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Modelling secondary succession on old fields using Markov chain and an overview of mathematical modelling of successional process

S. Shahid Shaukat and Moazzam Ali Khan

In search for models of succession a number of mathematical and statistical models have been tried by various ecologists and range workers including, descriptive, based on ordinary or partial differential equations, cellular automata, fractals and stoichiometric models as well as ordination techniques and matrix models including Markov chains. This paper examines the old-field succession using Markov chain stochastic model to describe, predict and simulate the vegetation dynamics of the abandoned fields at Malir-Landhi area, southern Sind, Pakistan. Recorded data over 4-years period from permanent plots (patches) permitted an estimation of transition probabilities using the frequency of plots in various states that moved to other states over a period of one year at various sampling times. Average transition matrix using four years data was employed for the sake of accuracy in the estimation of probabilities. The paper discusses the Markov properties and its features, studies and exemplifies the test of first order Markov chain. The results indicate that the secondary succession under study conform to first-order Markovian process since the observed field data was found to fit closely to the first–order transition process. Transition matrix successfully exposed the nature and mechanism of succession and provided insights into the process of secondary succession. Succession was found to be almost unidirectional. Stability of the system was also checked which disclosed relatively greater stability at the later stage of succession pointing it to be the disclimax of the area. Though not all assumptions of Morkovian process were held by the data it appears that the transition matrices provide useful descriptive devices even when the system is not absolutely Markovian. The succession was related to second law of thermodynamics and entropy. The entropy of the successional ecosystem changed with the onward march of the succession. The overall system Entropy of the successional ecosystem was moderately high

To Cite this article: Shaukat, S.S. and M.A. Khan. 2023. Modelling secondary succession on old fields using Markov chain and an overview of mathematical modelling of successional process. Pak. J. Bot., 55(1): DOI:  

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