Inference of transmission modes from cultural frequency
data
Anne Kandler
City University London
Complexity Science Workshop
Systems & Control Research Centre
18.6.- 19.6.2015
Social learning
Social learning/cultural transmission: learning that is
facilitated by observations of, or interactions with, another
individual or its products (Heyes 1994, Hoppitt and Laland 2013)
Inference of transmission modes from frequency data
Social learning
Review
Trends in Cognitive Sciences February 2011, Vol. 15, No. 2
Copy if
uncertain [96]
Copy if personal
information outdated [86]
State
based
Copy if
dissatisfied [11]
Unbiased or random
copying [9,66]
Copy depending on
reproductive state [90]
Copy rare
behaviour [54]
Copy if demonstrators
consistent [53]
Copy the majority,
conformist bias [5,91]
Frequency
dependent
Context
dependent
Familiarity−based [48,59,95]
Social
learning
strategies
Bias derived from
emotional reaction
(e.g. disgust [30])
Content
dependent
Copy variants that
are increasing
in frequency [47]
Dominance rank
based [97]
Number of
demonstrators [39]
Prestige−based [31]
Bias for social
information [28]
Bias for
memorable or
attractive
variants [29]
Kin−based [62]
Model
based
Guided variation [5] (trial−and−error
learning combined with unbiased
transmission)
Based on
model’s knowledge [43]
Copy if payoff
better [87]
Success
−based
Copy in proportion
to payoff [88]
Size−based [93]
Copy most successful
individual [35]
Age−based [92]
Gender−based [98]
TRENDS in Cognitive Sciences
Figure 1. Social learning strategies for which there is significant theoretical or empirical support. The tree structure is purely conceptual and not based on any empirical data
on homology or similarity of cognition. The sources given are not necessarily the first descriptions or the strongest evidence, but are intended as literature entry points for
readers.
to both when it is best to choose social sources to acquire
information and from whom one should learn. These latter
[11,32]. A recent example is the social learning strategies
Inference
of entrants
transmission
tournament [32], an open competition
in which
Rendell et al. (2011)
modes from frequency data
Previous work
Research to establish the presence of particular learning
strategies in human populations is mainly centered around
Laboratory-based approaches: ‘Microsocieties’ (e.g. Coultas
2004, Baum et al. 2004, McElreath et al. 2008, Morgan et al. 2012) and diffusion chain
experiments (e.g. Mesoudi and O’Brien 2008, Caldwell and Millen 2008, Kirby et al. 2008)
Inference-based approaches: adoption curves (e.g.
Cavalli-Sforza and Feldman 1981, Boyd and Richerson 1985, Rogers 2003, Henrich 2001, Reader 2004,
, power-law distributions (e.g. Hahn and Bentley
, model selection
Kendal et al. 2007, Hoppitt et al. 2010)
2003, Herzog et al. 2004, Bentley et al. 2004, Mesoudi and Lycett 2009)
frameworks (McElreath et al. 2008, Franz and Nunn 2009, Hoppitt et al. 2010)
Modelling-based approaches (e.g. Boyd and Richerson et al., Feldman et al.)
For a comprehensive review see Kandler and Powell (2015)
Inference of transmission modes from frequency data
Previous work
Modelling-based approaches (e.g. Boyd and Richerson et al., Feldman et al.)
→ Evolutionary advantage or disadvantage of social learning
over its counterpart, asocial learning
→ Learning strategies that are expected in human
populations especially in spatially and temporally changing
environments at equilibrium
→ Important insight into what human populations are expected
to do if the cultural system is at equilibrium
Inference of transmission modes from frequency data
Inference framework
→ Framework that infers learning processes directly from
available data without any equilibrium/optimality assumption
→ What kind of data is available?
→ Time series data detailing the usage or occurrence of
different variants of a cultural trait in a population
Inference of transmission modes from frequency data
Inference framework
1
Generative model: Non-equilibrium framework capturing
the main cultural and demographic dynamics of the
considered system
→ Frequency changes of different cultural variants present
in a population under the assumed learning hypothesis
→ Causal relationship between learning processes and
observable patterns of frequency change
2
Statistical comparison (ABC): Conclusions about which
(mixtures of) learning strategies are consistent with the
observable frequency data and which are not.
