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Range Wrangler I: Guided Tour and Analyses of New World Mammal Distributions Nick Gotelli Department of Biology University of Vermont Burlington, VT 05405.

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Presentation on theme: "Range Wrangler I: Guided Tour and Analyses of New World Mammal Distributions Nick Gotelli Department of Biology University of Vermont Burlington, VT 05405."— Presentation transcript:

1 Range Wrangler I: Guided Tour and Analyses of New World Mammal Distributions Nick Gotelli Department of Biology University of Vermont Burlington, VT 05405 NCEAS, October 11, 2008

2 Range Wrangler 1 Inputs & Model Structure Goodness of Fit Statistics Independent Origins Models Ancestry Models Best Model Comparisons Applications to Other Taxa Conclusions

3 THANK YOU To Thiago Rangel!

4 Range Wrangler 1 Inputs & Model Structure Goodness of Fit Statistics Independent Origins Models Ancestry Models Best Model Comparisons Applications to Other Taxa Conclusions

5 New World Mammals Data Set Gridded Domain: 383 2° x 2° grid cells Environmental Layers: MinTemp, NPP, PET, AET 879 species Species Density: 11 to 228 species/grid cell Geographic Ranges: 1 to 350 grid cells

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8 Range Wrangler 1 Inputs & Model Structure Goodness of Fit Statistics Independent Origins Models Ancestry Models Best Model Comparisons Applications to Other Taxa Conclusions

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10 r 2 = 0.08 Slope = 0.60 Intercept = 54.5 AICc = 4147

11 r 2 = 1.0 Slope = 1.0 Intercept = 0.0 AICc = 2.0 r 2 = 0.08 Slope = 0.60 Intercept = 54.5 AICc = 4147

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19 Range Wrangler 1 Inputs & Model Structure Goodness of Fit Statistics Independent Origins Models Ancestry Models Best Model Comparisons Applications to Other Taxa Conclusions

20 Model Parameters SEED CELL – Equiprobable – Proportional to Environmental Variable (linear) – Single Cell (= center of origin)

21 Center of Origin Model

22 Model Parameters DISPERSAL DISTANCE – 1.0 TO 512.0 standard deviations of map cell distance

23 Model Parameters TARGET CELL – Equiprobable – Proportional to Environmental Variable (Linear) – Proportional to Similarity of Source Cell (Niche)

24 Model Parameters SEED CELL (Equiprobable, Linear, Single Cell) DISPERSAL DISTANCE (1,2,4,8,16,32,64,128,256,512) TARGET CELL (Equiprobable, Linear, Niche) 3 x 10 x 3 = 90 orthogonal parameter settings

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31 Df Sum of Sq Mean Sq F Value Pr(F) Seed.Cell 2 2.256552 1.128276 81.90621 0.00000000 Target.Cell 2 1.379895 0.689947 50.08612 0.00000000 DD 1 0.174349 0.174349 12.65670 0.00062169 DDSquared 1 0.072209 0.072209 5.24197 0.02458728 Residuals 83 1.143343 0.013775

32 Df Sum of Sq Mean Sq F Value Pr(F) Seed.Cell 2 2.256552 1.128276 75.74525 0.0000000000 Target.Cell 2 1.379895 0.689947 46.31866 0.0000000000 Seed.Cell:Target.Cell 4 0.353634 0.088408 5.93518 0.0003066929 Residuals 81 1.206549 0.014896

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37 Df Sum of Sq Mean Sq F Value Pr(F) Seed.Cell 2 27.62234 13.81117 36.27824 0.0000000 Target.Cell 2 3.97279 1.98640 5.21773 0.0073368 DD 1 0.87346 0.87346 2.29435 0.1336450 DDSquared 1 0.00026 0.00026 0.00068 0.9792425 Residuals 83 31.59820 0.38070

