1 data and mathematical approaches to the neolithic transition joaquim fort universitat de girona...
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Data and mathematical approaches to the neolithic transition
Joaquim FortUniversitat de Girona
Catalonia, Spain
FEPRE European project3rd annual workshopGirona, 16-18 March 2009
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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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!!! !!! !! !! !
!!! ! !!!!
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!!
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!
!!
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!!!
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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