theories and models of language change

RolandMühlenbernd

Review: Evolut.Approaches toLanguage Change

A Simulation Modelof Language ChangeLinguistic Items

The Threshold Problem

Social Impact Theory

The Simulation Model

Simulation Results

Further ’Spatial’Simulation Models

Homeworks

Theories and Models of Language ChangeSession 5: Models I - Social Factors and Structure

Roland Mühlenbernd

May 19, 2015

RolandMühlenbernd






Simulation Results


Homeworks

Review: Universal Darwinism

Mechanisms of universal evolution:

1. variation: continuing abundance of different elements

2. selection : number/probability of copies of elements -depending on interaction between element features andenvironmental features

3. replication: reproduction/copying of elements

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Review: Evol. Approaches to Language Change

Evolution and Language Change:

1. variation: how come new variants to a speechcommunity?

I innovation/actuationI language contact: borrowing, structure primingI transformation of already existing material:

recombination, reanalysis, adaptation2. selection : how are (competing) variants selected

I substitution vs differential replicationI selection vs evolutionary driftI social vs functional factors

3. replication: how do linguistic variants reproduce?I types vs tokensI replication units and replicatorsI mechanism of replication: e.g. social learning,

imitation, priming

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Language Change - Broad and Narrow Sense

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Methods

What is the Scientific Method?I research, data acquisitionI theorizeI testI evaluate

TheoryField Work,Experiments

Comp. Model,Simulation

structure, behaviour

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Language Change: Linguistic Items

”Languages are evolving populations of linguistic items.”(Nettle, 1999)

I isolatable elements of phonological and grammaticalstructure

I that can be individually learned and changed in languagehistory

I cultural traits, linguistic memes, linguemes

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Exercise I

What is according to Nettle (1999) the source of variation inlanguage-related cultural evolution?

I imperfect learning√

I language contactI speaker innovation

The source of variation in cultural evolution modelsis of the imperfect-learning type, and for convenienceI will adopt the same strategy here...

David Nettle (1999): Using Social Impact Theory to simulatelanguage change

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Biological, Cultural and Linguistic Evolution

I in biological evolution an individual inherits genes fromits parents with even probability getting the variant ofmother or father

I cultural evolution models assume infinite populationswithout particular structure (mean field)

I in linguistic evolutionI an individual ”inherits genes” (acquires linguistic items)

from a wider range of sourcesI the speech communities are finite and socially and

spatially structuredI new variants cannot be expected to cause change as the

next generation will simply discount it in favor of the morecommon old pendant (threshold problem)

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The Threshold Problem (Exercise II)

What is Nettle’s description of the ’threshold problem’?I In language change a new variant can only spread, if the

innovator of it passes a threshold of social status andinfluence, and this threshold is unrealistically high.

I In language change the new variant can only spreadsociety-wide, if the the degree of ’locality’ or’parochialism’ of the social structure passes a particularthreshold.

I In language change new variants can only establish if theypass the threshold of frequency, which in the beginningthey never have.

√

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I if the learner always adopts the common norm, the resultafter a few generations is homogeneity

I if the learner is biased towards new variants, those have achance of overcoming the threshold

I two possibilities of such a bias:1. social: influential people are bearers of new variants2. functional: new variant has attribute that makes it easier to

acquire or use

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Exercise III

What is according to Nettle (1999) the principal feature thatdefines the functional bias of a linguistic item?

I learnability√

I brevityI specificity

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Social Impact Theory (Latane 1981): The likelihood that aperson will respond to social influence will increase with:

I Strength: how important the influencing group of peopleare to you.

I Immediacy: how close the group are to you (in space andtime) at the time of the attempted influence.

I Number: How many people there are in the group.

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I Idea: a speaker will adopt the variant with the greatestimpact on him

I the impact of variant p is influenced by social andfunctional parameters: Ip = bp × f (Sp,Dp,Np), whereby

I bp represents acquisitional bias for using pI Np is the number of individuals using p (number)I Sp is the status of a individual using p (strength)I Dp is the social distance to a individual using p

(immediacy)

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Social Impact TheoryNettle’s formula:

Ip = bp × Nap ×

∑i si × 1

d2i

Np

0 1 2 3 4 5 6 7 80

0.2

0.4

0.6

0.8

1.0

di

1d2

0 1 2 3 4 5 6 7 80

1

2

3

4

Np

Nap

a = .7a = .5a = .3

I Why 1/d2? Answer: established in SIT, apparently by analogywith gravitation laws, where effects decrease with the square ofdistance

I Why exponent a? Answer: The persuasiveness of a belief doesnot rise linearly with the number of people holding it.

