Runestones gather in family groups by the grave fields – neighbouring stones name the same people eight times as often

Gunnar Ekholm (1950) asked where the runestones were raised and was sceptical of the idea that lone stones mark grave fields that have been ploughed away. Torun Zachrisson (1998), in her study of Uppland and Gästrikland, set the runestones in relation to farm, boundary and grave field and proposed that stones at a farm's boundaries protected the farm. Lydia Klos (2009) argued that most runestones were originally raised at grave fields, a conclusion that Shane McLeod (2014) holds overstates the grave fields at the expense of other places, such as roads. Birgit Sawyer (2000) read the stones as expressions of family and inheritance, and groups such as Jarlabanke's stones at Täby and Vallentuna have long been seen as a lineage's monuments.

What is missing is a measure on the whole material: whether the stones actually form groups beyond chance when the density of settlement is held constant, whether the stones of a group belong together through people or through roads and bridges, and whether the groups stand in other places than the lone stones. The aim of the study is to measure that, in four steps, each pre-registered before it was run.

The study consists of four pre-registered steps and an addendum plan. Each plan was written down and time-stamped in the project's version control before the analysis was run; the checksums (SHA-256) are given below and the files under Data and code.

1. The spacing (28 October 2026, 9e7f6be50cd5b932…, addendum 663cae7ff05a94e2…; replication 31 October, e1fb9abc5cf9ec88…): do stones still in place stand closer together than chance would give at 100–1,000 metres, with the density of settlement constant? Tested in Uppland and Södermanland, and with the same method on the stones of Östergötland, Västergötland and Småland.
2. The neighbouring stones (29 October, dae9035c05fe5ba3…): do near pairs of stones (25–500 metres) more often share a personal name, a carver, a style group or a message than pairs at 2–10 kilometres? Six tests, Holm-corrected.
3. The family's place (29 October, 68361374fa670187…): do stones in a group (another stone 25–500 metres away) more often than lone stones (nearest stone over 1 kilometre away) stand by grave fields, burial mounds, roads, boundary markers, churches and certain place names? Fifteen tests, Holm-corrected.
4. One generation (29 October, 17798b75004cd30c…): do the groups have fewer different style groups than as many stones drawn from the same district?
5. The addendum plan (31 October, ec4a17c59132e058…): the same fixed series of sensitivity analyses that every other association in the project passes, applied to step 2 (the names) and step 3 (the grave fields). It was written after the four results were known but before the sensitivity analyses were run, and it adds no new outcomes.

Two things must be said about the order. Step 4 was formulated after an observation in step 3: there a one-sided test of more style groups than chance had been set, and the result went strongly the other way. The new plan tested the opposite with a stricter comparison (permutation within the district instead of within the province), but on the same stones. Step 4 is thus pre-registered, but not tested on independent data. In step 1 the method had to be corrected after the first run in Uppland and Södermanland (see 4.6). The corrected method was therefore tested unchanged, under a new locked plan, on the stones of Östergötland, Västergötland and Småland, which had been in no spacing analysis. It is that test that carries step 1.

• Source. The Scandinavian Runic-text Database (Rundata), Department of Scandinavian Languages, Uppsala University, in the version frozen for the analyses on 28–29 October 2026. Grave fields, burial mounds, roads and boundary markers from the Swedish National Heritage Board's register; place names from the project's place-name table.
• The stones. Only runestones that according to Rundata stand at their original place and have a known location; moved and lost stones are not included, since their place does not say where they were raised. Steps 1 and 2 concern Uppland and Södermanland, where the stones are most numerous (458 and 168 stones, 420 and 149 sites when stones within 25 metres count as one site). The replication of step 1 concerns 167 stones in place in Östergötland (59), Västergötland (56) and Småland (52), the only provinces besides Uppland and Södermanland with enough stones still in place. Step 3 concerns all Swedish provinces: 185 stones in a group and 472 lone ones.
• The personal names are the sponsors' and the dead's names, read from the inscription with the project's name model. The 20 most common names in the whole material are not counted, so that a pair does not share a name merely because the name was common.
• Dating by the stone's ornamental style (Gräslund 2006). A style group covers 25–50 years.
• The carver. The carver Rundata gives, secure or uncertain.

