Using hybridization networks to retrace the evolution of Indo-European languages
© The Author(s). 2016
Received: 30 March 2016
Accepted: 17 August 2016
Published: 6 September 2016
Curious parallels between the processes of species and language evolution have been observed by many researchers. Retracing the evolution of Indo-European (IE) languages remains one of the most intriguing intellectual challenges in historical linguistics. Most of the IE language studies use the traditional phylogenetic tree model to represent the evolution of natural languages, thus not taking into account reticulate evolutionary events, such as language hybridization and word borrowing which can be associated with species hybridization and horizontal gene transfer, respectively. More recently, implicit evolutionary networks, such as split graphs and minimal lateral networks, have been used to account for reticulate evolution in linguistics.
Striking parallels existing between the evolution of species and natural languages allowed us to apply three computational biology methods for reconstruction of phylogenetic networks to model the evolution of IE languages. We show how the transfer of methods between the two disciplines can be achieved, making necessary methodological adaptations. Considering basic vocabulary data from the well-known Dyen’s lexical database, which contains word forms in 84 IE languages for the meanings of a 200-meaning Swadesh list, we adapt a recently developed computational biology algorithm for building explicit hybridization networks to study the evolution of IE languages and compare our findings to the results provided by the split graph and galled network methods.
We conclude that explicit phylogenetic networks can be successfully used to identify donors and recipients of lexical material as well as the degree of influence of each donor language on the corresponding recipient languages. We show that our algorithm is well suited to detect reticulate relationships among languages, and present some historical and linguistic justification for the results obtained. Our findings could be further refined if relevant syntactic, phonological and morphological data could be analyzed along with the available lexical data.
KeywordsHistorical linguistics Phylogenetic trees Phylogenetic networks Reticulate evolution
Many curious similarities between the processes of species and language evolution have been observed since Darwin’s The Descent of Man . But even earlier, in 1863, August Schleicher  sent a letter to Ernst Haeckel in which he discussed some of these similarities, comparing, for example, mixed languages to hybridized plants in botany. Atkinson and Gray  presented a table that highlights the most important conceptual parallels which can be drawn between these evolutionary phenomena. In particular, the latter study compares the process of social selection in linguistics to natural selection of species, borrowing of words across languages to horizontal transfer of genes, creole languages to plant hybrids, ancient texts to fossils, and cognates to homologies. There are also a few differences between these processes . For instance, the biological alphabet (e.g., DNA) is universal, whereas the set of sounds used to form words is specific to each language. Moreover, the sequence data are usually much longer in molecular biology than in linguistics, and the selection of a perfect list of basic meanings suitable for the application of phylogenetic methods in the context of language evolution remains a challenging task. Nevertheless, the similarities and parallels between the two disciplines make it possible for researchers to use several well-developed computational biology methods for studying the evolution of species, and in particular reticulate evolution, in the field of linguistics. Obviously, it's not possible to apply these computational biology methods directly, without an appropriate adaptation, which is critical in interdisciplinary research. Thus, the existing phylogenetic algorithms should be modified and workflows adapted in order to obtain meaningful linguistic results and interpretations.
Two nucleotide sequences observed in two distinct species are said to be homologous if they have evolved from a common ancestral sequence . Similarly, in linguistics, a group of cognates is a group of word forms in different languages that have been inherited from a common ancestral word form . The main difference between these concepts is that the concept of homology includes the possibility of lateral transfers, whereas the concept of cognacy excludes all potential processes of borrowing. Cognates and phylogenetic trees play a fundamental role when studying the evolution of natural languages using phylogenetic methods . For instance, a phylogenetic tree representing the main traits of lexical evolution is equivalent to a species phylogeny depicting the key speciation events [3, 7, 8]. Several linguistic studies used phylogenetic methods to better understand the evolution of Indo-European (IE) languages [7–11]. Discovering the origin and main evolutionary trends characterizing the IE language family is one of the most recalcitrant intellectual challenges in historical linguistics [7, 12]. Two opposing theories, Kurgan and Anatolian, concerning early Indo-European origins are generally considered . The Kurgan theory [13, 14] postulates that IE languages originate from the Kurgan culture dated around 3000 to 4000 BC, whereas the Anatolian theory  dates the origin of IE languages around 7000 BC. For example, the works of Gray and Atkinson  and Bouckaert et al. , which focus on inferring and dating the divergence times of the contemporary and extinct IE languages using Bayesian phylogenetic methods, support the Anatolian theory of IE origin.
