Mathematical Modeling of the growth of Acinetobacter baumannii YNWH 226 on Azo dye Congo red

Industrial effluents (Azo dyes) are brightly coloured, making their disposal into receiving waters undesirable not only because many Azo dyes and their breakdown products are toxic to aquatic life and mutagenic to humans, but also because many Azo dyes and their breakdown products are harmful to aquatic life due to the presence of aromatics and metals, chlorides, and other chemicals. Various kinetic models, including modified Gompertz, Baranyi-Roberts, modified Richards, Von Bertalanffy, modified Logistics, modified Schnute, Buchanan three-phase, and the most recently presented Huang, were used in this study. Based on statistical tests, the modified Schnute model provided the best fit, with the lowest values for RMSE and corrected Akaike Information Criteria (AICc), the greatest value for adjusted R2, and the closest to unity for both Accuracy and Bias Factor. The Modified Schnute parameters such as λ (lag time), µmax (maximum specific bacterial growth rate) and curve fitting parameters α and β (Constant), were found to be -4.39 (95% confidence interval of -77.58 to 68.79), 57.00 (95% confidence interval of -2854.30 to 2968.30), 0.78 (95% confidence interval of -0.34 to 1.89) and 0.96 (95% confidence interval of -0.85 to 2.78, respectively.

Growth curves of the yellowlegs shrimp Penaeus californiensis Holmes, 1900 (Decapoda, Penaeidae), using length data

The yellowlegs shrimp Penaeus californiensis is an oceanic species that approaches the coastal zone for its reproduction. However, in the southern Gulf of California, this species also enters coastal lagoons to grow and reproduce. To test the hypothesis that the growth of P. californiensis differs between these two environments, monthly samplings of shrimp were made in the interior of the Navachiste coastal lagoon and its adjacent marine area. To determine growth, age groups were identified using the size structures over time. Five cases of the Schnute model were adjusted to the data, and the best case was selected using a multi-model selection approach. A sigmoid-shaped curve best represented the female data (case 2), and the inverted exponential curve (case 5; equivalent to the Von Bertalanffy growth function) was best for males. Average growth differed between sexes () but not between environments ().

Age and growth of thread herring Opisthonema libertate, in the southern Gulf of California

To fit a growth model to Opisthonema libertate, the most common thread herring in a small pelagic fishery in the southern Gulf of California, size data of commercial landings and age were generated from sagittal otoliths assessed during three different years, 2005, 2008 and 2015, representing Neutral, La Niña and El Niño environmental conditions, respectively. A multimodel select approach on five special submodels of generalized Schnute model, including one, equivalent to the Von Bertalanffy model, were used. A total of 573 otoliths were analyzed; 219 from Neutral, 149 from El Niño and 205 from The Niña events. An opaque zone of otoliths formed in winter-spring when chlorophyll a (Chl-a) concentrations were at a maximum. However, a hyaline zone of otoliths formed during the summer of the reproductive period. Schnute submodel 1 was the best model selected in all three environmental conditions, but submodel 3 was the best on pooled data. Length of thread herring aged 0.5 years old in the El Niño year was lower than other environmental-years analyzed. A possible compensatory effect on growth with age was observed in the data because environmental conditions affected the growth of 0.5-year-old thread herring, as was evident in size variance in this age group under all three conditions, but variance decreased in the older age groups. Thus, a multimodel average of Schnute submodels 1 and 3 could be used to describe the growth of O. libertate in the southern Gulf of California.

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

Age and growth estimates of the jumbo flying squid (Dosidicus gigas) off Peru

Mantle length (ML) and age data were analyzed to describe the growth patterns of the flying jumbo squid, Dosidicus gigas, in Peruvian waters. Six non-asymptotic growth models and four asymptotic growth models were fitted. Length-at-age data for males and females were analysed separately to assess the growth pattern. Multi-model inference and Akaike's information criterion were used to identify the best fitting model. For females, the best candidate growth model was the Schnute model with L∞ = 106.96 cm ML (CI 101.23–110.27 cm ML, P < 0.05), age at growth inflection 244.71 days (CI 232.82–284.86 days, P < 0.05), and length at growth inflection 57.26 cm ML (CI 55.42–58.51 cm ML, P < 0.05). The growth pattern in males was best described by a Gompertz growth model with L∞ = 127.58 cm ML (CI 115.27–131.80 cm ML, P < 0.05), t0 = 21.8 (CI 20.06–22.41, P < 0.05), and k = 0.007 (CI 0.006–0.007, P < 0.05). These results contrast with the growth model previously reported for D. gigas in the region, where the growth pattern was identified as non-asymptotic.

