Schnute Models Research Articles

Allometry and Individual Growth of the Temperate Pacific Sardine (Sardinops sagax) Stock in the Southern California Current System

We analyzed individual growth and body mass allometry of the temperate stock of Sardinops sagax from samples collected on commercial fleet during 2005 to 2014 in the southern California Current System. Ages were estimated on otolith growth ring reading. Age (years) and standard length (SL; mm) data were fitted using four growth models: von Bertalanffy (VBM), Gompertz (GM), logistic (LM), and Schnute (SM) models. Parameters of each model were calculated by the maximum likelihood method using Akaike information criterion and Akaike’s weight (WAICi) to select the model with the greatest plausibility. Additionally, the interannual growth performance (φ′) variation was described. Body mass allometry was established from the relationship between total body mass (TM; g) and standard length. The sardine samples ranged in size from 114 to 226 mm SL and in weight from 20 to 192 g TM; ages varied from 0.5 to 6.0 years. The allometric parameter (b) was estimated to be 3.155 (3.154–3.156), showing a hyper-allometry growth type. On the basis of raw data, we found that the LM model fit the original data better (WAICi ~35%). When models were fitted to data bolstered with simulated values, the VBM model obtained the greatest weight (WAICi = 60.9%), but the LM model had null plausibility. Consequently, we determined that the Pacific sardine growth pattern was best described by the VBM model, which appears to be more robust against biased data. The φ′ showed interannual variation (2.13–2.51), with an average of φ′ = 2.25. An apparent inverse relationship was observed between φ′ and the Oceanic Niño Index (ONI) or the Pacific Decadal Oscillation (PDO) and the apparent positive relationship between Upwelling Index (UI) and φ’.

Estimating the total allowable catch and management of Threadfin porgy (Evynnis cardinalis) fisheries in the northern South China Sea based on sampling surveys conducted at fishing ports

In order to develop a method that apply sampling survey data randomly obtained at fishing ports to fish stock assessments, based on fish landing surveys conducted at fishing ports in the northern South China Sea (SCS), 19 Threadfin porgy (Evynnis cardinalis) catch per unit effort (CPUE) datasets were collected for fishing vessels with different gear types and engine powers and incorporated into surplus production models. Considering only the fitting performance, the Schaefer model had the best overall goodness of fit, followed by the Fox, CYP, W–H, and Schnute models. Among fishing vessels with different gears and engine powers, the data were best fitted for single-trawl vessels powered by 301–400-kW engines and for gillnet vessels powered by > 200-kW engines. Eight model expressions were superior and selected for subsequent analyses based on their goodness of fit and relative residuals. The Kobe plot analysis results showed an optimistic fish stock status when using the four model expressions, required more caution when using three model expressions and output pessimistic estimations using one model expression. Considering the incomplete information acquired, a compromising decision-making method was used to derive a 2017 northern SCS E. cardinalis total allowed catch (TAC) of 44,691.21 t. The different conclusions drawn from estimations using CPUEs reflect variable exploitation and utilization fish stock statuses among fishing vessels with different gears and engine powers. Hence, the fishing operations were grouped according to their CPUE relationship, and recommendations regarding optimum fishing efforts were assigned to the groups following a fundamental principle: to improve fishery TAC management, fishing efforts should be reduced if the fish stock assessment is pessimistic and maintained if the assessment is optimistic. This study providing a feasible technical method for the TAC management of China's offshore fisheries.

Effects of stochastic growth on population dynamics and management quantities estimated from an integrated catch-at-length assessment model: Panopea globosa as case study

In size-based stock assessment models, the stochastic growth of individuals is expressed through a transition matrix representing the growth variability as probability of shift from one length class to another during a time period. This process is important because it describes the changes in population size structure brought about by the increase in length or weight of organisms over time. In this study, four stochastic growth matrices were developed within an integrated catch-at-length assessment model (ICLAM), and the changes in the population dynamics and quantities relevant to fishery management of Panopea globosa were analyzed. The growth increments were estimated through von Bertalanffy, Gompertz, Logistic, and Schnute models using a gamma probabilistic density function. A corrected Akaike information criterion was used to select the best performance among the four ICLAMs. The ICLAM associated with the von Bertalanffy matrix was the best for describing the catch-at-length data, providing conservative estimates on the condition of the stock; while the ICLAM for the Logistic matrix showed low performance, exhibiting the highest estimates for all the components of population dynamics, such as an increase of 75.3% in the recruitment and 58.5% in the total abundance with regard to the von Bertalanffy matrix. These differences emphasize the importance of determining a suitable stochastic growth matrix because it has serious implications in biasing stock assessments, resulting in inadequate management strategies.

