Estimation of the present status of the species based on the theoretical bounds of environmental noise intensity: An illustration through a big abundance data and simulation

Sibly et al. (2005) described that most species have a fundamental characteristic to follow the theta-logistic growth trait with the convex downward trend. The fundamental yardstick of this research work builds under the deterministic setup, whereas the involvement of the external noise in any growth system is inevitable. But, the involvement of external affairs in any species growth can not be well judged only through its density dependence; it requires a further assessment. So, we frame the theta-logistic model with the stochastic analog in two directions, i.e., the discrete and continuous setup. The analysis of the discrete stochastic model is manifested by the bifurcation analysis, which shows that the attainment of the chaotic regime enhances with the increase in noise intensity level. Although the role of chaos in species extinction is debatable, a literature survey suggests that chaos with stochasticity accelerates the extinction of species. Similarly, in the case of the continuous version, we performed a theoretical study on the stochastic theta-logistic model to provide a critical value of the noise intensity parameter. This threshold magnitude acts as the sustainability criterion of any species environmental tolerability. In this connection, we use the data of four major taxonomic groups, i.e., Bird, Insect, Mammal, and Fish, from the GPDD database and classifies the species based on environmental sensitivity. The highly sensitive species have a low tolerance level, associated with the small magnitude of environmental noise intensity parameter. Moreover, the simulation prediction model on these four taxonomic classes also shows that the overall extinction probability of the considered birds in our research work is almost negligible for the current time window.