Range Wrangler I: Guided Tour and Analyses of New World Mammal Distributions Nick Gotelli Department...

Range Wrangler I: Guided Tour and Analyses of New World

Mammal DistributionsNick Gotelli

Department of BiologyUniversity of VermontBurlington, VT 05405

NCEAS, October 11, 2008

Range Wrangler 1

• Inputs & Model Structure• Goodness of Fit Statistics• Independent Origins Models• Ancestry Models• Best Model Comparisons• Applications to Other Taxa• Conclusions

THANK YOU To Thiago Rangel!

Range Wrangler 1

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

Range Wrangler 1

Expected Species Richness0 50 100 150 200 250Obs

r2 = 0.08Slope = 0.60Intercept = 54.5AICc = 4147

Expected Species Richness0 50 100 150 200 250Obs

r2 = 1.0Slope = 1.0Intercept = 0.0AICc = 2.0

r2 = 0.08Slope = 0.60Intercept = 54.5AICc = 4147

Intercept

-500 -300 -100 100

0 1 2 3 4 5

0.0 0.2 0.4 0.6 0.8

3600370038003900400041004200

Intercept

-500 -300 -100 100

0 1 2 3 4 5

0.0 0.2 0.4 0.6 0.8

3600370038003900400041004200

Intercept

-500 -300 -100 100

0 1 2 3 4 5

0.0 0.2 0.4 0.6 0.8

3600370038003900400041004200

Intercept

-500 -300 -100 100

0 1 2 3 4 5

0.0 0.2 0.4 0.6 0.8

3600370038003900400041004200

Intercept

-500 -300 -100 100

0 1 2 3 4 5

0.0 0.2 0.4 0.6 0.8

3600370038003900400041004200

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Range Wrangler 1

Model Parameters

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

Center of Origin Model

Model Parameters

• DISPERSAL DISTANCE– 1.0 TO 512.0 standard deviations of map cell

distance

Model Parameters

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

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

Equiprobable

Linear

Equiprobable

Linear

SingleCell

DISPERSAL DISTANCE

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.2 0.8 1.4 2.1 2.7 3.4 4.0 4.7

Equiprobable Linear SingleCell

Seed Cell

Equiprobable Linear Niche

Target Cell

Dispersal Distance (SD)

0.1 1 10 100 1000

EquiprobableLinearSingle Cell

Df Sum of Sq Mean Sq F Value Pr(F) Seed.Cell 2 2.256552 1.128276 81.90621 0.00000000Target.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

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 0.0000000000Seed.Cell:Target.Cell 4 0.353634 0.088408 5.93518 0.0003066929 Residuals 81 1.206549 0.014896

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.2 0.8 1.4 2.1 2.7 3.4 4.0 4.7

Equiprobable Linear SingleCell

Seed Cell

Equiprobable Linear Niche

Target Cell

Df Sum of Sq Mean Sq F Value Pr(F) Seed.Cell 2 27.62234 13.81117 36.27824 0.0000000Target.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

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 0.008898663Seed.Cell:Target.Cell 4 11.00685 2.75171 6.93765 0.000074570 Residuals 81 32.12739 0.39663

Best 12 Models Based on Slope

Model # Seed Cell for Clade AncestorSD of Dispersal

Distance Target Cell Slope r2

42 Linear 2 Linear 0.995 0.524

72 Linear 2 Niche 1.010 0.514

71 Linear 1 Niche 1.012 0.514

12 Linear 2 Equiprobable 1.013 0.507

34 Equiprobable 8 Linear 0.985 0.361

73 Linear 4 Niche 1.016 0.539

5 Equiprobable 16 Equiprobable 0.947 0.085

72 Linear 2 Niche 1.010 0.514

71 Linear 1 Niche 1.012 0.514

73 Linear 4 Niche 1.016 0.539

Environmental Effects on SpeciationShort Dispersal DistancesEnvironmental or Niche Effects on Dispersal

72 Linear 2 Niche 1.010 0.514

71 Linear 1 Niche 1.012 0.514

73 Linear 4 Niche 1.016 0.539

Worst 12 Models Based on Slope

52 SingleCell 2 Linear 0.196 0.177

23 SingleCell 4 Equiprobable 0.195 0.149

81 SingleCell 1 Niche 0.187 0.168

Center of Origin or Environmental Effects on SpeciationLong or Short Dispersal DistancesEquiprobable Dispersal

Best 12 Models Based on r2

49 Linear 256 Linear 1.227 0.766

50 Linear 512 Linear 1.231 0.765

47 Linear 64 Linear 1.197 0.761

48 Linear 128 Linear 1.213 0.761

46 Linear 32 Linear 1.146 0.751

45 Linear 16 Linear 1.063 0.721

79 Linear 256 Niche 1.479 0.716

77 Linear 64 Niche 1.435 0.715

49 Linear 256 Linear 1.227 0.766

50 Linear 512 Linear 1.231 0.765

47 Linear 64 Linear 1.197 0.761

48 Linear 128 Linear 1.213 0.761

46 Linear 32 Linear 1.146 0.751

45 Linear 16 Linear 1.063 0.721

79 Linear 256 Niche 1.479 0.716

77 Linear 64 Niche 1.435 0.715

Environmental Effects on SpeciationLong Dispersal DistancesEnvironmental Effects on Dispersal

