You are employed as a consultant at a large paper company, because the company i
ID: 214331 • Letter: Y
Question
You are employed as a consultant at a large paper company, because the company is concerned about defoliation caused by insects in its poplar plantations. Insect damage can have severe effects on tree health, and can even cause tree mortality in large areas of forest. The paper company is considering altering the way it grows trees from a one-species plantation to more of a natural multi-species forest setting, in response to the insect damage. After consulting with a forest entomologist, you find out that the insect most prevalent in the poplar plantations is the poplar tentmaker (Icthyura inclusa), but you also find the cottonwood leaf beetle (Chrysomela scripta) present. Most trees can reproduce both vegetatively (asexual clones) and sexually; poplar trees are known to produce huge tracts of clonal shoots, and a single tree can produce hundreds of thousands of seeds per year.
Given that there can be both sexual and asexual reproduction in poplar trees, you decide that it would be a good idea to test the changing-environment hypothesis for this site, in comparison to a nearby natural forest that has a mixture of poplar, red oak, and black cherry. You collect data at ten 10-m2 plots at each site (plantation and forest) based on two factors: percentage of infected trees and percentage of trees that are clonal versus sexually reproduced. The data you collect are provided in the chart below.
Plantation Site
Forest Site
Percent
infected trees
Percent clonal
Percent
infected trees
Percent
clonal
Mean
24.6
80.2
12.1
49.8
SD (Standard Deviation)
3.27
4.52
3.90
4.18
N (Number of samples)
10
10
10
10
SE (Standard Error)
1.03
1.43
1.23
1.32
a) In your own words, describe the changing-environment hypothesis (in reference to sexual vs. asexual reproduction, was discussed in the lecture video or you can look it up in the textbook or internet).
b) Do the data above support or refute the changing-environment hypothesis? What would you recommend to the paper company?
Plantation Site
Forest Site
Percent
infected trees
Percent clonal
Percent
infected trees
Percent
clonal
Mean
24.6
80.2
12.1
49.8
SD (Standard Deviation)
3.27
4.52
3.90
4.18
N (Number of samples)
10
10
10
10
SE (Standard Error)
1.03
1.43
1.23
1.32
Explanation / Answer
Formulae:
An associated statistic that is also relevant is the standard deviation because it is in the same units as the mean.
The mean is the average value of the distribution. Two distribution can have the same mean, but widely different shapes.
The sample mean is an unbiased estimate of the population mean. Its precision can be estimated from the standard error: SE = sx n.
Plantation Site
Forest Site
Percent
infected trees
Percent clonal
Percent
infected trees
Percent
clonal
Mean
24.6
80.2
12.1
49.8
SD (Standard Deviation)
3.27
4.52
3.90
4.18
N (Number of samples)
10
10
10
10
SE (Standard Error)
1.03
1.43
1.23
1.32
1. Even though the mean percent of infected trees of forest site is smaller, the standard deviation is larger. This suggests that it is more variable than the Percent infected trees of plantation site. This suggests that plantation site is good.
2. A larger standard deviation suggests that the distribution is wider than one with a smaller standard deviation so plantation site is wider than forest site because the standard deviation of percent clonal of plantation site is more than forest site.
3. As standard error of infected plants of plantation site is less than forest site but percent clonal is more in forest site so more likely to present in forest site.
B. The data above support the changing-environment hypothesis. I recommend to the paper company to take plantation site for work because there is less infected plants are present than forest site.
Plantation Site
Forest Site
Percent
infected trees
Percent clonal
Percent
infected trees
Percent
clonal
Mean
24.6
80.2
12.1
49.8
SD (Standard Deviation)
3.27
4.52
3.90
4.18
N (Number of samples)
10
10
10
10
SE (Standard Error)
1.03
1.43
1.23
1.32
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