Dataset

Our dataset (S2 Dataset; sources detailed in S1 Appendix), contains 48 ‘lists of the nights of the Moon’ from all the major archipelagos and transmitted in all East Polynesian languages, except for the Rapan-speaking island of Rapa Iti: Aotearoa/New Zealand (n = 10) and Moriori/Chatham Islands (n = 1), Hawai’i (n = 2), Mangareva (n = 1), the Marquesas (n = 8), Raivavae in the Austral Islands (n = 1), Rapa Nui/Easter Island (n = 4), the southern (n = 5) and northern Cook (n = 3) groups, Tahiti and neighboring islands (n = 4), and the Tuamotuan archipelago (n = 9). Therefore, it is representative of the divergence of the lists throughout East Polynesia.

Analysis of cognacy

We define cognate names (or cognate components of names) of nights as those that (1) originate from the same etymological source and (2) occupy a similar relative position in the calendrical list, regardless of whether their phonological form in a given East Polynesian language strictly follows that language’s regular sound laws. This cognacy relationship is similar to the connection between the names for ’January’ in different languages, such as French janvier, German Januar, Italian gennaio, Portuguese janeiro, and Spanish enero.

Etymologies used to determine (1), as per above, follow for the most those of POLLEX (Polynesian Lexicon Project) Online. POLLEX is a large-scale comparative dictionary of Polynesian languages, which uses reference dictionaries and other scholarly works as primary sources [15]. One notable exception involves a series of nights attested in lists from many locations, and whose names were already identified as cognates by J. F. Stimson in the 1930s: Marquesan Maheama, Mangarevan Ma[ʔ]ema, Tahitian Hamiāma, Rurutu (Austral islands) ʔamia, Tongarevan Samia, Tuamotuan Hania or Hanīa [21]. Stimson assumed the following development: Samia > Hamia > Hamia-ma(-tahi, etc.)> Mahiama > Maheama / Ma[ʔ]ema. Yet this leaves the etymology of the name unexplained, as most forms are opaque. We argue that the path was the opposite. The starting form is Proto-East Polynesian *ma-seʔa ‘(be) perceptible’ [15], originating the structure *maseʔa(-maa)-NUMERAL, where *maa is a numeral connective particle that became lexicalized and fossilized as part of the names of nights only in some calendars. Thus, *Maseʔa(-maa)- developed not just into Marquesan Mahea-ma / Mangarevan Ma[ʔ]ema (with *s > h), but also into *Same[ʔ]a(-ma), which, following metathesis (and the irregular shift e > i) finally became Tongarevan Samia, Tahitian Hamiama (with e > i), and Tuamotuan *Hamia > Hania (irregular m > n). The etymology is supported by the semantics of Hawaiian māhea ‘hazy (moonlight)’, Rapanui maʔeha ‘brightness; lighten/brighten up’, and Tahitian maheahea ‘turn pale; fade’, keeping in mind that this series of nocturnal names referred to some of the first nights after the new moon, when the latter is barely visible.

In addressing the proximity between any pair of calendrical lists, we did not just compute which forms of night names, and how many, were shared (the ‘lexical’ aspect). We also considered how much the relative position of a pair of cognate forms diverged within the sequence of ca. 30 nights (the ‘structural’ aspect). Moreover, we analyzed cognacy among names or components of names (here referred to as ‘forms’) of the lunar nights, rather than focusing on segments or phonemes (see next subsection).

Notation of the data

For compiling the dataset, our notation of the names of lunar nights from the calendrical lists followed seven (1–7) principles:

