Phylogenetic models and MCMC methods for the reconstruction of language history

Robin J. RyderCEREMADE – Paris Dauphine / CREST – INSEE

Joint work with Geoff K. Nichollsat the Department of Statistics, University of Oxford

www.slideshare.net/robinryder

Carles li reis, nostre emper[er]e magnesSet 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 (11th 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 boireJ'ai vu tous les soleils y venir se mirerS'y jeter à mourir tous les désespérésTes 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 porteChill c'est trop fort ! baisse le son merde ! j'connaisA chaque fois c'est pareil tant pis il faut qu'ça pèteEt 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

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

Description of the model (2)

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.

Description of the model (3)

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

Registration process

Registration process

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/languageBorrowing: 10%

Consensus tree

Influence of borrowing (2)

Consensus treeTrue tree, ~40 words/languageBorrowing: 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

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