Problems of Modeling Growth and Yield of Renewable Resources

Mathematical models are now influential and widely used tools in renewable resource management. Managers of forests, fisheries, wildlife, range, and other resources routinely consult quantitative predictions on harvesting policies. The types of models used are as varied as the resources, from regression models predicting growth increment from dozens of environmental variables to complex systems of nonlinear differential equations reflecting intricate webs of species interactions. The modern-day resource manager trained at a university typically has received a battery of courses in mathematics, statistics, computing, and modeling and simulation in the appropriate resource. Despite the acceptance and growing use of models by resource managers, there are many aspects of resource modeling for which challenging problems exist. One of the main problems is the ever-present variability in the abundance of the resources. Forests, fish populations, and wildlife populations undergo large, irregular fluctuations due to a wide range of causes. Resource modelers have typically concentrated on extracting the “signal” from these fluctuations, building deterministic models that are sometimes fit to complete scatter-clouds of data. Managers in turn make decisions primarily based on the forecast mean behavior of the systems. This article identifies some of the main quantitative obstacles to more effective modeling of the growth and yield of renewable resources. We concentrate in particular on statistical problems associated with modeling forests and marine fisheries. Our goal is to describe areas in which resource modeling and decision making might benefit from explicitly acknowledging and including stochastic factors in the models. Section 2 of this article briefly looks at the ecological underpinnings of resource modeling. The ecological modeling tradition has arisen over many decades, mainly from studies of populations growing in the laboratory. We discuss the modeling of laboratory populations, before undertaking the “real” resources in forestry and fisheries, to emphasize the importance of stochastic forces in population growth. Life is stochastic, even under controlled environmental conditions. Section 3 tackles some prevailing issues in modeling forest growth and yield. We discuss usual regression models