In many species a fundamental feature of genetic diversity is that genetic similarity decays with geographic distance; however, this relationship is often complex, and may vary across space and time. Methods to uncover and visualize such relationships have widespread use for analyses in molecular ecology, conservation genetics, evolutionary genetics, and human genetics. While several frameworks exist, a promising approach is to infer maps of how migration rates vary across geographic space. Such maps could, in principle, be estimated across time to reveal the full complexity of population histories. Here, we take a step in this direction: we present a method to infer maps of population sizes and migration rates associated with different time periods from a matrix of genetic similarity between every pair of individuals. Specifically, genetic similarity is measured by counting the number of long segments of haplotype sharing (also known as identity-by-descent tracts). By varying the length of these segments we obtain parameter estimates associated with different time periods. Using simulations, we show that the method can reveal time-varying migration rates and population sizes, including changes that are not detectable when using a similar method that ignores haplotypic structure. We apply the method to a dataset of contemporary European individuals (POPRES), and provide an integrated analysis of recent population structure and growth over the last ∼3,000 years in Europe.

The island of Sardinia has been of particular interest to geneticists for decades. The current model for Sardinia's genetic history describes the island as harboring a founder population that was established largely from the Neolithic peoples of southern Europe and remained isolated from later Bronze Age expansions on the mainland. To evaluate this model, we generate genome-wide ancient DNA data for 70 individuals from 21 Sardinian archaeological sites spanning the Middle Neolithic through the Medieval period. The earliest individuals show a strong affinity to western Mediterranean Neolithic populations, followed by an extended period of genetic continuity on the island through the Nuragic period (second millennium BCE). Beginning with individuals from Phoenician/Punic sites (first millennium BCE), we observe spatially-varying signals of admixture with sources principally from the eastern and northern Mediterranean. Overall, our analysis sheds light on the genetic history of Sardinia, revealing how relationships to mainland populations shifted over time.

The population of the Mediterranean island of Sardinia has made important contributions to genome-wide association studies of complex disease traits and, based on ancient DNA studies of mainland Europe, Sardinia is hypothesized to be a unique refuge for early Neolithic ancestry. To provide new insights on the genetic history of this flagship population, we analyzed 3,514 whole-genome sequenced individuals from Sardinia. Sardinian samples show elevated levels of shared ancestry with Basque individuals, especially samples from the more historically isolated regions of Sardinia. Our analysis also uniquely illuminates how levels of genetic similarity with mainland ancient DNA samples varies subtly across the island. Together, our results indicate that within-island substructure and sex-biased processes have substantially impacted the genetic history of Sardinia. These results give new insight into the demography of ancestral Sardinians and help further the understanding of sharing of disease risk alleles between Sardinia and mainland populations.

34Recent ancient DNA studies of western Eurasia have revealed a dynamic history of admixture, 35 with evidence for major migrations during the Neolithic and Bronze Age. The population of the 36 Mediterranean island of Sardinia has been notable in these studies -Neolithic individuals from 37 mainland Europe cluster more closely with Sardinian individuals than with all other present-day 38 Europeans. The current model to explain this result is that Sardinia received an initial influx 39 of Neolithic ancestry and then remained relatively isolated from expansions in the later Ne-40 olithic and Bronze Age that took place in continental Europe. To test this model, we generated 41 genome-wide capture data (approximately 1.2 million variants) for 43 ancient Sardinian individu-42 als spanning the Neolithic through the Bronze Age, including individuals from Sardinia's Nuragic 43 culture, which is known for the construction of numerous large stone towers throughout the is-44 land. We analyze these new samples in the context of previously generated genome-wide ancient 45 DNA data from 972 ancient individuals across western Eurasia and whole-genome sequence data 46 from approximately 1,500 modern individuals from Sardinia. The ancient Sardinian individuals 47 show a strong affinity to western Mediterranean Neolithic populations and we infer a high degree 48of genetic continuity on the island from the Neolithic (around fifth millennium BCE) through 49 the Nuragic period (second millennium BCE). In particular, during the Bronze Age in Sardinia, 50 we do not find significant levels of the "Steppe" ancestry that was spreading in many other parts 51 of Europe at that time. We also characterize subsequent genetic influx between the Nuragic 52 period and the present. We detect novel, modest signals of admixture between 1,000 BCE and 53 present-day, from ancestry sources in the eastern and northern Mediterranean. Within Sardinia, 54 we confirm that populations from the more geographically isolated mountainous provinces have 55 experienced elevated levels of genetic drift and that northern and southwestern regions of the 56 island received more gene flow from outside Sardinia. Overall, our genetic analysis sheds new 57 light on the origin of Neolithic settlement on Sardinia, reinforces models of genetic continuity on 58 the island, and provides enhanced power to detect post-Bronze-Age gene flow. Together, these 59 findings offer a refined demographic model for future medical genetic studies in Sardinia.60

The population of the Mediterranean island of Sardinia has made important contributions to genome-wide association studies of traits and diseases. The history of the Sardinian population has also been the focus of much research, and in recent ancient DNA (aDNA) studies, Sardinia has provided unique insight into the peopling of Europe and the spread of agriculture. In this study, we analyze whole-genome sequences of 3,514 Sardinians to address hypotheses regarding the founding of Sardinia and its relation to the peopling of Europe, including examining fine-scale substructure, population size history, and signals of admixture. We find the population of the mountainous Gennargentu region shows elevated genetic isolation with higher levels of ancestry associated with mainland Neolithic farmers and depleted ancestry associated with more recent Bronze Age Steppe migrations on the mainland. Notably, the Gennargentu region also has elevated levels of pre-Neolithic hunter-gatherer ancestry and increased affinity to Basque populations. Further, allele sharing with pre-Neolithic and Neolithic mainland populations is larger on the X chromosome compared to the autosome, providing evidence for a sex-biased demographic history in Sardinia. These results give new insight to the demography of ancestral Sardinians and help further the understanding of sharing of disease risk alleles between Sardinia and mainland populations.