Post by Caleb Aldridge.— In my last blog post I discussed modifying a simple experimental design to one slightly more complicated but allowed more alternatives in herbicide choice. (If you haven’t read it, now’s a good time–much of the material ahead relies on part I). I also alluded to budget and coverage (ha). These are important elements in deciding which herbicide to choose to control the invasive.
Let’s simplify the problem a little, so we can concentrate on why considering decision elements in the design of experiments is important. I’m going to focus on one fundamental objective, increase suitable habitat, and its two means objectives, maximize percentage dead stems per meter-squared and maximize area treated (ha). Let’s also assume that $500 (USD) has been allocated for the purchase of herbicide, so we’ll use the full amount.
Recall from our experiment that we had two herbicides (Herbicide 1 & 2) at two concentration levels (Suggested and Below) we compared. We knew that the two herbicides may not have equal effectiveness, and we assumed this was even more the case when they were diluted. But we also knew that the below suggested concentration treatments would likely give us more coverage (area treated). The coverage area is important because we’ve surveyed about 90 ha where the invasive grass is growing. We’d like to get at least 100 ha of coverage, but because each herbicide is sold in different volumes were uncertain if we will meet our 100 ha goal.
From our experiment we were able to determine probabilities for the three outcomes of percentage of dead stems per meter-squared. For Herbicide 1 Suggested the probabilities were: 0.02 for = 60%, 0.58 for 61-79%, and 0.40 for = 80%. Probabilities for other treatments were:
- Herbicide 1 Below = 0.10, 0.70, and 0.20;
- Herbicide 2 Suggested = 0.20, 0.70, and 0.10;
- and Herbicide 2 Below = 0.45, 0.50, and 0.05, for = 60%, 61-79%, and = 80%, respectively.
We also placed probabilities on above or below 100 ha coverage. For Herbicide 1 Suggested we gave it equal chance (0.50-0.50), Herbicide 1 Below 0.65 > 100 ha and 0.35 < 100 ha, Herbicide 2 Suggested 0.60 > 100 ha and 0.40 < 100 ha, and for Herbicide 2 Below we assigned probabilities of 0.70 and 0.30 for > 100 ha and < 100 ha, respectively.
We then valued the outcomes of percentage of dead stems per meter-squared and coverage. We did this on a scale of 1 to 9, 1 being the least valuable outcome and 9 being the most valuable outcome. The dead stems outcome of = 60% was valued at 1, 61-79% as 7, and = 80% as
- The coverage outcome of > 100 ha was valued at 9 and < 100 ha was valued at 3. The ‘value’ is subjective but should be consistent with the management objectives. There are other was that are less subjective but suffice this method in our example. We can then map the values and probabilities for each herbicide treatment (decision) in a tree. If we’d like to know the probabilities of each outcome, we can leave out choice of herbicide as equally uncertain (Fig. 1). But if we make the herbicide node a decision node the herbicide with the highest chance of a desired outcome (i.e., value) will be highlighted (dark green and bold lines; Fig. 2).
Figure 1. Decision tree with uncertainty in herbicide choice—probability of outcomes are given in blue next to terminal (green) triabgles.
Figure 2. Decision tree with herbicide node as decision node. Other branches have been folded for convenience and probability of outcomes are in blue next to green triangles.
Take-home points
Experiments being used to solve problems should think about the possible decisions to be made once the experiment is included. Decisions about what to do aren’t as simple as pick the one that was statistically shown to be most effective (highest proportion of in = 80% dead stems bin). Decisions need to consider objectives (i.e., herbicide effectiveness in killing invasive grass AND coverage to maximize suitable habitat) and constraints (i.e., volume of each herbicide treatment the allocated budget can afford). These can be considered before the experiment takes place–it just takes a little more planning. You can also imagine how quickly decision in natural resource management can become really complex; we’ve only looked at a simple example and it was still pretty hairy…
If you liked this post and want to learn more about the things our lab does please shoot us an email!