1. [1] The basic unit of analysis is a ‘form’, which represents the name of a night or part thereof. This choice responds to the intricacies of the data. On the one hand, in Polynesian studies (especially in early or non-linguistic publications) the notation of morphemes varies, leading to instances where the same combination of morphemes can be spelled as one or multiple words: e.g., Rongo nui / Rongo-nui / Rongonui ‘Big Rongo’. On the other hand, many night names are composite. Therefore, our unit of analysis comprises any name or part of a night name that we can examine separately for its presence or absence across calendrical lists. This unit, which we termed ‘form’, comprises both full words and morphemes, as well as repeated parts of morphemes (such as ‘ko’, which is the partial reduplication of the morpheme ‘kore’ in ‘kokore’). We defined our set of forms inductively, by examining the dataset and the established relations of cognacy among night names (see the index of forms in S1 Appendix).
2. [2] Forms (not character strings) were compared as whole units and notated in normalized ways—either reconstructed proto-forms or language-specific reflexes—disregarding phonological variation and linguistic change. For instance, East Polynesian *Roŋo [15] appears as Roŋo (Maori, Rapanui, and Tuamotuan), ʔOno, ʔOko (Marquesan), Lono (Hawaiian), and Roʔo (Tahitian) in different lists and languages. To encode all these forms as cognates, we notated them as ‘roŋo’, after the proto-form.
3. [3] The ‘nights of the moon’ were often recited using extended formulas: e.g., Tahitian ʔO Roʔo-nui te pō “Roʔo-nui is the night”, Maori He Otāne “It is O Tāne” (where O Tāne is literally “[night] of Tāne”), or Rakahanga-Manihiki Ko maraŋi “Marangi”, with a prominence marker (see S1 Appendix). Thus, in considering only basic forms to compare the names of nights, we excluded from the analysis most grammatical words (‘particles’) such as markers ko / ʔo, he, o, and the article te.
4. [4] Use of symbol ‘/’: Where there are variants of a form that can be diagnostic of relatedness between lists, both ‘form’ and ‘variant’ were annotated for computational analysis, following the scheme FORM/VARIANT. For example, while most calendrical lists have a reflex of *ʔAri, Mangaian, Rarotongan and Tuamotuan lists have Vari, probably due to lexical reinterpretation (as mentioned above). The presence of one or the other variant was notated as ‘ʔari/ʔari’ vs ‘ʔari/vari’. The part before ‘/’ shows that some (any) form of the night occurs, while the part after ‘/’ indicates the specific variant. They are distinct features, each of which may or may not be shared by any given pair of lists.
5. [5] Use of symbol ‘#’: This was used for two purposes: (i) the comparison of lexicalized complexes of the type of FORM#FORM against a single FORM (e.g., ‘maseʔa#maa’ is fully cognate with another ‘maseʔa#maa’ but only partially cognate with ‘maseʔa’); (ii) the comparison of reduplicated vs partially reduplicated vs non-reduplicated expressions of the same form; notice that reduplication is a common morphological process in Polynesian languages and it affects some night names (e.g., ‘kore#kore’ vs ‘ko#kore’ vs ‘kore’).
6. [6] Use of symbol ‘_’: This was used to detect full cognacy between composite night names of the type of FORM_FORM, regardless of the fact that the forms changed syntactical position (especially in ordered series of nights). For instance, different Tuamotuan lists feature the variant names Hania fakaoti ‘Final Hania’ and Te fakaotiga na Hania ‘The finalizing of Hania’, but we treated them as cognate despite changes in word order (and exact grammatical form), so as not to generate artifacts.
7. [7] Added numbers (FORM1, FORM2, etc.) distinguish non-cognate homographic forms. To illustrate this point: some lists share the composite ‘roŋo#nui’ while others have a standalone ‘roŋo’, a subtle difference we needed to consider. Similarly, we needed to compute the greater proximity between nights called ‘fotu#nui’ as opposed to nights called simply ‘fotu’. However, we did not count as cognates ‘fotu#nui’ and ‘roŋo#nui’. Even though both forms are modified by an adjective nui ‘big’, they are nights with quite different positions in their lists and the addition is most probably a trivial innovation that occurred independently. To put it simply, the addition of the adjective ‘big’ to *Fotu is a separate phenomenon from its addition to *Roŋo. To handle this, we added numerical labels to homographic words—both lexical and grammatical—to mark them as non-cognate forms: e.g., tuu#nui1 vs. tamatea_nui2 vs. fotu/fotu#nui3, etc.; tuu#faka1#so#ʔata vs faka2#pau vs faka3#ʔoti, etc. (see S1 Appendix).

Exclusion of other calendrical types

We did not explore the divergence between the ‘naming’ lists of East Polynesia and the ‘numbering’ lists of West Polynesia and other areas, although some of the latter include a few related forms (e.g., there are cognates of *tuu, *matofi, *fakaʔoti, *mate, etc.; see S1 Appendix). Three reasons hinder the application of our comparative method to a set containing both types. First, while we have complete records of lists for several locations that use the ‘numbering’ type (Pukapuka, Rennell and Bellona, Samoa, Takuu, Tokelau, Tonga, and Vaitupu), in other instances we located only partial data (Nanumea, Niue, and Sikaiana). Second, in some cases nights were described with long sentences (e.g., the 28th night in the Pukapukan list is Koa wakatau wenake ma te ulu o te ata matua “[The moon] rises at the same time as the darkness before dawn”) making it difficult to isolate diagnostic and comparable lexical forms. Third, and most importantly, number words are pervasive in most West Polynesian and other lists, with some sequences of nights numbered from ‘one’ to as many as ‘ten’. This creates a risk for our method, as it might falsely indicate greater similarity with the East Polynesian calendars that have longer numbered series (such as those from Rapa Nui), which may be an independent innovation.