4.1 The point pattern. Ripley's L-function for the stones' sites, compared with an inhomogeneous Poisson pattern whose intensity is that of the settled land (kernel smoothing with a 10-kilometre bandwidth and a floor of 5 percent of the mean intensity), with a DCLF test over 100–1,000 metres against 999 simulations (Baddeley et al. 2015). Uppland and Södermanland separately, Holm-corrected. The replication uses exactly the same method, with the three provinces of Götaland as one pattern; it counts as successful if p is below 0.05, the pattern is clustered and the same direction holds in both halves.

4.2 The neighbouring stones. For each trait: the share of near pairs that share it, divided by the share of comparison pairs that share it. The p-value comes from 9,999 permutations of the stones' traits within the province, with the sites fixed.

4.3 The grave fields. Logistic regression: grave field within 500 metres ~ in a group + province + dating period + local density of stones, so that a dense district does not in itself count as a grave-field pattern.

4.4 One generation. For each group with at least two style-dated stones: the number of different style groups, compared with as many stones drawn 9,999 times from the same district (within 10 kilometres, except the group's own site).

4.5 Sensitivity analyses (the addendum plan). Grave fields: raw model; the plan's model; the carver as a random effect (Bates et al. 2015); the parish as a random effect; the stone's location as a spatial surface (Wood 2017); each half on its own; without one province at a time; without stones that the National Heritage Board's register Runor (2020) records as moved. Names: the main measure; each half on its own; each province on its own; without pairs with the same secure carver; without stones moved according to Runor. The halves are the project's fixed ones: whole parishes dealt alternately within each province. A step holds when the effect goes the same way and p is below 0.05; when a province is removed, or a province is tested alone, significance is required only where at least two thirds of the material remains.

4.6 Deviations from the plans. In step 1 the plan's 2-kilometre bandwidth gave stones without neighbours an intensity near zero, so that the test measured nothing; a calibration on random patterns revealed the error. The run is reported as invalid, and an addendum with a 10-kilometre bandwidth and a floor was locked before the new run. Since the method was corrected after a run on the same stones, it was then tested unchanged on new stones (the replication); there only one test run with 19 simulations was made to find code errors. In step 3 provinces with fewer than ten stones were merged. Otherwise no deviations.

5.1 The stones form groups. The stones lie closer together than chance would give at 100–1,000 metres: Uppland p = 0.004, Södermanland p = 0.003 (Holm-corrected 0.006 both), in both halves and with every bandwidth and floor in the robustness checks (p between 0.001 and 0.005). The median distance to the nearest stone is 1.1 kilometres in Uppland and 1.4 in Södermanland, but one stone in ten has a neighbour within about 200 metres. The replication on the stones of Östergötland, Västergötland and Småland gives the same result: clustered, p = 0.004, and in both halves (west p = 0.02, east p = 0.01). On their own, Västergötland (p = 0.003) and Småland (p = 0.02) are clustered; Östergötland goes the same way but is too small to be sure (p = 0.20). One stone per farm, evenly spread, finds no support.

5.2 Neighbouring stones name the same people. Of the near pairs where both stones carry names, 17.6 percent share a personal name (74 pairs), against 2.2 percent of the comparison pairs (4983 pairs): 7.9 times as often, Holm-corrected p = 0.001. The same carver (2.2 times) and the same style group (1.6 times) are indications; bridges, journeys and Christian features do not make neighbours more alike. The sensitivity analyses all hold:

• Half A: ratio 9.3 (34 near pairs), p = 0.002. Half B: 5.8 (40), p = 0.004.
• Uppland only: 8.2 (63 near pairs, 85 percent of the pairs), p < 0.001. Södermanland only: 5.8 (11 near pairs), p = 0.09 – the same direction, but too few pairs to be sure.
• Without pairs in which both stones have the same secure carver: 7.1, p < 0.001.
• Without stones that Runor records as moved: 9.6, p < 0.001.

