FW 544: Quantitative Decision Analysis for Fish and Wildlife Management
Winter quarter 2013
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Class exercise: What follows is a description of a course project that included the participation of the entire class. Here we develop a decision model to address a contemporary management issue and used the resulting model to illustrate various steps and techniques needed to complete a decision analysis from start to finish. I usually try to have two of these examples a term. However this term, technical difficulties with the equipment in the computer lab prevented us from completing both examples. C'est la vie. Now on to our exercise!
Red-legged frog conservation in Oregon (Idea for problem: Jennifer Rowe-- good job!)
The northern red-legged frog (Rana aurora draytonii) was listed as threatened in 1996. It historically occurred occur along the Pacific Coast from southwestern Vancouver Island and Sullivan Bay, British Columbia to the California coast north of Mendocino County. Populations in the Willamette Valley OR are believe to be the most at risk of extirpation due to fragmentation associated with intensive agricultural land use and presence of non-native predators, chiefly introduced Centrarchids (i.e., sunfish and black basses) and bull frogs In the Willamette Valley, northern red-legged frogs breed in winter through early spring with adults frequently undertaking long migrations from summer habitats in mesic forests and riparian areas to breeding areas. Females lay eggs in vegetated shallows with little or no current. Eggs take approximately 6 weeks to hatch and an additional 3 months to reach metamorphosis. The wetlands can be temporary or permanent but they need to hold sufficient water until the juvenile frogs metamorphose in late June-July. Metamorphosed juveniles general remain at or near natal wetlands for several weeks before dispersing to summer habitats. Larval northern red-legged frogs consume epiphytic algae and generally use areas of dense vegetative cover, presumably to minimize predation risk.
Spatial and temporal dimensions
The spatial extent of this decision is the Willamette River Valley from Eugene OR north to Portland. Land use within the watershed is primarily a mixture of irrigated row crop agriculture and with heavily forested riparian zones. The valley is highly fragmented with wetlands occurring primarily is areas adjacent to the river. Riparian buffers are highly variable throughout the basin but tended to be smallest nearest urban areas. The grain of the decision is individual wetlands.
Legal, regulatory, and institutional constraints
The management of natural resources within the state of Oregon is the responsibility of the Oregon Department of Fisheries and Wildlife (ODFW). The broad responsibility lies in managing public lands and establishing best management practices standards, and setting wildlife conservation laws. Management of the Federally-listed species is the responsibility of the US Fish and Wildlife Service (USFWS) under the framework of the endangered species act.
Stakeholders
Identifying stakeholders was not part of this exercise. However, if I were to guess, the stakeholders for the decision would include: ODFW, USFWS, and landowners and managers in the Willamette Valley.
Objectives
During class,we created a mean objectives network and identified two fundamental objectives. One of the fundamental objectives was the long term persistence of northern red-legged frog and the other was to minimize the cost of management actions. To maximize northern red-legged frog persistence, the class believed that we should maximize the distribution and abundance of northern red-legged frogs in the Willamette Valley. A quantifiable attribute of this objectives at the wetland scale (i.e., the grain) was the presence of juvenile frogs during the early to mid summer. Thus, the quantifiable attributes of our fundamental objectives were maximizing juvenile from occupancy and minimizing costs.
Decision alternatives
After a brainstorming exercise, we arrived at three decision alternatives that could be applied to individual wetlands: mow exotic vegetation, remove exotic vegetation and replant native vegetation, and control (remove) exotic bull frogs. (Real world decision alternatives would probably more complex and exhaustive, but give us a break we only had 1/2 hr to brainstorm!!)
Valuation of outcomes
We used proportional scoring to standardize the objective specific outcomes. Here, objective specific utilities are rescaled as (actual outcome - worst outcome)/(best outcome - worst outcome). This results in utilities with a maximum value of 1 and a minimum value of 0. For example, the maximum cost for an action ( worst case replanting) was $20 K and the minimum cost ( best case mowing) was $0.5 K , so if the actual cost of an action was $5 K, the cost utility was: (5 - 20)/(0.5 - 20) = 0.769. For occupancy, the best outcome was 1 (100%) and the worst outcome was 0. The two utilities were weighted and combined as: combined utility = U.cost*0.375 + U.occupancy*0.625. The weights 0.375 and 0.625 needed to sum to one and the values were based on a majority vote by the class. The weights mean that the stakeholders value frog occupancy 0.625/0.375 = 1.67 times more than cost.