38 Df Sum of Sq Mean Sq F Value Pr(F) Seed.Cell 2 27.62234 13.81117 34.82090 0.000000000 Target.Cell 2 3.97279 1.98640 5.00813 0.008898663 Seed.Cell:Target.Cell 4 11.00685 2.75171 6.93765 0.000074570 Residuals 81 32.12739 0.39663

39 Best 12 Models Based on Slope Model #Seed Cell for Clade Ancestor SD of Dispersal DistanceTarget CellSloper2 42Linear2 0.9950.524 72Linear2Niche1.0100.514 71Linear1Niche1.0120.514 12Linear2Equiprobable1.0130.507 34Equiprobable8Linear0.9850.361 41Linear1 1.0160.522 73Linear4Niche1.0160.539 44Linear8 0.9830.631 11Linear1Equiprobable1.0180.521 43Linear4 0.9820.559 13Linear4Equiprobable1.0190.497 5Equiprobable16Equiprobable0.9470.085

40 Best 12 Models Based on Slope Model #Seed Cell for Clade Ancestor SD of Dispersal DistanceTarget CellSloper2 42Linear2 0.9950.524 72Linear2Niche1.0100.514 71Linear1Niche1.0120.514 12Linear2Equiprobable1.0130.507 34Equiprobable8Linear0.9850.361 41Linear1 1.0160.522 73Linear4Niche1.0160.539 44Linear8 0.9830.631 11Linear1Equiprobable1.0180.521 43Linear4 0.9820.559 13Linear4Equiprobable1.0190.497 5Equiprobable16Equiprobable0.9470.085 Environmental Effects on Speciation Short Dispersal Distances Environmental or Niche Effects on Dispersal Environmental Effects on Speciation Short Dispersal Distances Environmental or Niche Effects on Dispersal

41 Best 12 Models Based on Slope Model #Seed Cell for Clade Ancestor SD of Dispersal DistanceTarget CellSloper2 42Linear2 0.9950.524 72Linear2Niche1.0100.514 71Linear1Niche1.0120.514 12Linear2Equiprobable1.0130.507 34Equiprobable8Linear0.9850.361 41Linear1 1.0160.522 73Linear4Niche1.0160.539 44Linear8 0.9830.631 11Linear1Equiprobable1.0180.521 43Linear4 0.9820.559 13Linear4Equiprobable1.0190.497 5Equiprobable16Equiprobable0.9470.085

42 Worst 12 Models Based on Slope Model #Seed Cell for Clade Ancestor SD of Dispersal DistanceTarget CellSloper2 10Equiprobable512Equiprobable1.7930.032 52SingleCell2Linear0.1960.177 23SingleCell4Equiprobable0.1950.149 81SingleCell1Niche0.1870.168 51SingleCell1Linear0.1800.155 22SingleCell2Equiprobable0.1680.129 21SingleCell1Equiprobable0.1610.124 16Linear32Equiprobable2.7080.443 17Linear64Equiprobable3.8540.448 18Linear128Equiprobable4.4220.412 19Linear256Equiprobable4.8090.414 20Linear512Equiprobable4.9730.410

43 Worst 12 Models Based on Slope Model #Seed Cell for Clade Ancestor SD of Dispersal DistanceTarget CellSloper2 10Equiprobable512Equiprobable1.7930.032 52SingleCell2Linear0.1960.177 23SingleCell4Equiprobable0.1950.149 81SingleCell1Niche0.1870.168 51SingleCell1Linear0.1800.155 22SingleCell2Equiprobable0.1680.129 21SingleCell1Equiprobable0.1610.124 16Linear32Equiprobable2.7080.443 17Linear64Equiprobable3.8540.448 18Linear128Equiprobable4.4220.412 19Linear256Equiprobable4.8090.414 20Linear512Equiprobable4.9730.410 Center of Origin or Environmental Effects on Speciation Long or Short Dispersal Distances Equiprobable Dispersal Center of Origin or Environmental Effects on Speciation Long or Short Dispersal Distances Equiprobable Dispersal

