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

University of Tokyo - Japan
Forecast
• Language evolution

• Two strategies for the fittest

• How big can a language grow ?
2
Language, the (most) complex adaptive system
• Language displays organized
complexity, i.e. the
characteristics of a CAS
(...
Evolutionary Linguistics
4
<source:Kirby2007>
Which linguistic units?
• Linguistic replicators, units of information (Szatmary 2000, Croft 2000)

• phonemes

• morpheme...
Language Evolution
• Major contributions come from many different areas 

• animal communication and social behaviors (Marl...
Biology and Language Evolution
7
• In biology, trait selection leads
to a trade-off between
strategies r and K (MacArthur &
Wilson 1967)

• Species have alw...
r vs K strategy
Opportunistic
r-strategists
• They produce many offspring
and care less about them

• Individuals have a lo...
r vs K strategy
<source : extremescience.com>
Stable K-strategists
• They produce fewer larger
offspring. Every child is ta...
• The r/K theory places every individual on a continuum ranging from fully
opportunistic to purely competitive behaviour
1...
• Study the population dynamics of language evolution

• Using the tools from mathematical biology
Population r-strategy
K...
• Study of language evolution suffers from a lack of empirical data

• r/K-like theories provide ready-to-use heuristics to...
r/K in Language Evolution
14
• [r] Some words are used a lot,
in a lot of different forms
(usually different contexts)

• [r...
Unpredictability in the language sphere
• Noisy communication channel,
narrow learning bottleneck

• Differences between th...
Linguistic adaptive capacity
• Linguistic units adapt their strategy of transmission

• Adaptive capacity confers resilien...
Lexicon size
• The number of words is hard to count

• What is a word ? 

• A string of linguistic stuff that is arbitraril...
Lexicon size
• A word’s reproductive ratio (Nowak 2000)
• R = teachers per child B x probability of learning a word Q

• W...
Transmission Channel
• Imperfect communication medium between speakers

• As a result, language is forced through a narrow...
A Linguistic Carrying capacity
• A carrying capacity can be defined in the case of language Ktot = f (K1, K2) as
a combinat...
Agent-based Simulation
• After formulating these hypotheses, one possible validation can be brought
by computational simul...
• The process of language transmission can be modelled via an iterated multi-
agent simulation (Kirby & Hurford 2002, Niyo...
Iterated Learning Model
Learning agent
Generation 1
Generation 2
Generation 3
S M
S M
S M
Bayesian learning
Bayesian learn...
Iterated Learning Model
Generation 1
Generation 2
Generation 3
Population of learning agents
Partial mesh
Partial mesh
S M...
Conclusion
• r/K tendencies can be observed in simulations. Experiments are still in
progress

• The carrying capacity is ...
A Two-Speed Language Evolution: Exploring the
Linguistic Carrying Capacity
Olaf Witkowski

University of Tokyo - Japan
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A Two-Speed Language Evolution - Protolang Torun - September 2011

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A Two-Speed Language Evolution - Protolang Torun - September 2011

  1. 1. A Two-Speed Language Evolution: Exploring the Linguistic Carrying Capacity Olaf Witkowski University of Tokyo - Japan
  2. 2. Forecast • Language evolution • Two strategies for the fittest • How big can a language grow ? 2
  3. 3. 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 3 SYS EXT
  4. 4. Evolutionary Linguistics 4 <source:Kirby2007>
  5. 5. Which linguistic units? • Linguistic replicators, units of information (Szatmary 2000, Croft 2000) • phonemes • morphemes • constructions • Transmitted between humans by means of linguistic utterances 5
  6. 6. 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. 6
  7. 7. Biology and Language Evolution 7
  8. 8. • 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> 8
  9. 9. 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> 9
  10. 10. 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 10
  11. 11. • The r/K theory places every individual on a continuum ranging from fully opportunistic to purely competitive behaviour 11 r/K Continuum r-strategist K-strategist trees rabbits humans t flies bacteria lions
  12. 12. • Study the population dynamics of language evolution • Using the tools from mathematical biology Population r-strategy K-strategy Intermediate strategy 12 r/K Dynamics
  13. 13. • 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) 13 Why r/K can be interesting for Language Evolution
  14. 14. r/K in Language Evolution 14 • [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
  15. 15. Unpredictability in the language sphere • Noisy communication channel, narrow learning bottleneck • Differences between the speakers’ shared backgrounds, generalization algorithms • Unstable community of speakers 15
  16. 16. 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) 16
  17. 17. 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) 17
  18. 18. 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 18
  19. 19. 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 19
  20. 20. 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 20
  21. 21. 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 21
  22. 22. • 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 Meaning 1 2 3 4 Language 22
  23. 23. Iterated Learning Model Learning agent Generation 1 Generation 2 Generation 3 S M S M S M Bayesian learning Bayesian learning 23
  24. 24. 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 24
  25. 25. 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 25
  26. 26. A Two-Speed Language Evolution: Exploring the Linguistic Carrying Capacity Olaf Witkowski University of Tokyo - Japan

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