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Evolutionary paths of language
Bert Vaux
2020, EPL (Europhysics Letters)
October 11, 2025
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Abstract
We introduce a stochastic model of language change in a population of speakers who are divided into social or geographical groups. We assume that sequences of language changes are driven by the inference of grammatical rules from memorised linguistic patterns. These paths of inference are controlled by an inferability matrix which can be structured to model a wide range of linguistic change processes. The extent to which speakers are able to determine the dominant linguistic patterns in their speech community is captured by a temperature-like parameter. This can induce symmetry breaking phase transitions, where communities select one of two or more possible branches in the evolutionary tree of language. We use the model to investigate a grammatical change (the rise of the phrasal possessive) which took place in English and Continental North Germanic languages during the Middle Ages. Competing hypotheses regarding the sequences of precursor changes which allowed this to occur each generate a different structure of inference matrix. We show that the inference matrix of a "Norway Hypothesis" is consistent with Norwegian historical data, and because of the close relationships between these languages, we suggest that this hypothesis might explain similar changes in all of them.
Key takeaways
AI
The model explores stochastic language evolution influenced by social and geographical group structures.
Inferability matrices capture the dynamics of language change, notably during the rise of phrasal possessives.
The 'Norway Hypothesis' aligns with historical data, suggesting commonality in language evolution across similar languages.
Conformity and inference interact in shaping linguistic transitions, potentially trapping changes until random fluctuations occur.
Symmetry breaking may result in communities selecting distinct grammatical paths based on conformity levels.
Figures (7)
Fig. 1: A linguistic subspace in which stick people are evolving toward one of two grammars. Arrows from state 7 to 7 indicate that Siz = €, Sii = déwithe > dand Sj; = 1 es Sij- Dashed lines indicate transitions not based on inference.
Fig. 2: Symmetry breaking at a grammar branch. Parameter values T = 5,€ = 0.1,6 = 0.01, G = 1.05. Inset plot has 6 = 1.0. speakers cannot independently adopt grammars which are not inferable from their native (parental) grammar, they can do so if sufficiently large numbers of the speech com- munity are using the target grammar. In fig. 1, a tran- sition of this kind is illustrated between 4 and 6. Fig. 2 shows the evolution of a population beginning with gram- mar 0. When conformity is sufficiently strong the popula- tion arbitrarily select one final dominant grammar. Fig. 2 (inset) shows the evolution of a similar community with lower conformity. Here the symmetry between grammars 4 and 6 is unbroken. At much longer time scales, fluctua- tions may lead to one state dominating: a different form of symmetry breaking. We can understand the interaction between conformity
Fig. 3: Equilibrium of two state model (10) where «; = 0.05,€2 = 0.06 and 6 = 1.3. Each dot is a group and Ki; x exp(—rj;/o7) where ri; is the distance between groups i and j, and o = 5. Blue groups are dominated by state Y and red by X. The spatial distribution of groups takes the form of two gaussian blobs centred at (50,50) and (150, 50).
Fig. 4: (a) Transitions in a linguistic subspace of two features; each can exist in C' = 2 contexts. (b) Inference matrices for the three hypotheses. Red: Norwegian, Green: English, Blue: Swedish. An arrow from states i to j implies that Si; > Si; > 0. No arrow implies S;; = 0.
Fig. 5: The evolution of two equivalent features, each of which can occur in C = 5 contexts. Speakers start in state (0,0). €1 = 0.035,€ = 0.075,6 = 0.02,7 = 5 and 6 = 1.04 where 6 is the inferability of reverse transitions. Inset shows detail of spontaneous transition in feature X.
Fig. 6: Solid lines show features evolving according to the Nor- way hypothesis with 7 = 5. Parameter values found by least squares optimization @ = 1.1,So0g = 0.19,Sg9 = 0.19, S913 = 0.40, Soir = 0.25, Sitis = 0.06,Si315 = 0.11. The inference values for all reversals (taken all equal) were constrained to match the incomplete transition in concord and genitive, yield- ing an optimized value 0.03. Crosses show historical data col- lected for the same features. Features 2 and 3 have smaller data sets (table 1), and greater ambiguity in identification than 1. Time origin adjusted to match start of historical changes.
Fig. 7: Evolution of features amongst a single group (NV = 100) evolving according to the English hypothesis. In these examples tT = 20 epochs, 8 = 1.06 and all green (English) arrows in fig. 4 correspond to inferability « = 0.0175.
