If you are looking at just distribution modelling and not dispersal, you won't need the duplicate records, the fact that the same or (very close) points are sampled as presences at different times gives you assurance that your presences are more accurate, as clearly the case is still found there. but leaving duplicate points in the modelling process will only inflate your model accuracy, as it is calculated on the basis of how many presences you got right in your prediction, and including the duplicates will only either exaggerate or deflate the model accuracy based on whether those points were predicted accurately or not. So if you are using Maxent (or any model for that matter), I'd suggest removing duplicates and be very careful not to use Maxent for a big study area, like regional or global studies. MAXENT being a presence -only model it is not best for extrapolating into new areas (this is a problem for all models, but it is accentuated with presence-only models as they are only based on presence information and no absence data).

I also suggest reading

1) Phillips, S. J., Anderson, R. P., & Schapire, R. E. (2006). Maximum entropy modeling of species geographic distributions. Ecological Modelling, 190(3–4), 231-259.

2) Phillips, S. J., & Dudík, M. (2008). Modeling of species distributions with Maxent: new extensions and a comprehensive evaluation. Ecography, 31(2), 161-175. doi:10.1111/j.0906-7590.2008.5203.x

3) Elith, J., Phillips, S. J., Hastie, T., Dudík, M., Chee, Y. E., & Yates, C. J. (2011). A statistical explanation of MaxEnt for ecologists. Diversity and Distributions, 17(1), 43-57. doi:10.1111/j.1472-4642.2010.00725.x

4)Royle, J. A., Chandler, R. B., Yackulic, C., & Nichols, J. D. (2012). Likelihood analysis of species occurrence probability from presence-only data for modelling species distributions. Methods in Ecology and Evolution, 3(3), 545-554. doi:10.1111/j.2041-210X.2011.00182.x

Environmental data: you can use variables that you believe affect the species you are modelling, in this case you are looking at a mosquito so i'd imagine, temperature, rainfall, moisture, and if you have it topographic features, that prob. show swampy areas? but with asian tiger mosquito...that is not the case as they are container breeders, so you might want to include urban areas too..if you want a fine scale distribution. for global prediction you can look at the bioclimatic variables found http://www.worldclim.org/bioclim for 19 variables with temp, and rainfall derived data... or https://www.climond.org/ for 35 variables derived from temp. rainfall, mositure and radiation. they have datasets with resolutions at 30', 10", and 30" depending on the dataset.

Thanks for your answers, but "duplicated" points are not just presence data of the specie, actually this points are quantity of the captured mosquitoes that varies with time so I`m trying to evaluate possible associations between this variation in time and space, and the occurence of Dengue cases (georeferenced as well), temp, rain, etc., in an overlapping time period.

With correlative models like MAXENT, the quantity really doesn't tell you much (in that case you better find programs that take species abundance into consideration) with correlative models its not density that matters it is knowing for a fact that the species is established there and it finds that locality environmentally suitable. From then on it’s all the model's work to extract environmental information from those points and find areas that environmental match these conditions in the rest of your study area.

In any way what I believe you can do is.

1) Take geo-referenced species presence points from your time step and do a prediction map.

2) Separately make a map of the Dengue incidence

3) Overlay and compare the species distribution on 1 to the Dengue incidence map on step 2

Repeat step 1-3 for all your time steps.

make inference based on your overlay analysis if the vector presence maps from these time steps show a trend of increasing Dengue incidence ... if these two events match spatially , provided that your distribution model is fairly (accurate) and that your Dengue incidence data is also accurate, then you can discuss the correlation or the lack thereof between these two events.

One idea might be to use the observation data to train a classifier by fitting an abundance model to the environmental variables. You could use various machine learning techniques to fit the model, e.g. random forest or neural nets. The classifier would learn from the available observations to use the environmental variables to predict the likelihood of presence at a particular place and time. This might allow you to measure the importance of each of the environmental variables in the model. With cross-validation (holding back some of the data from the training phase and trying to predict it with the resulting model) you could assess how predictive the environmental variables are.

Thank you for all your answers. The overlay analysis is an interesting idea, but how do you evaluate the statictical significance of these observations in the different time periods? with just a mean comparation analysis? there`s some kind of analysis that consider the abundance (not just the presence) of the specie that could evaluate the correlation with this kind of incidence variable?

If you Google community species distribution or niche models you will find models that take abundance and species richness and that sort of density related information, sorry I’ve not worked with community models so can't help there. BUT unless you have a logical reason to believe that the population established have been eradicated ever since, if you knew for sure that the population was established when you took it into analysis, the assumption should most likely be that the population still exists. It might require a bit more info digging on your part whether you use abundance based model or not, to make sure all the populations are still reported to be present in those locations. One easy place to see this is the GBIF portal, Google it, it is a global biodiversity database, you will find datasets full of information on most insect species, date of collection, sighting etc…... just make sure to cite them as they are doing an excellent job for all of us :). You are right, correlation is not causation..., but in cases like this with a vector-pathogene relationship if the disease increased when the vectors number increase I would say it is a straight forward cause and effect, unless I got your question wrong (and/or unless other effects like treatment, or eradication control interfered with the interaction)