RESUMO
The size at which a certain fraction of a fish population reaches sexual maturity is an important parameter of life history. The estimation of this parameter based on logistic or sigmoid models could provide different ogives and values of length at maturity, which must be analyzed and considered as a basic feature of biological reproduction for the species. A total of 305 individuals of Narcine entemedor (N. entemedor) were obtained from artisanal fisheries in the Bahía de La Paz, Mexico. For the organisms sampled, sexes were determined and total length (TL) in cm was measured from October 2013 to December 2015. The results indicated that the females were larger, ranging from 48.5 cm to 84 cm TL, while males varied from 41.5 cm to 58.5 cm TL. The sex ratio was dominated by males ranging from 45-55 cm TL, while females were more abundant from 60 to 85 cm TL. Mature females were present all year long, exhibiting a continuous annual reproductive cycle. The length at maturity data were described by the Gompertz model with value of 55.87 cm TL. The comparison between models, and the model selection between them, showed that the Gompertz model had maximum likelihood and smaller Akaike information criterion, indicating that this model was a better fit to the maturity proportion data of N. entemedor.
RESUMO
Essential oils (EO) are a great antimicrobial resource against bacterial resistance in public health. Math models are useful in describing the growth, survival, and inactivation of microorganisms against antimicrobials. We evaluated the antimicrobial activity of Melaleuca armillaris EO obtained from plants placed in the province of Buenos Aires (Argentina) against Staphylococcus aureus. The minimum inhibitory and bactericidal concentrations were close and decreased, slightly acidifying the medium from pH 7.4 to 6.5 and 5.0. This result was also evidenced by applying a sigmoid model, where the time and EO concentration necessaries to achieve 50% of the maximum effect decreased when the medium was acidified. Moreover, at pH 7.4, applying the Gompertz model, we found that subinhibitory concentrations of EO decreased the growth rate and the maximum population density and increased the latency period concerning the control. Additionally, we established physicochemical parameters for quality control and standardization of M. armillaris EO. Mathematical modeling allowed us to estimate key parameters in the behavior of S. aureus and Melaleuca armillaris EO at different pH. This is interesting in situations where the pH changes are relevant, such as the control of intracellular infections in public health or the development of preservatives for the food industry.