1

Data and mathematical approaches to the neolithic transition

Joaquim FortUniversitat de Girona

Catalonia, Spain

FEPRE European project3rd annual workshopGirona, 16-18 March 2009

2

1. Archaeological data: Speed versus neolithisation time

2. Mathematical models: Interpretation of the data

3. Archaeological data: Speed versus latitude

Plan of this talkPlan of this talk

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MotivationMotivation

If some hunter-gatherers become farmers:If some hunter-gatherers become farmers:· The front speed should be faster, and· The front speed should be faster, and· The · The neolithisation time*neolithisation time* should be shorter should be shorter

*Time necessary for the population of *Time necessary for the population of farmers to reach saturation densityfarmers to reach saturation density

· Theory: New J Phys (2008)· Comparison to archaeological data: this talk

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Neolithisation timeNeolithisation time

2400 yrData from Gkiasta et al., Antiquity (2003)Data from Gkiasta et al., Antiquity (2003) 2000 yr

Time necessary for the population Time necessary for the population of farmers to reach saturation densityof farmers to reach saturation density

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Legend! 2008_10_23a_fepre_context_ppnb9000CALyrBP Events

lakes

country

2008_10_23a

<VALUE>

<6.669 cal yr BP (>73 gen)

6.669 - 7.264 cal yr BP (73-54 gen)

7.265 - 7.859 cal yr BP (54-36 gen)

7.860 - 8.454 cal yr BP (36-17 gen)

>8.455 cal yr BP (<17 gen)

DATA INTERPOLATION: 903 FEPRE sites and 16 PPNB CONTEXT sites, all set to 9000 CAL yr BP2008_10_23a_fepre_context_ppnb9000CALyrBP.mxd2008_10_23b_fepre_context_ppnb9000CALyrBP.pdf

0 generations corresponds to 9000 cal yr BP

!

!

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! !! !!! !!! !! !

!!!

!! !! !!! !!! !!! !! !!! !!!!! ! !! ! ! !! !!! ! ! !! ! !! !! !!!!! !! ! !!!! !! !! !! !

!!! !! ! !!! !! !! !!! !!!! ! !! ! ! !!! ! ! !! !! !! ! !! !!! ! !!!! !!!! !! ! !!

! !! !!! !!! !! !! !! !!! ! !!!! !! ! ! !! !! ! ! !! ! !!! !! ! !! !!! ! ! !!! !! ! !!!! ! !! !!! ! !! !! ! !! !!!!!! ! ! !! ! !! !!! ! !! !! ! ! !! !!! ! !! !!! !! ! !!! !! !! !!!! ! ! ! ! ! !! !!! ! ! !! !!! ! !! ! !!!!! !! !! ! ! !!! !! ! !!! !! !!! ! !!!!! ! !!! ! !! ! !!! !! !! !! !!! !! ! !!! !! ! !! !! ! !! ! !!! ! ! !! !! ! ! !! !! !!!! ! !! ! !!! !!! ! !!! ! !! !! !! ! !! !! !!!

! !!! ! ! !! !! !! ! !!!! !! ! !! !!! ! !! ! !! ! ! !!! !! ! !!! ! !! !!!! ! !!! !! ! !! !! ! !!! !! !! ! ! !! !! ! !!! ! !!! !! ! ! ! !! !! !!! ! !! ! !!!! ! !!!! !! !! ! !! ! !!! ! !! ! ! !!! !! !!! !!!!!!!!!!! !! !!!! !! !! ! !! ! !!!! ! ! !! ! !!!! ! !!!! !! !! !!! ! !! !!! !!!!! !! !!! !! !!! ! !! !!! ! !!! !! !! ! !! !! !!! !! ! ! !!! ! !! ! !! !! !! ! !! !! !! ! !! !!! !! !! ! ! !! ! !!! !! !! !!! !! ! !! !!! !! !!! !! ! !!! ! !! !! ! !!! !! !!!! !! !!! !!! !!! !!!!! ! !! ! !!! !! ! !!! !! !! !!! ! !! ! !! !!! !! !!! ! !! !!!! !! ! ! ! !! ! !! ! !!!! ! !! !! !!!! !! !! !!! !! !! !! !!! ! !! ! !! !! ! !! ! !!! ! !! !!! !!! !! ! !! !! !! !!!! ! !! !! !! !! !!! !!

