Management of California Oak Woodlands: Uncertainties and Modeling

A mathematical policy model of oak woodlands is presented. The model illustrates the policy uncertainties that exist in the management of oak woodlands. These uncertainties include: (1) selection of a policy criterion function, (2) woodland dynamics, (3) initial and final state of the woodland stock. The paper provides a review of each of the uncertainty issues. The final section of the paper describes a modeling approach that can be developed to assist policy makers in evaluating alternative oak woodland policy actions. The management of natural resources is the topic of numerous academic journals, and hundreds of books and popular articles. Natural resource management has different meanings to different groups of people. Natural resources can be viewed as environmental assets which provide value to society in any number of ways. This value can be gained from using the natural resource as an input into the productive process, as a sources of raw materials, as a provider of life-sustaining services, and as a provider of esthetic and recreational amenities. The management of a natural resource is further complicated by various uncertainties. Uncertainty exists in determining the exact composition or stock (size) of the natural resource, in understanding the ecological dynamics of the natural resource, and with respect to whether the resource can be managed to achieve some socially preferred state. It is then not surprising that, when one suggests that we need to better manage our natural resources, controversy erupts concerning how the natural resource should managed and for whose benefit. One segment of society may wish to have natural resources managed to improve their short-run and/or longrun productivity (e.g., range management for livestock) while another group may wish to have the natural resource managed to sustain or improve its amenity qualities (e.g. wildlife habitat). Ideally, the highest value of the natural resource to society could be attained by maximizing the discounted net social value of the resource. This can be a difficult natural resource management problem since it requires information on the prices and costs of differing natural resource uses. Some of these have market values and cost (e.g. firewood), and other uses may have observable costs, but not have observable market prices (e.g. open space). These uses must have values measured through non-market evaluation techniques. Nevertheless, management of a natural resource requires that choices be made between competing resources uses and over time and space. These choices will not only affect differing groups in society but also potentially affect the ecological dynamics of the natural resource system. Effects on natural resource systems are typically valued in terms of their ultimate impact on human society although this is not universally accepted. Commoner (1972) presents a principle of minimum interference, which suggests that there should be minimal to no management of natural resource systems by society. However, the obvious is that society does attempt to manage natural resource assets and that the outcome of that management is judged by whether it is consistent with collectively desired outcomes. 1An abbreviated version of this paper was presented at the Sym­ posium on Oak Woodlands: Ecol­ ogy, Management, and Urban Interface Issues, March 19-22, 1996, San Luis Obispo, Calif. 2Associate Professor, Agribuiness Department, and Professor, Natu­ ral Resources Management De­ partment, California Polytechnic State University, San Luis Obispo, CA 93407. USDA Forest Service Gen. Tech. Rep. PSW-GTR-160. 1997. 603 Noel and Thompson Management of California Oak Woodlands A California natural resource that is subject to such complex debate over its allocative uses is the oak woodlands. There are about 10 million acres of oak woodlands (also known as hardwood rangelands) in California. Oak woodlands provide a number of valuable economic uses. These include cattle grazing, water resource development, wildlife habitat, open space, hardwood lumber and firewood, and land for urban development. There is a long history of concern about the public and private management of California’s oak woodlands. These concerns include conflicts over changing land use, rights and responsibilities of ownership, and the extent and character of urban forces reshaping the oak woodlands, and the long-run sustainability of these woodlands. Local, state, and federal agencies are under increasing pressure to deal with a wide diversity of private and public interests in a comprehensive and economically sound manner. To achieve this goal, improved oak woodland management guidelines are needed for land use planning and for ecologically and economically sustainable management practices in water production, grazing, wildlife, hardwood lumber, and housing. The California Department of Forestry and Fire Protection has summarized the policy issues and objectives for state action (California Dept. of Forestry 1988). The broad objectives of this paper are to provide an overview of the problems associated with managing California’s oak woodlands as a natural resource management problem and the development of a comprehensive oak woodlands control model that could assist policy-makers in achieving collectively desired outcomes. The modeling approach takes a systems view of the oak woodland’s management problem. The model is intended to be an evaluative, not prescriptive, tool. Oak Woodlands Management: The Uncertainty Problems The following control problem is a mathematical representation of the oak woodlands management problem. It is presented to facilitate discussion of the uncertainty that exists in establishing oak woodland management policies. t1 I S t ,U t , t , Maximize or Minimize ∫ ( ( ) ( ) ) subject to: t0 • S (t)=f(S(t),U(t),t), the oak woodland ecosystem dynamics, (t0) = S0, initial state of the oak woodlands, S(t) = Gt(S(t)), the final state or terminal value of the oak woodlands, ht(S(t), U(t), t) ( 0, oak woodland constraints. S(t) is the state of the oak woodlands at any given period of time between t0 (current time period) and t1 (future time period). The state describes those attributes that compose a specific oak woodland. For example, acres of land suitable for cattle range, volume of wood available for firewood and other hardwood uses, acres available for housing development, acres suitable for amenity purposes, acres suitable for wildlife habitat, and water development potential could characterize a specific oak woodland state. U(t) represents the control variables which affect the state of the oak woodlands from one period of time to the next. These controls could include the amount of cattle grazing in some specified time period, amount of oak harvested for firewood, amount of land utilized for wildlife habitat or housing. X(t) are the random disturbances that can affect the oak woodland state and include natural phenomena such as drought, fire, wind, and plant diseases and insect infestations. USDA Forest Service Gen. Tech. Rep. PSW-GTR-160. 