Phylogenetic tree model widely considered in linguistics assumes that the frequency of lateral word exchanges across languages has been relatively low. For example, Gray and Atkinson  and Bouckaert et al.  removed known loanwords from the basic vocabulary data before inferring their IE language trees. Obviously, linguistic phenomena such as word borrowing  and birth and evolution of hybrid languages , resulting from languages in contact, cannot be adequately represented by a tree model. For instance, a study of 80,000 words of the old Shorter Oxford Dictionary points out that English, which is a Germanic language, has borrowed 56.5 % of its total lexicon from Old French (Langue d’oïl) and Latin, 5.3 % from Greek, 13.2 % from other languages, and has inherited only 25 % of its current lexicon from its direct ancestor, Old Germanic [17, 18]. In this work, we analyzed basic vocabulary data from a 200-meaning Swadesh list . While the use of this list may lead to a certain decrease in the number of loanwords , it remains helpful for detecting the most important word borrowing trends . For example, the traditional 200-meaning English Swadesh list includes 33 confirmed loanwords (16.5 %)  and 10 additional “irregular phylogenetic patterns” which might be suggestive of unrecognized borrowings . Moreover, in a recent revision of the Albanian Swadesh list 31.8 % of its entries were identified as probable borrowings .
Word borrowing can be viewed as one of the main development mechanisms leading to the emergence of hybrid (i.e., mixed or contact) languages. There exists a variety of hybrid languages, including pidgins, creoles, and lexical hybrids . In a pidgin, the lexand minimum hybridization scoreicon usually comes from one parent language and the syntax comes from another one. A creole language, which arises from a pidgin, is a stable natural language spoken as a mother tongue. There are however many other types of lexical and grammatical transmission that produce a variety of linguistic outcomes. For example, Michif, which is the language of the Métis people of Canada and the United States, combines noun phrase phonology, lexicon, syntax and morphology from Métis French and verb phrase phonology, lexicon, syntax and morphology from Cree. As our analysis is based on lexical data only, here we address the problem of detection of lexical hybrids and word borrowing events.
Clearly, phylogenetic networks, and not phylogenetic trees, should be used to represent hybrid languages and word borrowing events. In fact, some drawbacks of the tree model in historical linguistic were already pointed out by Schmidt  in 1872. Nakhleh, Ringe and Warnow  were among the first to use directed phylogenetic networks to identify lexical contacts among 24 IE languages. These contacts have been represented by bidirectional reticulations, but the donor languages were not clearly distinguished from the recipient languages in the presented “perfect linguistic networks”. The study of Nakhleh and colleagues was restricted to the earliest attested languages of 12 subgroups of the IE family. Some other works that address the topic of modeling reticulate evolution in linguistics rely on the use of split graphs [3, 27, 28], minimal lateral networks (MLN) [10, 11, 21], and horizontal word transfer networks (HWTN) . While the MLN and HWTN methods can be applied to detect word borrowing events, split graphs can be used to identify hybrid-like features of certain natural languages. For example, the split graph topology obtained for nine Germanic languages  allows one to identify Sranan, a language spoken in Suriname, as a hybrid of English and Dutch. However, split graphs were not specifically designed to detect and explicitly represent network relationships among languages. For instance, they cannot be used to identify explicitly the hybrid language, its parent languages and the corresponding hybridization/reticulation degree (i.e., percentage of lexical material transferred from each of the parent languages). Split graphs cannot be used to quantify the frequency of word borrowing events either. Furthermore, Wichmann and colleagues  proposed to infer reticulations based on distances retrieved from the Levenshtein metric  scores. Wang and Minett  used maximum parsimony to detect language contacts. The test, they designed, is based on the distribution of lexical similarities between languages. Köllner and Deller  proposed an ancestral state reconstruction method, which is specific to linguistics. The latter authors used the dissimilarities between a given node and its immediate ancestor in the tree in order to identify potential word borrowing events. In all these methods, the exact source and destination of the detected word borrowings cannot be identified explicitly. Only a few methods offer the advantage of finding the direction of reticulation events in linguistics. Mention here the work of Van der Ark et al. , who used the Levenshtein distance  to identify the source and the destination of word borrowing events, and that of Delz , who applied the horizontal gene transfer algorithm  from the T-Rex web server [37, 38] to detect loanwords and the corresponding word borrowings.
