England from the Neolithic to Today: Gaussian-Process Match Maps

Where do contemporaneous genomes that resemble people of England come from? Fourteen groups of 6 to 32 persons are read in seven periods, from the Neolithic to the present day: Hazleton North and England Neolithic, England Beaker and England Middle Bronze Age, England Early and Middle Iron Age, two Roman-period groups, England Anglo-Saxon and England Viking Age, two groups from medieval to early modern Cambridgeshire, and Modern English from Kent and from Cornwall and Devon. Each person is placed on a spatio-temporal Gaussian-process map at their own date, following the principle of Mobest¹, on four PCA coordinates of 12,990 ancient individuals, and the map of a group is the mean of its individual maps. Of the probability that falls on land, the largest or joint-largest share goes to France for the Neolithic, Iron Age and present-day groups, to Germany for the Bronze Age groups, to Poland for the Roman-period groups and to Russia for the early medieval and Cambridgeshire groups. The share of persons whose single most similar place lies inside Britain and Ireland ranges from 0 % to 47 % between groups, and 34 % to 51 % of the probability falls on sea cells. The method is an exploratory own implementation of the Mobest principle. Peaks follow where DNA has been sampled, not necessarily where people lived.

A PCA position says whom a person resembles, not where they lived. Mobest¹ turns this into a map: for a person at a given date, it asks in which places contemporaneous genomes resemble them. This article asks the same question for 14 groups of people from England, in seven periods from the Neolithic to the present day, and reports the result as shares of the map by country.

The maps are an own Gaussian-process implementation following the principle of Mobest¹; they are not made with the Mobest software, and they are neither PANE nor qpAdm. Each person is placed separately at their own date. A Gaussian-process regression over space and time (kernel exp[−(Δs²/800² + Δt²/800²)], that is 800 km and 800 years) models four PCA coordinates: the Nexju N25 European PC1 and PC2 and the Nexju N25 Middle-Eastern PC1 and PC2, which stand in for the West-Eurasian and the European PCAs of the Mobest paper. The training set is 12,990 ancient individuals of the AADR v66 (29.9–70 °N, −24–70 °E, 150–8500 BP, at least 15,000 SNPs, one version per person) within a window of ±2000 years around the person.

The nugget differs between the maps (Table 1). On the Neolithic map it was fitted by marginal likelihood; on the six later maps it is stated as a value (0.3, 0.4 or 0.6), and the variance of each coordinate was fitted by marginal likelihood on a random subset of 5,008 reference individuals of the training window (6,653 to 9,727 individuals, depending on the map).

The map shows, for each cell, the probability that the person's PCA position belongs to that cell (product of normal densities, normalised to 1 over the whole map). It is computed on a 40 km grid without land mask and smoothed to 10 km by cubic interpolation. On the six later maps, colours are shown on land only; sea cells are computed and normalised but left blank, and white triangles mark the sampling sites of the persons shown (for the present-day groups, the sampling districts of the Nexju annotation). The map of a group is the mean of the maps of its persons. A group written as n=30 of N is shown as a random sample (seed 7) of 30 of the N persons of the group. The persons shown are excluded from the reference (294 on the six ancient maps, 64 on the present-day map); on the ancient maps other English samples remain. Shares by country refer to land only.

On the present-day map, England itself is empty by construction: all 1000 Genomes British and English genomes are excluded from the reference. The present-day part of the reference (991 individuals of Human Origins, HGDP and SGDP, at most 30 per population, placed at the sampling place of their population) has no genomes from Germany, Scandinavia (except Norway and Iceland), the Netherlands or Ireland; ancient persons of 150–1000 years ago fill these regions.

The results are given period by period. Table 2 lists the five largest shares of the land probability by country for every group; Table 3 lists the share of persons whose single most similar place lies inside Britain and Ireland and the share of the probability that falls on sea cells.

Neolithic. France carries the largest share for Hazleton North (22 %) and for England Neolithic (21 %). Britain and Ireland follow with 14 % and 12 %, Spain with 11 % and 14 %; Poland (8 % and 8 %) and Germany (8 % and 7 %) come next (Table 2). The best match of a person lies inside Britain and Ireland for 3 % of the persons of Hazleton North and for 11 % of England Neolithic (Table 3).

Bronze Age. Germany carries the largest share for England Beaker (13 %) and for England Middle Bronze Age (12 %). For England Beaker, Sweden (10 %) and France (10 %) follow, and Britain and Ireland are not among the five largest shares; for England Middle Bronze Age, Britain and Ireland come second (11 %), then France (10 %). The best match lies inside Britain and Ireland for none of the persons of England Beaker (0 %) and for 12 % of England Middle Bronze Age.