!!! !!! !! !! !

!!! ! !!!!

! !!!!!!

!

!!

! !!

!

!!

!

!

!!!

!

!

!

How to estimate local speeds?How to estimate local speeds? One way is from isochronesOne way is from isochrones

Data by M. Vander Linden Data by M. Vander Linden (919 sites) (919 sites)

Interpolation with GIS software Interpolation with GIS software

Legend! 2008_10_23a_fepre_context_ppnb9000CALyrBP Events

lakes

country

2008_10_23a

<VALUE>

<6.669 cal yr BP (>73 gen)

6.669 - 7.264 cal yr BP (73-54 gen)

7.265 - 7.859 cal yr BP (54-36 gen)

7.860 - 8.454 cal yr BP (36-17 gen)

>8.455 cal yr BP (<17 gen)

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Bocquet-Appel et al., Bocquet-Appel et al., J. Arch. Sci.J. Arch. Sci. (2009), Fig. 8 (2009), Fig. 8Another way is to fit a surface of C-14 dates

and estimate the gradient

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400 600 800 1000 1200 1400 1600 1800 2000 2200

0.4

0.6

0.8

1.0

1.2

1.4

1.6

SP

EE

D

T NEOL

No trend.

Is the effect too small?

France >47ºN

France <47ºN

Greece

Italy

Germany

Belgium

Yugoslavia

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400 600 800 1000 1200 1400 1600 1800 2000 2200

0.4

0.6

0.8

1.0

1.2

1.4

1.6

SP

EE

D

T NEOL

No trend.

Is the effect too small?

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1. Archaeological data: Speed versus neolithisation time→ no trend

2. Mathematical models: Do they predict that this effect is too small?

3. Archaeological data: Speed versus latitude

Plan of this talkPlan of this talk

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““Predator-prey” modelsPredator-prey” models

1. Ammerman and Cavalli-Sforza→ (1984)

2. Lotka-Volterra:

PNP

PPP

P

PNN

NNN

N

ppP

ppa

tp

ppP

ppa

tp

max

max

1

1

2

2

2

2

max

2

2

2

2

max

1

1

y

p

x

pDpp

pp

pat

p

y

p

x

pDpp

pp

pat

p

PPPPN

P

PPP

P

NNNPN

N

NNN

N

2

2

km

gatherers-hunter ofnumber km

farmers ofnumber

P

N

p

p

births-deaths

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3. Cohabitation models 2km

farmers ofnumber Np

before migration cohabitation non-cohabitation

(e.g., Lotka-Volterra)

pN time t gen time t + 1 gen time t + 1 gen

x x-r x x+r x-r x x+r

Example: if all individuals disperse:

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Cohabitation modelsCohabitation models

F et al, Phys Rev E (2007) F et al, New J Phys (2008) Isern et al, J Stat Mechs (2008)

2

2

km

gatherers-hunter ofnumber km

farmers ofnumber

P

N

p

p

fecunditynet

generation 1

),(

),(),(),(),(

0

0

N

N

PNNNN

R

T

rdtrx

trxPtrxPtrxPRTtxP

Dispersal probability distribution

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How to estimate the interaction parameter How to estimate the interaction parameter ΓΓ ? ?Effect of the interaction (no dispersal and Effect of the interaction (no dispersal and RR00NN=1)=1)

generation 1

)()()()(

T

tPtPtPTtPP PNNNN

)(max tPP PN

)(1

)()()(

)()( tPtPtPtP

tPtPP

NPN

P

PN

N

maxmax

1

NP

0 Γ 1/PN max 1/PN

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R0N = 2.2 (Birdsell 1957)

T = 32 yr (Stauder 1971) Currant & Excoffier (2005):

pe = 0.38 (Stauder 1971) Pmax P = 0.064 people/km2

r = 50 km (Stauder 1971) Pmax N =20 Pmax P=1.28people/km2

Speed of the neolithic frontSpeed of the neolithic front

km/yr 09.10 c

km/yr 10.11

maxmax c

P N

T

rpppRc eePN

)1))(cosh(1(2ln

0

min max0

This maximum difference of speeds is only 1% !!

