Optimal management strategies in variable environments: Stochastic optimal control methods

Abstract

Dynamic optimization was used to investigate the optimal defoliation of salt desert shrubs in north-western Utah. Management was formulated in the context of optimal stochastic control theory, with objective functions composed of discounted or time-averaged biomass yields. Climatic variability and community patterns of salt desert shrublands make the application of stochastic optimal control both feasible and necessary. A primary production model was used to simulate shrub responses and harvest yields under a variety of climatic regimes and defoliation patterns. The simulation results then were used in an optimization model to determine optimal defoliation strategies. The latter model encodes an algorithm for finite state, finite action, infinite discrete time horizon Markov decision processes. Three questions were addressed: (i) What effect do changes in weather patterns have on optimal management strategies? (ii) What effect does the discounting of future returns have? (iii) How do the optimal strategies perform relative to certain fixed defoliation strategies? An analysis was performed for the three shrub species, winterfat (Ceratoides lanata), shadscale (Atriplex confertifolia) and big sagebrush (Artemisia tridentata). In general, the results indicate substantial differences among species in optimal control strategies, which are associated with differences in physiological and morphological characteristics. Optimal policies for big sagebrush varied less with variation in climate, reserve levels and discount rates than did either shadscale or winterfat. This was attributed primarily to the overwintering of photosynthetically active tissue and to metabolic activity early in the growing season. Optimal defoliation of shadscale and winterfat generally was more responsive to differences in plant vigor and climate, reflecting the sensitivity of these species to utilization and replenishment of carbohydrate reserves. Similarities could be seen in the influence of both the discount rate and the climatic patterns on optimal harvest strategics. In general, decreases in either the discount rate or in the frequency of favorable weather patterns lcd to a more conservative defoliation policy. This did not hold, however, for plants in states of low vigor. Optimal control for shadscale and winterfat tended to stabilize on a policy of heavy defoliation stress, followed by one or more seasons of rest. Big sagebrush required a policy of heavy summer defoliation when sufficient active shoot material is present at the beginning of the growing season. The comparison of fixed and optimal strategies indicated considerable improvement in defoliation yields when optimal strategies are followed. The superior performance was attributable to increased defoliation of plants in states of high vigor. Improvements were found for both discounted and undiscounted yields.