Iron Age. France (16 % in both groups), Germany (11 %) and Britain and Ireland (10 %) head both maps with identical shares. Ukraine (8 %) and Poland (7 %) fill the fourth and fifth places for England Early Iron Age, Russia (8 %) and Sweden (7 %) for England Middle Iron Age. The best match lies inside Britain and Ireland for 25 % and 47 % of the persons.

Roman period. Poland (13 % in both groups) and Britain and Ireland (13 % and 12 %) head the maps, followed by Germany (11 % and 12 %). The best match lies inside Britain and Ireland for 29 % and 33 % of the persons (7 and 6 persons in the groups).

Early Middle Ages. Russia carries the largest share for England Anglo-Saxon (13 %, level with Germany and Britain and Ireland) and for England Viking Age (19 %). For England Viking Age, Sweden follows with 14 %, then France (10 %), Norway (8 %) and Poland (8 %). The best match lies inside Britain and Ireland for 3 % and 4 % of the persons.

Medieval Cambridgeshire. Russia (15 % and 16 %) and France (12 % and 13 %) head both maps, and Britain and Ireland have 8 % on both. The best match lies inside Britain and Ireland for 20 % of the persons of Medieval Cambridgeshire and for 27 % of Medieval to early modern Cambridgeshire.

Present day. France carries 14 % on both maps, followed by Poland (9 %), Ukraine (9 %), Germany (8 %) and Russia (8 %). England is empty by construction, so Britain and Ireland are not among the five largest shares. The best match lies inside Britain and Ireland for 9 % of the persons in both groups.

Across the periods. The country with the largest or joint-largest share changes from map to map: France for the two Neolithic groups, Germany for the two Bronze Age groups, France for the two Iron Age groups, Poland for the two Roman-period groups (level with Britain and Ireland for England Roman period), Russia for the early medieval and the two Cambridgeshire groups (level with Germany and Britain and Ireland for England Anglo-Saxon), and France again for the two present-day groups (Table 2). The share of persons whose best match lies inside Britain and Ireland is lowest for England Beaker (0 %), Hazleton North (3 %), England Anglo-Saxon (3 %) and England Viking Age (4 %), and highest for England Middle Iron Age (47 %) (Table 3).

Within a period, the two groups give the same picture at the level of countries on five of the seven maps: Neolithic, Iron Age, Roman period, Cambridgeshire and present day. On the Bronze Age map they differ in the rank of Britain and Ireland, which are second for England Middle Bronze Age and outside the five largest shares for England Beaker. On the early medieval map they differ in the countries after Russia: England Viking Age has Sweden, France and Norway, England Anglo-Saxon has Germany and Britain and Ireland. The largest difference within a period in the share of best matches inside Britain and Ireland is on the Iron Age map (25 % against 47 %).

The maps do not show origins. A cell has a high value where genomes similar to the person have been sampled in the training window, and sampling is uneven in space and time. Shares by country grow with the area of the country. A high value for a country does not mean that the person's ancestors came from there: the maps are not ancestry shares and give no model of how the groups formed.

Data and methods. Own Gaussian-process implementation following the principle of Mobest (Schmid & Schiffels 2023); not the Mobest software, not PANE, not qpAdm; exploratory, post hoc. Training data: 12,990 ancient individuals of the AADR v66 (29.9–70 °N, −24–70 °E, 150–8500 BP, at least 15,000 SNPs, one version per person, training window ±2000 years); on the present-day map plus 991 present-day individuals (Human Origins, HGDP and SGDP, at most 30 per population, placed at the sampling place of their population; 1000 Genomes persons excluded because of placeholder locations). Kernel exp[−(Δs²/800² + Δt²/800²)], 800 km and 800 years. Nugget per map in Table 1; on the six later maps the variance of each coordinate fitted by marginal likelihood on a random subset of 5,008 reference individuals of the training window (Bronze Age 9,271 individuals dated 1,080–6,328 BP; Iron Age 9,727, 150–4,612 BP; Roman period 8,364, 150–3,766 BP; early Middle Ages 7,879, 150–3,450 BP; Medieval Cambridgeshire 7,072, 150–2,700 BP; present day 6,653, 0–2,000 BP). Response: four PCA coordinates (Nexju N25 European PC1–2 and Middle-Eastern PC1–2). Map: product of normal densities, normalised to 1; 40 km grid without land mask, smoothed to 10 km by cubic interpolation; group map is the mean of the individual maps. On the six later maps colours are shown on land only (sea cells are computed and normalised but left blank) and white triangles mark the sampling sites (present-day groups: sampling districts of the Nexju annotation). The 358 persons shown are excluded from the reference; on the present-day map also all other 1000 Genomes British and English genomes. Validation: on Albania, a Balkan peak appeared for 2 of 4 test persons. The maps were computed with the author's own code; they are not a Nexju analysis run.

Schmid, C. & Schiffels, S. Estimating human mobility in Holocene Western Eurasia with large-scale ancient genomic data. Proc Natl Acad Sci USA 120(9), e2218375120 (2023).

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