44 Best 12 Models Based on r 2 Model #Seed Cell for Clade Ancestor SD of Dispersal DistanceTarget CellSloper2 49Linear256Linear1.2270.766 50Linear512Linear1.2310.765 47Linear64Linear1.1970.761 48Linear128Linear1.2130.761 40Equiprobable512Linear1.3560.753 46Linear32Linear1.1460.751 38Equiprobable128Linear1.3480.747 39Equiprobable256Linear1.3590.746 37Equiprobable64Linear1.3320.731 45Linear16Linear1.0630.721 79Linear256Niche1.4790.716 77Linear64Niche1.4350.715

45 Best 12 Models Based on r 2 Model #Seed Cell for Clade Ancestor SD of Dispersal DistanceTarget CellSloper2 49Linear256Linear1.2270.766 50Linear512Linear1.2310.765 47Linear64Linear1.1970.761 48Linear128Linear1.2130.761 40Equiprobable512Linear1.3560.753 46Linear32Linear1.1460.751 38Equiprobable128Linear1.3480.747 39Equiprobable256Linear1.3590.746 37Equiprobable64Linear1.3320.731 45Linear16Linear1.0630.721 79Linear256Niche1.4790.716 77Linear64Niche1.4350.715 Environmental Effects on Speciation Long Dispersal Distances Environmental Effects on Dispersal Environmental Effects on Speciation Long Dispersal Distances Environmental Effects on Dispersal

46 Worst 12 Models Based on r 2 Model #Seed Cell for Clade Ancestor SD of Dispersal DistanceTarget CellSloper2 1Equiprobable1 0.5870.080 61Equiprobable1Niche0.5840.079 26SingleCell32Equiprobable0.2540.069 6Equiprobable32Equiprobable1.4270.067 27SingleCell64Equiprobable0.2320.051 7Equiprobable64Equiprobable1.7590.050 28SingleCell128Equiprobable0.2200.044 29SingleCell256Equiprobable0.2120.040 30SingleCell512Equiprobable0.2100.039 8Equiprobable128Equiprobable1.7480.037 10Equiprobable512Equiprobable1.7930.032 9Equiprobable256Equiprobable1.4630.023

47 Worst 12 Models Based on r 2 Model #Seed Cell for Clade Ancestor SD of Dispersal DistanceTarget CellSloper2 1Equiprobable1 0.5870.080 61Equiprobable1Niche0.5840.079 26SingleCell32Equiprobable0.2540.069 6Equiprobable32Equiprobable1.4270.067 27SingleCell64Equiprobable0.2320.051 7Equiprobable64Equiprobable1.7590.050 28SingleCell128Equiprobable0.2200.044 29SingleCell256Equiprobable0.2120.040 30SingleCell512Equiprobable0.2100.039 8Equiprobable128Equiprobable1.7480.037 10Equiprobable512Equiprobable1.7930.032 9Equiprobable256Equiprobable1.4630.023 Center of Origin or Equiprobable Speciation Long Dispersal Distances Equiprobable Dispersal Center of Origin or Equiprobable Speciation Long Dispersal Distances Equiprobable Dispersal

48 Single “Best” Model based on Slope, r2, and Residuals Model #Seed Cell for Clade Ancestor SD of Dispersal DistanceTarget CellSloper2 42Linear2 0.9950.524 72Linear2Niche1.0100.514 71Linear1Niche1.0120.514 12Linear2Equiprobable1.0130.507 34Equiprobable8Linear0.9850.361 41Linear1 1.0160.522 73Linear4Niche1.0160.539 44Linear8 0.9830.631 11Linear1Equiprobable1.0180.521 43Linear4 0.9820.559 13Linear4Equiprobable1.0190.497 5Equiprobable16Equiprobable0.9470.085

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50 Residuals From “Best” Model

