A Markov Chain Model for Simulating Wood Supply from Any-Aged Forest Management Based on National Forest Inventory (NFI) Data
Markov chain models have been applied for a long time to simulate forest dynamics based on transitions in matrices of tree diameter classes or areas of forest size and structure types. To date, area-based matrix models have been applied assuming either even-aged or uneven-aged forest management. However, both management systems may be applied simultaneously due to land-use constraints or the rationality of combining the systems, which is called any-aged management. We integrated two different
... ted two different Markov chain models, one for even-aged and another for uneven-aged forest management, in an area-based approach to analyze wood supply from any-aged forest management. We evaluate the impacts of parameterizing the model based on available data sets, namely permanent and temporary Finnish National Forest Inventory (NFI) sample plots and a plot-level simulator to determine transitions due to different types of thinning treatments, and present recommendations for the related methodological choices. Our overall observation is that the combined modelling chain simulated the development of both the even-and uneven-aged forest structures realistically. Due to the flexibility of the implementation, the approach is very well suited for situations where scenario assumptions need to be varied according to expected changes in silvicultural practices or land-use constraints, for example. of 22 for example, availability of forests for wood supply at the European level may lead to serious under-or overestimates when downscaling the results to the national levels  . In Europe, the wood supply analyses have been based on different approaches from increment-based estimates  to modelling of future biomass supply  . In countries where wood-based industry is important, analyses of harvesting potential are based on data from National Forest Inventories (NFIs) and plot-or stand-level simulations     and similar approaches can be applied to simulate the provisioning of non-wood forest products or other ecosystem services. Also less data-intensive models, such as the European Forest Information Scenario Model (EFISCEN,  ) have been applied [20, 21] . The EFISCEN model originates from the so called International Institute for Applied System Analysis (IIASA) model developed by Nilsson et al.  and is based on the concept of Markov chain matrix models adopted by Sallnäs  from the ideas of Usher    . EFISCEN has been used to model forest dynamics from regional to European levels [11,    27] , but only in the context of even-aged forestry, although the Markov chain approach is fundamentally applicable for simulations of uneven-aged forest management    . A more recent Markov chain model, the European Forest Dynamics Model (EFDM,  ) was tested also for modelling the development of uneven-aged forests  . However, rational forestry practices combine both even-and uneven-aged management  and, in many countries in Europe, both management systems and shifts between systems appear with implications on future wood supply. Yet, none of the area-based matrix models used in Europe is applicable for simulating combined even-and uneven-aged management, also known as any-aged forest management    . The aim of this study is to analyze wood supply from any-aged forest management based on NFI data. The main objective is to integrate two different Markov chain models, one for even-aged and another for uneven-aged forest management, in a single simulation run based on the EFDM approach. The second objective is to evaluate the impact of different choices when selecting the parameterization of the model based on available data sets. Author Contributions: T.P. developed the research idea; J.V. and T.P. designed the experiments; J.V. carried out all computations and analyses; J.V. and T.P. wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.