A Two-Speed Language Evolution: Exploring the Linguistic Carrying Capacity

Olaf WitkowskiUniversity of Tokyo - Japan

Forecast

• Language evolution

• Two strategies for the fittest

• How big can a language grow ?

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Language, the (most) complex adaptive system

• Language displays organized complexity, i.e. the characteristics of a CAS (Hruschka et al. 2009) :

• dissipative with the environment

• all relations are nonlinear

• memory/feedback

• can achieve and maintain an intricate structure over time

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SYS EXT

Evolutionary Linguistics

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<sou

rce

: Kirb

y200

7>

Which linguistic units?

• Linguistic replicators, units of information (Szatmary 2000, Croft 2000)

• phonemes

• morphemes

• constructions

• Transmitted between humans by means of linguistic utterances

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Language Evolution

• Major contributions come from many different areas

• animal communication and social behaviors (Marler 1970, Hauser 1996)

• cultural evolution (Boyd & Richerson 1985, Niyogi & Berwick 1997)

• language development in children (Hurford 1991, Bates 1992),

• genetic and physical facets of language competence (Lieberman 1991, Deacon 1997)

• etc.

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Biology and Language Evolution7

• In biology, trait selection leads to a trade-off between strategies r and K (MacArthur & Wilson 1967)

• Species have always alternated between r and K strategies

• r-strategists focus on the quantity of their progeny

• K-strategists focus on on the survival of fewer but more competitive children

r/K selection

<source : New Yorker>

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r vs K strategy

Opportunistic r-strategists• They produce many offspring

and care less about them

• Individuals have a low probability of survival

• The individuals are usually smaller, reproduce quickly, early and spread widely

• They are better primary colonizers

<source : anthonyspestcontrol.com>

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r vs K strategy<source : extremescience.com>

Stable K-strategists• They produce fewer larger

offspring. Every child is taken care of and trained longer,

• They are usually larger with a longer life expectancy

• They procreate slower and later

• They are strong in crowded niches, once the population approaches carrying capacity

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• The r/K theory places every individual on a continuum ranging from fully opportunistic to purely competitive behaviour

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r/K Continuum

r-strategist K-strategist

treesrabbits

humans

tree

fliesbacterialions

• Study the population dynamics of language evolution

• Using the tools from mathematical biology

Population r-strategy

K-strategy

Intermediate strategy

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r/K Dynamics

• Study of language evolution suffers from a lack of empirical data

• r/K-like theories provide ready-to-use heuristics to predict future states of the system in absence of complete information about its constituents (Fog 1996)

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Why r/K can be interesting for Language Evolution

r/K in Language Evolution

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• [r] Some words are used a lot, in a lot of different forms (usually different contexts)

• [r] They are usually short or easy to remember, viral or specific to some contexts

• [r] They are a better way to communicate in case of an unpredictable environment

• E.g. non-native speakers

• [K] Some words are transmitted in specific lexical fields

• [K] They have evolved to be used in specific situations

• [K] They are strong in stable languages, stable contexts, but may disappear when the linguistic environment changes

• E.g. technology vocabulary

Unpredictability in the language sphere

• Noisy communication channel, narrow learning bottleneck

• Differences between the speakers’ shared backgrounds, generalization algorithms

• Unstable community of speakers

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Linguistic adaptive capacity

• Linguistic units adapt their strategy of transmission

• Adaptive capacity confers resilience to perturbation, giving words the ability to reconfigure themselves with minimum loss of function

• r-strategist words do well in unpredictable environments, where specialized adaptations are unhelpful (e.g. noisy environments)

• K-strategist words do better in more predictable environments, where large gains can be made through specialization (e.g. specific contexts in everyday life)

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Lexicon size

• The number of words is hard to count

• What is a word ?

• A string of linguistic stuff that is arbitrarily formulated with a particular meaning (Pinker 1995)

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Lexicon size

• A word’s reproductive ratio (Nowak 2000)

• R = teachers per child B x probability of learning a word Q

• We can compute analytically a minimum frequency of occurrence in the language:

• fmin > (B number of words Zq)-1

• If we consider a Zipf’s Law distribution, this means for the maximal lexicon size:

• nmax log nmax = BZq

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Transmission Channel

• Imperfect communication medium between speakers

• As a result, language is forced through a narrow bottleneck of linguistic experience (limited amount of time for communication)

• If we lower the probability to learn an utterance, an r-strategy becomes more efficient

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A Linguistic Carrying capacity

• A carrying capacity can be defined in the case of language Ktot = f (K1, K2) as a combination of the capacity of the individuals’ memory and the capacity of the transmission channel

• Passed this carrying capacity K, a K-strategy is more appropriate for linguistic replicators than an r- one

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Agent-based Simulation

• After formulating these hypotheses, one possible validation can be brought by computational simulations

• Iterated modelling recreates language evolution in a small world

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• The process of language transmission can be modelled via an iterated multi-agent simulation (Kirby & Hurford 2002, Niyogi & Berwick 2009)

• The model implements repeated learning and transmission of an initial random "language" between successive generations of Bayesian learners

Multi-Agent Model

Agent Signal Meaning1234

Language

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Iterated Learning Model

Learning agent

Generation 1

Generation 2

Generation 3

S M

S M

S M

Bayesian learning

Bayesian learning

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Iterated Learning Model

Generation 1

Generation 2

Generation 3

Population of learning agents

Partial mesh

Partial mesh

S M S M S M S M

S M S M S M S M

S M S M S M S M

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Conclusion

• r/K tendencies can be observed in simulations. Experiments are still in progress

• The carrying capacity is linked to the limits to human memory, both for grammar complexity and lexicon size

• More dimensions can be included into the carrying capacity function

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A Two-Speed Language Evolution: Exploring the Linguistic Carrying Capacity

Olaf WitkowskiUniversity of Tokyo - Japan