We also did not apply our method to the year calendar used in both West and East Polynesia, which had months also with specific names [1,7,13]. This calendar has been the focus of comparative studies and is found in similar forms across several archipelagos, but some locations lack comprehensive documentation or show disruptions. Notably, the Marquesan lists suffer from transcription issues, and the surviving Rapa Nui month names have minimal to no similarities with other Polynesian calendars. Moreover, establishing cognacy and patterns of divergence is challenging due to the practice of renaming months after the stars marking their beginning in certain islands.

The issue of borrowability

While the lexicon is typically the most easily borrowed part of a language—and lunar calendars could in principle fall into this category—the high degree of isolation of many East Polynesian islands makes the borrowing of individual lunar night names unlikely in most cases. Indeed, we found little linguistic evidence for horizontal transmission (borrowing) in our dataset. We examined the lists for forms of night names that potentially did not conform to known patterns of historical phonology in the local language but instead matched those of another archipelago; yet, we were unable to identify any compelling cases. Moreover, calques—that is, night names borrowed from another island’s language but adapted to the local phonology—are virtually impossible to detect.

Nevertheless, it remains plausible that borrowing of night names and mutual influence occurred within specific archipelagos. In cases in which contact was significative in relatively recent times, the wholesale borrowing of calendrical lists is conceivable (see below on historical contact between Tongareva and Rarotonga). Accordingly, we should note at the outset that the Society, Tuamotu, southern Cook and Austral islands represent some of the least isolated archipelagos within East Polynesia. In addition, during the late 18th and early 19th centuries a newly-formed Tahitian kingdom expanded its influence in the region [22]. This facilitated increased contact across these islands. As a result, the calendrical lists from Tahiti, Tuamotu, the Southern Cook, and Raivavae islands are the most likely candidates to have undergone horizontal transmission, a factor we took into account when evaluating the phylogeny derived from our analysis. The case of Tongareva (Northern Cook) is also noteworthy. Although the island is geographically closest to Rakahanga and Manihiki, historical records indicate that it maintained close contact with Rarotonga (Southern Cook) for nearly seven decades (1864–1929) before its calendrical list was collected [23]. Therefore, we considered the possibility that the Tongarevan calendar (NCOOK_TGV) reflects Rarotongan interference. Continued contact with Rarotongan-speaking communities may also explain why a recent source registers the first lunar night in Tongareva as Tiroe (instead of older Tireo), a form otherwise only attested in the Atiu atoll (Southern Cook; see list 27 in S1 Appendix). In this instance, however, an earlier version of the Tongarevan list is preserved that contains the older and regular form (Tireo). This version—without the potential borrowed night—was the one used in our study.

Computational comparison of pairs of names of nights

To quantify similarity/difference between forms of night names in any pair of calendrical lists, we applied an algorithmic method that yielded numerical distances (see below). First, we introduced an adapted version of the Edit Distance metric to compare single forms of names. To find the probable cognate names of nights across pairs of lists, we produced a matching between nights with the lowest cumulative distance (i.e., the sum of all distances between matched nights). This yielded a first measure termed ‘lexical similarity’ (). Second, the algorithm analyzed how lexically cognate nights differ in their relative positions in any pair of lists, with the aim of computing the lists’ structural divergence (). The algorithm considers the cyclical pattern of lunar calendars: for example, if two nights are found in the 29th and 30th positions in one list, but their counterparts in another list occur in the 30th and 1st positions, respectively, this means that their relative positions are the same. Lastly, we combined the measures and to obtain the final distance between any pair of lists (see below).

We represented ‘forms’ (i.e., names or parts of names of calendrical nights, as collected in S1 Appendix and S1 Dataset) as . To accurately identify cognate names of nights, even in cases where linguistic phenomena changed the syntactical order of forms within a name (e.g., Tuamotuan Hania fakaoti and Fakaoti-Hania), we processed every possible permutation: . As the name of a night is comprised of only 1–4 forms, combinatorial explosion was not an issue. We compared pairs of names using a variation of the well-known Edit Distance, as defined in Fig 2.

