Qualitative network modeling, as shown in the previous post in Our Water Ways, is focused on actions that create either positive or negative results for actors in the model. This modeling approach is useful for considering the possible outcomes triggered by various actions, especially when data are lacking to develop mathematical relationships between the actors.

Another type of causal model, called a Bayesian network model, takes the process one step further by including probabilities that certain actions will take place among the actors in the model. Data from field studies can help establish the probabilities, or experts can make informed predictions about the likelihood of various actions, given a set of conditions outlined in the model.

King County’s Department of Natural Resources and Parks developed a rather extensive group of models to describe how improving water quality can increase shellfish harvesting and recreation while producing positive effects for fish and Southern Resident killer whales. Check out Water Quality Benefits Evaluation.

As a simple example of a Bayesian model, let’s look at a small slice of a massive King County model used to account for factors that can affect orca health and population growth (or decline). The major factors — each described within a “submodel” — are human disturbance, chemical contaminants, and prey (quantity and quality).

Let’s zoom in on a sliver of the model dealing with prey — the ability of the killer whales to find food. This piece is from a preliminary draft of the model, later simplified but described further in a video. Two major influencers of hunting success are featured. They are 1) the number or availability of Chinook salmon, the orcas’ primary prey, and 2) human-induced harm, such as noise and interference from boats that can keep the whales from finding the available prey.

Each of these factors, referred to as “nodes” in a diagram, are assigned possible conditions or “states.” For this part of the model, three states were clearly defined for each of the factors 1) “improved,” 2) “same as today” and 3) “degraded.” The definition of “improved” Chinook availability is a 25 percent increase or more in the average number of fish returning to local waters.

The essence of the Bayesian model emerges when experts, using their best judgment, decide what probabilities to apply to each of the possible states. Combining the three possible states for Chinook availability with the three states for human interference leads to nine possible combinations. For each combination, percentages are assigned to show the likelihood that the outcome (hunting success) will be 1) “improved,” 2) “same as today” or 3) “degraded.” All the various conditions along with the 27 percentage predictions can be displayed in a “conditional probability table.”

Once the probabilities are all estimated, one can run various scenarios to see the predicted effects. With preliminary assumptions in this example, reducing human-induced harms by 20 percent with no change in Chinook availability is predicted to lead to a 16 percent increase in hunting success. A 20 percent increase in Chinook with no change in the human factor would lead to a 20 percent hunting success. A 20 percent increase in Chinook along with a 20 percent decrease in human effects would boost hunting success by 30 percent, as described by this particular model.

Of course, hunting success is just one factor in determining the overall health of orcas and their population changes. The full Bayesian network model developed by King County also considers how toxic chemicals, disease and other factors affects body condition, mortality and ultimately population. The model includes probabilities for each step in the conceptual diagram, and it uses Bayesian statistics to calculate a “degree of belief” in the possible outcomes. A video produced by King County is based on a preliminary version of the model related to killer whale health.

To run the model, the operator provides inputs by specifying changes in the levels of toxic chemicals in Chinook; the amount of human disturbance and human-induced injury; prey quality; and salmon run size. In real life, some factors are easier for people to fix than others, but one can imagine a wide variety of possibilities.

Outputs are a prediction of the increase or decrease in a defined condition that combines orca population with orca health. The idea is that health can be a short-term change and population is the long-term result.

In the end, the model’s numeric outputs depend on the probabilities assigned by the experts, noted Carly Greyell, water quality project manager for King County. But the value of the model, she said, lies in observing all the cause-and-effect linkages and determining which potential changes could have the greatest effect on orca health and population.

The completed model, described in detail in a final report, has shown that making changes in King County alone is not adequate to improve the Southern Residents’ health or population, but it suggests that making specific changes on a regional level could have positive outcomes.

Storymaps describing the King County models, including the orca model, are being developed for public release on the county’s website before the end of this month. Earlier documents can be found on the webpage dealing with causal models.