You might look at generalized additive models (GAM)s or generalized additive mixed models (GAMMS) possibly

Spatio-temporal hypothesis may be modelled and tested using STEM approach and software: https://code.google.com/p/d-stem/

well really depends upon the nature of data collected. You can see time-series analysis if the data is taken at intervals. R statistical package is very useful in this regard (package tseries)

These two papers may be of interest to you if you are looking for ordination techniques such as PCA or Factor analysis

• Malik RN, Nadeem M [2011]. Spatial and temporal characterization of trace elements and nutrients in the Rawal Lake Reservoir, Pakistan using multivariate analysis techniques. Environmental Geochemistry and Health, 33[6]:525-41.

• Qadir A, Malik RN and Husain SZ [2008]. Spatio-temporal variations in water quality of Nullah Aik-tributary of the River Chenab, Pakistan. Environmental Monitoring and Assessment, 140:43-59.

I don't know if this is useful to you, but have a look to the work of Ethan P. White (University of New Mexico, Albuquerque, NM, USA) on spatio temporal scaling of biodiversity.

Depends on what you're interested in exactly, and the nature of the data indeed (high vs low frequency?...)

You can for example detrend the data and then explore the anomalies (as in http://www.pnas.org/content/104/38/14889.full.pdf, for example).

Another possibility is to work with a moving window (as we did for a short time series in Vicca et al 2009, Geobiology).

Wavelet analysis is another tool that has been used by for example Vargas et al., 2011. On the multi-temporal correlation between photosynthesis and soil CO2 efflux: reconciling lags and observations; New Phytologist).

Thanks everybody! Actually, we are going to work on a couple of different datasets and I think all your suggestions can apply. For one project we have on one hand biodiversity data with relatively low frequency, whereas for other purposes we should analyse photosyntetic efficiency vs. environmental and spatial predictors at 10 periods. I know more or less how to manage spatial variability, but I have to look at your suggestions for integrating the temporal variability.

I guess you'll have to be careful with collinearities then (when environmental and spatial variables covary, and vary over time). A tool that I found useful for dealing with collinearities was stepwise regression analysis (as applied in Vicca et al., 2012; Ecology Letters where we analyzed the NPP:GPP ratio of forests). If you use it, don't forget to calculate the variance inflation factor (VIF), which gives you an indication for the collinearities of the different predictor variables.

Another useful (and easy) tool for exploring which predictor variables are related to the dependent variable is a regression or classification tree.

Multivariate analysis PCA, Discriminant analysis, cluster analysis, dendogram depictions are possible options for spatio and temporal anaysis.

For joint depictions contour plots could be applied.