Prior to divergence, we find a 10-fold decline in the global joint ancestral population ( Table S3 ). Polar bears declined in population size after the split from brown bears, although we were unable to confidently estimate the timing of the bottleneck. However, both the IBS tract method and ∂a∂i indicate that the population size decrease in polar bears was either of a greater magnitude or of a longer duration than in brown bears, in agreement with our other indicators of relative population sizes.

We find evidence of smaller long-term effective population sizes in polar bears than in brown bears ( Figure 2 A). Genetic diversity is a function of effective population size, and the number of private SNPs in polar bears (2.6 million, Figure S1 B) is about one third of that in brown bears (7.7 million, Figure S1 C). Similarly, patterns of linkage disequilibrium (LD) can be informative about demographic history () and we find a slower rate of LD decay in polar bears ( Figure S3 A).

(B–E)PCA of (B) 79 low-coverage polar bears (the gray insert is a blow up of the individuals in the smaller dashed square); (C) 18 high-coverage polar bears from West and East Greenland; (D) ten high-coverage brown bears; (E) 79 low-coverage polar bear using a novel method which takes genotype uncertainty into account ( https://github.com/mfumagalli/ngsTools ). Samples from West (WG) and East Greenland (EG) are indicated. For sample details, see Table S2 . See also “Population Diversity, Structure, and Linkage Disequilibrium” Extended Experimental Procedures

(A–C) Joint demographic model for polar bear and North American brown bear populations inferred using the IBS tract method (A). Joint past population is in gray, polar bear in blue and brown bear in brown. Estimated effective population sizes are indicated and the migration rate is in genetic replacements per generation. The recent brown bear population size has been downscaled by a factor of 20, the recent polar bear population size is to scale. (B), (C) Distribution of IBS tract length from our observed data (solid line) and from model prediction (dotted line) inferring gene flow from polar bear into brown bear (B) or using a simple isolation-with-migration (IM) model (C), which does not account for past population size changes. There are only two black dotted curves in (C) because the IM model constrains the within-polar bear and within-brown bear tract lengths to be the same. See also Figure S4 B and Table S3

To infer the joint demographic history of polar bears and brown bears, we used a novel method based on identity by state (IBS) tracts of DNA shared within and between populations () and ∂a∂i (diffusion approximation for demographic inference []), which infers demographic parameters based on a diffusion approximation to the site frequency spectrum. The two models differed in their individual parameter estimates ( Table S3 ), in part reflecting the fact that the IBS tract method uses both recombination rate and mutation rate, and ∂a∂i uses only the latter. However, despite the inherent uncertainty in the genome-wide mutation rate estimate, which we calibrated using deep fossil divergence dates ( Figure S2 A), the estimates from the two models are in fact quite similar with regards to divergence time, relative effective population sizes, and direction of gene flow.

(C) Phylogenetic tree of mitochondrial genomes, using black bear as an outgroup. GenBank accession numbers of published sequences included in the analysis are included (after the underscore). For sample details, see Table S2

(B) Phylogenetic tree of polar and brown bear nuclear genomes, based on 9,597,347 SNPs and using giant panda as an outgroup; the 95% confidence intervals of the internal divergence times are included.

(A) Phylogenetic tree based on 5,990 single-copy orthologous genes, using the 4D sites of the whole coding regions. The nodes leading to horse, cat and dog, show the two internal fossil calibrations used in the analysis (black hollow circles). The 95% confidence interval of split time is indicated.

The timing of polar bear origin coincides with Marine Isotope Stage (MIS) 11. MIS 11 was a warm period, which spanned ca. 424–374 kya. It was the longest interglacial in half a million years () and lasted almost 50 kyr (). The period was associated with a substantial decrease in Greenland ice-sheet volume; DNA from the basal part of the Dye 3 ice core from southern central Greenland () and abundant spruce pollen from the shore off southwest Greenland () both suggest that boreal coniferous forest developed at least over southern Greenland. Such a prolonged interglacial could have enabled an ancestral brown bear population to colonize northern latitudes that were previously uninhabitable for the species, setting the stage for future allopatric speciation, as subsequent climatic and environmental change caused population isolation ().

We assessed the effect of using our more complex demographic models versus simpler models by analyzing our data using a simple isolation-with-migration model similar to that used byand. The procedure yielded an older divergence date in the range of 1.6–0.8 Mya ( Table S3 ). However, we found that our complex model with a more recent divergence time estimate was a better fit to our empirical data ( Figures 2 B and 2C). Discrepancies between our divergence date and previous genomic estimates highlight the impact of accounting for past population size changes on divergence time estimates, suggesting that models that do not account for past population size changes have the potential to overestimate divergence times (e.g.,).

To reliably estimate when polar bears and brown bears diverged, we used the IBS tract method () and ∂a∂i (), which both take past population size changes into account. The approaches indicated that the two species diverged only ca. 479–343 kya ( Figure 2 A, Table S3 ). Because genotyping errors appear as singletons and given that in both methods singletons lead to increasing divergence time estimates, we can conclude that the polar bear likely emerged closer to the lower bound of our estimate. Our date greatly decreases the age of polar bear origin and agrees with fossil evidence ().

Gene Flow between Polar Bears and Brown Bears after Divergence

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Cahill et al. (2013) Cahill J.A.

Green R.E.

Fulton T.L.

Stiller M.

Jay F.

Ovsyanikov N.

Salamzade R.

St John J.

Stirling I.

Slatkin M.

Shapiro B. Genomic evidence for island population conversion resolves conflicting theories of polar bear evolution. Based on the IBS tract method, we find strong evidence of continuous gene flow from polar bears into North American brown bears after the species diverged ( Figure 2 A, Table S3 ). We used the IBS tract method to compare likelihoods of two scenarios with parsimonious one-way gene flow, finding that gene flow from polar bears to North American brown bears explained the data better than the reverse scenario ( Figures 2 B, S4B, Table S3 ). In the former scenario, we estimate a migration rate of 0.0018% genetic replacement per generation. As a complementary approach, we used ∂a∂i to infer the parameters of a model with asymmetric two-way gene flow between polar bears and North American brown bears. With this approach, we observe nonzero migration in both directions but infer a substantially higher migration rate in the polar-to-brown bear direction ( Table S3 ). These results suggest that the major direction of introgression has historically been from polar bears into North American brown bears, in agreement with