Modeling Results
The three modeling methods of generalized linear models, boosted
regression trees and maximum entropy all generated fair to excellent
results, as measured by AUC values, with values ranging from 0.80–0.88.
Boosted regression trees (BRT) produced the best models, as measured by
AUC values, 10-fold cross validation, model deviance versus null
deviance and relevance of information regarding predictors and their
contributions to the models. The model results presented below are
derived from BRT analysis. The first model presented here is a model
that included soil type, which was the best performing BRT model. The
map of predicted suitable habitat shows a low probability of
colonization of the peninsula, especially to the east of localized,
immediately adjacent regions on the western edge of Bahía Magdalena. The
highest predicted probabilities on the peninsula are near the town of
Puerto San Carlos, where the only known peninsular population occurs.
(Fig. 3).
Annual temperature range, a simple subtraction of the annual high
temperature minus the annual low temperature, has the highest marginal
response, which shows a sudden drop in the suitability of habitat forCochemiea halei under an annual temperature range greater than
approximately 21.5○ C. The optimal mean temperature of
the warmest quarter is ranges from 24○ C to
26○ C, with an increased contribution to occurrence at
26○ C, but then a sharp drop off , with temperatures
above approximate 26.5○ C negatively correlated to
occurrence. Precipitation of the warmest quarter is positively
correlated with occurrence below 30 mm, but negatively correlated above
30 mm. Precipitation of the coldest quarter shows approximately the same
reponse of precipitation of the warmest quarter. (Fig. 4).
The percent relative contributions for each variable to the predictive
ability of the model described above show that the most significant
predictor is annual temperature range, accounting for nearly 66% of
model performance. Thermal energy in general is a strong predictor of
suitable habitat, with the top two predictors accounting for 78.3% of
model performance. (Fig.5).
In order to gauge the impact of soil type on the habitat suitability ofC. halei , a model was created with the same predictor variables
as the above model, but without soil type. The habitat suitability map
without soil type shows a higher probability of occurrence on the
peninsula, where the species does not occur in any large populations and
where ultramafic soils do not occur. A higher suitability is also
predicted within the islands themselves overall, with a higher
saturation in general of suitable habitat. Suitable habitat is also
predicted on some pure sand features, such as the sand that connects
Isla Magdalena with Cabo San Lazaro. There is also a higher predicted
probability on basalt and non-ultramafic soil types on the islands. The
low, sandy trough in the middle of Isla Margarita, however, remains an
area of low suitability, as does the peninsular region to the east of
the small footholds predicted for C. halei . The 10-fold
cross-validated AUC of this model was .85, slightly lower than the model
with soil type. (Fig. 6)