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BIOL 4312 Analysis of Biological Communities Assignment - University of Manitoba, Canada

Assignment - Diversity and Cluster Analysis

BOVID DATA SET - A complete description of these data, and numerous analyses using R, is given in Part 2 of the "R" Manual (Data Set 2, pages%6.19); read over this material carefully, and undertake the exercises and analyses in R on your own. Information required to answer the questions in the Assignment is attached.

DIVERSITY: BOVID TRIBES IN AFRICA

Question 1: [Richness, effective richness and evenness values are given in TABLE 2; from page 11 of "R" Manual]

(a) Summarize and discuss trends in the herbivore tribe group richness (N₀ = S) across the 16 parks (e.g. which parks have the highest and lowest number of tribe; what is the range of values; and so forth).

(b) Summarize and discuss trends in the effective richness N₁ (Shannon Index) and N₂ (Simpson Index) of herbivore tribe groups across the 16 parks (e.g. highest and lowest values, range of values, and so forth). Do high values of richness (N₀ = S) always correspond high values for N₁ and N₂); if not, why not? HINT: e.g. compare parks with high N₀ = 8; why do the N₁ and N₂ values differ among these 3 parks? Provide examples to support your answer [refer to raw data, TABLE 1].

(c) Summarize the evenness (E₂₁) values across the 16 parks. Why do parks KRU and MKU have relatively low evenness? Why does park TUR have the highest evenness value, even though it has the lowest herbivore tribe group richness (N₀ = 3)? Use the raw data values (TABLE 1) to support your answer.

Question 2: (a) To what degree are the diversity measures N₀ N₁, N₂ and E₂₁ correlated for these data? Refer to the correlation matrix (TABLE 3), and the pair wise scatterplots (FIGURE 1).

(b) Discuss why these measures are, or are not, correlated, e.g. why are N₁ and N₂ highly correlated, but not N₀ and N₁?; why is E₁₂ poorly correlated with N_α?; and so forth.

Question 3: (a) Examine, and briefly summarize, the Renyi diversity profiles (as effective richness N_α) for the 16 parks (FIGURE 2).

(b) Compare the results for parks KRU, MAN, BIC and TUR, relating the differences in these four profiles to their corresponding bovid tribe abundance distributions (given in TABLE 1 - attached).

CLUSTER ANALYSIS: BOVID TRIBES IN AFRICA

The R commands to produce these results are given in Part 2 of the "R" Manual, pages 13-15. Note that for all of the cluster analyses undertaken, CHORD DISTANCE was utilized.

Question4: (a) Why was Chord Distance, rather than Euclidean distance, used to quantify the associations among the 16 African game parks?

(b) What aspect of the data would have been emphasized if Euclidean Distance had been used? Summarize how the standardization "built into" Chord Distance alleviates this problem.

Question 5: (a) Compare the dendrograms of Single and Complete Linkage cluster analyses of the 16 parks (FIGURE 3). How similar are the two dendrograms, and how do they differ?

(b) What do the similarities/differences between the Single and Complete Linkage dendrograms tell you about the robustness of group structure in the bovid tribe data?

Question 6: (a) Compare and contract group structure of Single, Complete, Average, and Ward (Sum of Squares) dendrograms for the 16 parks, at the 4Ngroup level (FIGURE 4).

(b) Which cluster methods produce similar/different 4Ngroup results? Summarize your findings in tabular format.

Question 7: HINT: In answering this question, refer to and interpret the sorted Bovid Density file (with data (standardized to percent abundance, i.e. sum of values for each park = 100%) shown in TABLE 4.

(a) Using the sums of squares cluster dendrograms for the 16 parks, and for the 9 tribes (FIGURE 5), summarize (in tabular format) and comment on the relationships between the bovid parks at the 4-group level and the 9 tribes at the 3-group level.

(b) Which tribe groups are most affiliated with which park groups?

Note - All required tables and figures are attached.

Attachment:- Analysis of Biological Communities Assignment File.rar