Note Your answers to the questions below should follow the expectations for homework found here. Due date is on the Dates page.

Crayfish and Periphyton Abundance

Snail grazing

Luttenton et al. (1998) tested the implications of littoral zone food web changes for periphyton abundance by comparing algal removal rates of three Orconectes crayfishes and a grazing snail (Amnicola spp.) in a laboratory experiment. Periphyton communities were established on unglazed clay tiles incubated in grazer-free enclosures in the littoral zone of Carrol Lake, Wisconsin. In the laboratory, tiles were placed in individual “arenas”” that were randomly assigned to one of four grazing treatments (with a species of crayfish or the snail) or a control treatment (no crayfish or snails). After 96 h, total algal biovolume (μm3/cm2) was measured on seven tiles in each treatment. The three crayfishes (with abbreviations) tested were Orconectes rusticus (Or), O. virilis (Ov), and O. propinquus (Op). The observed total algal biovolumes are shown below. Load these data into R and answer the questions below. [Note: you may need to change the default order of groups from being alphabetical. Use factor() with levels= as shown in Section 1.1.3 of the first reading.]

Control: 16.7, 59.2, 30.2, 20.2, 17.6, 24.3, 38.5
Op:      10.0, 10.9, 10.2, 14.7, 16.5,  8.8,  9.4 
Or:      26.3,  6.5, 14.6, 16.8, 22.4, 11.8, 12.4
Ov:       3.3,  8.5,  5.1,  6.4, 13.3,  8.1, 16.4
Am:       8.6, 15.0,  5.5,  4.3, 10.7,  6.2, 11.8
  1. Test the assumptions of a One-way ANOVA model.
  2. If the assumptions are not met on the original scale then identify an appropriate transformation. Transform the variable(s) to this scale and test the assumptions again.
  3. Test if the mean (transformed?) algal biovolumes differed among the treatment groups.
  4. If a difference among treatment group means was identified, then use an appropriate method to determine which of the grazers differed significantly from the control treatment.
  5. Provide, for the grazer that is most different from the control treatment, an appropriate statement that describes the difference between the means (with a CI) on the original scale (not the transformed scale). [Hint: You may need to back-transform the results.]