Worst 12 Models Based on r2

61 Equiprobable 1 Niche 0.584 0.079

Center of Origin or Equiprobable SpeciationLong Dispersal DistancesEquiprobable Dispersal

Single “Best” Model based on Slope, r2, and Residuals

72 Linear 2 Niche 1.010 0.514

71 Linear 1 Niche 1.012 0.514

73 Linear 4 Niche 1.016 0.539

Equiprobable

Linear

Equiprobable

Linear

SingleCell

DISPERSAL DISTANCE

Residuals From “Best” Model

“Best” Model

Range Wrangler 1

Model Parameters

• ANCESTOR SPECIES– Equiprobable– Proportional to Geographic Range (Direct)– Inversely Proportional to Geographic Range (Inverse)

Model Parameters

• NICHE CONSERVATISM OF DESCENDANT– 0.0 Evolution to new environmental conditions– 1.0 Strict Niche Conservatism (perfectly inherited

ancestral niche)

Model Parameters

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

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

Equiprobable

Linear

Equiprobable

Linear

SingleCell

DISPERSAL DISTANCE

Equiprobable

Linear

Equiprobable

Linear

SingleCell

DISPERSAL DISTANCE

Linear

Equiprobable

Direct

Inverse

0.00.2

0.40.6

0.81.0

Conservatism <-> Evolution

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.40 0.45 0.50 0.55 0.60 0.65

0.2 0.8 1.4 2.1 2.7 3.4 4.0 4.7

0.7 0.8 0.9 1.0 1.1 1.2

Direct Equiprobable Inverse

Ancestor Range

Linear Niche

Speciation Cell

-0.1 0.1 0.3 0.5 0.7 0.9 1.1

Conservatism

Direct Equiprobable Inverse

Ancestor Range

Linear Niche

Speciation Cell

Model # Ancestor Choice Target Cell Niche Conservatism Slope r2

77 Equiprobable Niche 1 0.999 0.508

81 Direct Niche 0.3 0.999 0.484

84 Direct Niche 0.6 0.999 0.495

82 Direct Niche 0.4 1.002 0.488

86 Direct Niche 0.8 0.998 0.51

83 Direct Niche 0.5 1.008 0.497

85 Direct Niche 0.7 0.992 0.488

87 Direct Niche 0.9 1.009 0.506

51 Direct Linear 0.6 1.014 0.522

53 Direct Linear 0.8 1.015 0.511

50 Direct Linear 0.5 1.016 0.505

81 Direct Niche 0.3 0.999 0.484

84 Direct Niche 0.6 0.999 0.495

82 Direct Niche 0.4 1.002 0.488

86 Direct Niche 0.8 0.998 0.51

83 Direct Niche 0.5 1.008 0.497

85 Direct Niche 0.7 0.992 0.488

87 Direct Niche 0.9 1.009 0.506

51 Direct Linear 0.6 1.014 0.522

53 Direct Linear 0.8 1.015 0.511

50 Direct Linear 0.5 1.016 0.505

Speciation Proportional To Range SizeTarget Cell Similar to AncestorNiche Conservatism Variable

62 Inverse Linear 0.6 0.896 0.575

97 Inverse Niche 0.8 0.888 0.534

61 Inverse Linear 0.5 0.887 0.611

60 Inverse Linear 0.4 0.879 0.635

63 Inverse Linear 0.7 0.879 0.605

65 Inverse Linear 0.9 0.875 0.605

56 Inverse Linear 0 0.87 0.624

59 Inverse Linear 0.3 0.869 0.621

64 Inverse Linear 0.8 0.869 0.607

57 Inverse Linear 0.1 0.854 0.596

89 Inverse Niche 0 0.799 0.469

62 Inverse Linear 0.6 0.896 0.575

97 Inverse Niche 0.8 0.888 0.534

61 Inverse Linear 0.5 0.887 0.611

60 Inverse Linear 0.4 0.879 0.635

63 Inverse Linear 0.7 0.879 0.605

65 Inverse Linear 0.9 0.875 0.605

59 Inverse Linear 0.3 0.869 0.621

64 Inverse Linear 0.8 0.869 0.607

57 Inverse Linear 0.1 0.854 0.596

Speciation Inversely Proportional To Range SizeTarget Cell Proportional to AETNiche Conservatism Variable

60 Inverse Linear 0.4 0.879 0.635

59 Inverse Linear 0.3 0.869 0.621

58 Inverse Linear 0.2 0.908 0.619

61 Inverse Linear 0.5 0.887 0.611

64 Inverse Linear 0.8 0.869 0.607

63 Inverse Linear 0.7 0.879 0.605

65 Inverse Linear 0.9 0.875 0.605

57 Inverse Linear 0.1 0.854 0.596

36 Equiprobable Linear 0.2 0.915 0.592

60 Inverse Linear 0.4 0.879 0.635

59 Inverse Linear 0.3 0.869 0.621

58 Inverse Linear 0.2 0.908 0.619

61 Inverse Linear 0.5 0.887 0.611

64 Inverse Linear 0.8 0.869 0.607

63 Inverse Linear 0.7 0.879 0.605

65 Inverse Linear 0.9 0.875 0.605

57 Inverse Linear 0.1 0.854 0.596

Speciation Inversely Proportional To Range SizeTarget Cell Proportional to AETNiche Conservatism Variable

