Rémi DAVID 1, Chantal LEROYER 2, Philippe LANOS 3, Philippe DUFRESNE 3, Gisèle ALLENET DE RIBEMONT 4

1 PhD - UMR 6566 CReAAH – University Rennes 12 MCC - UMR 6566 CReAAH - University Rennes 1

3 CNRS - UMR 5060 IRAMAT-CRP2A – University Bordeaux 34 INRAP - UMR 6566 CReAAH Rennes 1

Context of the studyBayesian statistic

Application of Bayesian method

LinksThese age models will allow to apply various modeling methods: LANDCLIM (with

Florence Mazier), modern analogues (with Odile Peyron).

Our final objective will then be to better understand the climatic changes that

influenced, since the Neolithic, the evolution of the Paris Basin, in order to compare them

with the cultural changes that took place in this geographical area during the same periods

and thus try to distinguish climatic and anthropogenic determinisms on the environment.

Contribution of Bayesian statisticto characterize the chronological limits

of the Paris Basin palynozones

These regional pollen

assemblages zones (RPAZ) are

dated by 197 radiocarbon datings,

obtained on different analyzed cores,

supplemented by archaeological and

dendrochronological datings.

To determine the precise

chronological boundaries of these

palynozones, 14C dates have been

treated by Bayesian statistics. To do

this, we used the RenDateModel

software, developed by Ph. Lanos

and Ph. Dufresne.

Based on 91 cores (about 2000 pollen samples), the

palynological synthesis established by Ch.Leroyer in paleochannels of

flood plains of the Paris Basin summarizes the Holocene vegetation

history by the individualization of 7 regional palynozones (IV to X).

Download RenDateModel software→ https://sourcesup.cru.fr/projects/rendatemodel/

Download RenGraph software → http://sourcesup.cru.fr/projects/rengraph/

The calculation allows to obtain three probability distributions for each palynozone. The first (white background)

describes the extent of the phase itself. The two others (gray background) represent, for one, the uncertainty about the

start of this phase and, for the other, the uncertainty about its end.

These three distributions result from the integration of all 14C measures ( green background) relating to the RPAZ

considered. The Bayesian treatment of the data is very "robust" in the sense that distant 14C (outliers) in a RPAZ did not

influence significantly the calculation. Indeed, they will be assigned a high variance that will underestimate their impact

in the final equation.

For each of these distributions, we can determine a time interval with a confidence level of 95% (represented by

rectangles). We obtain four dates for each RPAZ, a start date and an end date for each distribution of start and end.

ProspectsThe definition of temporal limits for the various PAZ of the Paris Basin is

a major source of chronological information. All of the pollen sequences, whose

interpretation is based on the history of regional vegetation, can benefit from it.

This allows the construction of more accurate age models for these cores.

-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000

Fresnes Gord V C1-2

-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000

Fresnes Noues V

-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000

Lesches V C2

-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000

Lesches V C3

-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000

Neuilly V

-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000

Vignely V a

-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000

Vignely V b

-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000

Warluis V b C3

-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000

Warluis V a C3

-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000

95%

Boreal V

-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000

95%

Begin

-10000 -9500 -9000 -8500 -8000 -7500 -7000 -6500 -6000 -5500 -5000

95%

End

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500

Bazoches IX Cant

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500

Bazoches IX Cant

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500

Bazoches IX Cant

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500

Fresnes Gord IXb C3

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500

Beaurains IX C1

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500

Houdancourt IX Tr9

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500

Houdancourt IX Tr9

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500

Houdancourt IX C2

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500

Jouars IX Tr41 a

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500

Chatenay IXa P1

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500

Jouars IX Tr41 b

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500

Sacy IXa C2

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500

95%Ancient SubAtlantic IX

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500

95%

Begin

-3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500

95%

End

We can thus

represent all the results

obtained with RenDateModel

for the RPAZ of the Paris

basin during the Holocene,

and confront them to the

boundaries established in

the literature for the RPAZ

and the various cultural

phases.

2000

2000

-10000 -9000 -8000 -7000 -6000 -5000 -4000 -3000 -2000 -1000 0 1000

Preboreal IV

Boreal V

Ancient Atlantic VI

Recent Atlantic VII

SubBoreal VIII

Ancient SubAtlantic IX

-9000 -8000 -7000 -6000 -5000 -4000 -3000 -2000 -1000 0 1000

Recent SubAtlantic X

-10000

We obtain after

calculation some probability

densities for the RPAZ which are

in succession all over the

Holocene.