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epl draft
Evolutionary paths of language
J. Burridge1 , T. Blaxter2 and B. Vaux2
School of Mathematics and Physics - University of Portsmouth
Faculty of Modern and Medieval Languages and Linguistics - University of Cambridge
PACS 87.23.Ge – Dynamics of social systems
PACS 89.75.-k – Complex Systems
PACS 89.75.Hc – Networks and genealogical trees
Abstract – We introduce a stochastic model of language change in a population of speakers who
are divided into social or geographical groups. We assume that sequences of language changes are
driven by the inference of grammatical rules from memorised linguistic patterns. These paths of
inference are controlled by an inferability matrix which can be structured to model a wide range
of linguistic change processes. The extent to which speakers are able to determine the domi-
nant linguistic patterns in their speech community is captured by a temperature-like parameter.
This can induce symmetry breaking phase transitions, where communities select one of two or
more possible branches in the evolutionary tree of language. We use the model to investigate a
grammatical change (the rise of the phrasal possessive) which took place in English and Conti-
nental North Germanic languages during the Middle Ages. Competing hypotheses regarding the
sequences of precursor changes which allowed this to occur each generate a different structure
of inference matrix. We show that the inference matrix of a “Norway Hypothesis” is consistent
with Norwegian historical data, and because of the close relationships between these languages,
we suggest that this hypothesis might explain similar changes in all of them.
Introduction. – The last several decades have seen lution [11, 12]. Recognising language as a phenomenon
an explosion in cross-disciplinary applications of statisti- which emerges from interactions between large numbers
cal physics. This work encompasses a wide range of topics, of individuals, statistical physicists have constructed de-
from the motion of crowds [1] and the flocking of birds [2] liberately minimalist models to understand properties of
to the distribution of wealth [3], the behaviour of social its evolution [4–7, 13–16]. Simplicity is also recognised
systems [4] and, the focus of this letter, the evolution of as a virtue in the field of statistical (machine) learning,
language [5–9]. Linguistics (the study of human language) where sparsity can increase predictive power [17]. This
seeks to rigorously describe how the building blocks of lan- was also the goal of the locus classicus for phonological
guage may be combined to convey meanings [10]. Each theory: Chomsky and Halle (1968) [18]. Our aim is to
spoken language has a set of sounds or phones which are develop a simple model, which is flexible enough to cap-
typically generated by shaping airflow through the vocal ture a wide range of realistic linguistic processes, and to
tract in various ways. Phones are derived from the un- be calibrated to linguistic data sets which may be time
derlying inventory of contrastive elements in a language, dependent, geographically distributed and/or labelled by
called phonemes, by a set of phonological rules. Above social, gender or other factors.
the level of individual sounds, languages have morphologi-
Model definition. – We assume it is possible to write
cal rules for building words from morphemes (the smallest
down a detailed inventory of phones, phonological, mor-
units of meaning), and syntactic rules for combining words
phological, and syntactic rules, and lexical entries (with
together to form sentences. The world’s languages are de-
meanings) which fully define each speaker’s own version
fined by a vast array of sounds, generalizations (i.e. rules,
of their language. We refer to this as the full language
constraints, and/or associations) and lexicons, which are
state of a speaker. This inventory may be viewed as a
all constantly evolving, and it is well known to linguists
high dimensional feature vector [17]. Every speaker will
that the structures of social groups, identities, hierarchies
occupy a different location in feature space, but groups
and geography play powerful roles in controlling this evo-
of speakers may share many features in common, form-
p-1
J. Burridge et al.
ing clusters which represent distinct languages or dialects. Letting X(n, p) be a generic multinomial random vector
The process of language evolution is simply the progressive with n trials and probability vector p we have
alteration of the components of individual feature vectors. d
We divide time into epochs indexed by t ∈ {0, 1, . . .}. Ni (t) = X(ni , pi (t)) (5)
We consider a population of speakers, and focus on a sub- d
space of their language which has p different linguistic where = denotes equality in distribution. This completes
states or variants (possible feature vectors). At each time the specification of our dynamics.
