Maxent

 
Maximum entropy modelling is a general-purpose method for characterising probability distributions from incomplete information. In estimating the probability distribution defining a species distribution across a study area, Maxent formalises the principle that the estimated distribution must agree with everything that is known or inferred from the environmental conditions where the species has been observed, but should avoid making any assumptions that are not supported by the data. The approach is to find the probability distribution of maximum entropy (the distribution that is most spread-out, or closest to uniform) subject to the constraints imposed by the information available from the observed distribution of the species and environmental conditions across the study area.

The Maxent method does not require absence data for the species being modelled; instead it uses background environmental data for the entire study area. The method can utilize both continuous and categorical environmental variables and the output is a continuous prediction (a cumulative probability ranging from 0 to 100 that indicates relative suitability). One drawback is that it uses an exponential model that can predict unfeasibly high suitability for environmental conditions that are outside the range present in the study area (i.e. if used toextrapolate beyond the range of values of environmental variables to which the model was fitted). To alleviate this problem, when predicting for variable values that are outside the range found in the study area, these values are reset (or "clamped") to match the upper or lower values found in the study area.

For a concise mathematic definition of Maxent and for more detailed discussion of its application to species distribution modeling see Phillips et al. (2006, 2004, 2008).
 

References

Phillips, S.J., Dudik, M., & Schapire, R.E. (2004). A maximum entropy approach to species distribution modeling. In Proceedings of the 21st international conference on machine learning, pp. 655-662. AMC Press, New York.

 

Phillips, S.J., Anderson, R.P., & Schapire, R.E. (2006). Maximum entropy modeling of species geographic distributions. Ecological Modelling, 190, 231-259.
 
Phillips, S.J. & Dudík, M. (2008). Modeling of species distributions with Maxent: new extensions and a comprehensive evaluation. Ecography, 31, 161-175.