Evaluating management regimes for European beech forests using dynamic programming

<p><em>Aim of study:</em> This contribution describes a systematic search method for identifying optimum thinning regimes for beech forests (<em>Fagus sylvatica</em> L.) by using a combination of optimization heuristics and a simple whole stand growth prediction model. </p><p><em>Area of study: </em>Data to build the model come from standard and management forest inventories as well as yield tables from the Northern and Western part of Germany and from southern and central Denmark.</p><p><em>Material and Methods:</em> Growth projections are made from equations to project basal area and top height.  The remaining stand variables are recovered from additional equations fitted from forest inventory data or acquired from other authors.  Mortality is estimated through an algorithm based on the maximum density line. The optimization routine uses a two-state dynamic programming model. Thinning type is defined by the <em>NG</em> index, which describes the ratio of the proportion of removed trees and basal area with respect to the same proportion  before thinning. </p><p><em>Main results</em>: Growth equations fitted from inventory data show high goodness of fit with <em>R</em>² values larger than 0.85 and high significance levels for the parameter estimates. The mortality algorithm converges quickly providing mortality estimates within the expected range.</p><p><em>Research Highlights:</em> The combination of a simple growth and yield model within a Dynamic Programming framework in conjunction with <em>NG</em> values as indicators of thinning type yield good estimates of practical thinning schedules compared to thinning recommendations provided by diverse authors.</p><p><strong>Keywords: </strong>beech (<em>Fagus sylvatica L</em>.); <em>NG</em> ratio; thinning optimization; growth and yield simulation; mortality.</p>