t, each speaker will be in one of these p states. Language In this letter we focus on linguistic change which is
evolution is intrinsically coupled to the social and geo- driven by the inference of grammatical rules from cur-
graphical structure of society, and we may account for rent linguistic patterns observable in the PLD. In this case
this by dividing our population into n groups by some cri- speaker memories for grammar k may be viewed as the
terion or set of criteria (sex, location, social class [11,12]). PLD or patterns in the PLD generated by those rules,
Let Nik (t) be the number of speakers in group i who are rather than the rules themselves. Different rule sets may
in linguistic state k at epoch t. We define the relative generate similar patterns, so speakers may infer one gram-
frequency mar from the surface forms of another [21]. Typically, in-
Nik (t) ference is carried out by younger speakers as they learn
fik (t) = (1) their language [22]. The entries of S have the following
Ni
interpretation: subconsciously, a speaker selects the pat-
where Ni is the size of the ith group. Language evolu-
tern she is going to emulate, and then selects (infers) the
tion can be driven by children inferring altered versions
rules she believes are behind it. We have, for a speaker in
of the linguistic rules which generated the speech they
group i
have heard, and by adults switching their linguistic be-
haviour over time [19]. We allow for the possibility that P(attempt to emulate surface forms of k) = [mi ]k (6)
speakers preferentially select the most common patterns; P(infer grammar j in attempt to emulate k) = Skj (7)
an optimal strategy if matching language patterns with
interlocutors confers some advantage to a speaker. Such where [mi ]k denotes the kth component of mi . Gram-
non-linearity in decision making has been observed in hu- mar selection may therefore be viewed as a two step pro-
man social learning [20] and may be modelled by defining cess in our model. The first step – pattern selection – is
an adjusted frequency [13] driven by conformity, and the second – rule selection –
by inference from linguistic patterns. Expression (4) fol-
fik
vik = P β (2) lows by considering all possible ways in which grammar
j ij k could be inferred by this two step process using proba-
bilities (6) and (7). For other forms of linguistic change
which emphasizes more popular states when β > 1. When
like lexical change or vowel shifts its interpretation will
β < 1 higher frequencies are reduced, and lower ones em-
alter. In these cases S may be viewed as a linear re-
phasised. We call β the conformity number. We write
T weighting of frequency/conformity based selection proba-
vi = (vi1 , vi2 , . . . vip ) for the set of adjusted frequencies
bilities which captures bias effects originating from struc-
in group i. In principle each group can exhibit different
tural principles like maximal dispersion [23], automation
levels of conformity to each of the groups it is exposed to,
of production [24], ratchet effects [25] (in which changes
but for simplicity we set all conformity numbers equal.
acquire social momentum), phonetically systematic trans-
We assume that the speakers in each group are all ex-
mission errors (channel bias) and cognitive predispositions
posed to approximately the same primary linguistic data
(analytic bias) [26].
(PLD), and that this experience is captured by an n × n
We are motivated by the desire to model, in a simple
stochastic (unit row sums) matrix K where Kij is the frac-
and computationally efficient way, the evolutionary routes
tional observational weight placed on group j by speakers
of language change amongst populations that tend to con-
in group i. We call K the importance matrix. It encodes
form (find consensus) and are socially and spatially la-
all information that we wish to capture about social or
belled. Our computational implementation requires five
geographical groupings and their connectivity. We endow
lines of vectorized Python [27]. The modelling of language
each group with a time decaying memory for the confor-
change is by now well established and our model has its
mity adjusted states of other groups
X roots in existing approaches. A matrix with a similar in-
mi (t) = e−1/τ mi (t − 1) + (1 − e−1/τ ) Kij vj (t). (3) terpretation to our S appears in work on the evolution of
j Universal Grammar [16]. Time decaying speaker memo-
ries similar to (3) were studied in the utterance selection
Memories are related to current behaviour via a p × p
model [7], which also allowed linear re-weighting of selec-
stochastic inference matrix S: at each epoch we take the
tion probabilities, and our model of consensus may be seen
distribution of speakers using each variant to be multino-
as a modified majority rule [28]. The emergence of con-
mial with probability vector
sensus in language, including in spatial settings, is also
pi (t + 1) = mi (t)S. (4) explored in the naming game [15, 29].
p-2
Evolution of grammar
Symmetry breaking transition
0 1 2 impossible by inference alone
(conformity driven)
Fig. 1: A linguistic subspace in which stick people are evolving
toward one of two grammars. Arrows from state P i to j indicate
that Sij = ǫ, Sji = δ with ǫ > δ and Sii = 1− j6=i Sij . Dashed
lines indicate transitions not based on inference.
Fig. 2: Symmetry breaking at a grammar branch. Parameter
When S is the identity matrix then the probability that values τ = 5, ǫ = 0.1, δ = 0.01, β = 1.05. Inset plot has β = 1.0.
grammar k will be inferred by a speaker in group i is equal
to her memory [mi ]k for the frequency of that grammar.