In this study, we adapt a recently developed computational biology method , which was originally designed to detect hybrid species, their parents and the corresponding hybridization degrees, to identify explicitly hybrid languages (i.e., lexical hybrids in this study) and word borrowing events. One of the main advantages of our method over the MLN [10, 11, 21] and perfect networks  approaches is that it allows for determining the direction of reticulation events (e.g., word borrowing events) in addition to the quantification of influence of each of the donor languages on the corresponding recipient languages. For a more complete description of the benefits and shortcomings of the MLN approach, the reader is referred to [40–42]. We compare our explicit hybridization networks to the corresponding split graphs [43, 44] and galled networks . Finally, we present some historical evidence that supports the results of our analysis.
Several important studies dedicated to the classification of IE languages [7, 8, 10, 29] have examined the data from the 84 IE language database organized by Dyen and colleagues . The Dyen database contains word forms for the meanings of the 200-meaning Swadesh list . This list is one of a few lists of fundamental meanings collected by M. Swadesh in the 1940s and 50s. It is often used in lexicostatistics, which focuses on quantitative evaluation of lexical cognates, and in glottochronology, which focuses on dating divergence times of natural languages. Swadesh lists have been used by linguists to test the level of chronological separation of languages by comparing words, as they contain universal stable items with low levels of borrowing [7, 8]. However, it has been noticed that even though the use of Swadesh lists may decrease the level of borrowings to a certain degree, it cannot exclude all of them . For each of the 200 basic meanings of the Swadesh list, the Dyen database contains their word forms in 84 IE languages. These word forms have been regrouped in cognate sets . Two word forms were identified as cognate if they share an uninterrupted evolutionary history characterized by the presence of a common ancestral form. The word forms resulting from word borrowing (e.g., English word fruit which was borrowed from Old French) and those related by accidental similarity (e.g., the word form bad exists in both English and Farsi, but this is rather considered as an accidental similarity by linguists) were placed in a separate class. When it was difficult to differentiate between cognates and word forms resulting from borrowing or accidental similarities, the corresponding word forms, albeit not numerous, were categorized as doubtful cognates. For instance, this database was used by Gray and Atkinson  and Atkinson and Gray  to infer evolutionary trees of IE languages. In order to reconstruct our hybridization networks, we also considered some additional linguistic resources (Douglas Harper’s Online Etymology Dictionary , the IE Lexical Cognacy Database (IELex)  and the IE etymological dictionaries collection ), which include relevant etymological information regarding loanwords and accidental similarities. Using these resources, we modified some of the original cognate sets created by Dyen et al. . Precisely, the loanwords, put aside by Dyen and colleagues, were added to the corresponding cognate sets (i.e., cognate sets containing the donor forms for these loanwords). In some rare cases, the original cognate sets including doubtful cognates were either merged or eliminated. In total, our modified database included 1315 cognate sets. It is available at: http://www.trex.uqam.ca/biolinguistics.
Reconstruction of explicit linguistic hybridization networks
Note that Δ i,j h equals 0 if i and j are true neighbors in an additive tree.