5.3 The groups stand by the grave fields. 82 percent of the stones in a group have a grave field within 500 metres, against 55 percent of the lone ones. With province, dating period and local density constant the odds ratio is 2.38 (1.50–3.78), p < 0.001, Holm-corrected p = 0.003. The sensitivity analyses all hold:

• Raw model: odds ratio 3.59. Carver as a random effect (324 groups): 2.49, p < 0.001. Parish as a random effect (331 parishes): 2.45, p < 0.001. Location as a spatial surface: 2.45, p < 0.001.
• Half A: 2.27, p = 0.009. Half B: 2.53, p = 0.01.
• Without stones moved according to Runor (540 stones): 2.64, p < 0.001.
• Without one province at a time: the odds ratio lies between 2.18 and 2.70 without Östergötland, Småland, Södermanland and Västergötland. Without Uppland, when only 46 percent of the stones remain, it is 1.44 and not significant (p = 0.35); the direction holds, but the difference is carried to a large degree by Uppland.

Burial mounds, roads and boundary markers do not set the groups apart from the lone stones: road within 500 metres 26 against 16 percent, boundary marker 7 against 6 percent, both without a demonstrated difference. Place names in Husby and -tuna lie, on the contrary, somewhat less often near the groups when density is held constant (odds ratio 0.53, Holm 0.05, an indication).

5.4 A group was raised within one generation. 36 groups with 84 style-dated stones (32 in Uppland, 4 in Södermanland) have on average 1.58 different style groups, against 1.93 for as many stones from the same district, p < 0.001; half A p = 0.003, half B p = 0.004. 47 percent of the groups have all their stones in the same style group against 21 percent expected, and the span between a group's earliest and latest stone is on average 20 years against 36. Without groups in which one and the same carver made every stone (28 groups remain) it is 1.71 against 1.96, p = 0.01: weaker, but present. Examples are Täby (U 135, 136, 137 and 140, all in style group Pr2) and Skokloster (U 685, 686 and 689, all Pr2); counter-examples with time depth exist, such as Vårfrukyrka (Fp and Pr4).

What the findings say. Four measurements point the same way. Runestones gather in groups of a few hundred metres, the stones of a group name the same people, the groups stand by the grave fields, and a group was raised within a short time. The simplest reading is that the group is the family's place: a family that within one generation raised several stones by its grave field, for a father, sons and brothers. The roads and bridges do not explain the groups – neighbouring stones are not more often both bridge stones or journey stones, and the groups do not stand by roads more often than the lone stones.

Against earlier research. The findings support Klos (2009) in that the grave field was a main place for runestones, but sharpen it: it is above all the groups that stand by the grave fields, while somewhat more than half of the lone stones do so too. Zachrisson's (1998) boundary stones and the road stones emphasised by McLeod (2014) find no support in the comparison of group against lone stone – which does not rule out that single stones stood at boundaries and roads, but says that this is not what sets the family's gathered place apart from the lone stone. Ekholm's (1950) scepticism that lone stones mark ploughed-out grave fields agrees with the lone stones less often having a grave field nearby. That the groups were raised within one generation has, as far as we have been able to see, not been tested statistically before.

Weaknesses, in order of weight.

1. Uppland carries much. 32 of 36 groups in the generation test and 85 percent of the near pairs in the name test lie in Uppland, and without Uppland the grave-field difference is not significant. That the stones cluster holds also in Götaland, but the names, the grave fields and the generation apply first of all to Uppland, where the stones still stand and are most numerous.
2. Only stones in place. About a third of the runestones stand where they were raised. If moved stones more often came from groups or from lone places, that affects the comparisons.
3. The register is not complete. A grave field that has been ploughed away is not in the register. That can make lone stones lone in the register although they once stood by a grave field – Ekholm's objection the other way round.
4. Step 4 rests on the same stones as the observation behind it, and the style groups are 25–50 years wide. ”One generation” means here: a shorter time than chance gives in the same district.
5. The names are read by rules, and a name can be borne by different people. Removing the most common names reduces but does not remove that risk.

What would overturn the findings. That the name likeness disappeared when the carver or the sponsor's formula was held constant, that the groups turned out to follow roads when a more complete road register was used, or that the generation pattern did not recur in another province with many stones in place.

Runestones often stand in groups – in Uppland and Södermanland, and according to a pre-registered replication also in Götaland – and the groups belong to a family: stones within 500 metres of each other name the same people eight times as often as stones further apart, the groups stand by grave fields more often than lone stones, and a group was usually raised within one generation. It applies first of all to Uppland. The next step is to see whether the same families recur at several places, and what sets the lone stones' places apart.