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Fig 2. Definition of the Edit Distance: wD, wI, and wS represent the weight penalties for sign deletion, insertion, and substitution, respectively.

In this study, wD = wI = 1 and wS = 2.

https://doi.org/10.1371/journal.pone.0353287.g002

The function was extended to compute similarity between forms (notating them as described above). The general Edit Distance, including our variation, does not consider word length and is not ideal for comparing the distance between sets of words. Thus, various studies have introduced a form of normalization for Edit Distance values. We relied on the valuable properties [24] of the Generalized Edit Distance (as proposed and analyzed by [25]): it is a metric (which means it is non-negative, symmetric, and it satisfies the triangle inequality), its upper bound is 1, and it does not escalate repetitions. Thus, we normalized as

where represents the number of compounded forms, separated by the symbol ‘_’, and forming the name of a night (e.g., |faka1#ʔoti#ŋa1_maseʔa/samia| = 2). Given also the need to address trivial grammatical phenomena (including word-order changes), we defined the distance between the names of two nights as

searching for the pair of permutations of the two names of nights that have the minimal distance.

Lexical measure

Relations of cognacy between names of nights from two calendrical lists entail 1-to-1 mappings between cognate nights and require finding matching pairs across lists. To address this and facilitate accurate evaluation, we relied on the standard Linear Sum Assignment (LSA) problem for matching the calendars’ cognates, which can be solved by the Hungarian algorithm. We defined and , that is, any two calendrical lists to be compared, as two tuples of nights. We also assumed that , without any loss of generality, enabling the comparison of lists with different numbers of items. We can define a matching solution as a matrix over the variables representing the calendar alignment obtained by the LSA algorithm, with if and only if is assigned to and 0 otherwise. The LSA problem to be solved can then be expressed as

Note that: if , then nights are not matched.

Structural measure

The Lee Distance is a metric and for two general permutations of integers p₁ and p₂ of length n is:

Considering that a LSA matching can be expressed as two permutations of positions of nights in and , it can be adapted to our problem as

and then (following [26]) normalized as

In some instances, two lists are identical except for the presence of an extra night (e.g., RPN1 and RPN3). In these cases, is not a faithful measure as it counts a single shift multiple times. Thus, our method fixed the first list and shifted the nights of the second list in search for the best rotational matching:

Moreover, typically there was not a single best matching solution for any pair of lists, so we had to explore a set of equivalent solutions having the same value but different matching , and forming a set of possible solutions .

The final structural distance can thus be defined as

Calendrical distance

The final calendrical distance combined the lexical () and the structural () measures. We did not simply sum their contributions. If two lists are very different, then their score would be high—close to 1—and most of the distances between individual pairs of nights would also be high. This means that the LSA matching will, correctly, produce a high number of equivalent but poorly matching solutions, with nights matched almost randomly. If we searched for the best matching through double minimization in the definition of , we would certainly find a suitable solution with a very low score. This is evidently incongruous: the meaningfulness of the measure had to be modulated in some way to avoid such degenerate behavior. Given that the contribution of the distance must be maximal for near 0 and minimal for near 1, for deriving the final distance between two calendars and we can combine the two measures as

Note that was built starting from the Generalized Edit Distance and the Lee Distance (both provably metrics), only using additions and multiplication by positive scalars, so that it can be proved that is also a metric. The aim of this distance is precisely to create a metric that reduces the impact of the structural measure when the lexical one is very low, as a structural comparison between calendars with very little similarity in terms of the names of the nights does not constitute a meaningful measure. For this reason, the structural component in the formula is scaled by one minus the lexical component.

By combining the metrics described above to derive , we were then able to compare every calendrical list and produce a distance matrix suitable for the application of an algorithm that enabled us to construct a phylogenetic tree, as described next.

Construction of the phylogenetic tree

Before constructing a phylogenetic dendrogram, we assessed the extent to which our calendrical distance data were compatible with a tree-like representation. To this end, we used SplitsTree App [27] to calculate delta scores (Table 2) and to produce a split network graph (Fig 3A) based on the Neighbor-Net algorithm [28] from our distance matrix.

