a two-speed language evolution - protolang torun - september 2011
TRANSCRIPT
A Two-Speed Language Evolution: Exploring the Linguistic Carrying Capacity
Olaf WitkowskiUniversity of Tokyo - Japan
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
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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• 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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