In: Advanced Math
Elk, Fire and Aspen – Quaking aspen (Populus tremuloides) is one of the most widespread tree species in North America. Although quaking aspen has been a key component of forest ecosystems for more than ten thousand years, it is currently in decline across broad portions of its range. Historically, aspen recruitment has been favored by the occurrence of low intensity fires, which create openings that allow young aspens to grow and eventually reproduce. In recent decades, however, the number of fires per year and the area burned per fire has increased; these increases in the frequency and magnitude of fires are thought to be caused by the “hotter droughts” that have resulted from climate change and by previous fire suppression policies. Some recent fires have destroyed more than 400 km2 of forest; such fires are referred to as “mega-fires.” In addition to fire, browsing by elk can prevent young aspen trees from becoming large enough to reproduce. Field Experiment – Suppose that researchers wanted to examine the combined effects of a mega- fire and browsing by elk (Cervus elaphus) as factors that may be affecting the decline of quaking aspen. Immediately after a mega-fire, the researchers established fenced-in plots that prevented by browsing by elk (the “Elk absent” treatment) along with nearby plots from which elk were not excluded (the “Elk present” treatment). Five fenced-in plots and five unfenced plots were established in each of two areas: A section of forest that was burned in the mega-fire (the “burned” treatment), and a nearby section of forest that was not burned (the “unburned” treatment). After 6 years, the number and mean height of young aspen trees in each plot are shown in table
1. What is the total number of plots that were established in this experiment? How many of these plots were burned? How many were unburned?
2. The aspen height data were used draw the bar graph shown in Fig. 1. Summarize how elk and fire affect the height of young aspen trees by answering the following questions: 2.1. What are the overall effects of elk and fire on aspen height? 2.2. Does the impact of fire on aspen height depend on whether elk were present?
3. Summarize how elk and fire affect the number of young aspen trees by answering the following questions: What are the overall effects of fire and elk on the number of aspen? Does the impact of elk on aspen number depend on whether the plots were burned? Does the impact of burning on aspen depend on whether elk were present?
Treatment | Number of Trees | Mean Height |
Elk absent, burned | 2058 | 2.8 |
Elk absent, unburned | 738 | 1.2 |
Elk present, burned | 91 | 0.3 |
Elk present, unburned | 753 | 0.4 |
(1) Five fenced-in plots and five unfenced plots were established in each of two areas.
Thus the total number of plots=(5+5)X2=10X2=20.
A total of 20 plots were established in this experiment
A total of 10 plots were burned. [5 fenced-in plots and 5 unfenced plots.]
A total of 10 plots were unburned. [5 fenced-in plots and 5 unfenced plots.]
(2) (2.1) Overall, if elk were absent, the height is more if there was fire while if elk were present, the height is less if there was fire.
(2.2) Yes, the impact of fire on aspen height depends on whether elk were present. This is evident from the answer of part (2.1).
(3) Overall, if elk were absent, the number of aspen was more if there was fire while if elk were present, the number of aspen was less if there was fire.
Yes, the impact of elk on aspen number depends on whether the plots were burned. If the plots were burned, the number of aspen was more if elk were absent while if the plots were unburned, the number of aspen was less if elk were absent.
Yes, the impact of burning on number of aspen depends on whether elk were present. This is evident from the answer of the first part of (3).