1. Spent 22 Months Collecting Fine Scale Data on the Composition & Abundance of Bat Species in Caatinga & Edaphic Cerrado Biomes of Northeastern Brazil COMMUNITY ECOLOGIST

2. Time Consuming Narrow Specificity Insufficient for Addressing Broad Questions Unclear Comparative Context LIMITATIONS

3. RANGE MAPS: Wealth of Biogeographic, Ecological, and Evolutionary Information

4. BAT RANGE MAPS: Hall for North America Koopman for South America Supplemented by “Others”

5. RANGE MAPS: Expert Opinion Metadata Problems Heterogeneous Quality

6. GRADIENTS OF RICHNESS AND RANGE SIZE: BATS AND MARSUPIALS IN THE NEW WORLD

7. LATITUDINAL GRADIENT OF SPECIES RICHNESS

8. CAUSES Competition Population Size Growth Rates Epiphyte Load Harshness Predation Heterogeneity Niche Width Patchiness Host Diversity Mutualism Epidemics

9. CAUSES Stability Productivity Heterogeneity Aridity Habitat Number Predictability Rarefaction Area Seasonality Range Size Evolutionary Speed

10. LIMITATIONS Qualitative PredictionsQualitative Predictions Non Mutually ExclusiveNon Mutually Exclusive Unspecified FormUnspecified Form No Expected ValuesNo Expected Values

11. Hemispheric Patterns

12. CLASSICAL APPROACH RICHNESSRICHNESS L A T I T U D E HOHO H A1 H A2 CHANCE

13. STOCHASTIC PROCESSES AND NULL MODELS

14. SIMULATION NULL MODEL SIMULATION NULL MODEL LATITUDELATITUDE 0 134575322134575322 RICHNESSRICHNESS

15. SIMULATION APPROACH Randomly generate N & S termini for a speciesRandomly generate N & S termini for a species Repeat until S = richness of species poolsRepeat until S = richness of species pools Calculate richness at each latitudeCalculate richness at each latitude Repeat 1,000 timesRepeat 1,000 times Calculate mean and variance of richness per latitudeCalculate mean and variance of richness per latitude

16. EFFECT OF SPECIES POOL SIZE SIMULATION RESULTS

17. 1 q p P 0 PROBABALISTIC APPROACH

18. BINOMIAL NULL MODEL p + q = 1 ( p + q ) 2 = 1 p 2 + 2 pq + q 2 = 1 2 pq S = Richness at “P”

19. 1 0 q p P SPECIES RICHNESS GRAPHIC REPRESENTATION 2pqS Domain

20. NULL MODEL Predicts Form of RelationPredicts Form of Relation Quantitative PredictionsQuantitative Predictions FalsifiableFalsifiable

21. NEW WORLD BATS AND MARSUPIALS

22. Chrotopterus auritus

23. Neoplatymops mattogrossensis

24. BATS Species rich Trophically rich Abundant in tropics

25. BATS – ENTIRE CONTINENT

26. BATS – TAXON EXTENT

27. BATS – 95% OF EXTENT

28. Didelphis virginiana

29. Marmosa cinerea

30. MARSUPIALS Ancient group of mammals Moderate species richness Trophically diverse in past

31. MARSUPIALS – ENTIRE CONTINENT

32. MARSUPIALS – TAXON EXTENT

33. MARSUPIALS – 95% OF EXTENT

34. MODEL UTILITY Deviations from the model differ between bats and marsupialsDeviations from the model differ between bats and marsupials Deviations are not related to the area of latitudinal bandsDeviations are not related to the area of latitudinal bands

35. RANDOM SUBSETS 20 Ranges20 Ranges 20 o Latitude20 o Latitude 20 Species20 Species

36. RANDOM SUBSETS SPECIES RICHNESS 1 0 q p BATS 20 *** r = 0.77 MARSUPIALS 19 *** r = 0.73 P

37. ASSESSMENT Although stochastic mechanisms may not be the only factors affecting gradients, they play an appreciable role throughout the distribution of a biota

38. MODEL UTILITY Deviations from the model differ between bats and marsupialsDeviations from the model differ between bats and marsupials Deviations are not related to the area of latitudinal bandsDeviations are not related to the area of latitudinal bands

