1) The document discusses a two-speed model of language evolution based on r/K selection strategies from biology. r-strategist words spread widely and are useful in unpredictable environments, while K-strategist words are specialized for stable contexts. 2) It proposes the concept of a linguistic carrying capacity, determined by limits of individual memory and the transmission channel. Above this capacity, a K-strategy becomes more efficient than an r-strategy. 3) Agent-based simulations are suggested to model language transmission between generations of learners and observe the emergence of r/K tendencies, helping to validate hypotheses about factors influencing carrying capacity.

1. A Two-Speed Language Evolution: Exploring the
Linguistic Carrying Capacity
Olaf Witkowski
University of Tokyo - Japan

2. Forecast
• Language evolution
• Two strategies for the fittest
• How big can a language grow ?
2

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. Evolutionary Linguistics
4
<source:Kirby2007>

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. 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. Biology and Language Evolution
7

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. 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. 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. • 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. • 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. • 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. 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. 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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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. 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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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
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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
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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. 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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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. 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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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. 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. A Two-Speed Language Evolution: Exploring the
Linguistic Carrying Capacity
Olaf Witkowski
University of Tokyo - Japan