The Cedar Hollow Case File: Deer, Cattle and the Next Dry Year

Investigation question: Twelve years of monitoring records show rain, forage, cattle and deer in one valley. What limits the deer herd, did adding cattle change it, and what should the county do before a dry year that forecasters expect next spring?

Your role today

• Data analyst: Computes the forage-per-rain and deer-per-forage columns and the two averages; every number is read aloud so the others can check it.
• Grapher: Plots deer against forage with a different symbol before and after cattle, and draws a trend line by eye through each set.
• Skeptic: Leads the skeptic's round: reads each rival explanation and will not let the group move on until it names the years and numbers that support or rule it out.
• Planner and spokesperson: Runs the prediction and criteria tables, keeps track of costs, drafts the recommendation from the group's numbers and presents it to the class in one minute.

Safety

• Paper, pencil and calculator only; there are no physical hazards. Keep the discussion about the fictional valley rather than about any named local ranch or family.

Procedure

1. Read the background and the dataset. Answer q1 and q2: find the scarce years and describe how forage relates to rainfall.
2. Fill the work table. For every year, divide forage by rainfall (one decimal is enough) and compute the deer index: deer ÷ forage × 100, which is the number of deer counted for every 100 kg/ha of forage. Round to one decimal.
3. Average the deer index for years 1 to 6 (no cattle) and for years 8 to 12 (200 cattle). Leave year 7 out of both averages. Answer q3 and q4.
4. Graph deer counted against spring forage. Plot years 1 to 6 as dots in one color, years 8 to 12 as crosses in the other color, and year 7 as a triangle. Draw a trend line by eye through each set of points.
5. Skeptic's round. The skeptic reads each card aloud. For each one, the group finds the years and numbers that test it, decides whether the data support it or rule it out, and fills one row of the skeptic table.
6. Read the forecast and the plan menu. Predict the year-13 forage (2 kg/ha for every mm of rain). Fill the planning table with both methods for 0, 100 and 200 cattle kept, and the fawn mass column.
7. Fill the criteria table for plans A to D. If no plan meets every criterion and constraint, design plan E by choosing how many cattle to keep, compute its predictions and cost, and add it to both tables.
8. Decide. Write the recommendation (q5) using numbers from your tables, and present it to the class in one minute. If time runs short, finish the written recommendation as homework.
9. Answer the analysis questions on your own.

Record your observations

Lab 3 recording sheet: The Cedar Hollow case file

Cedar Hollow is a fictional valley of dry foothill rangeland, and every number in this file is a teaching dataset built to behave like real rangeland records. Mule deer live there all year. Each spring the county clips and weighs the grasses and leafy plants on sample plots to estimate spring forage in kilograms per hectare (kg/ha: the mass of plants grown on a square 100 m on a side). Each fall a team walks the same survey route to count the deer and weighs fawns caught for ear-tagging. Starting in year 7 the county leased the valley to a ranch for 200 cattle. A creek and two springs held water in every year of the record. Biologists think each fall count is within about 10 percent of the true number.

The forecast. Forecasters expect year 13 to be dry, with about 280 mm of rain. The herd at the end of year 12 was 260 deer. Two ways to predict the year-13 fall count. Method 1, the closest dry year: use the deer index from the most similar dry year (year 3, index 41.1, with no cattle; year 9, index 30.8, with 200 cattle), because those years started from a herd of similar size. Method 2, the long-run average: use your average index for that cattle level (years 1-6 or years 8-12). Either way, predicted deer = index × forage ÷ 100. For 100 cattle, use the index halfway between the 0-cattle and 200-cattle values. For any other number, move from the 0-cattle index toward the 200-cattle index by one quarter of the gap for every 50 cattle kept. Predict fawn mass the same way, from 25 kg (year 3) with no cattle to 23 kg (year 9) with 200. Criteria: C1, at least 180 deer in the year-13 fall count. C2, average fawn mass at least 24 kg (in real deer herds heavier fawns are more likely to survive their first winter; this 24 kg cutoff is part of the fictional case). Constraints: K1, the plan may cost the county at most $10,000. K2, the lease cannot be ended for good; cattle can be reduced or removed for year 13 only. The lease pays the county $60 per head of cattle per year, so every head kept off the range for year 13 costs $60 in refunds to the rancher.

Analysis questions