→ Generative inference frameworks have been already
successfully applied in genetics (e.g Veeramah et al. 2012, Eriksson et al. 2012,
Itan et al. 2009, Wilde et al. 2014)
Inference of transmission modes from frequency data
Linear Band Keramik data set
Frequencies of vessels decorated with specific motifs from excavated
settlements of the first farmers in SW Germany (c.5500-5000 BC)
Inference of transmission modes from frequency data
Linear Band Keramik data set
Data: Frequencies of different types of decorated pottery at the
beginning and end of 7 phases
Question: What are the underlying cultural transmission
processes that produced the observed changes between the
beginning and end of the phase?
Cultural transmission hypotheses:
Neutral evolution
Frequency-dependent selection (conformity,
anti-conformity)
Pro-novelty selection
Inference of transmission modes from frequency data
Generative model
Inference of transmission modes from frequency data
Generative model - Inference of population structure
Given: Sample S = [n1 , n2 , . . . , nk , 0] of k cultural variants
→ Population structure P = [R1 , . . . , Rk , Rk+1 ] from which the
sample S could have been drawn at random
Assuming the population structure P the probability of the
sample S is given by
P(S|P) = Qk
n!
i=1 ni !
R1n1 R2n2 · . . . · Rknk
Conjugate prior is given by the Dirichlet distribution of the form
α
k+1
P(P) ∝ R1α1 −1 R2α2 −1 · . . . · Rk+1
−1
Unnormalized posterior distribution of P:
α
k+1
P(P|S) ∝ P(P)P(S|P) = R1n1 +α1 −1 R2n2 +α2 −1 · . . . · Rk+1
−1
Inference of transmission modes from frequency data
Generative model
Inference of transmission modes from frequency data
Generative model - Cultural transmisson
Starting point: population structure P(t1 )
Assumptions:
Sample size is a fraction (s)
of total population size:
N(t1 ) = 1s n(t1 ),
N(t2 ) = 1s n(t2 )
Pottery is produces once a
year:
(t2 − t1 ) production events
During each year a fraction
(r ) of the population of
cultural variants is removed
and subsequently replaced
Inference of transmission modes from frequency data
Generative model - Cultural transmission
→ Transforming population P(t) of cultural variants at time t
into population P(t + 1) at time t + 1
Inference of transmission modes from frequency data
Generative model - Cultural transmission
→ Transforming population P(t) of cultural variants at time t
into population P(t + 1) at time t + 1
Inference of transmission modes from frequency data
Generative model - Cultural transmission
→ Transforming population P(t) of cultural variants at time t
into population P(t + 1) at time t + 1
Inference of transmission modes from frequency data
Generative model - Cultural transmission
→ Transforming population P(t) of cultural variants at time t
into population P(t + 1) at time t + 1
Inference of transmission modes from frequency data
Generative model - Cultural transmission
→ Transforming population P(t) of cultural variants at time t
into population P(t + 1) at time t + 1
Markov process with one-step transition probability:
P(P(t + 1)|P(t)) =
X
P(removing [u1 , . . . , uk+1 ] variants)
·P(adding [v1 , . . . , vk+1 ] variants)
→u=
Pk+1
i=1
ui variants are chosen to be removed at random
P
→ v = k+1
i=1 vi variants are chosen to be added according to
cultural transmission process
Inference of transmission modes from frequency data
Generative model - Cultural transmission
Transmission probabilities: Neutral evolution
pi (t) =
Ni (t) − ui
(1 − µ)
N(t) − u
k
pk+1 (t) =
X Nk+1 (t) − uk+1
Nk+1 (t) − uk+1
+µ
N(t) − u
N(t) − u
i=1
Inference of transmission modes from frequency data
Generative model - Cultural transmission
Transmission probabilities: Frequency-dependent selection
Ni (t) − ui
Ni (t) − ui
+ bfreq k̂
− 1 (1 − µ)
pi (t) =
N(t) − u
N(t) − u
Nk+1 (t) − uk+1
N (t) − uk+1
pk+1 (t) =
+ bfreq k̂ k+1
−1
N(t) − u
N(t) − u
k
X
Ni (t) − ui
Ni (t) − ui
+µ
+ bfreq k̂
−1
N(t) − u
N(t) − u
i=1
Inference of transmission modes from frequency data
Generative model - Cultural transmission
Transmission probabilities: Pro-novelty selection
pi (t) =
pk+1 (t) =
Ni (t) − ui bage ai (t)
e
(1 − µ)
N(t) − u
Nk+1 (t) − uk+1 bage ak +1 (t)
e
N(t) − u
k X
Ni (t) − ui bage ai (t)
e
+µ
