MaxEnt versus MaxLike: empirical comparisons with ant species distributions

MaxEnt is one of the most widely used tools in ecology, biogeography, and evolution for modeling and mapping species distributions using presence-only occurrence records and associated environmental covariates. Despite its popularity, the exponential model implemented by MaxEnt does not directly estimate occurrence probability, the natural quantity of interest when modeling species distributions. Instead, MaxEnt generates an index of relative habitat suitability. MaxLike, a newly introduced maximum-likelihood technique, has been shown to overcome the problem of directly estimating the probability of occurrence using presence-only data. However, the performance and relative merits of MaxEnt and MaxLike remain largely untested, especially when modeling species with relatively few occurrence data that encompass only a portion of the geographic range of the species. Using georeferenced occurrence records for six species of ants in New England, we provide comparisons of MaxEnt and MaxLike. We show that by most quantitative metrics, the performance of MaxLike exceeds that of MaxEnt, regardless of whether MaxEnt models account for sampling bias and include greater model complexity than implemented in MaxLike. More importantly, for most species, the relative suitability index estimated by MaxEnt often was poorly correlated with the probability of occurrence estimated by MaxLike, suggesting that the two methods are estimating different quantities. For species distribution modeling, MaxLike, and similar models that are based on an explicit sampling process and that directly estimate probability of occurrence, should be considered as important alternatives to the widely-used MaxEnt