progress in modeling human population fronts

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Progress in modeling human population frontsProgress in modeling human population fronts

Joaquim FortUniversitat de Girona

Catalonia, Spain

FEPRE European project2nd annual workshopSt Petersburg5-10 April 2008

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FEPRE work by the Girona groupFEPRE work by the Girona group

Manchester 2007 (1st FEPRE workshop):

1. Time-ordered models → SUBMITTED 2. Realistic dispersion kernels → IN PROGRESS

3. Non-isotropic models → PLANNED …

4. Genetic clines → PLANNED …

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FEPRE work by the Girona groupFEPRE work by the Girona group

St. Petersburg 2008 (2nd FEPRE workshop):

1. Time-ordered models → Phys. Rev. E 76, 031913 (2007)

2. Realistic dispersion kernels → talk by N. Isern

3. Non-isotropic models → New J. Phys. 76, 031913 (2007)

4. Genetic clines → 2-population models → New J. Phys. in press (2008)→ talk by J. Pérez-Losada

IMPACT FACTOR (SCI ) JOURNAL 7 Phys. Rev. Lett.

4 New J. Phys. 2 Phys. Rev. E

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Recent progressRecent progress

Other groups: M.J. Hamilton & B. Buchanan, PNAS 104 15625 (2007) G. J. Ackland et al., PNAS 104 8714 (2007)

IMPACT FACTOR (SCI ) JOURNAL 31 Science 29 Nature 14 PLoS Biology 10 PNAS

7 Phys. Rev. Lett. 4 New J. Phys. 2 Phys. Rev. E

Girona group:Non-isotropic models → New J. Phys. 76 031913 (2007)

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Time-delayed equationHamilton & Buchanan, PNAS (2007)

Girona group:Non-isotropic models → New J. Phys. (2007)

G. J. Ackland et al., PNAS (2007)

Plan of this talkPlan of this talk

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aDv 2FISHER FISHERDelayedDelayed Eq.

12

vv

aT

<

RecallRecall

2

4D

T

F+M, Phys. Rev. Lett. (1999)

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Hamilton & Buchanan, PNAS Hamilton & Buchanan, PNAS 104104 15625 (2007) 15625 (2007)

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Hamilton & Buchanan, PNAS Hamilton & Buchanan, PNAS 104104 15625 (2007) 15625 (2007)

→ predicted speed: 2 km/yr

→ observed speed: 8 km/yr

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Human prehistoric range expansion speedsHuman prehistoric range expansion speeds

Location

Dates

(uncal

yr BP)

Speed

(km/yr)

Mainly

boats?

Ref.

North America 12000-10000

8 ? Hamilton,

PNAS 2007

Oceania 4000-750

>8 YES Fort,

Antiquity 2003

Mediterranean 7000-6000

>10 YES Zilhao,

PNAS 2001

Levant+Europe Neolithic

11000-

40001 NO Pinhasi, Fort & Ammerman,

PLoS Biol 2005

Europe lateglacial

14000-12000

1 NO Fort, Pujol & Cavalli-Sforza,

CAJ 2004

Levant+Europe modern humans

42000-

360001 NO Fort, Pujol & Cavalli-Sforza,

CAJ 2004

10

max

1p

F app

22

2

2 1 + 12 2 2

12

x x

aT aT aTaD U U

vaT

x

pU

x

· Manchester group: · Davison, Dolukhanov, Sarson & Shukurov, J. Arch. Sci. (2006) · FEPRE project application· Girona group: F & Pujol, New J. Phys. 76 031913 (2007)

2 2

2 2

2 2

T p p p T FD F

t t x t

2

12

aDv

aT

2 2

2 2

T

2 2

p p p T FD F

t t x t

isotropic

non-isotropic

, 0 0p

r yy

Non-isotropic models

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Girona group: Non-isotropic models F & Pujol, New J. Phys. 76 031913 (2007)

non-isotropic

22

2

2 1 + 12 2 2

12

x x

aT aT aTaD U U

vaT

xU bT

probability cosa b

front

12

0.0 0.1 0.3 0.4 0.5 0.6 0.8 0.9 1.010

12

14

16

18

20

22

24

26

28

300.0 -1.5 -3.1 -4.6 -6.1 -7.7 -9.2 -10.7 -12.3

observed

Fisher (isotropic)

isotropic, time-delayed (HRD)

biased model

Fort and Pujol,New J Phys (2007)