51 “Best” Model

52 Range Wrangler 1 Inputs & Model Structure Goodness of Fit Statistics Independent Origins Models Ancestry Models Best Model Comparisons Applications to Other Taxa Conclusions

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54 Model Parameters ANCESTOR SPECIES – Equiprobable – Proportional to Geographic Range (Direct) – Inversely Proportional to Geographic Range (Inverse)

55 Model Parameters NICHE CONSERVATISM OF DESCENDANT – 0.0 Evolution to new environmental conditions – 1.0 Strict Niche Conservatism (perfectly inherited ancestral niche)

56 Model Parameters TARGET (SPECIATION) CELL – Equiprobable – Proportional to Environmental Variable (Linear) – Proportional to Similarity of Source Cell (Niche)

57 Model Parameters ANCESTOR SPECIES (Equiprobable, Direct, Inverse) CONSERVATISM (0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0) TARGET CELL (Equiprobable, Linear, Niche) 3 x 11 x 2 = 66 orthogonal parameter settings

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68 Best 12 Models Based on Slope Model #Ancestor ChoiceTarget CellNiche ConservatismSloper2 77EquiprobableNiche10.9990.508 81DirectNiche0.30.9990.484 84DirectNiche0.60.9990.495 82DirectNiche0.41.0020.488 86DirectNiche0.80.9980.51 83DirectNiche0.51.0080.497 85DirectNiche0.70.9920.488 87DirectNiche0.91.0090.506 51DirectLinear0.61.0140.522 53DirectLinear0.81.0150.511 67EquiprobableNiche01.0150.55 50DirectLinear0.51.0160.505

69 Best 12 Models Based on Slope Model #Ancestor ChoiceTarget CellNiche ConservatismSloper2 77EquiprobableNiche10.9990.508 81DirectNiche0.30.9990.484 84DirectNiche0.60.9990.495 82DirectNiche0.41.0020.488 86DirectNiche0.80.9980.51 83DirectNiche0.51.0080.497 85DirectNiche0.70.9920.488 87DirectNiche0.91.0090.506 51DirectLinear0.61.0140.522 53DirectLinear0.81.0150.511 67EquiprobableNiche01.0150.55 50DirectLinear0.51.0160.505 Speciation Proportional To Range Size Target Cell Similar to Ancestor Niche Conservatism Variable Speciation Proportional To Range Size Target Cell Similar to Ancestor Niche Conservatism Variable

70 Worst 12 Models Based on Slope Model #Ancestor ChoiceTarget CellNiche ConservatismSloper2 62InverseLinear0.60.8960.575 97InverseNiche0.80.8880.534 61InverseLinear0.50.8870.611 60InverseLinear0.40.8790.635 63InverseLinear0.70.8790.605 65InverseLinear0.90.8750.605 56InverseLinear00.870.624 59InverseLinear0.30.8690.621 64InverseLinear0.80.8690.607 66InverseLinear10.8630.627 57InverseLinear0.10.8540.596 89InverseNiche00.7990.469

71 Worst 12 Models Based on Slope Model #Ancestor ChoiceTarget CellNiche ConservatismSloper2 62InverseLinear0.60.8960.575 97InverseNiche0.80.8880.534 61InverseLinear0.50.8870.611 60InverseLinear0.40.8790.635 63InverseLinear0.70.8790.605 65InverseLinear0.90.8750.605 56InverseLinear00.870.624 59InverseLinear0.30.8690.621 64InverseLinear0.80.8690.607 66InverseLinear10.8630.627 57InverseLinear0.10.8540.596 89InverseNiche00.7990.469 Speciation Inversely Proportional To Range Size Target Cell Proportional to AET Niche Conservatism Variable Speciation Inversely Proportional To Range Size Target Cell Proportional to AET Niche Conservatism Variable