Prediction of Microbial Population in Sorghum Fermentation through Mathematical Models

The mathematical models can be used as a tool in predicting microbial population in sorghum fermentation, either spontaneous fermentation or fermentation with the addition of lactic acid bacteria (LAB) inoculum. Gompertz model modified by Gibson, Gompertz model modified by Zwietering, Baranyi-Robert model, Fujikawa model, Richards model, Schnute model were used in predicting the growth of lactic acid bacteria (LAB) and coliform bacteria during spontaneous fermentation, and also the growth of LAB during fermentation with the addition of inoculum. Meanwhile, there was death (inactivation) of coliform bacteria during sorghum fermentation with the addition of LAB inoculum. The Geeraerd model and the Gompertz model modified by Gil et al. were used to predict the inactivation. The accuracy and precision of models were evaluated based on the Root Mean of Sum Square Error (RMSE), coefficient of determination (R2), and curve fitting. Gompertz model modified by Gibson had the highest accuracy and precision, which was followed by the accuracy of the Fujikawa model and Baranyi-Robert model in predicting the growth of LAB and the growth of coliform bacteria during spontaneous fermentation. Meanwhile, in predicting LAB growth during fermentation with the addition of inoculum, high accuracy and precision was obtained from Richards and Schnute models. In predicting the inactivation of coliform bacteria, Geeraerd model provided higher accuracy and precision compared to Gompertz model modified by Gil et al. Keywords: fermentation; inoculum; mathematical; model; sorghum; spontaneous

Oxygen uptake rate as a tool for on-line estimation of cell biomass and bed temperature in a novel solid-state fermentation bioreactor.

Direct measurement of cell biomass is difficult in a solid-state fermentation (SSF) process involving filamentous fungi since the mycelium and the solid substrate are often inseparable. However, respiratory data are rich in information for real-time monitoring of microbial biomass production. In this regard, a correlation was obtained between oxygen uptake rate (OUR) and biomass concentration (X) of Rhizopus oryzae MTCC 1987, during phytase production, in an intermittently mixed novel SSF bioreactor. To obtain the correlation, various models describing sigmoidal growth were tested, namely the logistic, Gompertz, Stannard, and Schnute models. Regression analysis of experimental results, at different operating conditions of inlet air flow rate and relative humidity suggested that OUR and X were correlated well by the logistic model (R2 > 0.90). To corroborate the use of respiratory data for on-line measurement of metabolic activity, OUR was related to metabolic heat generation rate (Rq), and the logistic model was found to satisfactorily correlate Rq and X as well. The model parameter, YQ/X, when substituted into a heat transfer design equation, along with the values of other parameters and operating variables, gave reliable estimates of bed temperature. The correlations developed in the present study, between respiratory activity and biomass concentration may be extended on to other SSF processes for further validation and real-time monitoring of cell biomass and bed temperature.

Model Selection to Describe the Growth of the Squalid CallistaMegapitaria squalidafrom the Eastern Gulf of California

ABSTRACT In northwestern Mexico (Gulf of California and Pacific Coast), a fishery on the squalid callista Megapitaria squalida (Sowerby, 1835) was established four decades ago, but little is known about its growth. The objective of this study was to assess individual growth parameters by testing the best growth model fitted to M. squalida. Four growth models were tested, von Bertalanffy, Logistic, Gompertz, and Schnute. The best model was selected based on the Akaike information criterion (AIC) and Bayesian information criterion (BIC). The maximum log-likelihood algorithm was used to parametrize the models considering a multiplicative error structure. According to AIC and BIC, the Logistic model was hierarchically ordered in first place, but the Gompertz, von Bertalanffy, and Schnute models received strong support from the data with AIC and BIC. As no clear “best model” was found, the multimodel inference approach (MMI) was applied to estimate the asymptotic length (L∞). The averaged L∞ was 95.1 mm shell ...