N(t) − u
i=1
Inference of transmission modes from frequency data
Generative model - Cultural transmission
→ Transforming population P(t) of cultural variants at time t
into population P(t + 1) at time t + 1
Markov process with one-step transition probability:
P(P(t + 1)|P(t)) =
X
P(removing [u1 , . . . , uk+1 ] variants)
·P(adding [v1 , . . . , vk+1 ] variants)
→ Repeating this procedure (t2 − t1 ) times
Inference of transmission modes from frequency data
Generative model - Cultural transmission
Inference of transmission modes from frequency data
Generative model - Sampling
→ Theoretical sample conditioned on underlying cultural
transmission process
→ Strength of the selection process is given by model
parameters bfreq and bage
Inference of transmission modes from frequency data
Statistical inference
→ Which cultural transmission processes (parameterized by
θ = (r , bfreq ) and θ = (r , bage )) are consistent with the data?
Inference of transmission modes from frequency data
Approximate Bayesian Computation
→ Bayesian inference (approximate Bayesian computation)
→ Posterior distribution of selection strength (bfreq or bage ) and
fraction of the population that is replaced every year (r)
given a certain tolerance level
→ Widths of the posterior distribution can indicate how much
information we can extract from frequency data
Inference of transmission modes from frequency data
Proof of concept
→ Sample S = [1 2 5 10 20 40 60] at t = 0 generated
samples at t = 50 using the generative model with
bfreq = 0
bfreq = −0.01
bfreq = 0.01
0.6
0.25
0.2
0.18
0.5
0.16
0.15
0.1
0.4
Relative frequencies
Relative frequencies
Relative frequencies
0.2
0.3
0.2
0.14
0.12
0.1
0.08
0.06
0.05
0.04
0.1
0.02
0
−0.02
−0.015
−0.01
−0.005
0
0.005
0.01
Strenght b of frequency−dependent selection
0.015
0.02
0
−0.02
−0.015
−0.01
−0.005
0
0.005
0.01
Strenght b of frequency−dependent selection
0.015
0.02
0
−0.02
−0.015
−0.01
−0.005
0
0.005
0.01
Strenght b of frequency−dependent selection
0.015
0.02
→ There exist theoretical limits on the amount of information
that can be extracted from sparse population-level frequency
data
Inference of transmission modes from frequency data
Theoretical limits
→ Main insight: exclusion of cultural transmission processes
that could not have produced the observed sample based on
the used inference procedure and therefore the reduction
of the pool of potential hypotheses
→ Showing consistency of a single hypothesis with observed
data might not be enough
→ What is the temporal resolution that is needed to improve
inference results? (Wilder and Kandler (in press))
Inference of transmission modes from frequency data
Application to LBK data set
Results of the analysis
Rejection of the hypotheses of neutral evolution and
frequency-dependent selection
Evidence for consistency between pro-novelty selection
and the observed frecency changes in the different phases
Inference of transmission modes from frequency data
Application to LBK data set
0.5
0.45
0.3
0.3
0.25
0.2
Relative frequencies
0.4
0.35
Relative frequencies
Relative frequencies
0.4
0.35
0.3
0.25
0.2
0.15
0.15
0.1
0.1
0.05
0.05
0
0.35
0.5
0.45
0
0
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
Strength bage of age−dependent selection
0.01
0.25
0.2
0.15
0.1
0.05
0
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
Strength bage of age−dependent selection
0
0.01
0
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
Strength bage of age−dependent selection
0.01
0.15
0.2
0.15
0.1
0.15
Relative frequencies
Relative frequencies
Relative frequencies
0.2
0.1
0.1
0.05
0.05
0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Fraction r of the population to be replaced in every time step
0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Fraction r of the population to be replaced in every time step
0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Fraction r of the population to be replaced in every time step
0.5
Inference of transmission modes from frequency data
Summary
Population-level frequency data contain information about
the underlying transmission process but there exist
(theoretical) limits to inferences of transmission modes on
the base of sparse population level-data.