72 Best 12 Models Based on r 2 Model #Ancestor ChoiceTarget CellNiche ConservatismSloper2 60InverseLinear0.40.8790.635 66InverseLinear10.8630.627 56InverseLinear00.870.624 59InverseLinear0.30.8690.621 58InverseLinear0.20.9080.619 61InverseLinear0.50.8870.611 64InverseLinear0.80.8690.607 63InverseLinear0.70.8790.605 65InverseLinear0.90.8750.605 57InverseLinear0.10.8540.596 36EquiprobableLinear0.20.9150.592 35EquiprobableLinear0.10.9130.592

73 Best 12 Models Based on r 2 Model #Ancestor ChoiceTarget CellNiche ConservatismSloper2 60InverseLinear0.40.8790.635 66InverseLinear10.8630.627 56InverseLinear00.870.624 59InverseLinear0.30.8690.621 58InverseLinear0.20.9080.619 61InverseLinear0.50.8870.611 64InverseLinear0.80.8690.607 63InverseLinear0.70.8790.605 65InverseLinear0.90.8750.605 57InverseLinear0.10.8540.596 36EquiprobableLinear0.20.9150.592 35EquiprobableLinear0.10.9130.592 Speciation Inversely Proportional To Range Size Target Cell Proportional to AET Niche Conservatism Variable Speciation Inversely Proportional To Range Size Target Cell Proportional to AET Niche Conservatism Variable

74 Worst 12 Models Based on r 2 Model #Ancestor ChoiceTarget CellNiche ConservatismSloper2 79DirectNiche0.11.0240.503 80DirectNiche0.21.0290.503 96InverseNiche0.70.9220.502 78DirectNiche01.1010.501 83DirectNiche0.51.0080.497 84DirectNiche0.60.9990.495 82DirectNiche0.41.0020.488 85DirectNiche0.70.9920.488 81DirectNiche0.30.9990.484 88DirectNiche11.0840.471 89InverseNiche00.7990.469 99InverseNiche10.980.445

75 Worst 12 Models Based on r 2 Model #Ancestor ChoiceTarget CellNiche ConservatismSloper2 79DirectNiche0.11.0240.503 80DirectNiche0.21.0290.503 96InverseNiche0.70.9220.502 78DirectNiche01.1010.501 83DirectNiche0.51.0080.497 84DirectNiche0.60.9990.495 82DirectNiche0.41.0020.488 85DirectNiche0.70.9920.488 81DirectNiche0.30.9990.484 88DirectNiche11.0840.471 89InverseNiche00.7990.469 99InverseNiche10.980.445 Variable Effects of Range Size on Speciation Probability Target Cell Similar To Ancestor Niche Conservatism Variable Variable Effects of Range Size on Speciation Probability Target Cell Similar To Ancestor Niche Conservatism Variable

76 Best Models Based on Slope, r 2, and Residuals Model #Ancestor ChoiceTarget CellNiche ConservatismSloper2 77EquiprobableNiche10.9990.508 81DirectNiche0.30.9990.484 84DirectNiche0.60.9990.495 82DirectNiche0.41.0020.488 86DirectNiche0.80.9980.51 83DirectNiche0.51.0080.497 85DirectNiche0.70.9920.488 87DirectNiche0.91.0090.506 51DirectLinear0.61.0140.522 53DirectLinear0.81.0150.511 67EquiprobableNiche01.0150.55 50DirectLinear0.51.0160.505

77 Best Models Based on Slope, r 2, and Residuals Model #Ancestor ChoiceTarget CellNiche ConservatismSloper2 77EquiprobableNiche10.9990.508 81DirectNiche0.30.9990.484 84DirectNiche0.60.9990.495 82DirectNiche0.41.0020.488 86DirectNiche0.80.9980.51 83DirectNiche0.51.0080.497 85DirectNiche0.70.9920.488 87DirectNiche0.91.0090.506 51DirectLinear0.61.0140.522 53DirectLinear0.81.0150.511 67EquiprobableNiche01.0150.55 50DirectLinear0.51.0160.505