Decision model overview
The wetland decision model is a stochastic model that estimates the probability of juvenile northern red-legged frog occupancy in an individual wetland in response to a management decision. It is composed of the current state of a watershed: size, distance from nearest wetland, native vegetation buffer, and the presence of bull frog, population dynamics, and management components. The model went through three iterations before the final model. Here are the versions in Netica format (Version 1, Version 2, Version 3).
The final model is graphically represented as an influence diagram (below) that consists of model components, referred to as nodes with each node consisting of environmental states that are mutually exclusive and collectively exhaustive. The directed arcs indicate casual relationships between model components with parent nodes influencing (pointing into) child nodes. For instance, future native vegetation buffer (a child node) is influenced by current native vegetation buffer (a parent node) and the management decision (also a parent node). The relationships among components were parameterized using expert opinion. Elicitation of student experts included function elicitation, frequency elicitation, and value elicitation via the 4 step process. The excel file used to conduct the expert elicitation can be found here and the R script used for the 4 step process can be found here. Below we describe the model components and the sources of information that were used to parameterize the relations among model components.
Native vegetation buffer
Native vegetation buffer is influenced by the current buffet and the management decision. It is expressed as percent of the shoreline and was parameterized using function elicitation. The final parameters of the model were the average values of the experts. The initial (current) native vegetation buffer was simulated from a beta distribution x 100 to represent uncertainty or measurement error in the estimate of the current buffer. Future
native vegetation buffer affects water quality.
Water Quality Model
Water quality is influenced by future native vegetation buffer and is in one of 3 states based on 3 components of water qualty: dissolved oxygen > 6 ppm, maximum water temperature > 23 C, and total nitrogen to total phosphorous ratio < 5. Water quality is poor is less than 2 of these criteria are met, good if 2 criteria are met and excellent if all 3 criteria are met. The relationships are modeled using a multinomial logit model parameterized using function elicitation of experts.
Size of wetland
The size of wetland influenced the wetland extinction probability and was drawn from a gamma distribution to represent year to year variability or measurement error in the estimate of the size.
Distance from nearest wetland (patch)
The distance of the wetland from another wetland influenced the wetland colonization probability and was drawn from a gamma distribution to represent uncertainty or measurement error in the estimate of the distance.
Connectivity (Probability of fragmentation)
The connectivity component is an estimate of the probability that a watershed is isolated due to fragmentation. It influences the wetland colonization probability and the probability of bullfrog presence and was drawn from a beta distribution to represent uncertainty.
Bullfrog presence
Future bullfrog presence/absence is influenced by current bullfrog presence, the decision, and connectivity and the relations were parameterized using frequency elicitation. It influences the probability of wetland extinction. Current bullfrog presence was simulated using a beta binomial distribution to represent the uncertainty in bullfrog presence.
Extinction
The extinction probability is a function of the future bullfrog presence, the size of the wetland patch, and water quality and was parameterized using expert function elicitation. Wetland extinction influences the probability or rate of wetland patch occupancy.
Colonization
The colonization probability was modeled as a function of distance to the nearest patch and connectivity and was estimated using expert function elicitation. This relationship was developed through function value elicitation methods. Wetland colonization influences the probability or rate of wetland patch occupancy.
Occupancy rate
This component is influenced by extinction and colonization and represents the probability that the wetland is occupied by juvenile northern red-legged frog. Here we decided to estimate occupancy rate using an incidence function model as: colonization/(colonization + extinction). We could have modelel the colonization extinction process but opted to use this approach for simplicity.
Cost
The cost of each management action was elicited from our most experienced expert Jennifer who used the 4 step process to estimate the cost (and uncertainty) of each decision alternative. Uncertainty in the cost was incorporated using a gamma distribution.
Parameterization
Although we could have parameterized the model in the influence diagram format, I wanted to eventually use the model into a sequential dynamic decision making situation. Therefore, we created the model in R and modified the base code to learn how to use it for various aspects of decision analysis. I may eventually put the R code for parameterizing the influence diagram in Netica format. Note that you can find similar code at the Conroy and Peterson book companion website linked at the homepage.
Base model
Model with 3 sequential decisions
Model with sensitivity analysis of selected components
Model with indifference curve of utility weights
Dynamic decision model solved with exhaustive search of optimal sequence for decisions over 10 years (warning: this takes 23 hrs on my computer!!!)
Dynamic decision model solved using genetic algorithm
Step 1
Step 2
Step 3
Step 4
Model solved using Stochastic Dynamic Programming