Phylogenetic models and MCMC methods for the reconstruction of language history

Phylogenetic models and MCMC methods for the reconstruction of language history Robin J. Ryder CEREMADE – Paris Dauphine / CREST – INSEE Joint work with Geoff K. Nicholls at the Department of Statistics, University of Oxford www.slideshare.net/robinryder

Carles li reis, nostre emper[er]e magnes Set anz tuz pleins ad estet en Espaigne : Tresqu’en la mer cunquist la tere altaigne. N’i ad castel ki devant lui remaigne ; Mur ne citet n’i est remes a fraindre, Fors Sarraguce, ki est en une muntaigne. Chanson de Roland , 1r (11 th century)

La plus commune façon d'amollir les coeurs de ceux qu'on a offensez, lors qu'ayant la vengeance en main, ils nous tiennent à leur mercy, c'est de les esmouvoir par submission à commiseration et à pitié. Montaigne, Essais , I, 1 (1580)

Tes yeux sont si profonds qu'en me penchant pour boire J'ai vu tous les soleils y venir se mirer S'y jeter à mourir tous les désespérés Tes yeux sont si profonds que j'y perds la mémoire Aragon, Les Yeux d'Elsa (1942)

Et la piaule swingue au son du ghetto, on tape à la porte Chill c'est trop fort ! baisse le son merde ! j'connais A chaque fois c'est pareil tant pis il faut qu'ça pète Et profite en traître des nouveaux albums qu'Rod m'achète Akhénaton, Juste une pression (2005)

What to expect
Description of the data
Model of language diversification
MCMC for phylogenetic trees
Synthetic studies
Analysis of two data sets

Indo-European languages

Language diversification Languages change in a way comparable to biological species Similarities between languages indicate that they may be cousins. Most common model : phylogenetic tree

Questions
Topology
Internal ages
Age of the root: 6000-6500 BP or 8000-9500 BP?
(BP=Before Present)

Core vocabulary
100 or 200 meanings, present in almost all languages : bird, hand, to eat, red...
Borrowing is possible (non-tree-like change), but:
“ Easy” to detect
Uncommon
Does not introduce systematic bias

Data coding Old English: stierfþ Old High German: stirbit , touwit Avestan: miriiete Old Church Slavonic: umĭretŭ Latin: moritur Oscan: ? Cognacy classes: 1. {stierfþ, stirbit} 2. {touwit} 3. {miriiete, umĭretŭ, moritur}

Constraints
Constraints on parts of the topology
Constraints on some internal ages
We use these constraints to infer rates and other ages

Description of the model (1)‏
Traits are born at rate λ
Trait instances die at rate μ
λ and μ are constants

Catastrophes occur at rate ρ
At a catastrophe, each trait dies with probability κ and Poiss(ν) traits are born.
λ/μ=ν/κ: the number of traits is constant on average.

Observation model: each data point (0s and 1s) is missing with probability ξ
Some traits are not observed and are therefore deleted from the data

Registration process

Posterior distribution

Likelihood calculations

Prior distribution on trees
Our main focus is on the root age
We would like the marginal prior on the root age to be (approximately) uniform over (say) 5000-15000BP

MCMC moves
Random walk on the parameters
Various moves on the tree (Drummond et al., 2002)

Checking mixing and convergence
Auto-correlations
Need statistics on the tree
Length of the tree
Root age
Presence/Absence of a few subtrees

Synthetic data True tree, ~40 words/language Consensus tree

Synthetic data (2)‏ Death rate (μ)

Influence of borrowing True tree, ~40 words/language Borrowing: 10% Consensus tree

Influence of borrowing (2) Consensus tree True tree, ~40 words/language Borrowing: 50%

Influence of borrowing (3)
Topology is reconstructed correctly
Dates are underestimated for high levels of borrowing
Root age Death rate ( μ) Borrowing: 50%

Detecting borrowing Confirmed: hardly any borrowing!

Data used
Indo-European languages
Core vocabulary (Swadesh 100 or 200)
Two independent data sets
Dyen et al. (1997): 87 languages, mostly modern
Ringe et al. (2002): 24 languages, mostly ancient

Constraints

Cross-validation

Root age

Conclusions
Strong support for the Anatolian hypothesis: root age around 8000BP. No support for the Kurgan hypothesis.
Applicable to a variety of linguistic and cultural data sets
TraitLab: it's free!

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Phylogenetic models and MCMC methods for the reconstruction of language history

by Robin Ryder

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