Main insight from inference framework: exclusion of
cultural transmission processes that could not have
produced the observed sample
LBK data set: Pro-novelty selection is broadly consistent
with the observed frequency changes on pottery design
The generative framework is independent of the choice of
generative model!
Inference of transmission modes from frequency data
Thanks to
My collaborators
Stephen
Shennan
Kevin hfjd Adam
Laland
Powell
Bryan hfjd
hfjd Wilder
Laura hfjd
Fortunato
Inference of transmission modes from frequency data
Cultural evolution
Culture: Information capable of affecting individual’s behaviour
that they acquire from members of their species through social
learning (Richerson and Boyd 2005)
Social learning/cultural transmission: learning that is
facilitated by observations of, or interactions with, another
individual or its products (Heyes 1994, Hoppitt and Laland 2013)
Cultural change: Temporal frequency change of different
variants of a cultural trait
→ Social learning: one of the main causes of cultural change
→ Social learning can occur in many different ways (e.g. Boyd and
Richerson 1985, Laland 2004)
Inference of transmission modes from frequency data
Application to LBK data set
0.4
0.2
0.4
0.18
0.35
0.16
0.3
0.14
0.12
0.1
0.08
0.06
Rleative frequencies
Rleative frequencies
Rleative frequencies
0.35
0.25
0.2
0.15
0.1
0.3
0.25
0.2
0.15
0.1
0.04
0.05
0.05
0.02
0
−0.02
−0.015
−0.01 −0.005
0
0.005
0.01
Strength b of frequency−dependent selection
0.015
0
−0.02
0.02
−0.015
−0.01
−0.005
0
0.005
0.01
Strength b of frequency−dependent selection
0.015
0
−0.02
0.02
−0.015
−0.01
−0.005
0
0.005
0.01
Strength b of frequency−dependent selection
0.015
0.02
0.25
0.2
0.12
0.2
0.15
0.1
Relative frequencies
Relative frequencies
Relative frequencies
0.1
0.08
0.06
0.15
0.1
0.04
0.05
0.05
0.02
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Fraction r of the population to be replaced in every time step
0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Fraction r of the population to be replaced in every time step
0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Fraction r of the population to be replaced in every time step
0.5
Inference of transmission modes from frequency data
Application to LBK data set
→ Resulting marginal frequency distribution of the cultural
variants (present at the beginning of the phase) at the end of
the phase
0.45
0.35
0.3
0.4
0.3
0.25
0.35
0.2
0.15
0.3
Relative frequencies
Relative frequencies
Relative frequencies
0.25
0.25
0.2
0.15
0.2
0.15
0.1
0.1
0.1
0.05
0.05
0
0.05
1
2
3
4
5
6
Variant types
7
8
9
10
0
5
10
15
Variant types
20
25
0
5
10
15
20
Variant types
25
30
35
Inference of transmission modes from frequency data
Application to LBK data set
→ Resulting marginal frequency distribution of the cultural
variants (present at the beginning of the phase) at the end of
the phase
0.2
0.25
0.18
0.5
0.16
0.2
0.3
0.2
Relative frequency
0.14
Relative frequency
Relative frequency
0.4
0.15
0.1
0.12
0.1
0.08
0.06
0.1
0.05
0
0
0.04
0.02
1
2
3
4
5
6
Variant types
7
8
9
10
5
10
15
Variant types
20
25
0
5
10
15
20
Variant types
25
30
35
Inference of transmission modes from frequency data