1997. 604 Management of California Oak Woodlands Noel and Thompson The oak woodland management problem can now be stated as follows. Maximize or minimize I, some real valued policy criterion function, which has as its arguments S(t), the state of the oak woodlands in any time t; U(t) the uses of oak woodlands in any time t; and t time. This maximum or minimum is subject to S(t), the oak woodland ecosystem dynamics known as equations of motion; S(0), the initial state or value of the oak woodlands; Gt(S(t)), the final state or terminal value of the ending state; and h(S(t), U(t), t), specific ecological and policy constraints on the controls and states of the oak woodlands. This oak woodland management problem is dynamic and stochastic and can be characterized as a closed loop control problem. This implies that resource allocation policies are conditional upon learning more about the ecological and economic dynamics and the impact that resource uses of and policies for have on the dynamics. This model illustrates that managing oak woodlands is subject to varying degrees of uncertainty in the decision-making process. Uncertainty arises from (1) specification and selection of a policy criterion function and its parameters, (2) oak woodlands dynamics including the evolution of oak woodland ecology over time and the impacts that management decisions and random disturbance have on that evolution, and (3) the initial stock and final oak woodland stock or value. The next four sections discuss these uncertainties from the perspective of an investigator who is interested in developing a model to assist public policymakers in evaluating different oak woodland management policies. Policy Criterion Functions Policy criterion functions provide the basis for evaluating the desirability of management policies and actions which lead to specific outcomes. These outcomes can be viewed as the state of the oak woodland ecosystem in some given time period. Public-policy decision makers must choose between alternative management strategies (policies) and actions that influence different sectors of the society in various ways and have different welfare connotations to these segments of society. The uncertainty that must be addressed is the choice of a specific policy preference function and the estimation of its parameters. A number of researchers have attempted to address this issue including Theil (1968), Prescott (1972) , and Fromm (1969). Rausser and Freebairn (1974) discuss the issues associated with the selection of preference functions and estimate a preference function for United States beef import quotas. Policy preference functions can be viewed as the objective function of the public agency which has the management responsibility for the natural resource. This means that the public policy entity must combine its legal mandates with its perceptions of society’s wishes into a societal welfare function, which becomes its objective function. An attempt is then made to maximize this function given various constraints. Rarely, if ever, is the public agency certain as to what the societal welfare function looks like or whether, upon selecting a specific societal welfare function, it is the one which will maximize societal welfare. There are two basic approaches to the development of a policy preference function. The first approach is to develop an explicit objective function. The formalization of an explicit objective function and its optimization allows for the endogenous (internal to the system) determination of the control parameters and thus the time-dependent resource states. The controls and resultant states are then reviewed by the policy-maker for management feasibility. If the optimization set of controls and states is not considered practical by the policymaker then another objective function is selected and the process begins over again. This process would continue until a workable set of policies is determined. USDA Forest Service Gen. Tech. Rep. PSW-GTR-160. 1997. 605 Noel and Thompson Management of California Oak Woodlands The policy-maker would determine which is the more practical from a policy perspective. An example of this type of policy preference function is the maximization of a social welfare function. The function is composed of the benefits and costs that accrue to differing uses of the natural resource over time and space. A number of studies have used the optimization of an explicit objective function to evaluate natural resource issues. Noel and McLaughlin (1983) use this approach to address the problem of groundwater overdraft problem in the San Joaquin Valley. The second approach to the development of a policy preference function is an implicit approach. Such an approach assumes that the public policy decisionmaker has implicitly optimized a societal welfare function and has chosen a set of management options that targets specific state outcomes. These targets become the ideal levels the public-policy decision maker has for the natural resource system. A deviation from them is considered a loss or cost to societal welfare. The optimization criterion is to keep the evolution of the natural resource system as close to the target levels of controls (e.g., timber harvesting levels) and states (e.g., cubic feet of unharvested forest) as possible. An example of this type of policy criterion function is the quadratic tracking function (Athans 1972). The optimization of this function results in a minimization of the deviation of the targeted levels of states and controls. The deviation costs are measured by the relative weights placed on achieving a specific state versus achieving a specific control. The policy maker thus has the option of placing a greater weight on achieving a specific targeted state than control or vice versa. The optimization of the tracking function then is a minimization problem, which finds the minimum cost path of targeted state and control deviations. Dixon and Howitt (1979) use this type of policy preference function to evaluate an intertemporal forest harvesting problem. The choice of what type of policy preference function to use is a subject of theoretical and empirical debate. Rausser and Freebairn (1974) list