79 Direct Niche 0.1 1.024 0.503

80 Direct Niche 0.2 1.029 0.503

96 Inverse Niche 0.7 0.922 0.502

78 Direct Niche 0 1.101 0.501

83 Direct Niche 0.5 1.008 0.497

84 Direct Niche 0.6 0.999 0.495

82 Direct Niche 0.4 1.002 0.488

85 Direct Niche 0.7 0.992 0.488

81 Direct Niche 0.3 0.999 0.484

88 Direct Niche 1 1.084 0.471

79 Direct Niche 0.1 1.024 0.503

80 Direct Niche 0.2 1.029 0.503

96 Inverse Niche 0.7 0.922 0.502

78 Direct Niche 0 1.101 0.501

83 Direct Niche 0.5 1.008 0.497

84 Direct Niche 0.6 0.999 0.495

82 Direct Niche 0.4 1.002 0.488

85 Direct Niche 0.7 0.992 0.488

81 Direct Niche 0.3 0.999 0.484

88 Direct Niche 1 1.084 0.471

Variable Effects of Range Size on Speciation ProbabilityTarget Cell Similar To AncestorNiche Conservatism Variable

Best Models Based on Slope, r2, and Residuals

81 Direct Niche 0.3 0.999 0.484

84 Direct Niche 0.6 0.999 0.495

82 Direct Niche 0.4 1.002 0.488

86 Direct Niche 0.8 0.998 0.51

83 Direct Niche 0.5 1.008 0.497

85 Direct Niche 0.7 0.992 0.488

87 Direct Niche 0.9 1.009 0.506

51 Direct Linear 0.6 1.014 0.522

53 Direct Linear 0.8 1.015 0.511

50 Direct Linear 0.5 1.016 0.505

81 Direct Niche 0.3 0.999 0.484

84 Direct Niche 0.6 0.999 0.495

82 Direct Niche 0.4 1.002 0.488

86 Direct Niche 0.8 0.998 0.51

83 Direct Niche 0.5 1.008 0.497

85 Direct Niche 0.7 0.992 0.488

87 Direct Niche 0.9 1.009 0.506

51 Direct Linear 0.6 1.014 0.522

53 Direct Linear 0.8 1.015 0.511

50 Direct Linear 0.5 1.016 0.505

Range Wrangler 1

Model # Ancestor Choice Target CellNiche

Conservatism Slope r244 Independent Origins 0.983 0.63177 Equiprobable Niche 1 0.999 0.50883 Direct Niche 0.5 1.008 0.49767 Equiprobable Niche 0 1.015 0.55

Best Model SmackDown

Best Model: Independent Origins

Best Model: Ancestry, Direct, Niche, 0.5

Best Model: Ancestry, Equiprobable, Niche, 1.0

Best Model: Independent Origins

Best Model: Ancestry, Direct, Niche, 0.5

Model # Ancestor Choice Target CellNiche

Conservatism Slope r244 Independent Origins 0.983 0.63177 Equiprobable Niche 1 0.999 0.50883 Direct Niche 0.5 1.008 0.49767 Equiprobable Niche 0 1.015 0.55

Range Wrangler 1

Amphibians

Range Wrangler 1

Conclusions

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

Conclusions

• BFM includes ancestry, medium-distance dispersal, evolutionary shifts, and effects of AET on dispersal

Conclusions

• 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

Some Things That Don’t Work

• Equiprobable Dispersal

• Equiprobable Dispersal• Long-Distance Dispersal

• Equiprobable Dispersal• Long-Distance Dispersal• Speciation ~ Inverse of Geographic Ranges

• Equiprobable Dispersal• Long-Distance Dispersal• Speciation ~ Inverse of Geographic Ranges• Independent Origin of Species

Something for Everybody!

• “History” Fans• “Contemporary Climate” Fans• “Geometric Constraints” Fans

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

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.

For Geometric Constraints Fans….

Only models that included short- to medium-distance dispersal provided adequate fit and had good predictive

power.

Remaining Challenges

• Choice of “response variable” (r2 ≠ slope)

• Choice of “response variable” (r2 ≠ slope)• Efficient exploration of parameter space

• Choice of “response variable” (r2 ≠ slope)• Efficient exploration of parameter space• Goodness of Fit tests

• Choice of “response variable” (r2 ≠ slope)• Efficient exploration of parameter space• Goodness of Fit tests• Quantification of patterns in residuals

• Choice of “response variable” (r2 ≠ slope)• Efficient exploration of parameter space• Goodness of Fit tests• Quantification of patterns in residuals• Selecting among many competing alternative

models

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