Abstract
Forest dynamics is mostly concerned with the changes in forest structure and composition over time, including its behavior in response to anthropogenic and natural destructions which is one of the primary evidence of forest change. This study presents the dynamics of vegetation pattern formation taken into account all the interaction measure indices such as light, water, temperature and nutrients fertility. Michaelis-Menten Kinetics and a Continuous-Time Markov (CTM) method were employed to determine plant metabolism responses to all the inputs. The Continuous-Time Markov (CTM) technique was then used to obtain a simple plant growth component by synthesizing the four - measure indices or resources (light, water and nutrients and temperature). Stability analysis of the formulated model was carried out to determine the possible phase regions associated with the various stability states for a sufficiently precise representation of the essential features of the model. Results of the β values for the spatial patterns obtained indicate association or interaction among the various soil fertility levels under different water conditions. For instance, a β value of 0.05605 represents control fertility under arid conditions, indicates a vegetation pattern with numerous and wider patches of bare or almost bare land compared to patterns exhibited by the other fertility levels.
Highlights
Human activities affect forest growth in many diverse ways by influencing the vegetation composition, cover, age and density
The study observes that vegetation patterns on higher fertility level in a given area of rich water condition suggests mechanisms with increasing vegetation biomass, high fertility and a given water condition are responsible for pattern formation
Z which is a surrogate for a dimensionless infiltration capacity prohibits pattern formation, one may not expect vegetation patterns to exist in situations of high fertility level and rich water condition
Summary
Human activities affect forest growth in many diverse ways by influencing the vegetation composition, cover, age and density. Tree growth and forest destructions are primary evidence of forest dynamics These are determined by resources like radiation, water, nutrients supply and environmental conditions such as temperature, soil acidity, air pollution and human activities. Barber and Cushman [20], Smethurst et al [21] and Comerford et al [22] proposed model revisions to cover the major sub-processes of nutrient uptake and to accommodate a variety of additional conditions Other researchers such as Wu et al [23]; Wu et al [24] and Sharpe et al [25] modelled the physical growth of the forest by considering the influence of stem, crown and roots. This paper presents the dynamics of the forest by determining the influence of the interactions among multiple indices such as light, water, temperature and nutrients on vegetation pattern formation using Continuous Time Markov Chain
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