six points, which should be considered in the selection process. They conclude that the explicit function approach is preferred to the implicit approach since the arbitrariness of the former is less than that of the latter. Their view is not universally accepted (Naylor 1970). Whatever approach is taken, a policy preference function must be estimated. This is a three-step process involving: (1) selection of the relevant variables as arguments, (2) determination of the appropriate mathematical structure, and (3) obtaining an estimate of a set of values for the parameters of the function. Uncertainty in Dynamics of Oak Woodland Systems Management of oak woodlands is subject to ecological uncertainties. The areas of uncertainty that are important to both the modeler and decision-makers are structural uncertainty and functional uncertainty. Structural uncertainty is caused by a lack of knowledge concerning the exact mathematical form that represents the ecosystem dynamics and a lack of data to estimate the form even if it were known. Functional uncertainty is concerned with changes in structure arising from sampling and measurement error. Structural and functional uncertainties create a stochastic set of natural resource system parameters, which essentially means that decision-making is done with incomplete information. This implies that selection of a policy is conditional upon current information concerning the structural and functional aspects of the ecosystem. However, new data assist in updating knowledge, creating a sequential policy-making process. Thus, the oak woodlands management problem has a dual nature. The policies chosen to manage the system affect both the value of the objective function and quality of future information on the structural parameters of the ecosystem. This is an active learning problem, which recognizes the stochastic nature of the USDA Forest Service Gen. Tech. Rep. PSW-GTR-160. 1997. 606 Management of California Oak Woodlands Noel and Thompson ecosystem and represents a closed loop control problem, which seldom has an analytical solution (Aoki 1967). Given the structural and functional uncertainty problems associated with natural resource management, the modeling of complex ecological systems has received a considerable amount of attention from biologists, ecologists, engineers, and economists. The modeling efforts have been concentrated in two areas: those models whose purpose it is to provide an understanding of complex biological systems and those models which are directed to biological system control. Central to both is the difficulty in inferring the true model from the phenomena being modeled. An example of the research being done in this area is provided by Mees (1990). The second source of uncertainty in the mathematical modeling of natural resource systems is that of random disturbances, which can change the ecosystem parameters over time and space. These random disturbances include lightningcaused fire, floods, drought, erosion, disease, and insects. The impact of these disturbance processes on ecosystem management is discussed in detail by Averill and others (1994). The authors argue that these random disturbances can have both positive and negative effects on an ecosystem. It is not a question then of whether these disturbances can be ignored, but of finding a way to characterize these disturbances in physical and economic terms. Several tools are available to assist in this process including global positioning systems (GPS), geographic information systems (GIS) and geo-statistical technologies. Certainty equivalence is an approximation approach to the stochastic (uncertainty) problems created by both the structure and function issues and random disturbance issue discussed above. The certainty equivalence approach uses expectation of the stochastic parameters of the biological system functions. A number of restrictive assumptions underlie this approach (Chow 1975). However, it is likely that researchers and decision-makers will continue to approximate the complex, dynamic biological systems with linearized versions of models that use certainty equivalency to handle structural and functional uncertainty problems. Standiford and Howitt (1992) use certainty equivalency in their bioeconomic model of California’s hardwood rangelands. They derive production functions for forage, hunting, cattle, and oak firewood. A near optimal control was used to solve for state and control variables to give optimal time paths for oak density and cattle stocking. The Initial State of the Oak Woodland System This section discusses the biological, socio-political and economic criteria needed to adequately describe the initial state of the oak woodland ecosystem in California. This modeling phase should be the most straightforward to design and measure, but it is greatly complicated not only by the large amount of information needed on the parameters of the ecosystem but the more difficult problem of quantifying the relationships between the parameters. For example, one might be able to measure with reasonable accuracy the number of acres of various oak woodland types delineated by composition and structure. However, describing the habitat potential of each structural-composition type for various wildlife species is far more difficult. Another important issue to address in defining the initial state is the scope or scale of the ecosystem. As the scale of the model increases to statewide, for example, information must necessarily be more generalized, which increases the uncertainty and thereby reduces the model’s evaluative power. The result is either no feasible solution or a general one that is useless. On the other end of the spectrum, the project area could be scoped down to as small as a watershed scale where more detailed information could be (and has USDA Forest Service Gen. Tech. Rep. PSW-GTR-160. 1997. 607 Noel and Thompson Management of California Oak Woodlands been to varying degrees) collected, reducing uncertainties but providing solutions that disregard important landscape level concerns. Figure 1 briefly summarizes that state of knowledge necessary to develop a oak woodlands policy model. By no means is the summary exhaustive nor is it sufficiently detailed to show the distinction between studies related to state or control issues. It is basically designed to illustrate, in one glance, where past efforts have focused and where the major gaps in knowledge exist. Figure 1—Description of the current state of oak woodland research. Literature cited in this figure is not cited in the references section of the paper. 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