In this case groups of speakers can become fixed in one speakers cannot independently adopt grammars which are
grammar state when all others have been forgotten. Fix- not inferable from their native (parental) grammar, they
ation occurs because it is impossible to recreate any new can do so if sufficiently large numbers of the speech com-
grammars by mistaken inference. In the case β = 1 this munity are using the target grammar. In fig. 1, a tran-
process generates neutral evolution [30, 31], where vari- sition of this kind is illustrated between 4 and 6. Fig. 2
ants in future generations appear with a probability that shows the evolution of a population beginning with gram-
is proportional to their frequency in previous generations. mar 0. When conformity is sufficiently strong the popula-
Under some circumstances it is useful to consider the tion arbitrarily select one final dominant grammar. Fig. 2
large population (deterministic) limit of the model, which (inset) shows the evolution of a similar community with
for large τ may be approximated by the following set of lower conformity. Here the symmetry between grammars
coupled differential equations 4 and 6 is unbroken. At much longer time scales, fluctua-
tions may lead to one state dominating: a different form
1 X of symmetry breaking.
ṁi = Kij vj − mi (8) We can understand the interaction between conformity
τ j and inference transitions by considering a system with two
[mi S]βk grammar states X and Y . Such a system will have an
[vi ]k = P β
. (9) inferability matrix with general form
j [mi S]j
X Y
From this we see that in the deterministic setting, mem- X
1 − ǫ1 ǫ1
ory length τ linearly scales the rate of change of linguistic S= . (10)
Y ǫ2 1 − ǫ2
memory. In the stochastic case it also functions as the
window length of a time average, and so dampens fluctu- Suppose that our speech community consists of a single
ations. group, and let m = (v, 1 − v) then
Branching and symmetry breaking. – We now
p = (v(1 − ǫ1 − ǫ2 ) + ǫ2 , 1 − ǫ2 − v(1 − ǫ1 − ǫ2 )) . (11)
explore a simple inferability matrix which illustrates how
a speech community can select from two or more alterna- In statistical equilibrium the expected values of the entries
tive routes of linguistic evolution. Consider the linguistic of this vector are equal to the expectations of the current
subspace illustrated in fig. 1, where arrows between states frequencies of the two grammars in the population. Fluc-
indicate that one grammar is inferable from the other (the tuations of the true frequencies about these expectations
direction i → j indicates that j is easier to infer from i will be of order N −1/2 where N is the size of the commu-
than vice versa). In fig. 1 most speakers will eventually end nity. For large communities we can therefore approximate
up in state 4 or 6, so in a large and socially disjointed or ge- the true equilibrium frequencies with their expectations.
ographically dispersed speech community we would even- Replacing the memory values v with their expression in
tually expect to see both kinds of grammar. However, in a terms of the frequency, f , of X, we have the equilibrium
more strongly connected community with sufficiently large condition
conformity number, β, we may see a symmetry breaking fβ f − ǫ2
phase transition. To understand this we recall that while = . (12)
f β + (1 − f )β 1 − ǫ1 − ǫ2
p-3
J. Burridge et al.
(a) (b)
100
(2,0)
15
80 13
(1,0) (2,1)
60 9 11
10
40 14
(0,0) (1,1) (2,2)
12
20 8
1 4 6
0 (0,1) (1,2)
0 50 100 150 200 2
(0,2) 0
Fig. 3: Equilibrium of two state model (10) where ǫ1 =
0.05, ǫ2 = 0.06 and β = 1.3. Each dot is a group and Fig. 4: (a) Transitions in a linguistic subspace of two features;
Kij ∝ exp(−rij /σ 2 ) where rij is the distance between groups each can exist in C = 2 contexts. (b) Inference matrices for
i and j, and σ = 5. Blue groups are dominated by state Y and the three hypotheses. Red: Norwegian, Green: English, Blue:
red by X. The spatial distribution of groups takes the form of Swedish. An arrow from states i to j implies that Sij > Sij >
two gaussian blobs centred at (50, 50) and (150, 50). 0. No arrow implies Sij = 0.
For low conformity this equation has only one solution, but of dense population. Isogloss dynamics of this kind, which
for sufficiently large β a second appears, and the speech is driven by surface tension, is explored in [13, 14].
