Abstract
In this work, we employ autoregressive models developed in financial engineering for modeling of forest dynamics. Autoregressive models have some theoretical advantage over currently employed forest modeling approaches such as Markov chains and individual-based models, as autoregressive models are both analytically tractable and operate with continuous state space. We performed a time series statistical analysis of forest biomass and basal areas recorded in Quebec provincial forest inventories from 1970 to 2007. The geometric random walk model adequately describes the yearly average dynamics. For individual patches, we fit an autoregressive process (AR) of order 1 capable to model negative feedback (mean-reversion). Overall, the best fit also turned out to be geometric random walk; however, the normality tests for residuals failed. In contrast, yearly means were adequately described by normal fluctuations, with annual growth on average of 2.3%, but with a standard deviation of order of 40%. We used a Bayesian analysis to account for the uneven number of observations per year. This work demonstrates that autoregressive models represent a valuable tool for the modeling of forest dynamics. In particular, they quantify the stochastic effects of environmental disturbances and develop predictive empirical models on short and intermediate temporal scales.
Highlights
Markov chains are able to capture the effects of all these disturbances on forest biomass dynamics [10]
We develop a stochastic theory of forest dynamics using an analogy to stock market theory in financial mathematics
We propose a new method of modeling the biomass of an individual patch: An autoregressive model, where each year’s logarithm of biomass y(t + 1) is a weighted sum of the previous year’s logarithm of biomass y(t) and a random Gaussian noise
Summary
Self-organization occurs simultaneously on several levels of hierarchical ecosystem organization and involves dynamic processes operating on different temporal and spatial scales [2]. Forest dynamics refers to temporal and spatial changes that occur simultaneously at different levels of ecosystem organization. Various modeling approaches employed to understand and predict these changes include a number of discrete and continuous stochastic and deterministic models, such as Markov chains, individual-based models, ordinary and partial differential equations [3]. Markov chains are able to capture the effects of all these disturbances on forest biomass dynamics [10]. Their application is based on the discretization
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