How HEMI 2 Works

Overview

HEMI 2 works by fitting curves based on Bezier equations to your occurrences. It does this for each covariate independently and then combines the results to produce an output habitat map. The curves are placed to optimize the AIC of the model given the data.

The relationship of a species to it's fundamental niche, and thus to any covariate, should be based on a relatively simple interaction of physiological processes such as photosynthesis in plants. Hutchinson originally described the niche as having a "center optimal point" with less optimal areas on either side and then areas where a species could not survive. In addition, the sample data that we collect for any species will always be a sub-set of it's fundamental niche. For this reason, HEMI "smoothes" out the higher frequency noise in the sample data to find the lower-frequency signal buried within the data.

The Receiver Operator Curves (ROC) and Area Under the Curve (AUC) values are provided for evaluation but are not used in the model at this point

The Curves

The curves displayed are either categorical or continuous. The categorical curves are simply horizontal line segments that indicate the probability of the area being habitat. The user can move these lines up and down as desired.

The continuous curves are represented as three Bezier curves with control points. The control point on the left can move from the top of the left side (probability of habitat=1, covariate value=minimum) and across the bottom to the bottom-right corner (probability of habitat=0, covariate value=maximum). The right control point can move from the upper-left corner of the graph (probability of habitat=1, covariate value=maximum), down the right side and across the bottom to the lower-left side of the graph (probability of habitat=0, covariate value=minimum). The two additional points can move anywhere within the graph.

If our sample area contained the full range of covariate values for the species, then we should set the left and right control points to be at the bottom of the graph (probability of habitat=0). The points can be moved up the sides to allow for instances when where we have a sample area that does not control the full niche of a species.

Fitting the Curves

When the user presses "fit", or during Monte Carlo runs, the following steps are executed for each model:

1. If the model is categorical then the probability values are simply set to the proportion of occurrences in the histogram, otherwise,
2. The four control points are moved along the left, bottom, and right edges of the histogram chart. The number of moves and distance of each move are set in the "Fit" tab of the Individual Model settings dialogs.
3. The position of the control points with the best AIC are selected and the process is repeated until the
"Number of Checks" is 0.