1. Feiran Jiao and Barbara Monaco DETERMINING EFFECTS OF HABITAT AND TIME ON THE DIETS OF ANCIENT NATIVE AMERICANS

2. Specific Goals: Identify significant spatial (geography, habitat) and temporal variability in prey species use, as well as any association between time and space patterning Evaluate how well variability in data is explained by cultural (pop. changes, landuse practices, overhunting, new technology, etc.) and/or natural (climate change, vegetation differences) factors We focused on the first of Matt’s goals and looked at the variables Habitat (mountains, plains, alluvial valley) and Time Group (Paleoindian, Archaic, Woodlands, Late Prehistoric) to determine whether or not they significantly affect various responses regarding dietary habits. CLIENT’S ORIGINAL GOALS

3.  Simpson’s Index (D):[0,1] Measure of Evenness where  Margalef’s Diversity Index (0, ∞) Simple species richness index that attempts to compensate for sampling effects  Large Body Size [0,1] Proportion of bones that were classified as belonging to a large animal (mammoth, buffalo) Our data initially contained measures on three types of Function Groups (Kill, Camp, and Other). To match with Matt’s discipline, we eliminated the Kill and Other sites, analyzing only the Camp sites. RESPONSES

4.  Our initial analysis was to perform a Two-Way ANOVA for the three responses.  However, as you can see from the residual plots, the assumptions for the ANOVA are violated. INITIAL ANALYSIS

5. FINAL RESULTS  Since the assumptions for the Two-Way ANOVA using the original data were clearly violated we attempted to transform the data:  Simpson’s Index:  Margalef’s Diversity Index:  We could find no transformations that improved the residual plots enough that we could trust the p-values and hypothesis performed by the Two-Way ANOVA for Large Body Size

6. Anova Table (Type III tests) Response: neg.ln.D Sum Sq Df F value Pr(>F) (Intercept) 4.452 1 18.3976 0.00003 as.factor(Time.Group) 4.956 3 6.8267 0.0002 as.factor(Habitat) 2.143 2 4.4283 0.0132 as.factor(Time.Group):as.factor(Habitat) 5.337 6 3.6757 0.0018 Residuals 43.799 181 We have a significant interaction between Time Group and Habitat, thus our next step is to look at contrasts and interaction plots between these twelve group means. TRANSFORMED SIMPSON’S INDEX

9. Parameter Estimate Error t Value Pr > |t| valleyPaleo - mountainPaleo 0.27814841 0.17532388 1.59 0.1144 valleyPaleo - plainsPaleo 0.82207419 0.21999256 3.74 0.0002 mountainPaleo - plainsPaleo 0.54392578 0.17532388 3.10 0.0022 valleyArchaic - mountainArchaic -0.37336034 0.14200459 -2.63 0.0093 valleyArchaic - plainsArchaic -0.65476466 0.36004734 -1.82 0.0706 mountainArchaic - plainsArchaic -0.28140432 0.36402589 -0.77 0.4405 valleyWood - mountainWood -0.35735913 0.38455024 -0.93 0.3540 valleyWood - plainsWood -0.38085832 0.38455024 -0.99 0.3233 mountainWood - plainsWood -0.02349919 0.49191832 -0.05 0.9620 valleyLate - mountainLate 0.18490341 0.15094427 1.22 0.2222 valleyLate - plainsLate 0.29355680 0.15094427 1.94 0.0533 mountainLate - plainsLate 0.10865339 0.18592765 0.58 0.5597 Since we are making 12 comparisons, we need to adjust the cut- off alpha level using a Bonferroni correction. So we will take alpha and divide it by 12, so the new cut-off will be alpha=0.004167 Thus the only comparisons that are significantly different are Valley – Plains (Paleoindian), and Mountain-Plains(Paleoindian). SAS CONTRASTS

10. Anova Table (Type III tests) Response: sqrt.marg Sum Sq Df F value Pr(>F) (Intercept) 31.06 1 467.06 <0.001 as.factor(Time.Group) 0.24 3 1.19 0.314 as.factor(Habitat) 0.17 2 1.28 0.280 as.factor(Time.Group):as.factor(Habitat) 1.62 6 4.06 0.001 Residuals 12.44 187 We have a significant interaction between Time Group and Habitat, thus our next step is to look at contrasts and interaction plots between these twelve group means. TRANSFORMED MARGALEF’S INDEX

13. Standard Parameter Estimate Error t Value Pr > |t| valleyPaleo - mountainPaleo 0.05339427 0.09190836 0.58 0.5620 valleyPaleo - plainsPaleo 0.43098379 0.11267311 3.83 0.0002 mountainPaleo - plainsPaleo 0.37758952 0.08855853 4.26 <.0001 valleyArchaic - mountainArchaic -0.05500055 0.07444171 -0.74 0.4609 valleyArchaic - plainsArchaic -0.28760772 0.18874418 -1.52 0.1292 mountainArchaic - plainsArchaic -0.23260717 0.19082982 -1.22 0.2244 valleyWood - mountainWood -0.47380033 0.19822905 -2.39 0.0178 valleyWood - plainsWood -0.39761976 0.19822905 -2.01 0.0463 mountainWood - plainsWood 0.07618058 0.25787365 0.30 0.7680 valleyLate - mountainLate -0.09651651 0.07871177 -1.23 0.2217 valleyLate - plainsLate -0.02141871 0.07667386 -0.28 0.7803 mountainLate - plainsLate 0.07509781 0.09582886 0.78 0.4342 Since we are making 12 comparisons, we need to adjust the cut- off alpha level using a Bonferroni correction. So we will take alpha and divide it by 12, so the new cut-off will be alpha=0.004167 Thus the only comparisons that are significantly different are Valley – Plains (Paleoindian), and Mountain-Plains(Paleoindian), which are the same significant difference that we found for the transformed Simpson’s Index. SAS CONTRASTS

14. Since the Large Body Size variable had such a large proportions of 0’s and 1’s, it appeared to follow a Beta Density. We plotted the density histograms for each of the twelve group means (Habitat*Time Group) and fitted a Beta density to the data. We excluded the Woodlands since we had so few observations for each Habitat and felt that would not give an accurate fit to the density. We also dropped Plains/Rolling Hills for a similar reason. LARGE BODY SIZE

16. BETA REGRESSION

17. Since Beta Regression is not a commonly used (if ever) in Matt’s discipline, if he decides to move on with the Large Body Size analysis we have proposed then this would require additional work and collaboration between him and Feiran. NEXT STEPS

18. Hill, M. E. (2008). Variation in paleoindian fauna use on the great plains and rocky mountains of north america. Quaternary International, 191, 34-52. Magurran, A. E. (2004). Measuring Biological Diversity. Blackwell Science Ltd. REFERENCES

19. QUESTIONS?