community must select one, but we cannot tell in advance
which. Even if there is an inferability bias toward one The timing of linguistic changes. – We now con-
state, conformity may keep the community closer to the sider the conditions under which two or more linguis-
other by emphasising it in speakers’ memories. If ǫ1 = tic changes which are equally likely to be inferred from
ǫ2 = ǫ then we have a symmetry between the two states, the current grammar can spontaneously occur at different
and for low conformity the solution is f = 1/2. When times. Often grammatical changes spread though multiple
linguistic contexts over time (examples include the spread
β> (13) of do-support through different clause types in Middle En-
1 − 2ǫ
glish [33] and the spread of the new pronoun chdi between
then this single solution is replaced with two f = 1/2 ± a different syntactic contexts in northern Welsh [34]). To
for some a ∈ [0, 1/2], only one of which is selected by capture this we consider features which occur in C ∈ N
the community. Hence the term symmetry breaking [32], contexts, and simultaneously evolve two equally inferable
which we use to refer generically to the appearance of features X and Y . The state of a single speaker is then
multiple steady states from which the community selects. specified by the integer pair (i, j) indicating that she uses
In thermodynamic systems symmetry breaking generates feature X in i contexts, and Y in j contexts. Because the
macroscopic ordering, and is induced by non-linearity in spread of a feature from one context to another may be
the response of the microscopic constituents of the sys- easier to infer than its first appearance, we set the infer-
tem to their local environment. The strength of this non- ability of the first appearance of a features to be ǫ1 , with
linearity is typically controlled by temperature. In our later changes of the form (i, j) → (i+1, j) or (i, j +1) hav-
case the non-linearity which induces symmetry breaking ing inferability ǫ > ǫ1 . Such acceleration effects may also
lies in the relationship between v and f , and is controlled be caused by social factors [25,35]. A schematic diagram of
by β, which plays a role analogous to inverse temperature the square state space in the C = 2 case is shown in fig. 4
in thermodynamic systems. (a). The spread of a feature may be tracked by calculating
If we imagine the branch in fig. 1 being part of a much the average location of the population as its members nav-
larger network of grammars, then we see that symmetry igate the square. The appearance of new features may be
breaking will cause communities to select one particular prevented or delayed if conformity to the current dominant
route among many through the network. In spatially dis- linguistic state overwhelms any inferability bias toward
tributed cases, we might expect to see different routes new features. This conformity trapping may be overcome
taken in different places or amongst certain well defined by random fluctuations, where a large enough number of
and separated groups, leading to dialects and eventually speakers spontaneously adopt the new feature, reducing
distinct languages. A simple illustration of how a spatially the dominance of the (0, 0) state. A simulation example is
distributed system can support two equilibrium states is shown in fig. 5. Here, both features remain trapped at low
given in fig. 3, where the importance matrix K is struc- levels until fluctuations spontaneously allow one to emerge
tured to model a gaussian spatial interaction kernel be- fully, following the classic S-curve evolution [36, 37].
tween groups. Here we see that a domain wall or isogloss At any moment in time a language has the potential
(in linguistic terminology) has formed between two regions to undergo changes, but their timing appears difficult to
p-4
Evolution of grammar
Table 1: Features for a subspace of Norwegian / Swedish /
Danish / English grammar, and numbers of texts in datasets.
Label Feature Abbrev. Texts
1 uniform genitive endings Noun 3076
2 loss of concord for genitive Concord 933
3 loss of lexical genitives Genitive 1437
4 -s is a phrasal affix Affix NA
feature 4
{1, 2, 3} → 4. (14)
In another hypothesis (the ‘Swedish hypothesis’ [39]) the
reverse is true, with the reanalysis happening first in a
Fig. 5: The evolution of two equivalent features, each of which very restricted context and causing the latter changes
can occur in C = 5 contexts. Speakers start in state (0, 0).
ǫ1 = 0.035, ǫ = 0.075, δ = 0.02, τ = 5 and β = 1.04 where δ 4 → {1, 2, 3}. (15)
is the inferability of reverse transitions. Inset shows detail of
spontaneous transition in feature X. Our main focus is on a ‘Norwegian hypothesis’: that just
one of these changes, the change to uniform genitive end-
ings, is a necessary precondition for the reanlaysis, and
predict. One proposed explanation for major changes [35]
the other changes result from it
is the trigger event: some relatively small change in part of
the linguistic system which facilitates a much wider shift, 1 → 4 → {2, 3}. (16)
which may then accelerate. The natural question then
is: what triggered the trigger? In our simple model, it is Our model of these processes is simplified in a number
possible for changes to be trapped and waiting to happen of ways. First, we examine only a very small subsystem
with their release an inherently unpredictable event. of the grammar. In reality these changes took place in
The rise of phrasal marking of possessive. – We the context of a much more complex grammatical system
now use our model to provide a simplified account of his- and there are other changes, involving other grammati-
torical changes within a linguistic subspace relating to the cal features, which might be argued to have played a role.
genitive case. One function of the genitive is to signify Second, our four labelled features are abstractions from
possession (e.g. in modern English ‘Anna’s shoes’ ). The more complex sets of sub-features (loss of lexical genitives
change we are interested in took place in the grammar of in different contexts; spread of the uniform -(e)s ending to
English and Continental North Germanic (Swedish, Dan- different classes of words, or even to different individual
ish, Norwegian). In each language, a reanalysis of the words; loss of concord in different grammatical contexts
genitive ending -(e)s takes place where it goes from hav- and on different classes of words). Third, we assume that
ing scope over the preceding word to having scope over inferential changes (from the current grammar) occur in
the preceding phrase; for example one feature at a time, although speakers can of course
jump between any two grammar states provided there are
þe [kyng]is of ffraunce → [the king of France]’s. others in those states within the community. These sim-
| {z } | {z } plifications allow us to describe the model and its output
Middle English Modern English
in graspable terms.
