1. What is Rarity?

2. What is Rarity?

3. What is Rarity?

4. What is Rarity?

6. Characterizing Communities through the Relationships Among Species

7. Rank Abundance Curves
Community #1

8. Rank Abundance Curves
Community #1

9. Three Models Predicting Rank Abundance Patterns

10. Resources Divided Among Species

11. The Broken Stick Model
Resources are randomly divided among species.

12. The Broken Stick Model

13. The Niche Preemption Model (Geometric series)
Strong dominance with a few species acquiring most of the resources

14. The Broken Stick Model

15. The Log Normal Distribution
Assumption: A large number of factors influence species abundances
Veil line

16. Impact of Increased Sampling
1/8 yr
1 yr
4 yr

17. Sonoran Desert Example
veil line

18. The Broken Stick Model

19. Observed Patterns Broken stick Nesting bird pairs in West Virginia
Log Normal
Vascular plants of Great Smokey Mountains
Niche Preemption
Fir forest Great Smokey Mountains

20. General Trends Only in select groups of higher animals Broken stick:
Niche preemption:
Communities with few species and one dominant
Most common, particularly in communities with a large number of species
Log normal:

21. Comparing Communities
Community #1
Community #2
Subsampling
Stand level sampling

22. How do we make sense of all of this information?
Data Arrranged Listing Species in Each Sample Unit
How do we make sense of all of this information?

23. Braun-Blanquet: An Historical Approach

25. Step #1: Place Similar Stands Next to One Another

27. Step #2: Place Species with Similar Distributions Next to One Another

29. Step #3: Remove Species with Little Information Content
Rare
Supercommon
Not grouping well

31. Repeat Process Until Satisfied
Key species have:
(1) High fidelity (e.g., not in more than 20% of stands outside association)
(2) High constancy (e.g., are in most of the stands within the association)
Association c
Association a
Association b

32. This is a highly subjective approach
Criticism:
This is a highly subjective approach

33. Quantitative Approaches

34. Comparisons with Communities of One Species
dab= 10
dac= 20 50 A B C 30 20
dbc= 30

35. Comparisons with Communities of Two Species
dab= 10
dac= 20 50 A B C 30 20
dbc= 30

36. Comparisons with Communities of Two SpeciesB C A

37. Comparisons with Communities of Three SpeciesB C
Species 3 A

38. Comparisons with Communities of Lots of Species?

39. Multivariate Approaches

40. Step #1: Calculation of Site Similarities

41. Presence/Absence Data
Definitions
a = number of species in both sites
b = number of species only in second site
c = number of species only in first site

42. Presence/Absence Data
The Jacard Index
Definitions
a = number of species in both sites
b = number of species only in second site
c = number of species only in first site

43. Presence/Absence Data

44. Quantitative Data
Bray-Curtis Index
Definitions

45. Quantitative Data
Bray-Curtis Index
Definitions

47. Now What?
Similarity matrix

48. Dimension Reduction through Ordination