39. MULTIFACTORIAL Many FactorsMany Factors Species-Specific LimitsSpecies-Specific Limits Factor-Specific N and S LimitsFactor-Specific N and S Limits

40. EXTRAPOLATIONS Disturbance GradientsDisturbance Gradients Productivity GradientsProductivity Gradients Abiotic GradientsAbiotic Gradients

41. LATITUDINAL GRADIENT OF SPECIES RANGE SIZE

42. RAPOPORT’S RULE RAPOPORT’S RULE

43. METHODOLOGICAL BIASES Tropical Species Temperate Species 0o0o

44. SIMULATION APPROACH Randomly generate N & S termini for a speciesRandomly generate N & S termini for a species Repeat until S = richness of species poolsRepeat until S = richness of species pools Calculate correlation between latitudinal range size and mid-latitudeCalculate correlation between latitudinal range size and mid-latitude Repeat 1,000 timesRepeat 1,000 times Calculate mean and variance of correlationsCalculate mean and variance of correlations

45. SOUTH AMERICANORTH AMERICA LATITUDINAL RANGE 0 150 100 50 MID-LATITUDE -70 -50 -30 -10 10 30 50 70 BATS

46. SOUTH AMERICANORTH AMERICA LATITUDINAL RANGE 0 150 100 50 MID-LATITUDE -70 -50 -30 -10 10 30 50 70 MARSUPIALS

47. BATS 0 100 200 FREQUENCY -0.56 -0.53 -0.49 -0.45 -0.42 -0.38 -0.35 -0.31 CORRELATION COEFFICIENT MARSUPIALS -0.63 -0.56 -0.49 -0.42 -0.35 -0.29 -0.22 -0.15 0 100 200 MID-LATITUDE RESULTS Less Negative Less Negative

48. LATITUDE RANGE SIZE MID-LATITUDE RESULTS Rapoport’s Rule Empirical Pattern Stochastic Pattern

49. Comparisons of Gradients of Diversity at Two Scales: Communities Versus Regional Species Pools

50. SCALE Regional Patterns Local Patterns

51. LATITUDINAL GRADIENTS OF COMMUNITY ORGANIZATION

52. DESIGN Geographical Constraints (50 km)Geographical Constraints (50 km) Ecological Constraints (biome)Ecological Constraints (biome) Sampling Constraints (asymptote)Sampling Constraints (asymptote) Temporally Constrained (1-5 yr)Temporally Constrained (1-5 yr)

53. 32 Sites Temperate Subtropical Tropical Subtropical Temperate

54. DIVERSE HABITATS Riparian Temperate Forest (1) Desert (4) Montane Tropical Forest (6) Wet Tropical Forest (13) Dry Tropical Forest (2) Tropical Woodland-Savanna (1) Wet Semi-Tropical Forest (4) Dry Semi-Tropical Forest (1)

55. FAUNAL POOL - SPECIFIC DATA Number of species whose geographic range overlaps a communityNumber of species whose geographic range overlaps a community Identities of species whose range overlaps a communityIdentities of species whose range overlaps a community

56. COMMUNITY - SPECIFIC DATA Species identities & abundances in each communitySpecies identities & abundances in each community Indexes of diversity that are sensitive to richness (3), evenness (4), dominance (3), diversity (4)Indexes of diversity that are sensitive to richness (3), evenness (4), dominance (3), diversity (4)

57. BIODIVERSITY INDICIES RICHNESS Community Richness Margalef Index Menhinick Index EVENNESS Shannon Index PIE Index Camargo’s Index Shoener’s Index DIVERSITY Camargo Index Log Series Alpha Brillouin Index Shannon Index DOMINANCE Simpson’s Index Berger-Parker Index McIntosh Index

58. 3 -3 3 0 0 FACTOR 1 FACTOR 2 Tropical Subtropical Temperate Evenness Dominance Diversity Richness Factor Analysis CE O BP PIE SI MD SHD B CD A MAR R SHE MER

59. Latitudinal Gradients Richness Evenness B 1 = 0.0002; r 2 < 0.01; P = 0.999 B 1 = -0.055; r 2 = 0.37; P < 0.001

60. REGIONAL & LOCAL GRADIENTS Latitude Richness RegionalLocal 12O 90 60 90 1020 3040

61. LATITUDINAL GRADIENTS