Influence diagrams for environmental management
To establish the ecological objectives, the manager contemplates the populations that might be exposed. Several water bodies used by fisherfolk and others for recreation exist near the locations where adult mosquitoes congregate. The manager formulates a fundamental objective to make the best possible decisions about how to effectively spray to control West Nile Virus vectors while minimizing adverse ecological effects to nontarget organisms. The lower-level objectives for minimizing adverse ecological effects to nontarget organisms would be to minimize adverse ecological effects to fish and nontarget arthropods. Arthropods can be assumed to be susceptible to the adulticides because the target organisms (mosquitoes) fall into this taxonomic group. However, the manager is concerned about the generation time for fish in comparison to arthropods if a mortality event occurs. The manager realizes that these 2 attributes (fish and arthropods) are not independent in real-world scenarios. However, the probabilities of effects for each are independently specified from the output of PERPEST; the manager considers this pragmatic specification of independence to be acceptable.
The structure of the ID for the current example is given in Figure 3. The network has 5 chance nodes, 2 decision nodes, and 1 utility node. The chance nodes are based on circumstances important to minimizing adverse ecological effects and mosquito control. The important circumstances represented by the chance nodes are the downwind distance of the pond from the spraying location (access availability or pond distance from plane lines) and the wind speed during spraying. Each of these is a process outside of the decision-maker's control when a date, time, and location are selected. The influence of the latter variables could be modeled in the current ID if the decision-maker thought it would be valuable to capture this information. However, once the decision-maker knows where or when spraying should occur, she can input the parameters in the current decision model without losing information. The other 3 chance nodes specify potential outcomes from spraying. Adverse effects might occur to nontarget organisms and mortality to target organisms also might occur. There would be other outcomes after a spraying event, but these were deemed to be most important for management and stakeholders and so are the ones displayed for assessment. The outcome of each of these 3 variables influences the utility of the decision that is expressed with a pink utility node.
Risk managers are charged with confining risk estimates to levels that are needed for the purposes of their decisions and these risk estimates should not be too cautious nor too incautious (USEPA 2004). The Federal Insecticide Fungicide and Rodenticide Act stipulates that a pesticide use will not cause “unreasonable adverse effects on the environment” (USEPA 2003). Following this mandate, the standard USEPA consideration in evaluating pesticides is unreasonable risk to humans or ecology (USEPA 2000). Risk considerations in the current example will focus on probabilities of local extinction of a taxonomic group, given previous evidence from field or mesocosm scenarios.
Different choices for the spraying event are examined in Figure 3. Although evaluating risks and effectiveness is important, the value of the IDs in Figure 3 lies in the ability to examine the trade-offs in light of utilities. For the purpose of comparison, 2 IDs are displayed in Figure 3 with different spray characteristics highlighted. In Figure 3A, the pond downwind distance is far, the application rate is moderate, the drop size distribution is set to its coarsest value, and the wind speed is high. The resulting utilities (displayed in the decision nodes) are higher than the one in Figure 3B, indicating that this spray scenario is better. Examining the ecological effects and efficacy variables indicates that the risk is much lower in Figure 3A but the efficacy is less. This is interesting given that the efficacy outcome was weighted higher in the utility function than either of the ecological outcomes. In terms of trade-offs, the risk was low enough to compensate for having a lower probability of controlling adult mosquitoes. Changing some basic assumptions about the distance downwind from the pond, the application rate, and the drop size distribution causes a change in the utility values for our decisions. Some decisions might mitigate several issues and should be examined closer (Bierbaum 2002).
For each of the decisions to be made, we can estimate the probabilities of adverse effects for fish and arthropods as well as the efficacy of the spraying event. Table 2 presents the results based on the decisions of application rate and drop size distribution when spraying for a case scenario in which the pond downwind distance is known to be near and the wind speed is high. The potential risk of interest to fish is for the sum of the unknown recovery and the extirpation categories (adverse effects). Summing of the none, slight, and recovery node states would give a probability of low or negligible effects. Alternatively, they could be deduced from the adverse effects probabilities by subtracting them from 1 or 100 depending on whether the probabilities are expressed in decimal numbers or percents. As can be seen from Table 2, a higher application rate and smaller drop sizes will potentially give a more effective spraying. However, the same decisions increase potential risks to fish. The utility values were constructed as a way of measuring these trade-offs based on the value that is placed by stakeholders on chemically controlling adult mosquitoes or loss of fish. The highest expected utilities are generally found by deciding on moderate and low application rates with a coarse drop size distribution. The magnitude of changes in utility should be interpreted with caution. As observed in a decision analysis for a fisheries management context, conversions from their multiple attribute utility functions on a scale of 100 equated 1 utility score increase to $4.5 million in benefits (McDaniels 1995). The interpretation of expected utilities should consider the trade-off information as well as the risk attitudes incorporated into the utility function.
Table 2. Potential risk to fish (adverse effects probabilities), effectiveness, and expected utility of adulticide management decisions (application rate, drop size distribution) when pond downwind distance is near and the wind speed is high
|Application rate||Drop size distribution||p (fish adverse effects)||p (effective)||Expected utility|
Another advantage of placing probabilities of risk into an ID or BBN is the ability to project backwards to spraying factors that will lead to certain risk levels. Within the ID, we can specify likelihoods for ecological outcomes and observe what field characteristics are favored for these outcomes. Also, if the decision nodes are chance nodes or random variables in an inference problem, we might examine what application rate or drop size distribution would be most likely given high or low-risk levels. Figure 4 shows the 2 decision nodes (application rate and drop size distribution) as chance nodes (effectively turning the ID in Figure 3 to a BBN). By entering a finding of 100% extirpation to fish and arthropods in Figure 4A, we observe that the shortest pond downwind distance has the highest probability (39%) of causing this while wind speed is most likely to be high. In Figure 4B, evidence of no adverse ecological effects is entered into the BBN and the far pond downwind distance has the highest probability of causing no adverse ecological effects (35.5%). The low wind speed also has the greatest chance of causing no adverse ecological effects (38%). Also note from both figures that there is a lower probability of having an effective spraying when no adverse ecological effects are observed (82% vs 68%). Observations can be placed within a BBN for causes to compare and contrast probabilities of adverse ecological effects. Findings can also be specified for each of the effects categories and probabilities of various causes examined.
Figure 4. Bayesian belief network displaying probability distributions for spraying conditions when evidence is entered for (A) local extirpation to fish and arthropods and (B) no adverse effects to fish and arthropods.
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From Figure 4A, one can see that the 2 chance nodes related to decisions have states that are more likely given clear ecological effects than the other 2 root nodes, wind speed and pond downwind distance. The high application rate presents a much higher probability of having clear ecological effects on fish and arthropods than the other application rates. Also, the finest drop size distribution is more likely to produce adverse ecological effects. The opposite trend from Figure 4A was found for a scenario with no adverse effects to either fish or arthropods in Figure 4B.
All of these steps can also be done with the efficacy node. Thus, although the spraying outcomes were constructed from modeled data and expert opinion, the BBN allows us to clearly view what inputs are more likely to give certain outputs. This is an invaluable inference tool for risk management, but the ID should be used to ascertain the options that might bring the highest reward or lowest adverse effects under certain scenarios. To simplify the decision selection process, Netica can recommend policy options by optimizing decisions. Drawing arcs from wind speed and pond downwind distance to the 2 decision nodes would give recommended decisions for any combination of the site conditions that might be encountered. In addition, Netica can find optimal decisions via node absorption using methods described in Shachter (1986, 1988, 1990) and Norsys (1997).