Hypothesis TestingHypothesis Testing

• Are two species identical?• Are they more similar than you’d expect based on

the distribution of environmental variables in their allopatric ranges?

Hypothesis testingHypothesis testing

Actual Overlap

Distribution of overlaps under null hypothesis

OCCURRENCE RANDOMIZATIONOCCURRENCE RANDOMIZATION

Observed overlap

Overlap for pseudoreplicate

A. coelestinus A. chlorocyanus

• Incumbency• Steep environmental gradient• Ribbon of unsuitable habitat (tension zone)

Regularization and # Parameters

Model selectionModel selection

• ENMTools includes functions for calculating information criteria, so that models may be selected based on a combination of fit and complexity– AICc– BIC

Simulated DataSimulated Data

0.01002 0.01002 0.01001 0.01001 0.01001 0.01002 0.01001 0.01000 0.01001 0.01000

0.01001 0.01001 0.01001 0.01001 0.01001 0.01001 0.01000 0.01000 0.00999 0.00999

0.01002 0.01001 0.01000 0.01000 0.01000 0.00999 0.00999 0.00998 0.00998 0.00998

0.01001 0.01001 0.01000 0.01000 0.01001 0.01000 0.01000 0.00999 0.00999 0.00999

0.01001 0.01001 0.01000 0.01000 0.01000 0.00999 0.00999 0.00999 0.00999 0.00998

0.01002 0.01001 0.01000 0.01001 0.01000 0.01000 0.00999 0.00999 0.00998 0.00999

0.01001 0.01000 0.01001 0.01000 0.01000 0.00999 0.01000 0.01000 0.00999 0.00999

0.01002 0.01001 0.01001 0.01001 0.01000 0.01000 0.00999 0.00999 0.00999 0.00998

0.01002 0.01000 0.01001 0.01001 0.00999 0.01000 0.01000 0.00999 0.00999 0.00999

0.01001 0.01000 0.01001 0.01000 0.01000 0.01000 0.01000 0.00999 0.00999 0.00999

Simulated DataSimulated DataSpecies Latitude LongitudeHella_imaginarius 33.8103 -116.675Hella_imaginarius 34.744 -120.284Hella_imaginarius 34.744 -120.284Hella_imaginarius 34.744 -120.284Hella_imaginarius 34.744 -120.284Hella_imaginarius 34.744 -120.284Hella_imaginarius 34.744 -120.284Hella_imaginarius 34.744 -120.284Hella_imaginarius 34.744 -120.284Hella_imaginarius 34.744 -120.284Hella_imaginarius 34.744 -120.284Hella_imaginarius 34.744 -120.284Hella_imaginarius 34.744 -120.284Hella_imaginarius 34.744 -120.284Hella_imaginarius 35.6022 -120.17Hella_imaginarius 35.6022 -120.17Hella_imaginarius 35.3141 -120.658Hella_imaginarius 35.3141 -120.658Hella_imaginarius 35.6399 -120.19Hella_imaginarius 36.5056 -121.868Hella_imaginarius 36.3981 -121.647Hella_imaginarius 36.4427 -121.642Hella_imaginarius 36.9218 -121.833Hella_imaginarius 36.9218 -121.833Hella_imaginarius 36.9218 -121.833Hella_imaginarius 36.9218 -121.833Hella_imaginarius 36.9218 -121.833Hella_imaginarius 36.9218 -121.833Hella_imaginarius 36.9218 -121.833Hella_imaginarius 36.9218 -121.833

)...( 11)( nnxxexp

Inference

“Truth”

+

Other toolsOther tools

• Useful measurements– ENM “breadth”– Range overlap– Variable correlation

• Removal of duplicate occurrences• Jackknife, bootstrap, spatial cross-validation