Then, we select the triplet (h 0 , i 0 , k), here i 0 = i or i 0 = j, that provides the minimum of the least-squares function LS i,j h and satisfies the above-mentioned constraints. If LS i,j h < (Δ i,j h )2, we consider that h 0 is a hybrid of i 0 and k, and remove from the distance matrix the row and the column corresponding to h 0. Otherwise, we connect the languages i and j as in the conventional NJ algorithm . The time complexity of our network building algorithm is O(n 3), which is equivalent to the time complexity of NJ.
It’s important to mention that hybrid languages identified by our algorithm should not be always interpreted as real lexical hybrids or real mixed languages. In some cases, the detected parent-hybrid relationship may also represent the processes of word borrowing or even inheritance from the closest ancestor in the tree (see Fig. 2). This figure illustrates three possible network configurations which reflect the case where our algorithm detects a hybrid, h, which is a direct neighbour, or a very close neighbour, of one of its parents, Nb(h), in the phylogenetic tree (Fig. 2a). This tree is assumed to be inferred by a traditional tree reconstruction algorithm (e.g., NJ). For instance, language h may receive the proportion, α, of its lexicon either from its closest ancestor in the tree via direct inheritance (Fig. 2b), or from its neighbour Nb(h) in the tree as its lexical hybrid (Fig. 2c), or from both its closest ancestor via inheritance and from its neighbour Nb(h) via word borrowing (Fig. 2d; α is indicated in parentheses in this case).
We also conducted the analysis using the Levenshtein distance  between words of the same meaning but did not obtain convincing results using such an approach. This should be due to the fact that this distance tends to reflect chance similarity when the compared word forms are not cognate . The Levenshtein distance will be further used for inferring galled networks from word trees, but its application will be restricted to word forms belonging to the same cognate set.
The input parameters of our algorithm, MIN Sc , α MIN and α MAX , were chosen according to the size of the considered distance matrix (see  for a detailed discussion on the parameter selection). For smaller distance matrices corresponding to particular language groups, the following set of input parameters: (MIN Sc = 0, α MIN = 0.1 and α MAX = 0.9) was used. To avoid an excessive number of false positives, more restrictive parameters: (MIN Sc = 0.1, α MIN = 0.25 and α MAX = 0.75) were used for the entire distance matrix D 84. For the representation of our hybridization networks (Figs. 4, 5b, 6b and 7b), we used the backbone IE phylogenetic tree inferred by Gray and Atkinson (Fig. 1 in ), mapping into it the detected lexical hybrids and word borrowing events with their respective reticulation degrees. Our program for inferring explicit hybridization networks is available at:
www.info2.uqam.ca/~makarenkov_v/makarenv/hybrids_detection.zip. The data used in our study can be found at: www.trex.uqam.ca/biolinguistics/Biolinguistic_networks_data.zip.
Reconstruction of split graph-based linguistic networks
Reconstruction of galled linguistic networks from word trees
Several methods have been developed for inferring consensus phylogenetic networks from contradictory sets of two or more phylogenetic trees. They include, among others, cluster networks , galled networks  and level-k networks . A cluster network is a rooted phylogenetic network obtained from a given set of clusters (i.e., set of bipartitions). In such a network, every branch represents exactly one input cluster. A galled network is a rooted phylogenetic network in which each reticulation has a tree cycle. A tree cycle is an undirected cycle consisting of two disjoint tree paths between a tree node and a reticulation node. A level-k network is a rooted phylogenetic network, such that the maximum number of reticulations contained in a biconnected component equals k. A given set of clusters can always be represented by a galled network, but not necessarily by a level-k network . These three methods have been implemented in the Dendroscope software . We conducted our analyses with all of them but present here only the results of the galled network method which provided the “most interpretable” linguistic networks (i.e., networks in which the obtained reticulations correlate the best with known contacts between natural languages). Since for running this method we needed a set of phylogenetic trees, we reconstructed word phylogenies for each of the 200 meanings of the Swadesh list. We used the normalised Levenshtein metric , denoted here by d L , to calculate the distances between the cognate word forms of the same meaning; the distance between any two non cognate word forms was set to 1 (see below for more details). The Levenshtein distance between two words is defined as the minimum number of editing operations, consisting of insertions, deletions and substitution of a single letter, necessary to transform one word into the other. This distance was normalized by the maximum length of two words. The Levenshtein distance has been criticized as a poor distance for building language trees because of its reflection of chance similarity when the compared words are not cognate . Our comparative study presented below suggests that this distance can be used for building word trees from cognate data.