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Exercise IV

Ip = bp × Nap ×

∑i si × 1

d2i

Np

Given the ’Social Impact Theory’ formula (3) (on page 102) forthe impact of a variant p. Given the following values:

I variant p has a functional bias b of 0.5I the parameter a is 1I the language learner X is influenced by 3 persons using

variant p:I social status 5, social distance 2I social status 3, social distance 2I social status 8, social distance 4

What is the impact value of variant p on language learner X?

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Simulation Models

A simulation model

I takes the main relationships of real world situations andexplore effects across a range of conditions

I can cover complex iterated processes that cannot bepredicted by simple thought of deduction

I helps to explore under what assumptions and initialconditions does the system behave in the desired way

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The Simulation ModelNettle’s social map:

5 4 3 2 1 1 2 3 4 5 5 4 3 2 15 4 3 2 1 1 2 3 4 5 5 4 3 2 15 4 3 2 1 1 2 3 4 5 5 4 3 2 1

I horizontal: familial social ties (parents, children...)I vertical: horiz. social ties (own peer group, friends...)I In each life stage (simulation step) a whole cohort along

the vertical goes through language acquisitionI age 1-3: for possible variants p and q compute Ip and Iq;

acquire variant with higher impact valueI age 1 has no influenceI age 4-5: stay at acquired variantI age 1-2: 5% mutation, due to imperfect learning

I After each life stage: increase ages by one and replace age5 by age 1 (replace dead by newborn agents)

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Nettle’s toroidal social map:

5 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 55 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 5

Table: Nettle’s 20× 20 social map with initial age structure.

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Simulation ResultsParameter: ∀i, j : si = sj, a = 1

Percentage of individuals having p over 200 lifestages Simulation output after 100 lifestages

Parameter: ∀i, j : si = sj, a < .5

Percentage of individuals having p over 200 lifestages Simulation output after 100 lifestages

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Simulation ResultsChanging the effect of distance:

Ip = bp × N0.8p ×

∑i si × 1

d4i

Np

Percentage of individuals having p over 400 lifestages, with the variable of distance raised to the power 4 and threedifferent values of mutation rate.

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Simulation Results

Note:I a < 0.5 or distance raise to power 4 both pushed the

system to a 50/50 equilibrium (socially specializedvariants / differential replication)

I variable a > 0.5 is desirable to achieve communityconsensus

I the induced parochialism implied by raising power of thedistance variable reduces SIM to a cultural evolutionmodel with small number of cultural parents→ power 2 isrealistic assumption

Under what circumstances can the new variant replace the oldone totally? (threshold problem)

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Exercise 3

Nettle is discussing the distribution of features in a population.He mentions that many attributes are normally distributed(Gaussian distribution), but some are distributed according to aPoisson curve, like...

I weightI wealth

√

I height

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Simulation Results

Testing Social Selection:I A: different values of status, according to a Poisson curveI B: additional hyperinfluential agents (s = 100 with

probability .025)I result: with superinfluential agents the new variant

occasionally replaces the established oneagents with s

0.1

0.2

0.3

0.4

0.5

1-4 5-8 9-12 13-16 17-20s

Poisson distribution for status groups Percentage of individ. having p over 400 lifestages

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Simulation Results

Testing Social Selection:I different functional biases for new variant: 0.5, 1 and 2.0I result: only for similar biases variants replace each other -

but how similar?I note: functional bias has only impact in combination with

social selection!

Percentage of individuals having p over 400lifestages for different biases of q

Mean percentage having p averaged over 400lifestages for different biases of q

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Overall ResultsNettle’s conclusion:

I Emergence of separate dialects by decreasing theimportance learners give to conformity (decreasingparameter a, increasing power of distance factor)

I Changes are adopted if there are speakers which are muchmore influential than others (superinfluential agents)

I Functional biases determine the fate of competinglinguistic variants (bq >> 1)

Exercise 6:

“Without the potential for change provided by differences insocial influence, functionally favoured variants might neverovercome the threshold required to displace prior norms.Functional biases may therefore affect the direction of lan-guage change rather than providing sufficient conditions forit to occur.”

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Further ’Spatial’ Simulation Models

Language change and social networks (Ke, Gong, Wang 2008)

I more realistic network structures: small world structuresI adoption of Nettle’s age structureI simplification of SIT formula: F(U) = fu × qu

(functional bias and frequency, no status)I result: change can happen without superinfluential agents

Center and peripheries: Network roles in language change(Fagyal, Swarup, Escobar, Gasser, Lakkaraju 2010)

I directed networks (scale-free small world structures)I more than two competing variants (probabilistic adoption)I agents’ influence value (status)I result: i) peripheral low-connected agents preserve;

ii) central influential agents induce propagations

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Homeworks

Homeworks

I Read the article ‘Self-organization in vowel systems’ (deBoer, 2000)

I solve the appropriate exercises given on ILIAS

theories and models of language change

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