Phylogenetic inference from cognate word formsApril 08, 2026
AbstractLinguistic phylogenies are commonly inferred from abstract cognate classifications that encode relationships 1among lexemes. Although widespread, this practice has well-recognized limitations: it discards the 2phylogenetic signal contained in segmental word forms; restricts the range of evolutionary questions that 3can be addressed; and treats cognacy judgments, which are hypotheses, as observed data. We introduce a 4comparative framework that addresses these limitations by modeling the evolution of aligned cognate word 5forms directly. Our approach adapts the TKF91 model of molecular evolution, originally developed to 6account for insertion and deletion events in DNA sequences, to the domain of linguistic data. By operating 7on segmental strings rather than abstract character codings, the framework enables phylogenetic inference 8from observable word forms and supports quantitative investigation of sound change. We demonstrate its 9utility through analyses that illuminate patterns of segmental stability and the evolution of phonological 10inventories.11
LanguagesLatin (1)Romanian (2)Portuguese (3)Spanish (4)Catalan (5)French (6)Walloon (7)Friulian (8)Italian (9)
Root-meaning traitA root-meaning trait for the concept ‘hand.’ LanguagePhonemic RepresentationCognate ClassEnglish/hænd/0German/hant/0Dutch/ɦɑnd/0French/mɛ̃/1Spanish/mano/1Italian/mano/1Russian/ruka/2Polish/rɛŋka/2Lithuanian/ranka/2
An example of an aligned cognate setManual alignment of the words for the concept ‘what.’ LanguagePhonemic RepresentationAlignmentLatin/kʷid/kʷ-idRomanian/ʧe/ʧ-e-Portuguese/kɨ/k-ɨ-Spanish/ke/k-e-Catalan/kɛ/k-ɛ-French/kwa/kwa-Walloon/kwɛ/kwɛ-Friulian/ʧe/ʧ-e-Italian/ke/k-e-
Example TreeAn example tree showing the relationships of N = 9 languages.17Latin (1)16Romanian (2)1513Friulian (3)Italian (4)1411Catalan (5)10Portuguese (6)Spanish (7)12French (8)Walloon (9)
AlignmentAlignments (A) are formed from the observed segments (S) and a homology map (H). +SLatinpetramRomanianpjatrəPortuguesepɛdɾɐSpanishpjedɾaCatalanpedɾəFrenchpjɛʁWalloonpirFriulianpjereItalianpjɛtra+H1Latin001111101Romanian100011111Portuguese100011101Spanish011011011Catalan101010101French101010100Walloon101010000Friulian010011101Italian101011101↓=A1Latin--petra-mRomanianp---jatrəPortuguesep---ɛdɾ-ɐSpanish-pj-ed-ɾaCatalanp-e-d-ɾ-əFrenchp-j-ɛ-ʁ--Walloonp-i-r----Friulian-p--jer-eItalianp-j-ɛtr-aH2Latin1111100001Romanian1001111001Portuguese0101011010Spanish0001111110Catalan1010101001French0001010110Walloon0001001001Friulian1001110001Italian1111001001↓=A2Latinpetra----mRomanianp--jatr--əPortuguese-p-ɛ-dɾ-ɐ-Spanish---pjedɾa-Catalanp-e-d-ɾ--əFrench---p-j-ɛʁ-Walloon---p--i--rFriulianp--jer---eItalianpjɛt--r--a