In all four languages, other changes affect the genitive. We assume that each feature is either present or ab-
Among these: all endings are replaced by a uniform end- sent in each speaker, so that each speaker’s grammar
ing, -(e)s; all functions of this ending are lost except mark- has a representation of the form (σ1 , σ2 , σ3 , σ4 ) where
ing of possessive (loss of ‘lexical genitives’); a pattern by σk ∈ {0, 1} is the indicator of feature k. For brevity
which all elements of the phrase are independently marked we treat this state as the binary representation of an in-
for genitive (‘concord’) is lost. These changes are listed teger (σ1 , σ2 , σ3 , σ4 ) ≡ 8σ1 + 4σ2 + 2σ3 + σ4 . Within
and labelled in table 1. Different hypotheses about the this state space there are 16 possible grammars and all
relationships among these changes have been proposed, speakers start in state (0, 0, 0, 0) ≡ 0 and eventually reach
which can be expressed as different inferability matrices. (1, 1, 1, 1) ≡ 15. The set of inferable transitions for each
In one hypothesis (the ‘English hypothesis’ [38]), these lat- hypothesis is shown in fig. 4 (b).
ter changes create the ambiguity in surface forms which Fig. 6 shows linguistic data from the Annotated DN on-
are necessary for the reanalysis. That is, with reference line [40], a corpus of medieval Norwegian charters. To gen-
to table 1, features 1, 2 and 3 are needed in order to infer erate the data, for each change, a restricted context that
p-5
J. Burridge et al.
1.0 noun 1.0 noun
affix affix
0.8 concord 0.8 concord
1.0 noun
genitive genitive
affix
0.6 0.6
concord
0.8 genitive
0.4 0.4
Fraction of Speakers
0.2 0.2
0.6
0.0 0.0
0 200 400 600 0 200 400 600
0.4 1.0 noun 1.0 noun
affix affix
0.8 concord 0.8 concord
0.2 genitive genitive
0.6 0.6
0.4 0.4
0.0
1300 1350 1400 1450 1500 1550 0.2 0.2
Year
0.0 0.0
0 200 400 600 0 200 400 600
Fig. 6: Solid lines show features evolving according to the Nor-
way hypothesis with τ = 5. Parameter values found by least Fig. 7: Evolution of features amongst a single group (N =
squares optimization β = 1.1, S0 8 = 0.19, S8 9 = 0.19, S9 13 = 100) evolving according to the English hypothesis. In these
0.40, S9 11 = 0.25, S11 15 = 0.06, S13 15 = 0.11. The inference examples τ = 20 epochs, β = 1.06 and all green (English)
values for all reversals (taken all equal) were constrained to arrows in fig. 4 correspond to inferability ǫ = 0.0175.
match the incomplete transition in concord and genitive, yield-
ing an optimized value 0.03. Crosses show historical data col-
lected for the same features. Features 2 and 3 have smaller dataWe earlier demonstrated that the timing of linguistic
sets (table 1), and greater ambiguity in identification than 1.
changes in the stochastic model can be unpredictable un-
Time origin adjusted to match start of historical changes.
