In western Uppland ʀ was written with r five times as often as in the rest of the country

Runic Swedish had two r-sounds. One, r, is the ordinary one. The other, ʀ, goes back to an older z and stands, among other places, in endings such as æftiʀ ’after’, þæiʀ ’they’ and stæinaʀ ’stones’. It had a rune of its own, the yr-rune ᛦ. In time the sounds merged, and in the later Viking-Age inscriptions ʀ is written ever more often with the ordinary r-rune.

Patrik Larsson (2002), in his dissertation on the yr-rune, went through how older ʀ is written in all Scandinavian runic inscriptions. He shows that the share of spellings with the r-rune after a vowel is markedly higher in Uppland, Västergötland and on Gotland (18–28 percent) than in other provinces with many instances (section 7.2.2), and that the Uppland group in the Fp style consists largely of inscriptions by the carver Erik, who consistently writes the r-rune for ʀ (section 7.2.3). Per Stille (1999, p. 206), in his study of the carvers of Fjädrundaland, observed the same of Erik and concluded that r and ʀ had merged in his speech. Larsson places Erik among the carvers who seem to have kept no distinction between the sounds (section 7.2.1) and argues that the growing use of the r-rune on the whole reflects an ongoing language change, not an orthographic reform (section 7.3).

What that literature lacks is a measure of whether the spelling clusters geographically more than chance would give, independently of provincial boundaries, and whether such a cluster remains when the age of the stones and the habits of individual carvers are held constant. The aim of this study is to measure that, and to test what the measurement says about the explanation earlier research has given. Pronunciation is not tested directly, but section 6 takes a position on what the pattern says about it.

No analysis plan was locked for this question before the results were known. The finding is therefore not pre-registered, and it should be read as a discovery in a systematic search.

The search was a general method applied at once to 13 traits in the spelling and content of the runestones, r for ʀ among them. The method, its limits (circles holding at most a tenth of the stones, 999 simulations, adjustment across the traits) and the division of the material into two halves were fixed in the program code before the search was run, and they were the same for every trait. No hypothesis about r for ʀ or about western Uppland existed before the search.

Four things nonetheless keep the finding from being an artefact of our choosing it:

1. The scan statistic's p-value takes into account every circle that was tested; it is the probability that the most extreme area would be as extreme if the spelling were evenly distributed.
2. The p-values are adjusted for the 13 traits scanned, and in addition for all 48 associations the project reports.
3. The halves were set independently of the patterns, and the cluster must hold in each half on its own.
4. The same sensitivity analyses as for every other association.

The analyses in sections 5.1–5.3 are those the method prescribes for every trait. Section 5.4 on the carver Erik and on time is exploratory: it was computed after the cluster was known and is reported descriptively, with p-values that are not adjusted for the questions having been chosen afterwards.

• Source. The Scandinavian Runic-text Database (Rundata), Department of Scandinavian Languages, Uppsala University: transliteration, normalisation, province, parish, site, carver and style group for each inscription. The material was frozen for the analysis on 29 October 2026.
• The stones. Viking-Age runestones in the Swedish provinces. Runestones only; other objects with runes are not included. Skåne and Blekinge, Danish in the Viking Age, are counted as Denmark in Rundata and are not included. Of the stones, 1,097 have a known location and stand at their original site; stones moved according to Rundata or to the Swedish National Heritage Board's register Runor (2020) are not counted, since their location does not say where they were carved.
• The trait. For each stone, the words whose normalised form ends in ʀ and whose carved form ends in the r- or the yr-rune are taken. The stone counts as r for ʀ if at least one such ending is carved with the r-rune, and as ʀ-rune if all are carved with the yr-rune. The trait can be decided on 514 of the stones; 87 of them (17 percent) have r for ʀ. The measure rests on Rundata's normalisation, which places ʀ by the word's history, and on the transliteration of what the carver cut. It has not been checked against a reading of our own.
• The carver. The carver Rundata gives, with a note of whether the attribution is secure. The attributions rest on the editions in Sveriges runinskrifter and on Axelson (1993). Erik has twelve securely attributed stones where the trait can be decided and three uncertainly attributed ones (U 732, U 755, U 1151). His only signed stone, U 1165 at Rotbrunna, is not counted, since a gap in the text keeps its words from being paired with the normalisation; it has the r-rune in both the words where ʀ is expected (-ftir and the name airikr).
• Dating by the stone's ornamental style (Gräslund 2006). In section 5.4, RAK, Fp, Pr1 and Pr2 count as early and Pr3–Pr5 as late.

4.1 The search. Three measures, all in R (R 4.6.1) with the stones' locations in SWEREF 99 TM:

• Moran's I (Moran 1950) with the 8 nearest stones as neighbours: does the trait cluster geographically at all?
• Getis-Ord Gi∗ (Getis & Ord 1992) for each stone: does the stone lie in an area where the trait is more common among the neighbours than in the country? The local p-values are adjusted with Benjamini–Hochberg across the stones.
• Kulldorff's spatial scan statistic (Kulldorff 1997): every circle around every stone holding at most a tenth of the stones is tested, with the national share as the expected value. The circle where the trait is most over-represented is the cluster, and its p-value comes from 999 simulations in which the trait is distributed at random over the stones. The smallest possible p-value is then 0.001. The clusters' p-values are adjusted with Benjamini–Hochberg across the 13 traits.

