A mathematical model studying the survival of forest resource–dependent wildlife population in the presence of population pressure–induced mining activities

Abstract

Keeping human-wildlife conflicts in mind, that are taking place as a result of shrinking forest area due to overgrowing human population and consequently, due to augmentation of mining projects in the forest region, here, a nonlinear mathematical model is developed. The model is formulated under the assumption that continuously growing human population and its increasing demands impose population pressure on the environment, which results into augmentation of mining activities in the forest region. The model is analyzed qualitatively for boundedness, existence, and stability of equilibrium points, along with permanence of the model system. Quantitative analysis is also being performed by evaluating the numerical solutions of the model and analyzing them through graphical illustrations. The model analysis demonstrates that in order to have permanent model system, the growth of forest resources should be large as compared to their utilization for wildlife and human population. K E Y W O R D S forest resources, Holling type-II, human population, mining activities, permanence, stability, wildlife population Natural Resource Modeling. 2017;30:e12139. wileyonlinelibrary.com/journal/nrm Summary for Managers• It is important to understand that human-wildlife conflict is one of the serious implications of the impact generated through population pressure-induced mining activities on forest resources and wildlife population.• With the continuous depletion of forest resources, due to growth of mining activities in the region, the extinction of forest resources could take place and the survival of forest resource-dependent wildlife population comes under risk. Therefore, forests, which are natural habitats for wildlife species, should be protected.• Control measures on rampant mining activities through government intervention are required in order to protect forest resources from being unsustainably overharvested.• Proper planning of mining activities in a forest region should be implemented in order to develop balanced forest ecosystem, where the human and wildlife population can live in perfect harmony. * 1 ,

Dynamical behavior of tribal‐forest system in the presence of development activities: Leslie–Gower‐based nonlinear modeling study

“…Since the dynamics of forest resources depletion through tribal population and development activities is not same; therefore, they are represented through different mathematical functional responses. The utilization of forest resources by tribal population is exhibited through Holling Type II functional response, whereas their depletion through development activities is formulated through Holling Type I in (2.1a) with the term (Jyotsna & Tandon, 2017b). Besides this, keeping in mind the forced migration of tribal people due to excessive development activities, the term is being incorporated in (2.1b) to exhibit such type of decrease in tribal population. Development activities in the forest region are assumed to be having some constant growth rate In addition to constant growth, development activities also get accelerated by the utilization of forest resources, which is shown through the term However, the increase in rate of development activities due to migration of tribal population is assumed to be very small as compared with forest resources and hence, their direct interaction is not incorporated.…”

“…Since the dynamics of forest resources depletion through tribal population and development activities is not same; therefore, they are represented through different mathematical functional responses. The utilization of forest resources by tribal population is exhibited through Holling Type II functional response, whereas their depletion through development activities is formulated through Holling Type I in (2.1a) with the term (Jyotsna & Tandon, 2017b). Besides this, keeping in mind the forced migration of tribal people due to excessive development activities, the term is being incorporated in (2.1b) to exhibit such type of decrease in tribal population.…”

“…The formulation of mathematical models in terms of nonlinear dynamical system of differential equations is a popular tool for researchers to conduct studies of natural resource systems and their connected different population ecosystems and environment. Out of diverse natural resources, however, many nonlinear research studies concentrate on forest resources systems, where the effects of different population ecosystems and their associated activities have been investigated on forest resources using consumer–resource type interactions (Shukla & Dubey, 1997; Dubey, Upadhyay, & Hussain, 2003; Dubey, Sharma, Sinha, & Shukla, 2009; Shukla, Lata, & Misra, 2011; Misra, Lata, & Shukla, 2014; Misra & Lata, 2015; Jyotsna & Tandon, 2017a, 2017b). Shukla and Dubey (1997), in their nonlinear modeling study on the impact of population growth and its associated pollution on forest resources, found that the conservation of forest resources, along with control over excessive population growth and pollution should be properly addressed to maintain resource biomass at its required level.…”

“…They found the extinction of forest resource in the presence of unprecedented industrialization and therefore, suggested for employing control over industrialization growth to establish ecological stability. Recently, Jyotsna and Tandon (2017a and 2017b) demonstrated the behavior of forest resources along with their dependent wildlife and human populations, in the presence of perturbations caused due to mining activities. In these studies, authors qualitatively and quantitatively analyzed the forest resources based model system and obtained relevant conditions to maintain the stability of such type of systems.…”

Catastrophic or sustainable scenarios might occur when the carrying capacities of a tourism‐based socioecological system vary

“…The tourism industry is not the unique anthropogenic activity that has been analyzed using an interaction model; for example, in Agarwal et al (2010), Dubey (1997, 2012), Dubey and Das (1999), Dubey and Hussain (2003), Dubey et al (2009, 2003), Misra and Lata (2015), Misra et al (2014a,b), and Shukla et al (1989, 2011, 1988) they model the effects on the forest caused by the industrialization. Also, in Jyotsa and Tandon (2017) the impacts of mining activities on the forest resources and the wildlife populations are modeled.…”