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)