We applied our algorithm for inferring word borrowing events  to the word trees obtained with the normalized Levenshtein and the SCA distances (the inferred word tree topologies are available in Additional file 1). The results provided by using these distances can be considered as equivalent. The normalized Levenshtein distance allowed us to identify 23 of 28 suggested borrowings, while the SCA approach was able to detect 22 of them. For instance, the SCA-based algorithm was unable to recover the correct borrowings into English for the words flower, fruit and split (Table 1). The results of this analysis as well as the fact that orthographic cognate data are much more complete than phonological ones are the main reasons that justify the use of the normalized Levenshtein distance for inferring word trees. It is worth noting that one of the most significant differences between language history and biological evolution is that in the case of natural languages our alphabet systems change, while biological sequences change via mutation. Thus, methods using the Levenshtein distance as well as the more historically-oriented SCA distance may have shortcomings, since both of these distances are based on the idea that similarities and differences are due to mutations. For example, the distance between French tête and Latin testa should be 0 in linguistic terms, since the sound change was completely regular. Moreover, some words may contain cognate material, but only in parts. For example, the French word soleil is different from Italian sole, since it stems from a suffixed form of Latin sol, namely Latin soliculus. This case cannot be handled successfully by the Levenshtein and SCA distances, and the use of any of them will lead to the addition of noise to the distance matrix.
Borrowings can be seen as mutations in some parts, since they are not produced by regular sound change. Thus, methods based on sequence similarity, like those using the Levenshtein distance, may have advantages in identifying borrowings over methods that seek to ignore regular dissimilarities between words, like those using the SCA distance. Furthermore, the presented method could be modified to account for language-specific distances, which could be measured by other algorithms, as for example, the LexStat algorithm by List  or the algorithm proposed by Steiner et al. .
Results and Discussion
Hybrid languages emerge in a few generations as a new means of communication between two (or more) populations not sharing a common language. In many cases, e.g., when we found that Old Armenian is a lexical hybrid of Old Persian and Old Greek, we should interpret the results of our algorithm as the identification of the influence, e.g., cultural, political or military, which the two parent languages (i.e., the donors) had on their lexical hybrid (i.e., the recipient), at possibly different periods of time, and which could last over several centuries.
As known from evolutionary biology, the position of hybrid species in a phylogenetic tree or network is often uncertain . Furthermore, some of the hybrids added to the data can influence the position of their parents when a phylogenetic tree or network is inferred. Often a hybrid is placed as a direct neighbor of one of its parents in a phylogenetic tree or network, and the parents’ location may change when this hybrid is removed from the data set. Thus, some of the results presented in this section were obtained after rerunning our algorithm on the distance matrices from which the detected lexical hybrids, identified at the first run of this algorithm, were removed.
Here we present the most important reticulation events characterizing the evolution of IE languages which were identified by the three competing algorithms for inferring split graphs, galled networks and our explicit hybridization networks, respectively. The related historical facts and justifications are also discussed. Since only lexical data were considered in our study, the presented phylogenetic networks represent interactions between languages which are mainly based on lexical borrowings. They do not account for other language interactions, such as contact-induced syntactic restructuring, for example.
