[R-sig-eco] headache

[Yorick.Reyjol at mrnf.gouv.qc.ca]

Hello my dear fellows,

I would have a complicated -but not unusual- problem to offer you, as it is present in my mind for several months but I do not really succeed in handling it. It concerns the appropriate statistical treatment to use when dealing with a complex nested sampling design (we often have this in ecology!).

Here I go:

My data concern fish populations (trout) in streams of SW France. My sampling design is built according to four spatio-temporal scales of variation (why did I do this! sic…): 
  - Type of flow (natural vs. regulated section);
  - Type of micro-habitat (riffle vs. pool);
  - Year (2000 and 2001);
  - Season (Fall, Winter and Spring);

Each sampling site corresponds with one micro-habitat sequence (riffle-pool) in a given type of flow. One sample therefore corresponds with trout abundance (i.e., number of individuals) in a given type of micro-habitat and flow, for a given season of a given year (e.g. trout abundance in the riffle of a regulated section during summer of year 2001). My purpose is to predict trout abundance as a function of these four spatio-temporal scales of variation.

The first point I would need your confirmation -or not- is that as I have only one value of trout abundance for each combination of the modalities of the four spatio-temporal scales, I can only test for single effects but not for interaction among factors. Am I right?

The second point is that I think I should orientate toward mixed models as I have nested spatial (i.e., type of micro-habitat nested within type of flow) and temporal (i.e., season nested within year) scales. Am I still right and is it possible given point 1?

In this mixed model framework, my third point is the following one: is it better to consider that I have nested temporal scales (i.e. season nested within year) or to treat this as a repeated measure case? Is there a fundamental difference -in a statistical sense- between the two options? Another possibility could be to consider that type of microhabitat is nested within type of flow, itself being nested within season nested within year. But is it relevant to nest spatial scales in temporal scales (or conversely)?

Fourth, and perhaps most difficult, how do I handle the same case but in a multivariate scheme (e.g. redundancy analysis with restricted permutations test)? Is it possible to "translate" univariate mixed models into multivariate analyses? I know, for having doing in by myself, that it is possible in the case of a nested sampling design (e.g. sampling sites within different tributaries, see Reyjol et al. 2008 CJFAS) to handle the problem with RDA, but what about the case of you have such a complex sampling design with both nested spatial and temporal scales of variation or repeated measures, such as the one described here, which is typical of community ecology? Is it necessary to build covariate matrix for each single factor and to perform restricted permutations? That seems to me very difficult given the number of scales...

Fifth and last: are your answers would have been the same if I would have had more than only one value of trout abundance for each combination of the modalities of the four spatio-temporal scales (question 1)?

I sincerely thank you for your help, and hope I was enough clear, but this is a classical problem not really easy to solve, and usually not frontally tackle.

Cheers,

Yorick Reyjol, Ph.D.
Ministry of Natural Resources, Quebec, Canada