Ux (km/yr)

spe

ed

c (

km/y

r)

dimensionless bias = 2 b

Human colonization of the U.S. during the XIX century

Individual migrations are biased against the front propagation direction

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G. J. Ackland et al., PNAS G. J. Ackland et al., PNAS 104104 8714 (2007) 8714 (2007)

max max max

2 2

(1 ) ''

(1 ) ''

(1 ) ''

/ , /

/ , ''

( )

( ()

( )

)

/

F F F F FH FX F

H H H H HF HX H

X X X X XF XH X

i i i ij

F X F X

F

H F X

H

j j

X XF F X

i

n a n n n n D n

n a n n n n D n

n

n

a n n n n D n

n p p n n p p

n n t

n n n n

n

n n

n n n n n

n n r

n

H→Xacculturation

X→F or F→ X cultural competition(λ=0→Aoki,no cultural boundaries)

F= farmers with neolithic language, genes, etc.F= farmers with neolithic language, genes, etc.H= hunter-gatherers with paleolithic language, genes, etc.H= hunter-gatherers with paleolithic language, genes, etc.

X= converts = farmers with paleolithic language, genes, etc.X= converts = farmers with paleolithic language, genes, etc.

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0 500 1000 1500 2000 2500 30000.0

0.2

0.4

0.6

0.8

1.0

culturalboundary

Numerical integrations for an homogeneous landscape, by T. Pujol

H

t7

t10t

9t8t

6t5t

4t3t

2t1

X

X

H

F

n

r (km)

Farmers Hunters Converts

This is the only model known to predict cultural boundaries Neolithic culture & genes Paleolithic culture & genes

1611000 10000 9000 8000 7000 6000 5000 40000

1000

2000

3000

4000

5000

dates vs distances

distances vs dates

gre

at-

circ

le d

ista

nce

fro

m A

bu

Ma

di (

km)

date (uncalibrated yr BP)

13000 11000 10000 9000 8000 7000 6000 5000

Fort, Fig. 2adate (calibrated yr BP)

Open problemsOpen problems

Data fromPinhasi, Fort & Ammerman,PLoS Biol (2005)Impact Factor (SCI)=14

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11000 10000 9000 8000 7000 6000 5000 40000

1000

2000

3000

4000

5000

sites in Denmarkonly

dates vs distances

distances vs dates

gre

at-

circ

le d

ista

nce

fro

m A

bu

Ma

di (

km)

date (uncalibrated yr BP)

13000 11000 10000 9000 8000 7000 6000 5000

Fort, Fig. 2b

date (calibrated yr BP)

Open problemsOpen problems

Data fromPinhasi, Fort & Ammerman,PLoS Biol (2005)Impact Factor (SCI)=14

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Recent progressRecent progress Vlad, Cavalli-Sforza & Ross, PNAS Vlad, Cavalli-Sforza & Ross, PNAS 101101 10249 (2004) 10249 (2004)

Currant & Excoffier, Proc. Roy. Soc. B Currant & Excoffier, Proc. Roy. Soc. B 272272 679 (2005) 679 (2005)

Open problemOpen problemComparison between simulated & observed clinesComparison between simulated & observed clines

Spread of genetic mutations

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Aims of the FEPRE projectAims of the FEPRE project

Archaeological data + mathematical Archaeological data + mathematical modelling modelling → denied (2005)→ denied (2005)

RootsRoots in prehistory of in prehistory of present socio-present socio-culturalcultural diversity → approved (2006) diversity → approved (2006)

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Open problemOpen problem

progress in modeling human population fronts

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