Optimizing the management of a Picea abies stand under risk of butt rot

A simulation model was developed to predict the growth of a Norway spruce stand under risk of butt rot caused by Heterobasidion annosum stump infection and logging injuries. The simulation model was distance-dependent; tree growth was predicted with a distance-dependent model, and the spread of butt rot through root contacts depended on tree location. Infection of stumps and injured trees, and the spread of butt rot in the stand were stochastic processes whereas tree growth and mortality were treated as deterministic processes. The simulation model was used with the nonlinear optimization algorithm of HOOKE and JEEVES (J. Assoc. Comput. Mach, 8, 212-229, 1961) to find the most profitable management schedule for an even-aged, young stand. Optimization used four different stump infection rates and two spreading capacities from infected stumps. The profitability was evaluated by the expected soil expectation value (SEV) at a 3% interest rate. Two thinnings, both in winter-time, and hence without H. annosum infections, resulted in the highest SEV. If any stump infection by H, annosum occurred, only one thinning and a shortened rotation were suggested. The optimal thinning rate tended to decrease but also large trees were removed with the increasing infection rate. With one thinning during a rotation, stump treatment was profitable above a stump infection rate of 10%.