arXiv subjects

Anurag Sau

Publications and source records attributed to Anurag Sau.

4 recordsLinked to original sources

arXiv2026

Optimal harvesting under annuity and compound interest laws: economic-ecological trade-offs in a logistic growth model

The relationship between investment policy associated with species growth profile is essential in seeking the most appropriate strategy for a policymaker. Balancing maximum profit with the sustainability of species remains a central issue in both ecological and economic contexts. This study presents a comparative analysis of two interest principles, annuity and compounding, within the framework of optimal control. Various investment policies are examined from the perspective of capital theory, incorporating concepts such as future value, accumulation function, and force of interest, each contributing to the formulation of an optimal control strategy. Our analysis is based on a one dimensional logistic model incorporating linear harvesting. Key parameters include the species growth rate and interest rate, and optimality is evaluated with respect to these variables. Using Pontryagins Maximum Principle, we derive the optimal harvesting policies under both discounting laws and characterize the resulting steady state equilibria. The principal finding indicates that for species with low intrinsic growth rates and low annual interest rates, the annuity law of interest yields optimal outcomes. Conversely, for any annual interest rate, species exhibiting moderate or high growth rates maximize profit under the compound law of interest. The study also addresses maximum net revenue and optimal strategies for varying growth rates under each interest law.

econ.GN↗

arXiv2025

Interconnection between density-regulation and stability in competitive ecological network

In natural ecosystems, species can be characterized by the nonlinear density-dependent self-regulation of their growth profile. Species of many taxa show a substantial density-dependent reduction for low population size. Nevertheless, many show the opposite trend; density regulation is minimal for small populations and increases significantly when the population size is near the carrying capacity. The theta-logistic growth equation can portray the intraspecific density regulation in the growth profile, theta being the density regulation parameter. In this study, we examine the role of these different growth profiles on the stability of a competitive ecological community with the help of a mathematical model of competitive species interactions. This manuscript deals with the random matrix theory to understand the stability of the classical theta-logistic models of competitive interactions. Our results suggest that having more species with strong density dependence, which self-regulate at low densities, leads to more stable communities. With this, stability also depends on the complexity of the ecological network. Species network connectance (link density) shows a consistent trend of increasing stability, whereas community size (species richness) shows a context-dependent effect. We also interpret our results from the aspect of two different life history strategies: r and K-selection. Our results show that the stability of a competitive network increases with the fraction of r-selected species in the community. Our result is robust, irrespective of different network architectures.

q-bio.PE↗

arXiv2024

Evaluating the consequences: Impact of sex-selective harvesting on fish population and identifying tipping points via life-history parameters

Fish harvesting often targets larger individuals, which can be sex-specific due to size dimorphism or differences in behaviors like migration and spawning. Sex-selective harvesting can have dire consequences in the long run, potentially pushing fish populations towards collapse much earlier due to skewed sex ratios and reduced reproduction. To investigate this pressing issue, we used a single-species sex-structured mathematical model with a weak Allee effect on the fish population. Additionally, we incorporate a realistic harvesting mechanism resembling the Michaelis-Menten function. Our analysis illuminates the intricate interplay between life history traits, harvesting intensity, and population stability. The results demonstrate that fish life history traits, such as a higher reproductive rate, early maturation of juveniles, and increased longevity, confer advantages under intensive harvesting. To anticipate potential population collapse, we employ a novel early warning tool (EWT) based on the concept of basin stability to pinpoint tipping points before they occur. Harvesting yield at our proposed early indicator can act as a potential pathway to achieve optimal yield while keeping the population safely away from the brink of collapse, rather than relying solely on the established maximum sustainable yield (MSY), where the population dangerously approaches the point of no return. Furthermore, we show that density-dependent female stocking upon receiving an EWT signal significantly shifts the tipping point, allowing safe harvesting even at MSY levels, thus can act as a potential intervention strategy.

q-bio.PE↗

arXiv2021

Recognizing and prevention of probable regime shift in density regulated and Allee type stochastic harvesting model with application to herring conservation

An ecological system with multiple stable equilibria is prone to undergo catastrophic change or regime shift from one steady-state to another. It should be noted that, if one of the steady states is an extinction state, the catastrophic change may lead to extinction. A suitable manual measure may control the prevention of catastrophic changes of different species from one equilibrium to another. We consider two stochastic models with linear and nonlinear harvesting terms. We inspect either density regulation or Allee type density regulated models [Saha et al., Ecological Modelling, 2013], which have substantial applications in the herring fish population's viability study. Both the deterministic models we consider here contain bi-stability under certain restrictions, and in that case, one of the stable states is the extinction state. We assume that the dynamical system under consideration is closed, i.e., immigration and emigration are absent. The demographic noise is introduced in the system by substituting an ordinary differential equation with a stochastic differential equation model, where the birth and death rates of the deterministic process are used to obtain the instantaneous mean and variance in the stochastic differential equation. Our study reveals that, the catastrophic changes can be avoided manually by a suitable choice of handling time that will eventually help to prevent the sudden extinction of the harvested population. The entire study is illustrated through the herring population size data obtained from the Global Population Dynamics Database (GPDD) and simulation experiment.

q-bio.PE↗