Hello,

Concerning the limits of the extrapolation. MaxEnt uses the present climate conditions to "train the model' and then spatially project it onto the variables which you indicated to be your future climatic conditions. The model functions in the same manner as if it were to be projected onto the same environmental layers the model was trained on. 

The ability of MaxEnt to predict outside the range which it as calibrated on would be influenced by how well your observations have captured all the possible environmental conditions which the species can survive in. I.e the more occurrences the better change the model has of fully understanding the response of the species. 

The threshold to determine presence / absence of the species I think you should consider more carefully as this will have a greater impact on the predicted areas the species will occupy. 

I think the attached case study paper could be useful to you. 

Thank you very much, Joshua, for your prompt and useful response.

I am still wondering though if there are some defined limits for MaXent to extrapolate beyond the training range of the environmental variables. I imagine some sort of threshold that MaxEnt does not exceed. The problem is that I couldn't find any clear information on this issue in literature.

A case is attached where macro-meteorological variables predicted a distribution beyond the range of  some of these variables, but a broader set of environmental variables, including topo-climate proxies (elevation; vegetation) provides a different and arguably better prediction.

In other words, beyond the presence/absence data and the algorithm, the quality and completeness of the environmental variables deserves the same critical attention. There is an extensive literature on the impacts of various presence/absence 'biases' and the merits of various Species Distribution Modelling (SDM) algorithms (both insignificant in many cases), but the environmental variables rarely seem to receive the same level of scientific scrutiny. 

Article Where the bears roam in Majella National Park, Italy

Article Transferability of species distribution models: The case of ...

Really, there is not consensus on this matter. The "mess analysis" is very interesting to compare the current variables and the new conditions. You could take a look at the "response curves" and remove some variables if you confirm several problems caused by extrapolation (I have attached two examples).

And by the way, there is a release of Maxent (3.4) http://biodiversityinformatics.amnh.org/open_source/maxent/

@Oliver

Indeed, response curves are essential (attached) in interpretation of SDM output and in my opinion underused. Have said that, I would appreciate you explanation in your example in the context of the question?

Article Fine resolution distribution modelling of endemics in Majell...

Article Where the bears roam in Majella National Park, Italy

Species response curves are very useful if you have a properly extent of study area: based on the premise that you are working with a representative environmental domain both the calibration space and the projection space. If there are not truncated ecological response curves, probably you will have problems relate to the projection space beyond the range of the calibration space. This is an important problem in many projections across space (e.g. geographical transferability or extrapolation: Europa / North America) and time. Anoher case: care should be taken in the interpretation and applicability of the response curves in Biological Invasions Models: the range expansions are highly constrained by dispersal and colonization processes. 

Thank you for the very useful insights and for sharing the articles. Although I couldn't find explicit limits for 'clamping' (but I learned that this is an alternative word) I am better aware now of this issue and the importance of the response curves which will help me to develop species specific climate change threat maps. I will share the updates with you.

Here are some references to papers: 

*Beale CM, Lennon JJ, Gimona A. Opening the climate envelope reveals no macroscale associations with climate in European birds. Proc Natl Acad Sci U S A. 2008;105: 14908-14912. doi:10.1073/pnas.0803506105

*Barve N, Barve V, Jiménez-Valverde A, Lira-Noriega A, Maher SP, Peterson AT, et al. The crucial role of the accessible area in ecological niche modeling and species distribution modeling. Ecol Modell. Elsevier B.V.; 2011;222: 1810-1819. doi:10.1016/j.ecolmodel.2011.02.011

Harris RMB, Grose MR, Lee G, Bindoff NL, Porfirio LL, Fox-Hughes P. Climate projections for ecologists. Wiley Interdiscip Rev Clim Chang. 2014;5: 621-637. doi:10.1002/wcc.291

Mesgaran MB, Cousens RD, Webber BL. Here be dragons: A tool for quantifying novelty due to covariate range and correlation change when projecting species distribution models. Divers Distrib. 2014;20: 1147-1159. doi:10.1111/ddi.12209

*Peterson AT, Barve N, Bini LM, Diniz-Filho JA, Jiménez-Valverde A, Lira-Noriega A, et al. The climate envelope may not be empty. Proc Natl Acad Sci U S A. 2009;106: E47-E47. doi:10.1073/pnas.0809722106

Václavík T, Meentemeyer RK. Equilibrium or not? Modelling potential distribution of invasive species in different stages of invasion. Divers Distrib. 2012;18: 73-83. doi:10.1111/j.1472-4642.2011.00854.x

* Interesting discussion.