When a species has established itself across a broad geographic range, migrates relatively slowly, and outcrosses with reasonable frequency, isolation by distance is an inevitable outcome. Every time a new haplotype migrates to a nearby area it recombines with the local haplotypes creating organisms of intermediate relatedness. Occasional long-distance migration events may have only weak effects on this continuum, as crossing and back-crossing with local haplotypes would dilute the impact. Aggressively invading haplotypes and selective sweeps can, however, strongly disrupt this process. Both can allow individual haplotypes to spread over much greater distances before being broken apart by the locally established haplotype pools. This is consistent with the pattern that has previously been identified in smaller studies of Arabidopsis thaliana
within regions of Europe and Asia 
A species newly introduced to a region is expected to have a different pattern. As the species spreads across its new range its migration events bring it to previously unoccupied areas. Without established local haplotypes there is no recombination, no intermediate genotypes are formed, and single, un-recombined haplotypes can spread uninterrupted over great distances. As the new range becomes filled with the species, however, isolation by distance will begin to establish itself, first on very local scales and gradually spreading out as recombination creates geographically unique haplotypes and migration and recombination between occupied areas blends them together. These patterns are consistent with our observations. In Eurasia, where Arabidopsis thaliana
has flourished for thousands of years, it has established a strong gradient of isolation by distance. In North America, which has been colonized in the last three hundred years 
, haplotypes are spread across the entire continent but weak isolation by distance is emerging, particularly over shorter distances.
Arabidopsis thaliana is often a human commensal in both North America and Eurasia. The largest difference between its natural history on the two continents is that it has existed across Eurasia for thousands of years and in North America for only a couple of centuries. Human disturbance does not appear to have radically altered its natural population structure in Eurasia and the results suggest that the disturbance in North America is transitory and that a natural form of isolation by distance will emerge over time. This suggests that for organisms like Arabidopsis thaliana human disturbance only has a particularly large effect on population structure when established local populations are small or absent, or when an entire local gene-pool is replaced by artificial migrants. Otherwise, even moderate human disturbance can be swamped out by natural processes.
This kind of continuous isolation by distance is a type of population structure that the field of population genetics is poorly equipped to deal with. While there are several exceptions 
, most of population genetics theory is premised on the existence of discrete populations of exchangeable individuals. Even the modern field of landscape genetics 
is focused on finding discrete regions within continuous habitats that behave like classic populations. Organisms like Arabidopsis thaliana
, however, do not fit such models. With continuous geographic variation the probability of observing a particular set of alleles in an organism depends on the unique location of that organism and the alleles at the next closest organism are expected to have been drawn from a slightly different distribution. Sufficiently fine-scaled lattices of stepping-stone models may approximate many of the important features of this kind of structure, but it is not straightforward to determine the appropriate scale and having too coarse a scale may quickly degrade the numerical results (particularly for populations not at equilibrium) 
. Hierarchical models are particularly inappropriate. The migration rate is low compared to the outcrossing rate, which very quickly (on a scale generally less than a kilometer) creates a geographic blend of alleles and extremely rich pools of local haplotypes. There is no bifurcating process to be uncovered (Figure S4
, Figure S5
, Text S1
). To accurately estimate effective population size, gene flow, recombination, and natural selection in populations exhibiting continuous variation it will be necessary to reexamine the often over-looked theory of spatial genetics and develop new methods. A recent review of the subject 
suggests several promising approaches.
For researchers using Arabidopsis thaliana
as a model organism for ecological and evolutionary studies this paper provides several lessons and raises several new questions. One important point is that it is necessary to recognize that both genotype and environment are expected to vary spatially. Any study of local adaptation or gene by environment interaction should expect to find correlations between genotypes and environments simply through spatial correlation. Study design and analysis must take this into account and show that similarities between plants separated by a given distance within environments are greater than those at similar distances but between environments. Another point is that in terms of genetic diversity, Arabidopsis thaliana
needs to be thought of as a sexually reproducing species: the difference between outcrossing and highly selfing organisms is quantitative rather than qualitative. Each plant in the wild may contain multiple hybrid siliques. While the vast majority of individual seeds are self-fertilized, the outcrossing rate is sufficient to introduce considerable genetic recombination after just a few generations. This will help make natural samples of Arabidopsis thaliana
a powerful research subject for genome-wide association studies and linkage mapping 
, but create difficulties in reconstructing even fairly recent phylogeographic events such as the colonization of North America (let alone older events such as the re-colonization of Eurasia after the most recent ice age). Future studies using higher-density marker sets will have considerably more power to address these questions.