Network relationships within the Germanic group
Pennsylvania Dutch as a recipient of lexical material from English (by word borrowing) and German (by inheritance): Pennsylvania German or Pennsylvania Dutch (Penn Dutch) is a variant of German developed by the descendants of German, French (from Alsace and Lorraine) and Swiss emigrants to the East Coast of the United-States . These migrants settled in the Unites-States in the 17th and 18th centuries. Pennsylvania Dutch borrowed many words from English, particularly in the 19th century.
Frisian as a recipient of lexical material from Old English (by word borrowing) and the ancestor of Flemish, Afrikaans and Dutch (by word borrowing, but the inheritance from a close common ancestor is also possible here): The Frisian dialects are spoken in the northern parts of the Netherlands and Germany . They are the closest living languages to English, after Scots. Due to the long lasting influence of Old Dutch (since the Middle Ages), Frisian is now more similar to Dutch than to English (see a greater reticulation degree obtained for Old Dutch than for Old English in Fig. 5b, i.e., 0.71 vs. 0.29).
Sranan as a recipient of lexical material from English (by word borrowing) and Old Dutch (by word borrowing): Sranan is an English-based creole language spoken in Suriname . After the invasion of Suriname by the Dutch in 1667, Sranan’s vocabulary was greatly influenced by Dutch. Sranan also borrowed some Portuguese and African words.
Riksmål as a recipient of lexical material from Danish (by word borrowing) and Icelandic (by word borrowing, but the inheritance from a close common ancestor is also possible here): Historically, the North Germanic languages were divided into three main branches: East Scandinavian (Danish and Swedish), West Scandinavian (Icelandic, Faroese and Norwegian) and Old Gutnish . Riksmål (or Bokmål) is now the most widely-used written standard of contemporary Norwegian. It was strongly influenced by Danish, because of the political domination of Denmark over Norway during several centuries. Nowadays, Riksmål is closer to Danish than to Icelandic and Faroese (see the corresponding reticulation degrees in Fig. 6b).
The following common features can be observed when comparing the explicit networks provided by our algorithm to those given by the split graphs (Figs. 5a and 6a) and galled networks (Figs. 5c and 6c) methods. In the case of the North Germanic group, the split graph (Fig. 6a) allows us to identify Riksmål as a potential lexical hybrid of Danish and the ancestor of Icelandic and Faroese. Very similar reticulations were found by our method (Fig. 6b). However, the split graph does not yield any quantitative estimation of the influence of donor languages on recipient languages. In the case of the West Germanic group, the identification of network relationships in the split graph is more sophisticated (Fig. 5a). For example, we could implicitly identify in this graph the same lexical recipients as in our explicit network, but we could also see German as a recipient of lexical material from (Flemish, Afrikaans and Dutch) and Pennsylvania Dutch, or the ancestor of (Flemish, Afrikaans and Dutch) as a lexical recipient of German and Frisian. The galled network method yielded more explicit linguistic networks than split graphs. However, the galled network obtained for the North Germanic languages (Fig. 6c) incorrectly identifies Icelandic as a recipient of lexical material from Danish and the ancestor of (Faroese and Riksmål). For the West Germanic group (Fig. 5c), the reconstructed galled network was able to depict two correct recipients languages: Frisian and Pennsylvania Dutch. Nevertheless, Flemish was wrongly identified as a recipient of lexical material from Dutch and Afrikaans, and Sranan was not detected as a lexical hybrid but rather as one of the donors of Frisian.
Network relationships within the Latin group
Catalan as a recipient of lexical material from the ancestor of Spanish, Portuguese and Brazilian (by word borrowing, but the inheritance from a close common ancestor is also possible here) and from Old French (by word borrowing), and
Provençal as a recipient of lexical material from Catalan (by word borrowing) and Old French (by word borrowing, but the inheritance from a close common ancestor is also possible here).