4.2 Replication in the halves. The material was divided once, for all the project's analyses, into two halves parish by parish (whole parishes dealt alternately within each province). The share with the trait within and outside the cluster is compared in each half on its own with Fisher's exact test.

4.3 Sensitivity analyses. The cluster is tested as a comparison between stones within and outside it, with logistic regression: the raw model; the model adjusted for dating period; the carver as a random effect, so that a prolific carver's habits are not counted as a district's; the parish as a random effect; each half on its own; and without moved stones, both according to Rundata and also according to Runor 2020's record of the original site. Two analyses made for other associations are not made here: the model without one province at a time, since the cluster lies within one province, and the stone's location as a spatial surface, since the comparison itself is geographic. The sensitivity analyses test the cluster as it was found, not the choice of it; for the choice, the scan statistic's p-value and the halves stand. When the p-values are adjusted for all 48 associations the project reports, the larger of the sensitivity analyses' p and the scan statistic's own is therefore used. The model's assumptions are checked with simulated residuals (DHARMa; Hartig 2022).

4.4 Exploratory counts. The share with the trait within and outside the cluster, split by carver and dating period, is compared with Fisher's exact test. Those p-values are not adjusted.

4.5 Deviations and earlier versions. No plan existed, so no deviations can be reported. A popular article on the same pattern was published on 13 October 2026 on an earlier version of the material. After a correction of which stones count as moved, the cluster has a different centre (Holm in Vittinge instead of Grop-Norrby in Vårfrukyrka) and a different radius (30 instead of 22 kilometres). The figures in this report apply.

5.1 The cluster. The trait clusters clearly: Moran's I = 0.18 (p < 0.001). The most extreme area has its centre at U 1172 at Holm in Vittinge parish and a radius of 30.4 kilometres. There 24 of 36 stones have r for ʀ (67 percent), against 13 percent of the stones in the rest of the country: 5.06 times as common. Scan p = 0.001, the lowest value 999 simulations can give; adjusted for the 13 traits q = 0.013. Of the 13 traits it is the only one whose cluster passes the adjustment. The cluster's stones lie in 20 parishes, most in Simtuna (5), Vårfrukyrka, Tillinge, Nysätra, Fröslunda and Jumkil (3 each). In half A, 85 percent of the stones within the cluster have the trait against 12 outside (odds ratio 41, p < 0.001); in half B 57 against 15 percent (odds ratio 7.3, p < 0.001).

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5.2 The sensitivity analyses (514 stones, 87 with the trait). All 8 hold:

• Raw model: odds ratio 13.2 (6.3–27.7), p < 0.001.
• Adjusted for dating period: 13.0 (5.7–29.2), p < 0.001.
• Carver as a random effect (272 carvers and parish groups): 16.7 (5.6–49.8), p < 0.001. The cluster is thus not merely one carver's habit.
• Parish as a random effect (280 parishes): 15.9 (6.4–39.3), p < 0.001.
• Half A (262 stones): 10.0, p < 0.001. Half B (252 stones): 19.0, p < 0.001.
• Without moved stones according to Rundata: 13.0, p < 0.001. Also without stones that Runor 2020 records as moved (447 stones remain): 10.5 (4.2–26.1), p < 0.001.
• The difference in percentage points in the adjusted model: 63 against 13 percent, 50 points (probably between 32 and 67).
• The model's assumptions: residual distribution p = 0.10, overdispersion p = 0.08, remaining spatial pattern p = 0.15. Nothing amiss.
• Adjusted for all 48 associations the project reports: q = 0.02. The association is one of 15 that hold in every sensitivity analysis.

5.3 The hot stones. Getis-Ord Gi∗ singles out 32 stones in hot areas and none in cold ones. 23 of them lie in and around the cluster in Uppland and Västmanland. The other 9 lie in Västergötland (Vg 2, Vg 3, Vg 4, Vg 6, Vg 12, Vg 13, Vg 15, Vg 16, Vg 106), a second group too small for the scan statistic to test as a cluster of its own. Larsson (2002, chapter 7) noted the same inscriptions in Västergötland, where the preposition æftiʀ is written with the r-rune. In the rest of Uppland, outside the cluster, 39 of 244 stones have the trait (16 percent), in Södermanland 7 of 80 and in Västergötland 9 of 41.