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Table 2. Delta scores for the dataset of 48 East Polynesian lists of nights of the moon. Also included are the values for Q-residuals, which quantify departures from a strict tree (lower values indicate a better fit of the data to a phylogenetic tree) [29].

https://doi.org/10.1371/journal.pone.0353287.t002

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Fig 3. Phylogeny of 48 lists of ‘the nights of the moon’ from East Polynesia: split network graph using NeighborNet (A) and rooted phylogenetic tree using the MAD algorithm, with indication of node confidence values (B).

Key to the macro-provenances (islands or archipelagos) of the calendrical lists: AUSTR: Austral Islands; HAW: Hawai’i; MAO: Aotearoa/New Zealand; MGV: Mangareva (in the Gambier archipelago) MRQ: Marquesas Islands; MORI: Moriori/Chatham Islands; NCOOK: Northern Cook Islands; SCOOK: Southern Cook Islands; RPN: Rapa Nui/Easter Island; TAH: Tahiti and neighboring islands (Society Islands, French Polynesia); TUA: Tuamotu Islands. See S1 Appendix for the specific source of each list. Pale yellow and light purple highlight the lists corresponding to the two main branches of the rooted tree, Branch 1 and Branch 2, respectively.

https://doi.org/10.1371/journal.pone.0353287.g003

A split graph visualizes both tree-like and conflicting signals in the data: branching structures indicate tree-like relationships, whereas box-like structures indicate conflicting arrangements. In our network, most reticulations are confined to lists from the same archipelagos or islands, notably the Marquesas, New Zealand/Chatham Islands, the South Cook Islands, and the Tuamotu (Fig 3A). This pattern is consistent with local interaction and possible horizontal transmission among geographically proximate communities, but does not obscure the overall tree-like structure of the dataset. More substantial reticulation is observed in the central region encompassing the Society, Austral, South Cook, and Tuamotu archipelagos. As stated above, this is precisely the area for which historical evidence suggests sustained inter-island contact from the late 18th onwards.

Delta scores, introduced by Holland et al. [30], provide an exploratory measure of the extent to which the data from a distance matrix departs from a tree-like structure. The method assigns values between 0 and 1 to individual taxonomic units according to the extent to which each ‘taxon’ is involved in conflicting phylogenetic signals. These unit-specific values can then be averaged to obtain an overall estimate of the tree-likeness of the dataset, with higher values indicating a greater degree of conflicting signal and reticulation [29]. Crucially, as Gray et al. [29] noted, there is no generally accepted method for assessing the statistical significance of delta scores. The average delta score of our calendrical dataset is 0.2544, which is substantially lower than the values reported for applications of the method to datasets of Indo-European and Austronesian languages by the same authors [29]. This suggests that our calendrical data does not exhibit a high level of conflicting signal and is sufficiently tree-like to support phylogenetic reconstruction.

We therefore produced a dendrogram by applying the Neighbor-Joining algorithm [31] to the matrix containing all pairwise distances. The resulting tree was rooted using the MAD (Minimal Ancestor Deviation) algorithm [32], which has been shown to outperform other rooting methods based on experiments with biological phylogenies. An additional reason for adopting this method is its robustness to evolutionary rate heterogeneity. This property is particularly relevant in the present study, as we made no a priori assumptions about the tempo of change of the calendar systems we investigated. Finally, MAD rooting is especially useful when a suitable outgroup is unavailable. This is the case here, since, for the reasons discussed above, we considered it unfeasible to use the numbering-based calendrical lists from West Polynesia and other regions as an outgroup. With regard to the applicability of the Neighbor-Joining clustering method and the MAD rooting algorithm to our distance matrix: the assumptions underlying Neighbor-Joining (namely, positivity, symmetry, a zero diagonal, and additivity of distances) are satisfied by the fact that is a metric; the same preconditions hold also for the MAD algorithm [32].

After rooting the tree with MAD, we assessed the robustness of the inferred topology by estimating node confidence values using residual resampling. We followed the approach proposed by Waddell and Azad [33], which calculates residuals as the differences between the observed pairwise distances and the distances implied by the fitted tree. These residuals are then resampled with replacement to generate replicate distance matrices and reconstruct a Neighbor-Joining tree from each replicate. Ultimately, node confidence values correspond to the proportion of replicate trees in which a given clade was recovered. The resulting values indicate strong overall support for the inferred topology of our tree (Fig 3B).

Code availability

The code and data needed to repeat the analysis, and generate all figures and intermediate results are available from https://zenodo.org/records/20702913.