The detected reticulation events reflect the history of the Occitan language, which is a Romance language spoken in Southern France, Northern Italy and Eastern Spain . There have been many interactions between Occitan and French since the Middle Ages. For instance, “Langue d’Oïl”, from which evolved the modern French, was spoken in the North, and “Langue d’Oc”, the ancestor of Occitan, was spoken in the South. Catalan, which is the closest relative of Occitan, is sometimes considered as one of its dialects [66, 67]. After the union of Aragon and Castile in 1479, the influence of the Iberian languages, in particular that of Spanish, on Catalan became more noticeable. Provençal is a dialect of Occitan spoken in Southern France .
The split graph obtained for the entire Latin group (Fig. 7a) represents a highly implicit linguistic network, which is not easy to interpret. For example, we could identify here Provençal as a lexical recipient with donors Catalan and the ancestor of French, Walloon and French Creole, as well as Italian as a lexical recipient with donors Ladin and Sardinian. No interpretable galled network has been obtained for the Latin language group.
Network relationships within the Slavic group
Here we identified Lusatian as a lexical hybrid of Polish and Czech (both by word borrowing). The Sorbian (or Lusatian) languages are Slavic languages spoken in North East Germany . These languages have been strongly influenced by Czech and Polish, since Lusatia is located at the border between Germany, the Czech Republic and Poland.
Network relationships within the Persian and Sanskrit groups
Wakhi as a recipient of lexical material from Tadzik (by word borrowing) and Ossetic (by word borrowing, but the inheritance from a close common ancestor is also possible here). Wakhi is an Iranian language spoken in Pamir, a mountain region between Pakistan, Afghanistan, China and Tajikistan. For the small nations of Pamir the language of oral and written communication is Tadzik. Moreover, the Wakhi oral tradition is bilingual (Wakhi and Tadzik), and most Wakhs speak Tadzik quite fluently .
Ancestor of Nepali and Khaskura as a recipient of lexical material from Hindi (by word borrowing) and Kashmiri (by word borrowing). Nepali and Khaskura are spoken mainly in Nepal, India and Bhutan. They share about 80 % of their lexicon with Hindi .
Ancestor of Lahnda and Panjabi as a recipient of lexical material from Hindi (by word borrowing, but the inheritance from a close common ancestor is also possible here) and Romani (by word borrowing). Lahnda and Panjabi are the languages spoken in Pakistan and India . The Romani migrated from Northern India to Europe between the 6th and 11th centuries . They had numerous interactions with Northern Indian, Iranian and European languages during their migrations.
Network relationships within the Celtic and French/Iberian groups
We applied our algorithm to the union of the Celtic and French/Iberian groups excluding from our analysis the lexical hybrids that we had already identified when examining the Latin group alone, i.e., Catalan and Provençal. This way, we found that the Breton subgroup was a recipient of lexical material from Old Welsh (by word borrowing, but the inheritance from a close common ancestor is also possible here) and Old French (by word borrowing). The former reticulation shows a close etymological relationship between Welsh and Breton, whereas the latter accounts for the important number of words that Breton borrowed from Old French, namely in the 15th and 16th centuries .
Network relationships within the West Germanic and French/Iberian groups
We also applied our algorithm to the union of the West Germanic and French/Iberian groups ruling out the lexical hybrids we had already detected in these groups, i.e., Catalan, Provençal, Sranan, Pennsylvania Dutch and Frisian. This allowed us to identify English as a recipient of lexical material from the Old French (by word borrowing) and Old Dutch (by word borrowing, but the inheritance from a close common ancestor is also possible here) subgroups. Mention that these two reticulations do not exclude the direct inheritance of Old English from the Anglo-Frisian and North Germanic dialects originally spoken by Germanic tribes, traditionally known as the Angles, Saxons and Jutes . Moreover, the relationship between Dutch and English originates in Old Saxon, which was spoken in North West Germany and in the Netherlands by Saxon peoples. Old Saxon was closely related to both Old English and Old Dutch . After the Norman conquest of England in the 11th century, many French words were borrowed by Middle English. Furthermore, English was replaced as the language of the upper classes by Anglo-Norman, a relative of Old French, and Old English developed into the next historical form of English, known as the Middle English language .