Modeling Growth of the Cortes GeoduckPanopea globosafrom Unexploited and Exploited Beds in the Northern Gulf of California

In the upper Gulf of California, a lucrative fishery of the Cortes geoduck Panopea globosa (Dall 1898) is developing rapidly. Both exploited and unexploited areas for this fishery still exist in this area. The effect of the data source of the length-atage data on growth models fitted to Panopea globosa was evaluated. Five growth models were tested: von Bertalanffy, logistic, Gompertz, Schnute, and Schnute-Richards. The parameters of each model and their confidence intervals (CIs) were computed using the maximum likelihood method. Multimodel inference was used to average the asymptotic length for each area. The bestfitting model was selected using Akaike's information criterion (AIC). According to this criterion, the logistic growth model best described the growth of P. globosa in unexploited beds, and the Schnute models performed best in exploited beds. The asymptotic length values obtained frommultimodel inferencewere 161.88 mm (95% CI, 161.83–161.93 mm) in unexploited beds and 205.20 mm (95% CI, 197.60–212.96 mm) in exploited beds. The latter value is the largest asymptotic length obtained for any Panopea species worldwide. In conclusion, the data source of the length-at-age data clearly affects the performance of growth models.

Growth model selection for the jumbo squid Dosidicus gigas from the Gulf of California, Mexico

We analyzed mantle length and age data of the whole ontogenic cycle of the jumbo squid Dosidicus gigas in the Gulf of California, Mexico, to describe its growth pattern. Several individual growth models that included asymptotic and non-asymptotic patterns were fitted to the data, and Akaike’s information criterion and multimodel inference were used to identify the model that best fit the data. The length-at-age data were divided into males and females (recruits and adults) for analysis separately and then combined to assess the overall growth pattern. The Schnute general model (ρ≠0, η≠0, where ρis the constant relative rate of the relative growth rate, ηis the incremental relative rate of the relative growth rate) was the function that best described the growth of females, males and both sexes of D. gigas together. For females, the Akaike difference and Akaike weight were 0 and 0.91, respectively; for males, the Akaike difference was also 0, but the Akaike weight was 0.39, showing that alternative growth models could explain the individual growth; these growth models were the Gompertz (L0, length at time zero), Gompertz (L∞, asymptotic length) and Schnute (ρ≠0, η = 0) models. We estimated the age and mantle length at which the growth rate changes for both sexes, estimating an age of 162.36 d (separately, 167.51 d for females and 158.98 d for males), and a length of 299.52mm for the growth inflection point (separately, 312.84 mm for females and 292.86 mm for males). Once D. gigas reaches this point, the species exhibits more gradual growth until reaching an asymptotic mantle length of 859.45 mm (for females, 904.80 mm, and for males, 828.49 mm). A comparison of the growth patterns of D. gigas reported in the Eastern Pacific indicated nonasymptotic growth of this species in the Humboldt Current and Costa Rica Dome; in contrast, asymptotic growth was identified for the western coast of Baja California and Gulf of California. The reason for this difference is unclear, and this issue will be a topic of future studies.

Predictive modeling of β-carotene accumulation by Dunaliella salina as a function of pH, NaCI, and irradiance

Predictive modeling of β-carotene accumulation by Dunaliella salina as a function of NaCI, pH, and irradiance was studied. Modified Logistic, Gompertz, Schnute, Richards, and Stannard models were fitted to describe β-carotene accumulation by the alga under various environmental conditions. Lag time (λ, days), maximum accumulation (A, pg/cell), and the maximum production rate (μ, 1/day) for β-carotene accumulation were calculated by modified Logistic and Gompertz models. Values of λ, A, and μ for β-carotene accumulation varied between 0.26 and 20.14 days, 57.48 to 198.76 pg β-carotene/cell, and 1.80 to 3.68 1/day, respectively. Results revealed that Logistic and Gompertz models could be used to describe the accumulation of β-carotene by D. salina as a function of salt concentrations, pH, and irradiance. The highest asymptotic value was predicted from Logistic and Gompertz models at pH 9.0, 48 kerg/(cm2 s) light intensity, and 20% NaCl concentration.

