Looks good! Although this is already implied, it may be worth, to include a slide highlighting that naively we would use randomness as a null model, as is done frequently in most areas of statistics and in population genetic models (panmictic populations). One would then test for IBD as significant departure from randomness. In Landscape genetics, however, IBD is the starting point and needs to be built into the null model so as to test for significant departures related to landscape.

Dear Helene and Rolf -

Nice set of slides with good explanation of underlying assumptions in population genetics and how to think about in them in a landscape context. 

I think we should be thinking of randomness as the true null.  It is true that spatial structure has to be present in order to model landscape process (if there is not structure, then this is not possible).  So an underlying assumption with a landscape genetics study is that there is some spatial structure in the data.  However, distance (as a process) is not required in order to get spatial structure.  IBD implys that the resulting pattern (or some portion of it) is actually the result of some distance die-off.

Especially at fine scales, there may be spatial structure that is not the result of distance limitations.  What I mean is that without some landscape feature/process, the study area would be random (panmixia).  If we were to test IBD, we would get a significant result (assuming that the landscape feature(s) are autocorrelated).  But this result is misleading ("false autocorrlation", Legendre et al 2002) in that distance among individuals is not actually the process generating the observed pattern.  We demonstrated this in our Ecography paper (Murphy et al 2008) and I believe Niko saw the same result in his Ecography in press paper.

If we see spatial structure, it could be the result of one of three general hypotheses: 1) distance (distance die-off in probability of migration), 2) landscape feature(s)/process or 3) distance and landscape.  Although it is very likely and logical that distance is a factor, assuming that is must be present (as the actual generating process) in order to have landscape genetic structure is potentially misleading.

I'm think I agree with both of you.  IBD-like patterns can arise from purely spatial influences on gene flow, but also from environmental heterogeneity. 

Thinking about the underlying processes, panmixia should lead to spatial-genetic randomness, because all possibe pairs of mating partners in the study area have an equally likely chance of actually mating (i.e., successful mating between individuals is not dependent on their relative locations).  Thus, panmixia is a null, and one might consider IBD a deviation from this null, because it arises in situations where successful mating is more likely among individuals that are close in (environmental) space. 

On the other hand, panmixia is not a realistic null-model in an ecological sense, because it is highly unlikely that mating in natural populations really is spatially random.  (Aside fom the fact that space use of related individuals can really mess up our statistical analysis).  Thus, we will very often conclude that our data does not conform to the "expected null", simply because the null is only valid in theory.

So, maybe we need to distinguish between analytical and ecological null models?