78 Range Wrangler 1 Inputs & Model Structure Goodness of Fit Statistics Independent Origins Models Ancestry Models Best Model Comparisons Applications to Other Taxa Conclusions

79 Best Models Based on Slope, r 2, and Residuals Model #Ancestor ChoiceTarget Cell Niche ConservatismSloper2 44Independent Origins0.9830.631 77EquiprobableNiche10.9990.508 83DirectNiche0.51.0080.497 67EquiprobableNiche01.0150.55

80 Best Model SmackDown

81 Best Model: Independent Origins

82 Best Model: Ancestry, Direct, Niche, 0.5

83 Best Model: Ancestry, Equiprobable, Niche, 1.0

84 Best Model: Ancestry, Equiprobable, Niche, 0.0

85 Best Model: Independent Origins

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88 Best Model: Ancestry, Direct, Niche, 0.5

89 Best Model: Ancestry, Equiprobable, Niche, 1.0

90 Best Model: Ancestry, Equiprobable, Niche, 0.0

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92 Best Models Based on Slope, r 2, and Residuals Model #Ancestor ChoiceTarget Cell Niche ConservatismSloper2 44Independent Origins0.9830.631 77EquiprobableNiche10.9990.508 83DirectNiche0.51.0080.497 67EquiprobableNiche01.0150.55

93 Range Wrangler 1 Inputs & Model Structure Goodness of Fit Statistics Independent Origins Models Ancestry Models Best Model Comparisons Applications to Other Taxa Conclusions

94 Amphibians

95 Birds

96 Range Wrangler 1 Inputs & Model Structure Goodness of Fit Statistics Independent Origins Models Ancestry Models Best Model Comparisons Applications to Other Taxa Conclusions

97 Best fitting models (BFM) account for ~ 50% of variance

98 Conclusions Best fitting models (BFM) account for ~ 50% of variance BFM includes ancestry, medium-distance dispersal, evolutionary shifts, and effects of AET on dispersal

99 Conclusions Best fitting models (BFM) account for ~ 50% of variance BFM includes ancestry, medium-distance dispersal, evolutionary shifts, and effects of AET on dispersal BFM has acceptable residual distribution and better accounts for high-diversity residuals

100 Some Things That Don’t Work

101 Equiprobable Dispersal

102 Some Things That Don’t Work Equiprobable Dispersal Long-Distance Dispersal

103 Some Things That Don’t Work Equiprobable Dispersal Long-Distance Dispersal Speciation ~ Inverse of Geographic Ranges

104 Some Things That Don’t Work Equiprobable Dispersal Long-Distance Dispersal Speciation ~ Inverse of Geographic Ranges Independent Origin of Species

105 Something for Everybody! “History” Fans “Contemporary Climate” Fans “Geometric Constraints” Fans

106 For History Fans…. Only models that included ancestry and a simple form of speciation could generate a linear fit with good residuals and best account for high diversity sites

107 For Contemporary Climate Fans…. Only models that included an environmental layer representing contemporary climate (AET) could account for a substantial fraction of the variance in species richness.

108 For Geometric Constraints Fans…. Only models that included short- to medium-distance dispersal provided adequate fit and had good predictive power.

109 Remaining Challenges

110 Choice of “response variable” (r 2 ≠ slope)

111 Remaining Challenges Choice of “response variable” (r 2 ≠ slope) Efficient exploration of parameter space

112 Remaining Challenges Choice of “response variable” (r 2 ≠ slope) Efficient exploration of parameter space Goodness of Fit tests

113 Remaining Challenges Choice of “response variable” (r 2 ≠ slope) Efficient exploration of parameter space Goodness of Fit tests Quantification of patterns in residuals

114 Remaining Challenges Choice of “response variable” (r 2 ≠ slope) Efficient exploration of parameter space Goodness of Fit tests Quantification of patterns in residuals Selecting among many competing alternative models

115 Onward to Range Wrangler 2 !

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