This effect seems negligible. Reason: Pmax P << PmaxN

New J Phys (2008)

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1. Archaeological data: Speed versus neolithisation time

2. Mathematical models: The effect is too small

3. Archaeological data: Speed versus latitude

Plan of this talkPlan of this talk

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36 38 40 42 44 46 48 50 52

0.4

0.6

0.8

1.0

1.2

1.4

1.6

SPEED

SP

EE

D (

k/yr

)

LAT (º)

The same data versus latitudeItaly

GreeceYugoslavia

France>47ºFrance<47º

Germany

Belgium

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36 38 40 42 44 46 48 50 52

0.4

0.6

0.8

1.0

1.2

1.4

1.6

SPEED

SP

EE

D (

k/yr

)

LAT (º)

Is there

a trend?

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35 40 45 50 55 60

1

2

3

4

spe

ed

(km

/yr)

LATITUDE (º)

All grid nodes in Bocquet-Appel et al (2009)

But many nodes are on the sea...

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Bocquet-Appel et al., Bocquet-Appel et al., J. Arch. Sci.J. Arch. Sci. (2009), Fig. 8 (2009), Fig. 8

Is there a trend using all grid nodes?

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36 38 40 42 44 46 48 50 52 54 56

1

2

3

4

spe

ed

(km

/yr)

LAT

All grid nodes in 7 regions

But the

Mediterranean

spread is

faster

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22

36 38 40 42 44 46 48 50 52 54 56

1

2

3

4sp

ee

d (

km/y

r)

LAT

All grid nodes in 7 regions

MEDITERRANEAN

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48 49 50 51 52 53 54

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2sp

ee

d (

km/y

r)

LAT

All grid nodes in 7 regionswith latitude >=48ºN

Trend with latitude

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48 49 50 51 52 53 54

0.5

1.0

1.5

2.0

speed (km/yr)sp

ee

d (

km/y

r)

LAT

Germany

Trend also

in some

smaller regions

(but only at

latitude>47º)

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How to find the speed direction?How to find the speed direction?What should the surface of C14 arrival dates look like?

W

S

Nfast

slow

Near East

RussiaBritain

Portugal

E

t arrival

5000 cal yr BP

13000 cal yr BP

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How to find the speed direction?How to find the speed direction?The gradient is orthogonal to the level lines*

*N. Piskunov, Differential and Integral Calculus (Moscow, 1966), Sec. 8.15

y

x

t arrival surface

level line

level plane

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The speed is also orthogonal to the level lines of arrival time (isochrones):

How to find the speed direction?How to find the speed direction?

Speed vector 8500 CAL yr BP

8000 CAL yr BP

So the speed vector is parallel to the gradient

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GermanyGermany

6 8 10 12 14 16

48

50

52

54

56

LA

T (

º)

LON (º)

Gradients of dates surface (yr/km),as in Bocquet-Appel et al., JAS (2009), Fig. 8

6 7 8 9 10 11 12 13 14 1546

47

48

49

50

51

52

53

54

55

LA

T (

º)

LON (º)

Speed vectors (km/yr)

slowdownto the North

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1. Archaeological dataNo observed trend of speed versus neolithisation time

2. Mathematical models

The effect is too small because Pmax P << PmaxN

3. Archaeological dataLocal trends of speed versus latitude >47ºN. Cause?

ConclusionsConclusions

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Possible causesPossible causes

1. Reproduction and/or mobility decreases with increasing latitude NO DATA AVAILABLE

2. More density of hunter-gatherers to the North + resistance to farmers? DATA AVAILABLE?

3. Time needed for crop to adapt to colder climates to the North?

DATA AVAILABLE?

To model To model locallocal trends, the cause has to be known trends, the cause has to be known