2.1.1. Decision Model for Determining Preferred FRTs
The decision model determines the preferred FRTs over multiple, equal-length planning periods. The decision processes included in the model are as follows. First, the manager identifies the maximum hectares that can be treated with each FRT in each planning period. Maximum hectares treated are constrained by the fuel treatment budget for each planning period.
Second, for case 1, at the beginning of each planning period, the private manager selects and implements the preferred FRT, which is the FRT that maximizes expected net return for fuel treatment (ENRT) for that planning period. Because ENRT measures the profit earned from FRTs, if any, the management objective for FRTs for case 1 is to maximize the profit earned from fuel treatment in each planning period. For case 2, at the beginning of each planning period, the public manager selects and implements the most preferred FRT for that planning period with respect to three management objectives: maximizing ENRT; minimizing expected residential property losses from wildfire (ERLW); and maximizing expected ecological benefits of fuel treatment (EEBT). The preferred FRTs for planning periods in case 2 are determined using a multiple-objective decision-making procedure. The decision model is general enough to handle other management objectives besides the ones mentioned above.
Third, for both cases, managers select preferred FRTs for planning periods taking into account uncertainty about future climate change and its effects on management objectives for FRTs. Uncertainty about future climate change occurs because scientists that develop climate futures, such as the representative concentration pathways (RCPs) specified in the IPCC’s fifth assessment report [
13], are unwilling or unable to assign probabilities to those futures. In addition, managers are typically uncertain about how climate futures are likely to influence management objectives. Due to both sources of uncertainty, the preferred FRT for a planning period cannot be determined using stochastic decision-making rules that require probabilities for climate futures and the effects of climate futures on FRTs. Examples of such rules include the expected value criterion and Bayesian networks.
Fourth, the best adaptive management strategy for both cases is determined based on the preferred FRTs across planning periods.
Selecting the preferred FRT for a planning period involves two separate but related decisions: (1) determining the preferred FRT for each climate future in each planning period (first decision); and (2) identifying the best FRT across climate futures for each planning period (second decision).
For case 1, the preferred FRT for each climate future within a planning period is selected based on ENRT, which is stochastic because its determinants, such as wood prices and harvest costs, are stochastic. Therefore, the first decision for case 1 is to select the preferred FRT for each climate future at the beginning of the planning period based on the distributions of the estimated values of ENRT for that period. That decision can be made by applying the stochastic efficiency with respect to a function (SERF) criterion [
13] to the distributions of the estimated values of ENRT. The dominant or preferred FRT for each climate future with the SERF criterion is the one with the highest certainty equivalent [
14], which is the payoff amount a manager is willing to receive in exchange for accepting the variability in ENRT for a particular FRT. For example, the SERF criterion has been applied assuming: (1) the manager’s risk aversion coefficient (RAC) is in the range (0, 0.03), where 0 implies the manager is risk-neutral and RAC >0 implies the manager is risk-averse [
15]; (2) constant absolute risk aversion (
i.e., the risk premium a manager is willing to pay to reduce ENRT risk does not vary with the level of ENRT); and (3) the manager’s utility function is exponential in ENRT (
i.e., u[ENRT·I] = exp[−RAC × ENRT]) [
16]. The SERF criterion has the drawback that it requires specifying the manager’s risk preferences and the form of the manager’s utility function. Such specifications are usually arbitrary, which is undesirable.
Alternatively, the first decision for case 1 can be made using the minimax regret criterion (MRC). With the MRC, the preferred FRT for each climate future is the one that minimizes the average maximum loss in ENRT across those futures. The average maximum loss in ENRT with a particular FRT and climate future can be estimated by taking the difference between the expected value of the distribution of the estimated values of ENRT for that FRT with no future climate change minus the expected value of the distribution of the estimated values of ENRT for that FRT and climate future.
The second decision for case 1 involves choosing the preferred FRT across climate futures for each planning period. That decision is made by applying the MRC to the preferred FRTs for climate futures in each planning period.
The first decision for case 2 is to determine the preferred FRT for each climate future within a planning period based on three management objectives: maximizing ENRT; minimizing ERLW; and maximizing EEBT. A fuzzy logic decision model is used to make the first decision for case 2. That model uses a f, multiple-objective, decision-making rule that accounts for uncertainty. Fuzzy logic has been used to evaluate agricultural sustainability [
17,
18], ecological impacts [
19,
20], the behavior of environmental systems [
21,
22], suitability of sites as scientific natural reserves [
23], the efficacy of protected areas in nature conservation [
24], sustainable development [
25], and ecosystem management [
26,
27].
