FACULTY NOTES

This exercise is appropriate for sophomore to junior-level biology or environmental studies students with at least introductory knowledge of ecological principles such as food webs, predator-prey interactions and population dynamics, and with some experience interpreting graphs.

The "Step One-Step Two" approach is explained in the "Interpreting Figures and Tables" essay. As the essay explains, students often have difficulty interpreting figures because they do not realize that understanding figures takes time. This approach slows them down and requires them to pay attention to axes and other aspects of a figure.

Students should either read the background material, or be given a "mini-lecture" summary of the setting and background for the issue, and then work in pairs to interpret the figures. They should be able to recognize that the graphs show a significant decline in woody vegetation recruitment (for cottonwoods) and growth (for willows), starting as early as the 1930's, followed by a release of seedlings and an increase in willow height around 2001. (Note: In Figure 1-1 you might need to point out the black bar on the right hand side that indicates seedling abundance, and make sure students realize it is on a different scale.) They should also note that the observed distribution of cottonwood age classes is quite different than the expected distribution. The data on willow height are more qualitative (why?), but show a similar pattern. This should get the students thinking about what could have happened during the decades since 1930 to prevent the establishment and/or survival and growth of cottonwood seedlings and willows, and what happened in (or before) 2001 to allow for the establishment of so many seedlings and the increase in average height of willows.

I suggest letting students grapple with the figures on their own for several minutes before coming back to a question and answer session with the whole group. If the instructor circulates among pairs of students, s/he will probably get a feel for what the major sticking points are for students and can then address these via discussion with the whole class. Good discussion questions the instructor can use to help clarify students' confusion, and to guide them in correct and careful interpretation of the figures include the following, which address some common points of confusion for students:

• What are tree age classes, and how would you go about gathering the information to construct a figure such as this one (Figure 1-1)?
• The author did not core every tree and count its rings in order to determine tree age directly. Can you think of reasons for not measuring tree age directly, but doing it indirectly instead (as a function of tree diameter)?
• How did the author generate the expected distribution of tree age classes in Figure 1-1? Why is it shown as a swathe instead of a single line?
• Why would you expect numbers of trees in younger classes to increase? Why are seedlings so much more abundant than other age classes, even in the expected distribution?
• Why did Beschta keep the tree data from meander and floodplain sites separate?
• Why are the data for willows not based on age classes?
• Why are the willow height data qualitative instead of quantitative?
• Are qualitative data useful, or not? Should they be included in scientific research? What might be gained by using this approximate information instead of absolute, quantitative data (i.e. measurements of willow height)? (The best answer here is that we don't have a way to reconstruct willow height or abundance data quantitatively for the whole 20th century as we can for cottonwood trees; but we can use other methods to draw a general picture of the trends in willow abundance over this time frame, to see if it corresponds with what we know about trees in the region.)

Each instructor will have to read their class to determine how much, if any, of this large group discussion and de-briefing is needed before students are ready to move on to the next step, which is generating hypotheses to explain the trends shown in the two figures.

Students usually suggest two general categories of hypotheses (though other ideas may surface as well, and can be good fodder for discussion if time allows):

• climate-related hypotheses in some form (drought, low river flows, lack of spring floods...), depending upon the students' prior knowledge of riparian vegetation dynamics, or how much background information you choose to give them beforehand; and
  
• browsing-related hypotheses, given the title of this exercise, information in the Background section, and also the fact that the Yellowstone wolf-elk interaction has been in the news quite a bit in recent years.

You should call on some of the student pairs to write one or more of their hypotheses on the board for class discussion. The next figure set will allow them to address the two general categories of hypotheses listed above, so try to guide the class towards grouping similar hypotheses together, and possibly re-phrasing them as necessary. Each student pair should also turn in written versions of their hypotheses, to be assessed against a simple rubric such as the one included here. When the hypothesis papers are returned in the next class period, it would be a good idea to go over this rubric in detail with the students so they can learn from their mistakes and work towards writing cleaner hypotheses in the future.

Hypothesis Scoring Rubric

(Adapted from http://www.eastmont206.com/ejhs/html/profile/staff/thibault/rubrics/hypothesis%20rubric.htm)