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Now I'm curious, Marcelo. Do you think Maxent is inappropriate for presence-only modeling with large datasets?
One thing you haven't told us, Allison, is whether you're referring to AUC calculated on training data or test data, and if the latter, which data? I would be more surprised if this pattern arose with AUC calculated on your huge withheld dataset.
While Maxent can be effective with relatively small presence-only datasets, it's no less suitable for large ones. All else equal, it means there is more information available in order to better characterise the species-environment relationship. It still pays to check response curves to ensure they're sensible, and if there are signs of overfitting, adjust feature types and regularisation accordingly.
I'm still interested in whether people have recommendations for alternative approaches that might better exploit large sample size.