• Journal for History of Mathematics
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• v.27 no.3
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• pp.197-210
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• 2014

Species like insects and fishes have, in many cases, non-overlapping time intervals of one generation and their descendant one. So the population dynamics of such species can be formulated as discrete models. In this paper various discrete population models are introduced in chronological order. The author's investigation starts with the Malthusian model suggested in 1798, and continues through Verhulst model(the discrete logistic model), Ricker model, the Beverton-Holt stock-recruitment model, Shep-herd model, Hassell model and Sigmoid type Beverton-Holt model. We discuss the mathematical and practical significance of each model and analyze its properties. Also the stability properties of stationary solutions of the models are studied analytically and illustratively using GSP, a computer software. The visual outputs generated by GSP are compared with the analytical stability results.

• Fisheries and Aquatic Sciences
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• v.27 no.6
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• pp.392-409
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• 2024

The present study aims to analyze the biological aspects and population dynamics of Indian mackerel in Barru waters. Data was collected in Barru for 11 months, from June 2022 to April 2023. The observed parameters of biological aspects included gonadal maturation stages (GMSs), size at first gonadal maturation, and length-weight relationship. Meanwhile, the aspects of population dynamics encompass age group, growth, mortality rate, and exploitation rate. Data analysis consisted of morphological selection of general maturation stages, Spearman-Kärber method in estimating gonadal first maturation size, Bhattacharya method in identifying age group, von Bertalanffy function through FISAT II to measure growth (L_∞ and K), Pauly Model to estimate mortality rate, Beverton & Holt Model to estimate Y/R, and virtual population analysis (VPA) analysis to estimate stock and fish yield. The results demonstrated that GMS I was observed to be dominant, followed by stages II and III. The initial gonadal maturation was estimated to be 17.98-19.28 cm (FL) for females and 17.98-19.27 cm (FL) for males. The length-weight relationship in male and female Indian mackerels indicated a positive allometric growth. The mode grouping analysis results from the fork length measurement revealed three age groups. It was also identified that the asymptotic length (L_∞) = 29.5 cm (fork length), growth rate coefficient (K) = 0.46 per year, and theoretical age at zero length (t₀) = -0.3576 per year. Total mortality (Z) = 2.67 per year, natural mortality (M) = 1.10 per year, fishing mortality (F) = 1.57 per year, and exploitation rate (E) = 0.59, the actual Y/R = 0.083 gram/recruitment, and optimal Y/R 0.03 gram/recruitment. Fishing mortality is higher than the natural mortality rate, and a high exploitation value (E > 0.5) also reflects over-exploitation. VPA analysis on fish yields and stock estimation reported a highly exploited rate between the 11.5 cm and 14.5 cm length classes and an exceeding current yield of 467.07 tons/year with a recommended yield of 233.53 tons/year to ensure population sustainability.