Sounds like a great data set. Yes, it's important with the BioClim variables to reduce the overall number used in the models. I would pay close attention to those that are positively correlated, since they mean the exact same thing (in terms of inference). I have a tendency to retain variables that are negatively correlated as there may be some unmeasured variable.

A principal components analysis (PCA), or another factor reduction method that better accounts for the non-Gaussian nature of the BioClim data, may be a good approach. You can run your models on the first, second, and/or third principal component. Inference can then be made by looking at the factor loadings, once the final, reduced model is obtained. Reviewers will almost certainly have no problem with this approach. You mentioned that you have 30 sites, but I'm not sure how much replication you have for these sites. So, you definitely will want to reduce the number of terms in your model.

Concerning how to refine your model, I would most certainly use a model selection approach (using AICc or related information criterion). Others may weigh in with their preferred method for model reduction.

Dear J. Patrick,

Thanks for the reply. I tried to understand the species ecology and could confidently remove some of the bioclimatic variables. With correlation analysis I further removed few highly correlated variables. But at the end I am left with 3-4 variables and I am not sure if the prediction is reliable based on only these variables. The AUC values are good enough for prediction, but I am not satisfied with the low number of variables. Do you think low number of variables is a big problem?

Patrick´s answer is right, a PCA analysis allow to select the variables with the major loads in the componentes of the PCA. According to Hirzel et al. 2002 (http://www.whoi.edu/cms/files/Hirzel_etal_2002_53464.pdf), the variables with highest load in the first component of the PCA are important for the Marginality of the specie, and the variables important to others components of the PCA are important for the Specialization of the specie.

If you want to compare your model of 4 variable with the model of 20 variables, you can extract for example 200 random points of your Region of Interest, and using the probability in each point you can to do a comparison of the models, using a student-t or mann-whitney/wilcoxon test. I have never used the AIC comparison of models (how you do that). The comparison of the models using only the AUC is not recommended by Lobo et al. 2007 (http://www2.unil.ch/biomapper/Download/Lobo-GloEcoBioGeo-2007.pdf), you can try for example another modeling package like MaxLike and Biomapper (this last has a very strong multivariate statistical support) in order to compare you niche. Best regards,

Luís Enrique.

Have a look at our article on bears in Majella, Italy for how we dealt with your issue.

You should note that Harrell Jr. et al. (1996) suggested that no more than m/10 predictors should be included in the final model (where m is the total number of observations).

The leave-one-out approach (Alessandro) results in a few variables defining the distribution model. In our bear research (attached) only 2-3 variables, thus avoiding the overfitting that the rule of Harrell (Ali) aims to avoid. And the simpler a model, the better.

PCA mostly reduces the number of required variables to maximally 3 (Patrick). However, sometimes the PCs are more difficult to interpret ecologically than the primary variables.

The BioClim variables may be less suitable for fine-resolution distribution modelling when the number of meteorological point data underlying the extrapolation is small compared to the topographic climatic variation, as we reported in the same paper.

Article Where the bears roam in Majella National Park, Italy

I was following this interesting discussion! But  so far could figure out how do PCA on WORLDCLIM variables! From the technical perspective and after extracting 2-3 axes how model the potential distribution on that?! Any packages exist for these steps? Thanks in advance for your help!    

HI! I have the same question

I read the beautiful paper that Hein Van Gils suggested (Where the bears roam in Majella National Park ) and I want to make sure I understood the method...

You followed the hierarchical procedure, so you make a model in Maxent first, and choose to obtain the contribution values of each variable. Then you selected the ones with the higher % of contribution (successful predictors) to create a new model with less variables, an reducing the risk of over fitted models?

dear colleague, yes we followed the hierarchical approach as you outline above in our bear article (and in case you are more a plant than an animal ecologists, for plants as well in an earlier paper); others have done so before; what we did different is to divide the set of environmental variable into three subsets. climate, biophysical-without-climate (terrain and vegetation) and anthropogenic (in accordance with ecosystem theory and landscape ecological principles). We believe that our double hierarchical approach brought us additional ecological insights compared to enter the entire set only. For example climate variables would mostly not survive the step-wise elimination process using for the entire set of variables. For further examples of such insights please refer to the article.

Another uncommon approach we used was to subdivide the species presence points by season and run the maxent model per season; also this brought us new knowledge on our highly mobile species.

If you are only interested in the model, and not in the interpretation of variables that contributes to the model, you can use them all at once. There will be no difference in the predicted model.

Hi Carlos,

In my published experience, say feed 10 variables (co-variates; predictors) across the ecosystem components into the SDM, the AUC (or AIC) of the resulting SDM may be practically the same as after removal of the lesser predictors, the variables too many for  interpretation (as you highlighted), the response curves (helpful component of maxent) different, further minimizing interpretation potential (attached for response curves). Further, some SDM algorithms have been shown to be less transferable to other areas with a relative large number of environmental variables.