der certain conditions, and we now consider this possibility
along with the other two hypotheses. When the inferabil-
could be exhaustively searched and quantified was identi- ity values corresponding to each arrow in fig. 4 are small
fied: for uniform genitive endings, patronymics in the form in comparison to the conformity number (in the sense of
name-GEN+sonr (GEN stands for standard genitive end- eq. (13)) then the majority of the population may become
ing and sonr ≡ son); for the loss of concord, agreement be- trapped by conformity in its current state. In order to
tween genitive forename and patronymic; and for the loss escape this state and continue linguistic evolution, they
of lexical genitives, the case taken by the preposition mil- must be freed by random fluctuations. To demonstrate
lum ‘between’. Feature 4, the change in scope from word- the combined effect of conformity and fluctuations, fig. 7
to phrasal-level affix, is very hard to quantify from occur- shows four simulations of the English hypothesis, accord-
rences in texts as most potential examples exhibit surface ing to which features 1,2,3 must evolve before the phrasal
ambiguity between the older and newer structures; for this affix. Although the inference matrix treats each of these
reason, no linguistic data are presented for this feature. preliminary features as equivalent, because of the trap-
For simplicity we compare our data to the deterministic ping effects of conformity, the order in which they appear
form (8) of the model. We use calendar years as our unit is randomized, as in fig. 5. In the lower conformity, non-
of time, and set τ = 5, equivalent to ≈ 90% turnover of trapping regime all three features would evolve at the same
memory every 10 years. Although τ cannot be directly time, consistent with the deterministic model. Therefore,
measured, we are motivated by the fact that substantial in the presence of trapping, if we cannot be sure exactly
linguistic changes can take place over a decade for speakers when the phrasal affix arose in comparison to the other
across a wide range of ages [19]. To mimic the embedding features, then all three hypotheses may be consistent with
of the inference matrix (fig. 4 (b)) in a larger network, we any observed sequence of changes. We qualify this state-
incorporated a chain of three precursor states to state 0, ment as follows. Trapping of features which are all equally
and began the entire community in the first of these. To likely to evolve at a given time requires quite a delicate
generate the model fit in fig. 6 we performed a least squares balance between conformity and inferability, and features
optimization of the conformity number and elements of the tend to arise rapidly once they escape the trap. The time
inference matrix, restricted to the Norway form. The cor- intervals between feature appearance can also be highly
respondence between model and data in fig. 6 highlights variable. For these reasons the close fit to experimental
the plausibility of the Norway hypothesis. However the data shown in fig. 6 would be hard to achieve in the trap-
lack data on the rise of phrasal affix means that a range ping regime, both in terms of feature timing and S-curve
of inferability values, consistent with the hypothesis, yield shape. We therefore suggest that the non-trapping case
similarly good fits to data. We have therefore only estab- is the more likely of the two explanations that our model
lished that the structure of S implied by the hypothesis is provides for observations, at least in the case of Norway.
consistent with data; there is uncertainty as to the mag- What are the implications of this for the three hypothe-
nitudes of its non-zero entries. ses? Since each hypothesis applies to a different language,
p-6
Evolution of grammar
and Norwegian is the only one for which we currently have [11] Chambers, J. K. and Trudgill, P., Dialectology (Cam-
high quality quantitative data, then it is possible that all bridge University Press, Cambridge) 1998
three are correct. However, these languages are closely [12] Labov W., Principles of Linguistic Change (Blackwell,
related: medieval Danish, Swedish and Norwegian were Oxford) 1994
mutually comprehensible and formed a single, continuous [13] Burridge J., Phys. Rev. X, 7 (2017) 031008.
[14] Burridge J., Royal Society Open Science, 5 (2018)
dialect area [41]; English was a near geographical neigh-
171446.
bour and close relative. Given that such similar changes
[15] Baronchelli, A. and Felici, M. and Loreto, V. and
happened in all these languages at a similar time, it would Caglioti, E. and Steels, L., Journal of Statistical Me-
be surprising if the mechanisms by which they arose were chanics: Theory and Experiment, 2006 (P06014) .
different in each case. We have provided a simple model [16] Nowak, M. A. and Komarova, N. L. and Niyogi, P. ,
which matches the historical data for Norway, and sup- Nature, 291 (2001) 114.
ports the Norway hypothesis. While we offer no firm con- [17] Hastie T., Tibshirani R. and Friedman J. , The Ele-
clusion about the veracity of the three hypotheses, we sug- ments of Statistical Learning (Springer, New York) 1994
gest that the possibility of a single unifying explanation [18] Chomsky, N. and Halle, M., The Sound Pattern of En-
should be considered, requiring further data collection, glish (Harper and Row, New York) 1968
and a more sophisticated application of our model, involv- [19] Sankoff, G. and Blondeau, H. , Language, 83 (2007)
560.
ing geographical and cross-linguistic interactions, which
[20] Morgan, T. J. H., Rendell, L. E. Ehn, M. Hoppitt,
may be implemented using the importance matrix, K.
W. and K. N. Laland, Proc. R. Soc. B, 279 (2012) 653.
Summary. – We have introduced a model of language [21] Hale, M. and Reiss, C., The phonological enterprise
change which is driven by social conformity and the infer- (Oxford University Press, Oxford) 2008
ence of new linguistic rules from those currently in use. We [22] Yang, C., Language variation and change, 12 (2000) 231.
[23] Liljencrants, J. and Lindblom, B. , Language, 48
have explored some essential properties of the model, in-
(1972) 839.
cluding symmetry breaking and conformity trapping, and [24] Bybee, J., Language variation and change, 14 (2002) 261.
demonstrated how it may be used to quantitatively ad- [25] Lieberson, S., A Matter of Taste:How Names, Fashions
dress a specific linguistic question. The model in principle and Culture Change (Yale University Press, New Haven)
allows exploration of a variety of different processes and 2000
changes in greater detail (possibly requiring a reinterpre- [26] Moreton, E. , Phonology, 25 (2008) 25.
tation of S), including the effects of geographical distribu- [27] Van der Walt, S., Colbert, S. C., and Varoquaux,
tion, and interconnectivity of social groups. G. , Computing in Science and Engineering, 13 (2011) 22.