Concept ExamplesWoman-DominaDogLouseTreeLatindominamk-anemp-eːdu-kulumarboremRomaniando̯am-nə-k-ɨjne-p-ədu-k-je-arbore-Portuguesedo--nɐ-k-ww---pj--o---ʎu-aɾvuɾɨ-Spanishdoɲ--a-k-an--pj--o-x--o-aɾbol--Catalandɔ--nə-k-a---p-o----ʎ--a-b-ɾə-Frenchdam----ʃjɛ̃---p-u--------aʁb-ʁ--Walloondam----ʧ-ɛ̃---pju-------ɔ-p----Friuliandɔ--ne-c-an--p-edoː--li-arbul--Italiandɔn-na-k-ane-p-idɔkk-jo-albero-FruitSeed-SementiaSeed-GranumLeafLatinfruː-ktumseːm-entiaɡraːnumf-oliaRomanianfru-kt--səm-ɨnʦə-ɡrɨw---f-o̯a-jePortuguesefɾu--tɐ-sɨm-ẽ-tɨ-ɡɾww--f-oʎ-ɐSpanishfɾu--to-simjente-ɡɾano---ox-aCatalanfɾuj-t--səm-en---ɡɾa---f-uʎ-əFrenchfʁɥi----səm-ɑ̃-s--ɡʁɛ̃---f-œj--Walloonfry--t--sim-ẽ-s--ɡrin--f-ɔj--Friulianfru--t--sem-ɛnʧɛ-ɡran--fwe--eItalianfru-tto-sem-ente-ɡrano-f-ɔʎʎa
Segment Assignments0d1o2m3i4n5a6o̯a7ə8ɐ9ɲ10ɔ11e12k13ɨj14ɐ̃w15ʃ16j17ɛ̃18ʧ19c20p21eː22u23l24ʎ25x26oː27r28b29ɾ30v31ɨ32ʁ33f34uː35t36ɥ37y38s39ʦ40ẽ41ɑ̃42ɛ43ɡ44aː45ɨw46œ47ɔj48w49h50ʝ51ɑ52ɡʷ53ʤ54ɐ̃55ɔ̃56au̯57ø58iː59ej60ʀ61ɛj62kʲ63z64ʒ65θ66e̯a67kʷ68aj69õ70oj71ĩ72ɐj73øː74ɣ75ũ76œ̃77ŋ78ɐ̃j
Partition AssignmentsModel: “Natural Class”Long Voweleː oː uː aː iː øːNasal Vowelɐ̃w ɛ̃ ẽ ɑ̃ ɐ̃ ɔ̃ õ ĩ ũ œ̃ ɐ̃jDiphthongo̯a ɨj ɨw ɔj au̯ ej ɛj e̯a aj oj ɐjShort Vowelo i a ə ɐ ɔ e u ɨ y ɛ œ ɑ øNasal Consonantm n ɲ ŋLiquidl ʎ r ɾ ʁ ʀApproximantj ɥ wAffricateʧ ʦ ʤFricativeʃ x v f s h ʝ z ʒ θ ɣStopd k c p b t ɡ ɡʷ kʲ kʷ
Exchangability ParametersLongVowelNasalVowelDiphthongShortVowelNasalConsonantLiquidApproximantAffricateFricativeStopLong Vowel 0.01420.00955 0.00579 0.0006560.000217 0.0000164 0.0006920.000208 0.0000154 0.01830.00471 0.000119 0.003510.000903 0.0000422 0.01200.00794 0.00488 0.007790.00294 0.000265 0.07180.0452 0.0260 0.007270.00198 0.0000927 0.001420.000478 0.0000241Nasal Vowel 0.0006560.000217 0.0000164 0.05840.0452 0.0341 0.0005240.000131 0.00000648 0.1650.110 0.0637 0.009970.00485 0.00137 0.001250.000423 0.0000284 0.02000.0112 0.00518 0.004950.00136 0.0000527 0.1400.0914 0.0534 0.0007150.000212 0.00000262Diphthong 0.0006920.000208 0.0000154 0.0005240.000131 0.00000648 0.03390.0209 0.0113 0.01920.00518 0.000106 0.1020.0642 0.0369 0.002060.000612 0.0000187 0.003250.000909 0.0000631 0.008190.00223 0.0000768 0.006910.00191 0.0000393 0.0008560.000236 0.00000758Short Vowel 0.01830.00471 0.000119 0.1650.110 0.0637 0.01920.00518 0.000106 0.07960.0222 0.000660 0.04850.0132 0.000354 0.03320.00901 0.000392 0.05900.0155 0.000520 0.05390.0147 0.000440 0.06860.0183 0.000415 0.03210.00839 0.000232Nasal Consonant 0.003510.000903 0.0000422 0.009970.00485 0.00137 0.1020.0642 0.0369 0.04850.0132 0.000354 0.1550.0797 0.0216 0.005910.00169 0.0000452 0.01330.00366 0.0000822 0.02570.00736 0.000202 0.03440.00996 0.000154 0.003890.00108 0.0000536Liquid 0.01200.00794 0.00488 0.001250.000423 0.0000284 0.002060.000612 0.0000187 0.03320.00901 0.000392 0.005910.00169 0.0000452 0.05720.0368 0.0210 0.03650.0226 0.0115 0.1490.0963 0.0542 0.01060.00295 0.00000446 0.006470.00359 0.00163Approximant 0.007790.00294 0.000265 0.02000.0112 0.00518 0.003250.000909 0.0000631 0.05900.0155 0.000520 0.01330.00366 