Network relationships between IE language groups
In our final analysis, we removed from our data set the 12 lexical hybrids already identified in the original set of 84 IE languages, thus obtaining a reduced distance matrix D 72 of size (72×72). We applied our algorithm to this reduced matrix and limited the search of recipient and donor languages to the ancestor branches of the 11 main IE language groups (Armenian, Albanian, Baltic, Celtic, Greek, Latin, North Germanic, Persian, Sanskrit, Slavic and West Germanic).
First, we identified the Armenian group as a recipient of lexical material from the Albanian and Persian groups, and, second, the Albanian group as a recipient of lexical material from the Sanskrit and Latin groups. Since the reticulation (hybridization) score, which reflect the likelihood of a reticulation event (see Formula 3), of Albanian was much higher than that of Armenian, we applied our algorithm once again after removing from the distance matrix the data corresponding to the five languages of the Albanian group. It is worth noting that the position of the Albanian group in the IE language tree has been found to be unstable by many authors [7–9, 26]. The following application of our method to the reduced distance matrix D 67 of size (67×67) allowed us to identify Old Armenian as a recipient of lexical material from Old Persian and Old Greek (Fig. 4). A similar network pattern was found by the galled network method (Fig. 9). Thus, we could identify here:
- Old Albanian as a recipient of lexical material from Sanskrit (by word borrowing, but the inheritance from a close common ancestor is also possible here) and Latin (by word borrowing). Albanian borrowed many words from Latin, in particular between the 2nd century B.C. and the 5th century A.D. . The Albanian group is also a close relative of the union of the Sanskrit and Persian in the IE language tree (see for example Fig. 1 in ).
- Old Armenian as a recipient of lexical material from Old Greek (by word borrowing, but the inheritance from a close common ancestor is also possible here) and Old Persian (by word borrowing). The Armenians stayed under Persian rule for long periods of time from the 5th century BC to the 19th century AC and the Armenian language includes a large number of Iranian loanwords in its vocabulary . Moreover, the well-known “Graeco-Armenian” hypothesis postulates that Armenian is the closest relative of Greek .
The application of computational biology methods presented here in the context of historical linguistic can be viewed as a step towards a better understanding of the evolution of natural languages [79–82]. In this paper, we adapted a recently developed bioinformatics method for inferring explicit hybridization networks  to identify reticulate relationships between languages. We also showed how the well-known split graph [43, 44] and galled network  algorithms can be applied to analyze linguistic data. While all the three competing methods can be used to reconstruct evolutionary relationships between natural languages, our method has the important advantage of identifying these relationships explicitly. It also allows one to establish the extent of influence of each of the donor languages on the corresponding recipient languages through the computation of the reticulation degree parameter. Some recent studies have used syntactic distances to infer phylogenies of IE languages [83, 84]. Syntactic parameters reveal complementary relationships between languages which are often not reflected by lexicon . This type of syntactic distances could be further used to refine the inference of linguistic networks along with plausible phonological and morphological data. It would be also interesting to extend our method to infer the exact timing of the obtained reticulation events. This will allow us to discover new historical events that have shaped the evolution of natural languages.
We thank Dr. QD. Atkinson and two anonymous reviewers for their helpful comments and suggestions.
This work was supported by Natural Sciences and Engineering Research Council of Canada, Fonds de Recherche sur la Nature et Technologies of Québec, and Fonds de Recherche sur la Société et la Culture of Québec.
Availability of data and materials
All the data presented in this article, including linguistic and phonetic data, distance matrices, methods’ parameters, reconstructed trees and networks are available at: www.trex.uqam.ca/biolinguistics.
MW and VM wrote the article and carried out the experimental study. EL carried out the experimental study. VM, LL, GL, FJL and AMD participated in the design of the study and in the search of linguistic and historical justifications for the results obtained. All authors gave final approval for publication.
The authors declare that they have no competing interests.
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