared from one model to another and from one monitoring technique to another. Our results show that growth parameter estimates depended on the model used to fit data, whereas there were no systematic variations in the estimates of μmax and λ when the estimates were based on OD data instead of VCE data. By studying the evolution of OD and VCE simultaneously, we found that while log OD/VCE remained constant for some of our experiments, a visible linear increase occurred during the lag phase for other experiments. We developed a global model that fits both OD and VCE data. This model enabled us to detect for some of our strains an increase in OD during the lag phase. If not taken into account, this phenomenon may lead to an underestimate of λ.

scholarly journals Description of dermal denticles from the caudal region of Raja clavata and their use for the estimation of age and growth

2008 ◽  
Vol 65 (9) ◽  
pp. 1701-1709 ◽  
Author(s):  
B. Serra-Pereira ◽  
I. Figueiredo ◽  
I. Farias ◽  
T. Moura ◽  
L. S. Gordo
Keyword(s):  
Growth Parameters ◽  
Growth Models ◽  
Age Determination ◽  
Maximum Size ◽  
Age And Growth ◽  
Growth Band ◽  
Caudal Region ◽  
Vertebral Centra ◽  
Raja Clavata ◽  
Dermal Denticle

Abstract Serra-Pereira, B., Figueiredo, I., Farias, I., Moura, T., and Gordo, L. S. 2008. Description of dermal denticles from the caudal region of Raja clavata and their use for the estimation of age and growth. – ICES Journal of Marine Science, 65: 1701–1709. This work is a response to a lack of knowledge of the biology of Raja clavata in southern European waters, particularly in terms of age and growth. Two structures were analysed: dermal denticles and vertebral centra. Six types of dermal denticle were identified in the tail. Among those, small thorns were the most suitable for age determination owing to their fixed position, persistence throughout their lifespan, and defined growth-band pattern. Caudal thorns were more accurate than vertebral centra for age determination and were therefore selected as the most appropriate structure for ageing R. clavata. Based on edge analysis, annual band deposition was verified. The birthdate was established as 1 June based on the prevalence of hyaline edges in age-0 class specimens: prevalence peaked in May and June. Both von Bertalanffy and Gompertz growth models were fitted to age-at-length data, but the former was considered more appropriate based on similarity between the estimated L∞ and the maximum size recorded for the species. No significant differences in growth parameters were observed between sexes. The estimated growth parameters were L∞ = 1280 mm, k = 0.117 year−1, and t0 = −0.617 years. The maximum age estimated for R. clavata was 10 years, for a female of length 835 mm.

The use of caudal thorns for ageing Raja undulata from the Portuguese continental shelf, with comments on its reproductive cycle

2007 ◽  
Vol 58 (11) ◽  
pp. 983 ◽  
Author(s):  
Teresa Moura ◽  
Ivone Figueiredo ◽  
Inês Farias ◽  
Bárbara Serra-Pereira ◽  
Rui Coelho ◽  
...  
Keyword(s):  
Continental Shelf ◽  
Growth Parameters ◽  
Growth Models ◽  
Geographical Area ◽  
Growth Function ◽  
Age And Growth ◽  
Reproductive Analysis ◽  
First Maturity ◽  
Size At Age ◽  
Best Fit

The present study focuses on age estimation, with reproductive information contributing to the better understanding of the growth and the biology of Raja undulata. In the age and growth study, two calcified structures were used: caudal thorns and central vertebra. Results of readings showed that there were no significant differences in age estimates between the two structures. Both von Bertalanffy and Gompertz growth models were fitted to size-at-age data by sex and geographical area. No significant differences were found between sexes for the two models but significant differences were found between geographical areas (P = 0.05). The Gompertz growth function was selected as the best model to describe R. undulata growth because it presented the best fit and the most reasonable biological estimates. Reproductive analysis indicates one annual breeding season for R. undulata. The differences found in the estimates of length at first maturity between geographical areas (TL50% = 838 mm in Peniche and 762 mm in Algarve for females and TL50% = 781 mm in Peniche and 736 mm in Algarve for males), together with the regional differences found between growth parameters estimates (P = 0.05), may reflect the existence of different local populations of R. undulata on the Portuguese continental shelf.

Life history characteristics of the silky shark Carcharhinus falciformis from the central west Pacific

2018 ◽  
Vol 69 (4) ◽  
pp. 562 ◽  
Author(s):  
Michael I. Grant ◽  
Jonathan J. Smart ◽  
William T. White ◽  
Andrew Chin ◽  
Leontine Baje ◽  
...  
Keyword(s):  
Life History ◽  
Growth Parameters ◽  
Growth Models ◽  
Significant Risk ◽  
Growth Parameter ◽  
Parameter Estimates ◽  
West Pacific ◽  
Average Litter Size ◽  
Silky Shark ◽  
Carcharhinus Falciformis

In the central west Pacific region, silky sharks (Carcharhinus falciformis) are commonly taken in fisheries, forming up to 95% of incidental elasmobranch bycatch. The present study examined the life history of silky sharks (n=553) from Papua New Guinean waters. Age was analysed using sectioned vertebrae, and a multimodel approach was applied to the length-at-age data to fit growth models. Females ranged in length from 65.0- to 253.0-cm total length (TL), with the oldest estimated at 28 years. Males ranged in length from 68.4 to 271.3cm TL and were aged to a maximum of 23 years. The logistic model provided the best fitting growth parameter estimates of length at birth L0=82.7cm TL, growth coefficient g=0.14year–1 and asymptotic length L∞=261.3cm TL for the sexes combined. Females reached sexual maturity at 204cm TL and 14.0 years, whereas males reached maturity at 183cm TL and 11.6 years. The average litter size from 28 pregnant females was 8 (range of 3–13). The growth parameters and late ages of sexual maturation for silky sharks in the central west Pacific suggest a significant risk from fisheries exploitation without careful population management.

scholarly journals Improved Growth Estimates for Lethrinus harak: Measuring Increments, Adjusting Ages, and Fitting Flexible Growth Models

Fishes ◽  
2018 ◽  
Vol 3 (3) ◽  
pp. 31
Author(s):  
Stephen Midway ◽  
Andrew Ostrowski ◽  
Lindsey West ◽  
Mario Hernandez ◽  
Matthew Robertson
Keyword(s):  
Fishery Management ◽  
Growth Parameters ◽  
Growth Models ◽  
Age And Growth ◽  
Tropical Species ◽  
Parameter Estimates ◽  
Growth Coefficient ◽  
Asymptotic Size ◽  
Age Estimates ◽  
Edge Size

Thumbprint emperor (Lethrinus harak) are a widely distributed, tropical species ranging throughout the Indo-Pacific region. In coastal Tanzania, overfishing is likely occurring and thumbprint emperor are commonly represented in catches. The goal of this study was to estimate age and growth to provide basic life history information that may help inform future management. We sampled a total of n = 55 thumbprint emperors from both fishery-dependent and fishery-independent sources. Annular age estimates were improved with measurements of otolith markings. Fish ages ranged from zero to five years. We also evaluated the addition of otolith edge size (a proxy for fractional age) to age estimation, and fit two von Bertalanffy growth models—one for the whole ages and one for the fractional ages—using a flexible Bayesian framework. Growth parameters were similar between the two models, and ultimately, L ∞ (maximum asymptotic size parameter) estimates were comparable to other published values for the species, although our estimates of K (growth coefficient parameter) were smaller. Robust aging techniques for tropical fishes can provide a foundation for basic fishery management, which would help to sustain the future of this widely distributed fish.

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