5.4 Exploratory: the carver Erik and time.

• Erik. All Erik's 12 securely attributed stones where the trait can be decided have r for ʀ: 11 within the cluster and one outside (U 774). The three uncertainly attributed ones have it too. All are in the Fp style.
• The early stones. Within the cluster all 15 early stones have r for ʀ, and 13 of them are attributed to Erik. Outside the cluster 34 of 182 early stones have the trait (19 percent). In Uppland outside the cluster 7 of 9 stones in the Fp style have it.
• The cluster without Erik. Without every stone attributed to Erik, 11 of 23 stones within the cluster have the trait (48 percent), against 63 of 478 outside (13 percent), p < 0.001.
• The later stones. Among the stones in the style groups Pr3–Pr5, 7 of 16 within the cluster have the trait (44 percent), against 12 of 109 in the rest of Uppland (11 percent), p = 0.003.
• Balli, who carved in the district a generation after Erik, has r for ʀ on 3 of 5 stones within the cluster and 5 of 19 outside (p = 0.29); counting also the uncertainly attributed stones it is 5 of 7 against 6 of 20 (p = 0.08). The difference goes the way a local speech predicts, but the stones are too few for it to be certain.
• Åsmund, who carved in many parts of Uppland, wrote the yr-rune on all his 13 securely attributed stones where the trait can be decided, including the 3 that stand within the cluster.

What the finding says. Western Uppland is the area of Sweden where ʀ was most often written with the r-rune, and that is not because the stones there are early or because a single carver carved many of them: the cluster remains with dating period and carver constant, in each half and without moved stones. In the early generation it is carried almost wholly by Erik. That it remains without his stones, and that the later stones of the district write r four times as often as the rest of Uppland, shows that the spelling did not disappear with him.

Against earlier research. The result confirms and sharpens Larsson's (2002) observation that Uppland and Västergötland stand out. Within Uppland it singles out a definite area, and it recovers his group in Västergötland without having looked for it. It also confirms Stille's (1999) observation about Erik.

Where we depart from earlier research. Stille reads Erik's r as a sign that r and ʀ had merged in his speech, and Larsson holds that the advance of the r-rune on the whole reflects a language change, not an orthographic reform (section 7.3). Larsson's main reason is that the carvers at the same time mark palatalisation and use the s-rune for ʀ, which must reasonably follow pronunciation. That is an argument about runic writing at large. It shows that many carvers wrote by ear, but not that every carver did, and it does not explain why a single district differs so sharply from the rest of the country.

For western Uppland we propose another explanation: that r for ʀ there was a writing tradition that began with Erik and was passed on by the carvers of the district. Three observations support it.

1. Erik wrote r without a single exception, on all fifteen stones, including the one outside the district. Larsson, with Lena Peterson, takes the carvers' wavering between the runes as a sign of a sound change in progress (section 7.3). Erik does not waver at all; he writes as if by a rule.
2. Åsmund wrote the yr-rune on all his thirteen stones, including the three within the cluster. That speaks against the place or the patrons deciding the spelling. It followed the carver.
3. The spelling lives on in the same district after Erik, four times as common among the later stones as in the rest of Uppland, and the cluster remains when the carver is held constant.

The hypothesis is not proven, and Stille's and Larsson's explanation is not ruled out. The numbers are small: Erik has one stone outside the district and Åsmund three within it. If Erik and the carvers after him themselves spoke a variety in which the sounds had merged, that gives the same pattern as a writing tradition. Balli, moreover, points the other way: he wrote r more often within the cluster than outside it (3 of 5 against 5 of 19, p = 0.29; with the uncertainly attributed stones 5 of 7 against 6 of 20, p = 0.08). What separates the explanations is whether the later r-stones of the district stand in Erik's tradition – the same ornament, the same formulas, the same spelling otherwise – or merely in the same district. That is the next test.

Weaknesses, in order of weight.

1. The finding is discovered, not pre-registered. The cluster's boundary is chosen by the data. The scan statistic, the adjustment and the halves take that into account, but the radius and centre should be read as approximate.
2. Erik carries the early part. Thirteen of fifteen early stones in the cluster are attributed to him, and the attributions rest on style; several have been questioned (Larsson 2002, section 7.2.3). The cluster remains without him, but with a smaller margin.
3. The trait is decided on few words per stone. Many stones have only one or two endings with ʀ, most often in æftiʀ. A single r is enough for the stone to count as r for ʀ.
4. The measure is not checked by hand. It rests on Rundata's transliteration and normalisation. A misread yr-rune, or a normalisation placing ʀ where other scholars do not, would move individual stones.

What would overturn the finding. A hand reading showing that the r-forms within the cluster are more often uncertain readings than outside it, or new finds in the district with the yr-rune.

Within 30.4 kilometres of Holm in Vittinge, 67 percent of the runestones have r for ʀ, against 13 percent in the rest of the country, and the cluster withstands every sensitivity analysis. It begins with the carver Erik but remains without him and lives on among the later stones of the district. The spelling followed the carver rather than the place, and we propose that the cluster is a writing tradition. That it instead reflects the carvers' own pronunciation, as Stille and Larsson hold, the runestones cannot yet rule out; the test is whether the later r-stones stand in Erik's tradition or merely in his district.