HEMI 2 Hyper-Envelope Modeling Interface 2 Uses Bezier curves to minimize over- fitting Allows automatic fitting with manual adjustment Provides interactive mode for developing models and batch model (“Monte Carlo”) for validation and uncertainty analysis.

Germination Percentage Shrestha, A., E. S. Roman, A. G. Thomas, and C. J. Swanton Modeling germination and shoot-radicle elongation of Ambrosia artemisiifolia. Weed Science 47:

Maraghni, M., M. Gorai, and M. Neffati Seed germination at different temperatures and water stress levels, and seedling emergence from different depths of Ziziphus lotus. South African Journal of Botany 76: Over-fitting The Data? What should the model look like? Maxent model for Tamarix in the US: response to temperature when modeled with temperature and precipitation

Niche Temperature Salinity Population Growth Temperature Salinity From the Theory of Biogeography Brown, J.H., Lomolino, M.V. 1998, Biogeography: Second Edition. Sinauer Associates, Sinauer Massachusetts Environmental Space

Problems with Polynomials Lack flexibility Not well behaved at boundaries f(x) = a 0 + a 1 x + a 2 x a n x n, where a n ≠ 0 and n ≥ 2 Wikipedia.com

US Environmental Space

Tamarisk Occurrences United States Environmental Space

Alternatives to Polynomials BioClim – max and max boxes BioMapper – 25x25 grid of boxes DOMAIN – Distance to existing point NPMR Hyper-Envelope Modeling – Bezier Curves Multivariate adaptive regression splines

Bezier and Spline Curves Wikiepedia.com P1P1 P0P0 P2P2 P3P3

Modified Bezier Curves 08/10/2009International Biological Information Science P2P2 P3P3 P0P0 P1P1 S2S2 S1S1 S0S0 S3S3

Tamarisk Occurrences United States Environmental Space

HEMI Tamarix Model 08/10/2009International Biological Information Science Annual Precipitation (mm) Min Temp of coldest Month (°C*10) Potential Habitat Unsuitable Habitat 5 Points -> 10 Parameters AUC: 0.76

Models for Tamarisk in W.U.S.

Results MethodTrain AUC Number of Parameters Test AUC HEMI Automatic HEMI Edited BioClim BioMapper Median Maxent

Potential Habitat 08/10/2009International Biological Information Science Potential Habitat Unsuitable Habitat

Global Tamarisk Map? 08/10/2009International Biological Information Science 1.0 Habitat Suitability 2.0

Limits of HEMI 1 Computation limits as the number of predictors increased Problems visualizing combinations of predictors beyond 2

HEMI 2 Limited to one response curve per predictor –Similar to MaxEnt and traditional regression –Predictors can be transformed to adapt for this to some extent Up to 10 predictors New interactive interface with immediate feedback

HEMI Model 1 st point is “tied” to the left edge and the bottom Last point is “tied” to the left edge and the bottom Remaining Points can be moved vertically and horizontally