Hi Patrick

Yes, climatic variables are often highly correlated, negatively or positively; and removal of correlated variables is good from several perspectives; one is that in science the simple (less variable) solution is the better; empirical reasons are provided above; the real question is how to select which of the two correlated variables; the attached provide my approach, but in my other papers I have used other approaches as well, but found them less satisfactory.

My main point is however, that WorldClim is based on a double-biased data set; meteorological stations are distributed very uneven over geographic and environmental space and WorldClim has selected the stations with freely accessible data (e.g. airports) that also far from randomly distributed. Of course you will get a results with WorldClim data only, but it is unlikely to be meaningful from a fundamental or practical purpose. The limitations of using WorldClim only is less apparent at coarse resolution, but at fine ones failings become obvious (attached). For climate, I would use an measured proxy rather than an extrapolated, biased dataset; vegetation (phenology) as estimated by several remote sensing means, for example.

Article Where the bears roam in Majella National Park, Italy

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

Dear Pankai,

I am not expert in this respect, I do my first steps, but it seems you could use the SDM toolbox for reducing variables and exclude the high correlated ones. This tool is free, but match only for ArcGIs (ESRI) versions more than 10. There is a manual for using this tool as well.

Dear Pankaj,

ENMTools (http://enmtools.blogspot.in/) may help you in choosing the appropriate number of variables and data points. 

Regards

Following this discussion, Can we use only one climate variable in Maxent as predictor?

I think you can. But I cannot think in any example (taxa) for which that would be meaningful. 

Yasmin, there is no problem in using multiple climate variables as predictors in Maxent, so long as they are not highly correlated. This is where you can use something like ENMTools' 'correlation' tool to test for correlation and then select a subset of non-correlated climate variables (you will need to select a correlation threshold). Often, expert opinion on species ecology is used to inform the final selection of non-correlated predictor variables.

Thanks for recommendation of ENMTOOLS

Hello! If you're not interested in evaluating the species response curves to environmental variable, you could reduce the variables using a factorial analysis, like a NMDS, for instance, and then project the species distribution to the resulting dimesnions. I did that in a study that is under review. I think it could be a solution!

I am trying to remove highly correlated variables using SDM toolbox(Explore climate data).

I added climatic variables as per their decreasing importance and in the end Elevation and LULC layer, but model shows failed execution.

Please suggest solution to this.

Hi Seema, I recommend looking at the SDMtoolbox Google group for answers to your question. The SDMtoolbox author Jason is very proactive at answering questions and troubleshooting, but be sure to read the first post on self help before posting your question. I'd suggest being more specific i.e. what is the exact error message that you're getting?

https://groups.google.com/forum/#!forum/sdmtoolbox

Hi,

I'm currently trying to use Maxent for roadkill analysis, but one of my colleagues raised a question that using spatially correlated datasets in maximum entropy models leads to biased results and the dataset should be tested and correlated occurrences removed.

I have no clue how to test roadkill point dataset for spatial autocorrelation to get rid of correlated points. What's the easiest and the most common way to determine which points need to be removed to avoid the bias? 

If you know / have any information / articles / website for me to look over, please advise on this. 

Your direct advise to solve this issue is greatly appreciated. 

Best,

Bryan 

If you are using bioclimatic variables you should probably eliminate BIO8 and BIO9 (mean temperature of the wettest quarter and mean temperature of the driest quarter) right off the bat because they can be nonsensical for many study areas (see the attached picture) and can produce some odd-looking maps. I would also consider eliminating BIO 16 - 19 because the precipitation regime of a particular area may not coincide with quarters (Jan-Mar, Apr-June, July-Sept, Oct-Dec). That leaves 13 bioclimatic variables. I would recommend the correlation matrix approach keeping either a) the variable that makes the most biological sense or b) the easier to interpret variable. Also, be aware that elevation/altitude will make it difficult to transfer your models into the future or the past because essentially elevation will "lock in" those sites to their present-day locations. I would advocate against including elevation.

Hi Seema and Hoehun,

Your questions are somewhat separate from the original question by Pankaj because they have to do with sampling bias rather than the gridded covariates. The most common approach to dealing with sampling bias is spatial thinning, which can easily be implemented with Jason Brown's SDMToolbox or the ENMEval package in R by Muscallera, Kass, et al. The best paper discussing this issue (in my opinion) is Kramer‐Schadt, S., Niedballa, J., Pilgrim, J. D., Schröder, B., Lindenborn, J., Reinfelder, V., ... & Wilting, A. (2013). The importance of correcting for sampling bias in MaxEnt species distribution models. Diversity and Distributions, 19(11), 1366-1379. However, more research is needed to determine appropriate thinning distances and tools for identifying appropriate thinning distances.