Several fuzzy logic procedures can be used to make the first decision for case 2. The decision model uses the fuzzy Technique for Order Preference by Similarity of Ideal Solution, or fuzzy TOPSIS. Fuzzy TOPSIS evaluates and ranks decision alternatives based on how close (or how far away) the management objectives achieved by those alternatives are to the most (or least) desirable values of the positive (or negative) objectives [
28,
29,
30,
31,
32,
33]. A positive objective is one for which more of the objective is preferred and a negative objective is one for which less of the objective is preferred by the decision-maker.
General steps in the fuzzy TOPSIS procedure are as follows:
- (1)
Managers assign narrative descriptions known as linguistic variables to the estimated values of the objectives of FRTs under each climate future and the relative importance of the objectives. Linguistic variables can be assigned independently or collectively by managers.
- (2)
Fuzzy numbers are assigned to linguistic variables. For example, Chen [
30] and Prato [
33] assigned triangular fuzzy numbers to linguistic variables. If managers collectively assign linguistic variables, then the fuzzy numbers corresponding to the collective linguistic variables are used. If managers independently assign linguistic variables, then the fuzzy numbers corresponding to the linguistic variables chosen by individual managers are averaged to obtain collective fuzzy numbers.
- (3)
Fuzzy TOPSIS is used to rank FRTs for each climate future within a planning period. The preferred FRT for a climate future is the top-ranked FRT for that future.
The second decision for case 2 is to choose the preferred FRT across climate futures for each planning period using the MRC. This decision is more complicated than the second decision for case 1 because case 2 selects the preferred FRTs based on three objectives, whereas case 1 selects the preferred FRTs based on only one objective. In order to apply the MRC to the second decision for case 2, a maximum loss index (MLI) is calculated for the preferred FRT for each climate future. The MLI is an index of the expected maximum losses in the three objectives for a particular climate future. Expected maximum loss for an objective with a particular climate future is the average estimated value of the objective without future climate change minus the average estimated value of the objective with that climate future. Calculation of the MLI requires managers to assign weights to the objectives, such that the sum of the weights equals one. With the MRC, the preferred FRT for a planning period is the one that minimizes the MLI across climate futures.
2.1.2. Decision Model for Adapting FRTs to Climate Change
The decision model in the conceptual framework determines a manager’s best strategy for adapting FRTs to climate change over planning periods by applying adaptive management (AM) [
34,
35,
36] to the preferred FRTs for planning periods. AM is a form of integrated learning that acknowledges and accounts for the surprising and unpredictable nature of the outcomes of management alternatives due to uncertainty about future changes in system drivers and the effects of those drivers on management outcomes. Kohm and Franklin [
37] state that “adaptive management is the only logical approach under the circumstances of uncertainty.” The National Research Council (2004) [
38] states that “adaptive management [is a decision process that] promotes flexible decision making that can be adjusted in the face of uncertainties as outcomes from management actions and other events become better understood.”
Adaptive management can be either active or passive. Williams [
39] defines active AM as an approach that evaluates management alternatives for reducing uncertainty about ecological processes and how management decisions influence those processes, and passive AM as an approach that focuses on resource management objectives with less emphasis on learning about the effects of management alternatives on ecological processes. Nyberg [
40] and Prato [
41] define active AM as a management approach that designs and conducts experiments to test hypotheses about the efficacy of management alternatives and adapts management alternatives over time when warranted based on test results, and passive AM as a management approach that does not involve experiments and hypothesis testing. For the test results from active AM to be statistically reliable, the experiments must incorporate replicated, randomized, and independent treatments and controls.
Although active AM can provide statistically reliable information about the impacts of system drivers on management alternatives, it has three limitations. First, conducting experiments on management alternatives requires major investments in research, monitoring, and modeling, which can be expensive. Second, active AM cannot be used when the impacts of management alternatives or experimental treatments cannot be evaluated independently of one another; lack of independence among treatments violates one of the prerequisites of experimental design. Third, several of the prerequisites of active AM are difficult to satisfy [
41]. Passive AM does not involve experimental controls and replication or randomization of management alternatives, and, as a result, does not provide statistically reliable information about how management alternatives influence objectives. Nevertheless, passive AM is generally less expensive and easier to apply than active AM.
The decision model utilizes passive AM. Specifically, the best AM strategy for both cases is determined based on the preferred FRTs across planning periods. For example, if there are four FRTs, four planning periods, and the preferred FRTs are FRT3 for the first and second planning periods, FRT4 for the third planning period, and FRT1 for the fourth planning period, then the best passive AM strategy is to switch from FRT3 to FRT4 at the beginning of the third planning period, and switch from FRT4 to FRT1 at the beginning of the fourth planning period.