[28] Krapivsky, P. L. and Redner, S., Physcial Review Let-
∗∗∗ ters, 90 (2003) 238701.
[29] Castello, X. and Baronchelli, A. and Loreto V.,
The authors are grateful to the Royal Society for an The European Physical Journal B, 71 (2009) 557.
APEX award (2018-2020), funded by the Leverhulme [30] Blythe R. A. and McKane A. J., Journal of Statistical
Mechanics: Theory and Experiment, 2007 (P07018) .
Trust.
[31] Kauhanen H. , Journal of Linguistics, 53 (2016) 327.
[32] Blundell S. J. and Blundell K. M., Concepts in Ther-
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Liljencrants, J. and Lindblom, B. , Language, 48 (1972) 839.
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Blythe R. A. and McKane A. J., Journal of Statistical Mechanics: Theory and Experiment, 2007 (P07018) .
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Blythe R. A. and Croft W. , Language, 88 (2012) 269.
Ghanbarnejad F., Gerlach M., Miotto J. M. and Altmann E. G., J. R. Soc. Interface, 11 (2014) 20141044.
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Norde M. , The History of the Genitive in Swedish. A Case Study in Degrammaticalization (Universiteit van Am- sterdam, Amsterdam) 1997
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FAQs
AI
What explains the role of conformity in language evolution?
add
The model reveals that a high conformity number (β > 1) drives language communities towards dominant grammar states, while lower β allows for multiple grammatical evolutions to coexist.
How do speaker memories influence language change dynamics?
add
The study finds that speaker memories decay over time, influencing linguistic states' probabilities, which significantly affects the timing and nature of language evolution.
When did key changes in the genitive case occur in English?
add
The model suggests that major shifts in the genitive case began around the 14th century, coinciding with phonological simplifications observed in historical texts.
How did the model approach inferability and its impact on changes?
add
The research demonstrates that different inferability matrices dictate the sequence of linguistic changes, highlighting how speakers navigate and adopt grammatical features in evolving contexts.
What implications arise from exploring dialect formation through this model?
add
The findings indicate that spatial and social group interconnectivity substantially shapes dialect emergence, suggesting potential pathways for distinct language development across regions.
Bert Vaux
University of Cambridge, Faculty Member
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Monica Tamariz
2010
This paper describes evolutionary dynamics in language and presents a genetic framework of language akin to those of and Mufwene , where language is a complex system that inhabits, interacts with and evolves in communities of human speakers. The novelty of the present framework resides in the separation between form (phonology and syntax) and meaning (semantics), which are described as two different selection systems, connected by symbolic association and by probabilistic encoding of information.
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Evaluating the role of quantitative modelling in language evolution
Maurício de Jesus Dias Martins
The Past, Present and Future of Language Evolution, 2014
Models are a flourishing and indispensable area of research in language evolution. Here we highlight critical issues in using and interpreting models and suggests viable approaches. First, contrasting models can explain the same data and similar modelling techniques can lead to diverging conclusions. This should act as a reminder to use the extreme malleability of modelling parsimoniously when interpreting results. Second, quantitative techniques similar to those used in modelling language evolution have proven themselves inadequate in other disciplines. Cross-disciplinary fertilization is crucial to avoid mistakes previously occurred in other areas. Finally, experimental validation is necessary both to sharpen models' hypotheses, and to support their conclusions. Our belief is that models should be interpreted as quantitative demonstrations of logical possibilities, rather than direct sources of evidence. Only an integration of theoretical principles, quantitative proofs and empirical validation can allow research in the evolution of language to progress.
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Using spatial patterns of English folk speech to infer the universality class of linguistic copying
James Burridge
Physical Review Research, 2020
Both linguistic and genetic evolution involve copying and mutation of variants. The simplest copying process assumes that variants are reproduced at a rate equal to their current frequency, exemplified by Kimura's stepping stone model of neutral evolution, and the voter model. In this case, spatial patterns are driven by noise. In the linguistic context, an alternative possibility is that speakers preferentially select variants which are already popular, yielding patterns driven by surface tension, exemplified by the Ising model. In this paper, we model language change using a spatial network of speakers, inspired by the Hopfield neural network. The model's universality class-Voter or Ising-is determined by speakers' learning function. We view maps generated by the Survey of English Dialects as samples from our network. Maximum likelihood analysis, and comparison of spatial auto-correlations between real and simulated maps, indicates that the underlying copying processes is more likely to belong to the conformity-driven Ising class.
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