Growth, maturity and mortality of the blue crab Callinectes arcuatus Ordway, 1863 (Decapoda, Portunidae) in a Mexican coastal lagoon

In Mexico, swimming crabs are considered a strategic resource because it supports artisanal fishing when the main fish resource (shrimp) is in closed season. In “Marismas Nacionales” the blue crab fishery is relatively new, and the catches have been maintained due to the national demand and the availability of the resource. Individual growth, sexual maturity, sexual ratio and mortality were estimated for Callinectes arcuatus for providing information about its population dynamics. Samplings were carried out every 10 days from October 2002 to November 2003. A total of 6022 specimens of C. arcuatus were collected (70.05% were males and 29.95% females) with a maximum carapace width (CW) of 138.5 mm in males and 118.7 mm for females. For males, case 5 of the Schnute model was the best model for describing the individual growth ( and ), while case 2 ( and ) was a better fit for females. The size at sexual maturity was 88.9 mm CW in males (CI = 88-90 mm) and 82.2 mm CW in females (CI = 81.7-82.9 mm). The estimated age at sexual maturity was 0.79 and 0.91 years for males and females, respectively. The male/female sex ratio was 1 : 0.43, significantly different (, ) from the theoretical sexual ratio (1 : 1). Mortality rates in males were , and , and in females they were , and . The exploitation rate indicated the resource is below the optimum level of exploitation and the maximum yield per recruit.

Comparison and selection of growth models using the Schnute model

Forestmodellers have long faced the problem of selecting an appropriate mathematical model to describe tree ontogenetic or size-shape empirical relationships for tree species. A common practice is to develop many models (or a model pool) that include different functional forms, and then to select the most appropriate one for a given data set. However, this process may impose subjective restrictions on the functional form. In this process, little attention is paid to the features (e.g. asymptote and inflection point rather than asymptote and nonasymptote) of different functional forms, and to the intrinsic curve of a given data set. In order to find a better way of comparing and selecting the growth models, this paper describes and analyses the characteristics of the Schnute model. This model has both flexibility and versatility that have not been used in forestry. In this study, the Schnute model was applied to different data sets of selected forest species to determine their functional forms. The results indicate that the model shows some desirable properties for the examined data sets, and allows for discerning the different intrinsic curve shapes such as sigmoid, concave and other curve shapes. Since no suitable functional form for a given data set is usually known prior to the comparison of candidate models, it is recommended that the Schnute model be used as the first step to determine an appropriate functional form of the data set under investigation in order to avoid using a functional form a priori.

Using length data in the Schnute Model to describe growth in a metapenaeid from waters off Australia

This paper presents a novel approach for fitting length data to the Schnute growth model. Cohorts were fitted manually to a time series of length distributions from two stocks (Clarence and Hunter Rivers) of Metapenaeus macleayi and considered analogous to individuals from tag–recapture data, in order to estimate growth parameters. Data for Clarence males best fitted the three-parameter Schnute Model (L∞ = 21.3 mm CL, κ = 0.025 day–1 and γ = –1.35), whereas those for Hunter males were best fitted to a two-parameter version of the model (L∞ = 33.5 mm CL, κ = 0.009 day–1 and γ = 0 fixed). The equivalent to the von Bertalanffy growth function was the best fit to female data from both stocks (L∞ = 36.6 and 40.2 mm CL, κ = 0.004 and 0.005 day–1 and γ = 1 fixed for Clarence and Hunter respectively). Females grew larger than males and took longer to achieve their maximum size. No significant differences in female growth were found between stocks; however, males from the Hunter grew to a longer mean maximum length but at a slower rate than those from the Clarence. This study shows how the Schnute Model can be fitted to length based data and thus include the flexibility of comparing fits between asymptotic and non-asymptotic growth functions.

Growth of the tambaqui Colossoma macropomum (Cuvier) (Characiformes: Characidae): which is the best model?

In order to decide which is the best growth model for the tambaqui Colossoma macropomum Cuvier, 1818, we utilized 249 and 256 length-at-age ring readings in otholiths and scales respectively, for the same sample of individuals. The Schnute model was utilized and it is concluded that the Von Bertalanffy model is the most adequate for these data, because it proved highly stable for the data set, and only slightly sensitive to the initial values of the estimated parameters. The phi' values estimated from five different data sources presented a CV = 4.78%. The numerical discrepancies between these values are of not much concern due to the high negative correlation between k and L<FONT FACE=Symbol>¥</FONT> viz, so that when one of them increases, the other decreases and the final result in phi' remains nearly unchanged.