A multiscale landscape genomics analytical framework to identify local adaptive variation in the Buckler Mustard.
The question of finding an appropriate scale to study adaptation emerged only recently in landscape genomics, while in landscape ecology its components (extent and resolution or grain) have been addressed in many papers [1-3]. In fact, in landscape genetics only a couple of studies have considered different extents to study adaptation - Manel et al.  for example - but the spatial resolution of environmental variables was not considered. However, when these variables are derived from digital elevation models (DEMs), the question of resolution becomes crucial. Here we used a signal processing generalization technique to produce DEMs a multiple scales allowing for a continuous representation of the landscape. We then investigated the adaptive response of the buckler mustard (Biscutella laevigata L.) to solar radiation with the help of environmental variables derived from these DEMs.
Data and methods
Firstly, we produced a set of 266 AFLP markers in 361 individuals sampled and georeferenced on the ridge of “Les Rochers-de-Naye” in the Swiss Prealps (fig.1). Secondly, we acquired a very high resolution DEM (0.5m) for the same area. On the latter, we applied a multilevel spline generalization algorithm  implemented in SAGA GIS  to compute DEMs at resolutions of 1m to 32m with intervals of 1m. Thirdly we produced solar radiation variables (direct, diffuse and total), also in SAGA GIS (fig.1), at all resolutions and extracted their values at the coordinates of the sampling locations . Finally we used a correlative method based on generalized linear models  to calculate univariate association models between the genetic markers and the variables.
We found no significant models involving different solar radiation variables with the highest resolutions. In fact, most associations showed their strongest p-value at resolutions between 16 and 26m. Among the most significant associations, some show a gradually decreasing p-value coming along with coarser resolutions (see fig.2a). Other relationships are not significant (constant low p-value through resolutions) with a significant peak at 2 or 3 successive resolutions (fig.2b). In total, 98 models were significant with a 99% confidence level involving 14 different markers (5.3% of the 266 markers).
Although these results are preliminary, they show that resolution matters at a local scale and that a higher resolution does not imply a stronger association. However, the interpretation of an optimal resolution is tricky, particularly because of the high variability of significance from one resolution to the other. It is also important to remind that correlative approaches have been shown to generate a high rate of false positives , and that among significant models, they are not able to disentangle selection from demographic processes .
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