  Patterns of isolation-by-distance arise when population differentiation
increases with increasing geographic distances. Patterns of
isolation-by-distance are usually caused by local spatial dispersal, which
explains why differences of allele frequencies between populations accumulate
with distance. However, spatial variations of demographic parameters such as
migration rate or population density can generate non-stationary patterns of
isolation-by-distance where the rate at which genetic differentiation
accumulates varies across space. To characterize non-stationary patterns of
isolation-by-distance, we infer local genetic differentiation based on Bayesian
kriging. Local genetic differentiation for a sampled population is defined as
the average genetic differentiation between the sampled population and fictive
neighboring populations. To avoid defining populations in advance, the method
can also be applied at the scale of individuals making it relevant for
landscape genetics. Inference of local genetic differentiation relies on a
matrix of pairwise similarity or dissimilarity between populations or
individuals such as matrices of FST between pairs of populations. Simulation
studies show that maps of local genetic differentiation can reveal barriers to
gene flow but also other patterns such as continuous variations of gene flow
across habitat. The potential of the method is illustrated with 2 data sets:
genome-wide SNP data for human Swedish populations and AFLP markers for alpine
plant species. The software LocalDiff implementing the method is available at
http://membres-timc.imag.fr/Michael.Blum/LocalDiff.html
