Implications of Extreme and Mean Ratio in Near- Natural Forest Management Planning – Using a Diameter Class Modelling Approach

Near natural forest management is performed by use of domestic tree species that are able to regenerate naturally. One of the long-term key objectives is to achieve more structural richness in the form of uneven-aged mixed species forests dependent on so-called forest development types that are allocated with support in ecological mapping. A goal of perfection or an ideal structure may be sought by replication of the normal forest structure that takes the form of an inverse J-shape when analysing the stem number ha-1 as a function of diameter. Here alternative approaches applying the extreme and mean ratio (1.61803) are developed with the purpose to describe and analyse the ideal or perfect structure of an uneven-aged forest of European beech (Fagus sylvatica L.) site index 1. The so-called golden ratio is applied for example in determining midpoints of diameter classes based on the assumption that the relation between the stem number ha-1 in adjacent diameter classes is equal to the golden ratio. Solutions are found by use of Markov chains through solution of recursive equations applying linear programming. Alternative approaches where the golden ratio is applied as a structural goal are analysed.