0.0000822 0.03650.0226 0.0115 0.03090.00894 0.000396 0.06300.0237 0.00160 0.05360.0161 0.000670 0.02110.0127 0.00601Affricate 0.07180.0452 0.0260 0.004950.00136 0.0000527 0.008190.00223 0.0000768 0.05390.0147 0.000440 0.02570.00736 0.000202 0.1490.0963 0.0542 0.06300.0237 0.00160 0.06660.0179 0.000371 0.03490.00902 0.000251 0.01470.00498 0.000254Fricative 0.007270.00198 0.0000927 0.1400.0914 0.0534 0.006910.00191 0.0000393 0.06860.0183 0.000415 0.03440.00996 0.000154 0.01060.00295 0.00000446 0.05360.0161 0.000670 0.03490.00902 0.000251 0.05710.0158 0.000318 0.01100.00303 0.0000338Stop 0.001420.000478 0.0000241 0.0007150.000212 0.00000262 0.0008560.000236 0.00000758 0.03210.00839 0.000232 0.003890.00108 0.0000536 0.006470.00359 0.00163 0.02110.0127 0.00601 0.01470.00498 0.000254 0.01100.00303 0.0000338 0.1180.0862 0.0604
Natural Class RatesThe average rates of change between and within the ten groups of the Natural Class model. Circle area is proportional to the rate of change between groups (qij). Shaded area represents the 95% credible interval. Long VowelNasal VowelDiphthongShort VowelNasal ConsonantLiquidApproximantAffricateFricativeStopLong VowelNasal VowelDiphthongShort VowelNasal ConsonantLiquidApproximantAffricateFricativeStop
Transition Rates between PartitionsThe area of the circles is proportional to the estimated equilibrium frequencies. The width of the lines is proportional to the estimated rates. 1)● Long Vowel2)● Nasal Vowel3)● Diphthong4)● Short Vowel5)● Nasal Consonant6)● Liquid7)● Approximant8)● Affricate9)● Fricative10)● Stop12345678910
Highest probability alignments for 'Flower'Segments are colored according to natural class. Dashes denote gaps where there is no homologous segment for the alignment position. The alignments are ordered from the highest posterior probability (top-left alignment) to the lowest posterior probability (bottom-right alignment) in row order. Probability135791115200.00.20.40.60.81.0LatinRomanianPortugueseSpanishCatalanFrenchWalloonFriulianItalian0.789floːremflo̯are-floɾ--floɾ--flɔ---flœʁ--flœr--floːr--fjore-0.0153 (0.804)fl-oːremfl-o̯are-fl-oɾ--fl-oɾ--fl-ɔ---fl-œʁ--fl-œr--fl-oːr--f-jore-0.0147 (0.819)floːremflo̯are-floɾ--floɾ--fl-ɔ--flœʁ--flœr--floːr--fjore-0.0133 (0.832)f-loːremf-lo̯are-f-loɾ--f-loɾ--f-lɔ---f-lœʁ--f-lœr--f-loːr--fj-ore-0.0125 (0.844)floː-remfl-o̯are-fl-oɾ--fl-oɾ--fl-ɔ---fl-œʁ--fl-œr--fl-oːr--fj-ore-0.0120 (0.856)fl-oːremflo̯a-re-flo-ɾ--flo-ɾ--flɔ----flœ-ʁ--flœ-r--floː-r--fjo-re-0.0113 (0.868)floː-remfl-o̯are-flo-ɾ--flo-ɾ--flɔ----flœ-ʁ--flœ-r--floː-r--fjo-re-0.00903 (0.877)fl-oːremflo̯a-re-fl-oɾ--fl-oɾ--fl-ɔ---fl-œʁ--fl-œr--fl-oːr--fj-ore-0.00834 (0.885)floːr-emflo̯are--floɾ---floɾ---flɔ----flœʁ---flœr---floːr---fjore--0.00700 (0.892)floːre-mflo̯ar-e-floɾ---floɾ---flɔ----flœʁ---flœr---floːr---fjor-e-0.00689 (0.899)floːrem-flo̯ar--efloɾ---floɾ---flɔ----flœʁ---flœr---floːr---fjor--e0.00591 (0.905)floːremflo̯ar-efloɾ--floɾ--flɔ---flœʁ--flœr--floːr--fjor-e0.00394 (0.909)floːr-emflo̯a-re-flo-ɾ--flo-ɾ--flɔ----flœ-ʁ--flœ-r--floː-r--fjo-re-0.00383 (0.913)floːr-emflo̯are--floɾ---floɾ---flɔ----flœʁ---flœr---floːr---fjor-e-0.00371 (0.916)floːr-emflo̯ar-e-floɾ---floɾ---fl--ɔ--flœʁ---flœr---floːr---fjor-e-0.00314 (0.920)floːre-mflo̯ar-e-floɾ---floɾ---flɔ----flœʁ---flœr---floːr---fjore--0.00306 (0.923)floː-remflo̯ar-e-floɾ---floɾ---flɔ----flœʁ---flœr---floːr---fjor-e-0.00269 (0.925)floːremflo̯are-flo-ɾ-flo-ɾ-flɔ---flœ-ʁ-flœ-r-floː-r-fjore-0.00231 (0.928)floː-remflo̯a-re-flo-ɾ--flo-ɾ--fl-ɔ---fl-œʁ--fl-œr--floː-r--fjo-re-0.00209 (0.930)floːre-mflo̯are--flo--ɾ-flo--ɾ-flɔ----flœ--ʁ-flœ--r-floː--r-fjore--
Gap frequency comparison chartDistribution of alignment gaps across word positions for the 102 cognate sets analyzed in this study. The top panel shows the proportion of alignments with a given number of gaps at the word-initial segment, the middle panel at word-internal segments, and the bottom panel at the word-final segment. Since nine languages are analyzed, at most eight gaps can occur at a given position: a deletion event affecting all nine languages would not appear in the alignment and is explicitly conditioned on in the likelihood calculation (10). Gaps increase systematically from initial to final position, with word-final segments exhibiting substantially higher deletion rates. A likelihood-ratio test rejects the null hypothesis that the gap distributions are identical across positions, (χ2 = 425.62, d.f. = 16, p < 0.001), which confirms a statistically significant positional asymmetry. Proportion of AlignmentsWord-initial seg.01234567890.00.20.40.60.81.0Word-internal seg(s)01234567890.00.20.40.60.81.0Word-final seg.01234567890.00.20.40.60.81.0Number of Gaps
The majority-rule consensus treeLatin100Romanian100Italian100Friulian100100PortugueseSpanish100Catalan100FrenchWalloon
Alignment categoriesAll cognate categories showing the number of alignments to reach the 95% credible interval. At2And9And10In10You Singular11If14Salt18All182Belly218Black198Blood477Bone263Dog58Dry88Ear533Earth211Egg685Eye365Feather107Fingernail141Fire217Five242Flower33Foot734Four330Fruit601Full339Good340Grass204Green144Head77I169Knee1087Leaf804Liver642Long114Long120Louse777Meat55Moon37Mountain58Mouth141Narrow1022Near498New757Night334Not22Old1519One38Other65Rain958Red114River101Round860Sea25Seed158Seed358Skin285Sky226Star472Stone302Tail106There52Thick148Thin92Three148To Come149To Cut484To Drink1023To Fall425To Fight531To Flow427To Hear90To Hold195To Know1090To Laugh534To Lie As In A Bed723To Play254To Say700To See751To Sew387To Sing191To Sleep148To Smell146To Squeeze1016To Stand152To Swell1158To Swell347To Think153To Turn Intransitive112To Wash174Tongue479Tooth52Tree187Warm73Water542What50When178Wind207Woman149Year98You Plural142
Questions
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