Growth Models for Fisheries: The Effect of Unbalanced Sampling Error On Model Selection, Parameter Estimation, and Biological Predictions

Field studies that attempt to estimate the mean growth rates of individuals in a population usually yield unbalanced data and various forms of sampling error. If these data are a poor representation of a population, then the estimates of growth rates may also be unrepresentative of the population. We present an assessment of the performance and uncertainty in 4 growth models—the von Bertalanffy, Gompertz, inverse logistic, and Schnute models—fitted to data with various scenarios of sampling error. The performance of each model was determined by comparing highest likelihoods outcomes to known case outcomes. A Monte Carlo simulation framework was used to generate data consisting of 8 typical scenarios of sampling error common in tag-recapture data. Each growth model was evaluated according to 2 metrics: the error rate (i.e., a metric for model uncertainty) and the prediction error (i.e., the accuracy of biological predictions such as age). Results indicate that an inadequate size range in the data (i.e., a lack of juvenile size classes) would often lead to a high error rate. When negative growth increment data are included, the K parameter of the von Bertalanffy model increased, and the L∞ decreased. The inverse logistic model sometimes produced absurd parameter estimates but nevertheless generated the lowest prediction errors. A high prediction error can potentially have far more serious implications to fishery stock assessments than is currently appreciated. Given widespread use of the von Bertalanffy and Gompertz models, selected solely on the basis of model selection criteria, it is clear that greater care and scrutiny are warranted in the selection of growth models in the presence of sampling error.

Age and growth of the blacknose shark, Carcharhinus acronotus (Poey, 1860) off the northeastern Brazilian Coast

From August 1994 to January 1999 and July 2004 to December 2007, 369 blacknose sharks, Carcharhinus acronotus (Poey, 1860), (43.5–146 cm in total length, TL) were collected from gillnets and surveys (longline) carried out on the continental shelf off the state of Pernambuco, Brazil (07°15′45″S and 09°28′18″S). Vertebral sections from 131 males (43.5–124 cm TL) and 146 females (46–146 cm TL) were analyzed. The index of average percentage of error ( IAPE) estimated from two readings ranged from 1.61 to 4.83 (mean: 6.66%) in the vertebrae of specimens between 0 and 15 years of age. The monthly marginal increment ( MIR) ratio revealed a tendency toward band pair deposition between autumn and winter, whereas the monthly distribution of growth band pair classes revealed that the first band pair appears on the vertebrae of newborns (ages 0+) about 6 months after birth (by June). This deposition pattern was found in specimens with one, two and three band pairs on the vertebrae (1+ and 2+, respectively), thereby confirming annual band pair completion in winter. Growth parameters were derived using the von Bertalanffy model ( VBGM), VBGM b (modified by length at birth: L 0), the Richards, Gompertz and Schnute models. No significant differences in growth rates were detected between the two sampling periods (1994–1999 and 2004–2008). Models with multiple inflection points, particularly the Richards model, best represented growth for the species, which was evidenced by the lowest Akaike information criterion value. There were no differences in growth between sexes. Growth parameters estimated for both sexes were L ∞ = 129.34 cm (SE = 1.35), k = 0.24 (SE = 0.009) and m = 1.34 with the Richards model. The “average” model was determined by averaging L ∞ between the models with substantial statistical support that were considered the most plausible (Richards and Gompertz). Thus, a consensual L ∞ = 130.69 cm, estimated by multi-model inference, was employed to minimize the effects of sample size and selectivity. Males and females mature at 6 years of age and the largest specimen in the catches was 15 years of age (132 cm TL). Local fishing exploitation using gillnets caught only juveniles, whereas the longlines used for the surveys caught subadult and adult specimens. C. acronotus is a relatively fast-growing species inhabiting shallow coastal waters throughout its lifespan, which is a pattern to be taken into account in the years to come for the management of coastal exploitation targeting valuable teleosts.

