**The first three questions of this assignment are mathematically based and answers can be given in Excel, the final question should be answered in a word document. You will be graded on the strength of your argument, the graphical and statistical support of your statements and your grammar, sentence structure and writing style. Please proof read before submitting.**

A little about the data: the first data set to answer questions 1 and 2 was collected on the Lewis and Clark National Forest in the vicinity of the Tenderfoot Experimental Forest. This lodgepole pine (*pinus contorta*) forest and is fairly indicative to forests of the area that have not experience wildfires since 1910. Each row of data is indicative of 10 trees per acre on this location.

For questions 3 and 4: A drought-induced bark beetle outbreak resulted in high levels of ponderosa pine mortality throughout Arizona between 2001 and 2003 (USDA Forest Service 2004). Early in the outbreak, *Ips* species [*I. lecontei* Swaine and *I. pini* Say] were the primary tree-killing species, in particular at low to mid- elevations, whereas *Dendroctonus* species (*D. brevicomi*sLeConte, *D. adjunctus* Blandford, and *D. frontalis* Zimmermann) became increasingly important later in the outbreak at mid- to high elevations (USDA 2005, Williams et al. 2008). The data used here for the Cruz et al. (2003) calculations was data collected in undisturbed stands (site 1) and in stands with bark beetle outbreaks (site 2). Each row of data represents a 0.05 acre (0.02ha) plot.

1.

Using the data set provided (Brown 1978), please calculate the foliage, 1-hr and available canopy fuel loadings using the Brown equations. Assume that each tree represents 10 trees per acre. Present your data in a table (you will not have any measures of variability to report, but please make sure there is a title) (20)

2.

Using the Brown 1978 data set provided please calculate the canopy bulk density using the load over depth method. Use the median crown base height to estimate canopy base height and the 90th percentile tree height for tree height to estimate the crown length. (15)

3.

Using the Cruz et al (2003) data set estimate the available canopy fuel loading, canopy bulk density, and canopy base height for the 2 stands. Show your data in a table, and make sure you include a measure of variation (e.g. standard deviation, standard error, etc.). (20)

4.

How do these two sites vary? Support your answer with a graphical and/or statistical measure. Of the two sites in the Cruz et al. data set which one do you think has the largest fire hazard? Please explain why. For this question I expect you to write something similar to a results section of a paper. This is good practice for your final project and I will be able to provide feedback on what you could do to improve your argument. See below for information on what you will be graded on. The writing guide is also an excellent source of information on what you might want to include. (45)

**Writing the Results section**

The results section of a scientific paper is often the first section written, both because the results have to be finalized to complete the paper and because it’s a good section to warm up with. As with all science writing, there are conventions used when writing up the results section of a paper. The following guidelines will be used to grade question 4 of this assignment (worth 45 points). Some of the material you have already calculated above, I would just like to see you use the information to write a results section on the ** Cruz et al. data**:

Remain objective [5 pt]: The defining feature of the results section is that it contains only objective information about the outcomes of the study. The purpose of this section is to allow the reader to access the results of the study without any interpretations from the authors. Additionally, this section should only present information relevant to the conclusions you draw in the Discussion section; thus, even if you measured ten times as many variables as ultimately make into your discussion, you only present the variables needed to critically evaluate your interpretations. Your interpretations of the data are presented in the Discussion section, where you construct logical arguments based on information presented in the Results section and the existing state of knowledge in the field.

Use past tense, consistently [5 pt]: Convention differs between fields and authors, but for this class, you should use the past tense for verbs, and apply this consistently throughout the Results section.

For example, you should write \mean tree height differed significantly between treated and un-treated

stands” as opposed to \mean tree height differs significantly between treated and un-treated stands.”

Report information from statistical tests [10 pt]: Report the outcome of statistical tests in the results section, either upfront, or in parenthetical comments. In the Methods or Results section you may state that \for all statistical tests, the null hypothesis was rejected when p < 0.05.” If you do this, then you later on you may simple write, for example, mean tree heights differed significantly between treated and un-treated stands (two-sample t-test, p = 0.01)”. It is key that the reader knows what statistical test the p-value is based on. This can be presented in the results (as above), or, if only one or several statistical tests are used in the paper, this can be presented in the methods section.

Utilize tables and figures where appropriate [10 pt]: Tables are an excellent way to summarize results in one central location. They should not be repetitive with (a) the text itself, or (b) figures.

For example, one table might include the mean, median, and standard deviation for all variables of interest, as well the p-value for statistical tests between different populations.

Figures are powerful ways to help illustrate important aspects of your results, such as differences between populations or trends through time. As such, each figure should have a specific purpose, which determines its design and presentation. Do not show a box plot, for example, unless you are describing the distribution of a variable. Your goal is to construct a figure that highlights the key properties of the dataset, which will form the basis of your interpretations and conclusions. For example, if you want to highlight the absolute difference between variables displayed in different graphs, then it is important to keep the y-axis scales on those variables consistent; scaling the values to an individual variable could led to the misleading conclusion that the variables do not differ. All figures should have axis labels that include the units of measurement; Figures should not have a title within the figure itself.

Provide proper captions and place them appropriately [5 pt]: All tables and Figures should (a) be referenced from within the text, and (b) be labeled with an informative caption, including a brief title, followed by any information needed for the reader to interpret the information within. For example:

Table 1. Descriptive statistics for selected stand structure variables.” or Figure 1. Distribution of mean crown base height for treated and un-treated stands. The average value for treated stands (X) was significantly different from the average value from untreated stands(Y).” Captions should be placed above tables and below figure.

Write clearly, use proper grammar, and check your spelling [10 pt]: You will be evaluated on the clarity of your writing, the use of proper grammar, and spelling. Organizing your thoughts and communicating them effectively is a key component of science writing. If a reader cannot understand you, then (s)he will put down your paper and your work will go unread.