Interplay between strong Allee effect, harvesting and hydra effect of a single population discrete-time system

The dynamics of a single population with non-overlapping generations can be described deterministically by a scalar difference equation in this study. A discrete-time Beverton- Holt stock recruitment model with Allee effect, harvesting and hydra effect is proposed and studied. Model with strong Allee effect results from incorporating mate limitation in the Beverton-Holt model. We show that these simple models exhibit some interesting （and sometimes unexpected） phenomena such as the hydra effect, sudden collapses and essential extinction. Along with this, harvesting is a socio-economie issue to continue any system generation after generation. Different dynamical behaviors for these situations have been illustrated numerically also. The biological implications of our analytical and numerical findings are discussed critically.

Interplay between reproduction and age selective harvesting:A case study of Hilsa(Tenualosa ilisha)fish at Sundarban estuary of northern Bay of Bengal,India

New offspring due to sexual reproduction is not an instantaneous process from its birth,it takes time to be sexually mature.On the other hand,harvesting of commercially profitable fish population before the perfect size or weight is reached is not only a commercial loss but also risks the extinction of the population.Now,we discuss the issue of Ganges-Brahmaputra-Meghna basin,northern Bay of Bengal for the age-selective harvesting of Hilsa shad(Tenualosa ilisha)which lays eggs after its sexual maturation.Harvesting of hilsa before its sexual maturation risks its extinction and due to lamer body weight,it is not a commercially profitable policy.This is a reality of Sundarban estuary for hilsa fish harvesting,therefore,biologically and economically both India and Bangladesh are facing several problems.Empirical data of Frasergunje Fishing Harbor shows a clear picture as the supporting document of this mathematical problem.

A nonautonomous mat hematical model to assess the impact of algae on the abatement of atmospheric carbon dioxide

The world's oceans have played an important role in sequestering atmospheric carbon dioxide through solubility and the action of algae.Fixation of atmospheric carbon dioxide by photoautotrophic algal cultures has the potential to diminish the release of carbon dioxide into the atmosphere,thereby helping to alleviate the trend toward global warming.This work investigates the role of algae in controlling the level of atmospheric carbon dioxide.Partial Rank Correlation Coefficients(PRCCs)technique is used to address how the concentration of atmospheric carbon dioxide is affected by changes in a specific parameter disregarding the uncertainty over the rest of the model parameters.Parameters related to algal growth are shown to significantly reduce the level of atmospheric CO_(2).Further,we explore the dynamics of nonautonomous system by incorporating the seasonal variations of sonic ecologically important model parameters.Our nonautonomous system exhibits globally attractive positive periodic solution,and also the appearance of double periodic solution is observed.Moreover,by letting the seasonally forced parameters as almost periodic functions of time,we show almost periodic behavior of the system.Our findings suggest that the policy makers should focus on continuous addition of nutrients in the ocean to accelerate the algal growth thereby reducing the level of carbon dioxide in the atmosphere.