Impacts of distorted fishery statistical data on assessments of three surplus production models

We evaluated the effect of various error sources in fishery harvest/effort data on the maximum sustainable yield (MSY) and corresponding fishing effort (EMSY) using Monte Carlo simulation analyses. A high coefficient of variation (CV) of the catch and effort values biased the estimates of MSY and EMSY. Thus, the state of the fisheries resource and its exploitation was overestimated. We compared the effect using three surplus production models, Hilborn-Waters (H-W), Schnute, and Prager models. The estimates generated using the H-W model were significantly affected by the CV. The Schnute model was least affected by errors in the underlying data. The CV of the catch data had a greater impact on the assessment than the CV of the fishing effort. Similarly, the changes in CV had a greater impact on the estimated maximum sustainable yield (MSY) than on the corresponding estimate of fishing effort (EMSY). We discuss the likely effect of these biases on management efforts and provide suggestions for the improvement of fishery evaluations.

Growth model identification of short-finned squid Illex argentinus (Cephalopoda: Ommastrephidae) off southern Brazil using statoliths

Statoliths of 689 Illex argentinus specimens collected by national and foreign trawlers in Brazilian waters were analyzed. Catches occurred between 2001 and 2008, from 23° to 32° S and at depths of 80–730 m. Exponential, Power, Gompertz and Schnute models were fitted to size-at-age data and the logistic model was used for maturity modeling. Fitting procedures used the maximum log-likelihood and Akaike criteria for identification of best models. Total age estimates ranged between 56 and 320 days for squid between 35 and 376 mm mantle lengths. Gompertz and Schnute models, which suggest the positive acceleration of growth in the early stages of ontogeny followed by a decrease in the second phase, provided the best fit to the size-at-age dispersion in this study. The inflection point in the maturity curve was 137 days for males and 143 days for females. The age range for post-spawning squid was 116–250 (average 187) days for males and 133–280 (average 201) days for females showing a life cycle close to six months. None of the examined individuals reached one year of age. The wide range of sizes-at-age implied that catches of I. argentinus off southern Brazil probably include mixed micro-cohorts and different population units.

The biology and distribution of the monkfish Lophius vomerinus off South Africa

The monkfish Lophius vomerinus is economically the most important bycatch species in the South African demersal hake fishery. To assist in the development of a bycatch management plan for the species, age and growth characteristics, reproductive and feeding biology, and distribution patterns were investigated. Age was estimated from sectioned illicia and growth parameters were modelled using the Schnute and von Bertalanffy growth models. The error sum of squares was similar between the two models, so the latter was used to model growth. The oldest recorded fish were 17 years and 16 years for males and females respectively on the West Coast and 17 years for sexes combined on the South Coast. Growth differed significantly between West Coast males and females. Length-at-maturity ogives indicate that L50 for males and females was 376mm TL (total length) and 369mm TL respectively, corresponding to ages of approximately six years for each. Gonadosomatic indices for females suggested that spawning occurs in September. L. vomerinus is highly piscivorous, feeding mainly on demersal teleosts. Prey size increases with increase in predator length. Distribution data indicate that L. vomerinus move into deeper water as they grow, and that on the South Coast, this offshore movement is accompanied by eastward migration.

Predictive modeling of Yersinia enterocolitica inactivation in Turkish Feta cheese during storage

Several nonlinear models (Gompertz, Logistic-1, Logistic-2, Richards, Stannard and Schnute models) were compared to describe Yersinia enterocolitica and aerobic bacteria inactivation in Turkish Feta cheese during the storage period. They were compared statistically by using the F-test. The Gompertz model was decided as a sufficient model, which describes the inactivation of both Y. enterocolitica and aerobic bacteria. The biological parameters were calculated from the modified Gompertz model. The effect of starter culture ( Streptococcus cremoris), salt (150 or 200 g/l) and initial inoculum level of Y. enterocolitica on the phase of disappearance ( λ) and the rate of reduction ( μ) of Y. enterocolitica and aerobic bacteria were determined. Addition of starter culture had a significant ( P<0.05) inhibitory effect on both Y. enterocolitica and aerobic bacteria in Turkish Feta cheese. However, salt and inoculation rate of Y. enterocolitica had no significant ( P>0.10) effect on both λ and μ of microorganisms.

除去法によるSchnuteモデルへのAICの導入

除去法によるSchnuteモデルへのAICの導入