Modeling Intervention with Respect to Biodiversity Loss : A Case Study of Forest Resource Biomass Undergoing Changing Length of Growing Season

This paper examines the extent of a system interventions against the loss of biodiversity due to an increase in the length of the growing season. By using a computationally efficient numerical scheme, we have observed that a shorter length of the growing season dominantly predicts a biodiversity loss whereas a relatively increased length of the growing season has predicted a biodiversity gain which has sufficient implication for the availability of adequate ecological-forestry services which are capable to provide a useful insight for the management of the forestry conservation and sustainable development. The novel contributions of this pioneering research has not been seen elsewhere; it is fully presented and discussed in this paper. Keywords— Forest resource biomass, intervention strategies, environmental perturbation, biodiversity, growing season, numerical simulation.


Modeling Intervention with Respect to Biodiversity Loss: A Case Study of Forest Resource Biomass Undergoing Changing Length of Growing Season INTRODUCTION
It is a vital crop science ideology that the length of the growing season plays a significant role in the harvest of interacting legumes for a limited resource within an agricultural setting.In the same manner, the length of the growing season is equally an important model parameter in the distribution of the forest resource biomass over a specified duration of growth which we have considered to be in the unit of months and for our numerical simulation propose the length of the growing season to be twenty-five (25) months.In our intervention strategy against biodiversity loss, we have measured the extent to which environment provides protection to prey species by proposing a longer length of growing season which allows premature tress to mature.This present paper is modeled after the Leslie-Gower functional response Chaudhary et al (2015), Gupta & Chandra (2013) Yue (2015).Optional control policy as applied to fishery management (Clark 2010), Kar and Ghorai (2011), Ghosh and Kar (2014).From the theory of forest development and forest conservation, a relatively low environmental perturbation and a severe environmental perturbation have the potential to lead to early harvest for the forest resources biomass.There two (2) concepts were taken into consideration in our bid to provide a short term intervention strategy against the loss of biodiversity.

Mathematical Formulations
In this paper, we have adopted the model in respect of the depletion of forestry resources due to human population and human population activities developed by Ramdhani et al 2015.This mathematical model on the depletion of forestry resources has the structure of a system of continuous nonlinear first order ordinary differential equations.The model assumptions are specified follows: (i) The growth of forest resources biomass and human population are governed by the logistic type equation.(ii) The growth rate of population pressure is proportional to the density of human population (iii) The depletion of forestry resources is due the human population and industrialization.

Description of Model Parameters
B is the density of forestry resources biomass s is the intrinsic growth rate coefficientof the forestry resource biomass L is the carrying capacity of the forestry resource biomass N is the density of human population, P is the density of population pressure and Following the above, the governing equations of the model are: with the initial conditions

II. METHOD OF ANALYSIS
Since the proposed model formulations do not have a closeform solution, we have proposed to analyze our model formulation using a computationally efficient ODE 45 numerical scheme.The result we have obtained will be presented and discussed in the next section of this paper.

III.
RESULTS AND DISCUSSION Our five (5) phases of results are presented as follows:

Scenario one results
Here we present the impact of varying the length of the growing season by ten percent (10%).On the whole, we observe that biodiversity loss is highest at the 5 th month with a value of 97.07%which decreases to 61.38% at the 11 th month and decreases monotonically to 0.1013% at the 132 nd month.A biodiversity loss of 0.1013% dominantly predicts a biodiversity gain of over 99%, it is therefore clear that while biodiversity loss cannot be completely eradicated, maintaining a longer length of growing season is a powerful mitigation factor against biodiversity loss and a sustainable development strategy.
IV. CONCLUSION It is interesting to note that while biodiversity is being lost at an alarming rate and the intensity of environmental pressures behind the decline show no sign of abating, with many limitations of biodiversity indicators shared, models relate the response of biodiversity components to mechanisms of climate change.These mechanisms of change are often data deficient and assign qualitative classifications to intensities of change.We have by utilizing the ODE 45 numerical simulation scheme provided an insight into data associated with biodiversity loss due to climate change effects.With data on biodiversity and environmental change made available we have measured the response to biodiversity.

RECOMMENDATIONS (i)
The length of the growing season should be good and appropriate enough to avoid harvesting pre-mature species.(ii) There should be deliberate efforts to measure relationship between biodiversity and intensity of mechanisms for environmental change.

International Journal of Advanced Engineering, Management and Science (IJAEMS) [Vol-3, Issue-9, Sep-2017] https://dx.doi.org/10.24001/ijaems.3.9.5 ISSN: 2454-1311
What can we learn and deduce form Table1results? From this empirical numerically simulated results we have observed that a shorter duration of the length of the growing season in the magnitude of 2.5 months dominantly predicts biodiversity loss for which 3 days length of growing season is more vulnerable to biodiversity loss value of 68.4 percent (approx.)compared with a 34.6 percent loss of biodiversity when the length of the growing season is 72 days.Therefore, the vulnerability of the forest resource biomass to biodiversity loss tends to decrease from 3 days to 72 days.