In our case, the major interest is

the possibility of characterizing

successions of regional RPAZ

and to consider them as

"stratigraphic" entities that can be

used as references on all the

studied sites.

Annet Jablines IV

Beaurains IV C1 Fontainebleau IVa BEL Fresnes Gord IV C3

Fresnes Gord IVb C1-2

Fresnes Gord IVa C1-2 Joinville IV S3Neuilly IV

Noyen IV MN C23

Noyen IV MN C23 Sacy IV C2

Sevre IVWarluis IV C3

Fresnes Gord V C1-2Fresnes Noues V

Lesches V C2

Lesches V C3

Neuilly VVignely V a

Vignely V bWarluis V b C3

Warluis V a C3

Annet Jablines VI

Chatenay VI P2Fontvanne VI C3

Noyen VI a CXV

Noyen VI a CXV

Noyen VI e L196

Noyen VI d L196

Noyen VI c L196

Noyen VI b L196

Noyen VI a L196Sacy VI a C2

Sacy VI b C2

Verrieres Champs VI C7

Verrieres Cœurs VI P1

Verrieres Cœurs VI P1 b

Verrieres Cœurs VI P1 a Vignely VI

Annet Beuvronne VII C1

Annet Jablines VII

Armancourt VIIFresnes Noues VII a

Fresnes Noues VII b

Joinville VII S3 Lesches VII C3Noyen VIIa U211 a

Noyen VIIa L196 b

Noyen VIIa U211 c

Noyen VIIb MN

Noyen VIIb

Noyen VIIb

Noyen VIIb

Noyen VIIb

Bercy VIIb QS C21

Bercy VIIb QS C21

Bercy VIIb QS C21

Bercy VIIb QS C21

Bercy VIIb QS Struc7

Bercy VIIb Cap9

Bercy VIIa pirog1 Cap7

Bercy VIIb QS7

Bercy VIIb QS7Paris Harley VII

Pont St Max VII b

Pont St Max VII a

Verrieres Champs VIIa C7Verrieres Cœurs VIIa P1

Verrieres Cœurs VIIa P1

Annet Beuvronne VIII C1

Annet Jablines VIII

Armancourt VIII

Bazoches VIIIa BM

Bazoches VIIIa Csud

Champagne VIII

Champagne VIII

Champagne VIII

Champagne VIII

Champagne VIII

Chatenay VIII P3

Fresnes Noues VIIIb

Fresnes Gord VIIIa C1-2

Croix St Ouen VIIIa S2

Lesches VIII C3

Bercy VIIIa pirog3 cap6

Bercy VIIIa pirog3 cap6

Bercy VIIIa pirog3 Cap6

Bercy VIIIa pirog12 QS KIX

Bercy VIIIa pirog2 Cap7

Bercy VIIIa pirog2 Cap7

Bercy VIII QS6

Paris Harley VIII

Rueil VIII C6 a

Rueil VIII C6 a

Rueil VIII C6 b

Rueil VIII C6 c

Rueil VIII C6 c

Sacy VIIIb C2

Saint Pouange VIIIa C3 Vignely VIII a

Vignely VIII b

Bazoches IX Cant

Bazoches IX Cant

Bazoches IX Cant

Beaurains IX C1Chatenay IXa P1

Fresnes Gord IXb C3

Houdancourt IX Tr9

Houdancourt IX Tr9

Houdancourt IX C2Jouars IX Tr41 a

Jouars IX Tr41 b

Sacy IXa C2

Annet Beuvronne X C1

Baloy Xb C2

Baloy Xa C2

Beaurains X C1

Dourdan X c C12

Dourdan X b C12

Dourdan X a C12

Dourdan X c C13

Dourdan X b C13Dourdan X b C13

Dourdan X a C13

Estissac X

Fontainebleau X c BEL

Fontainebleau X b BEL

Fontainebleau X a BEL

Fontainebleau X c FRA

Fontainebleau X b FRA

Fontainebleau X a FRA

Fontainebleau X b COU

Fontainebleau X a COU

Fontainebleau X c MAJ

Fontainebleau X b MAJ

Fontainebleau X a MAJ

Fontvanne X C1Hirson X

Jouars X Tr41Lailly X c

Lailly X b

Lailly X a

Moussey XBranly X Branly XBranly X

Neauphles X a C3

Neauphles X b C3

Neauphles X C26

Neauphles X C13

Bercy X QS4

Senart X

Senart X

Senart X c

Senart X b

Senart X a

Septeuil Xb C2

Ann Jab IV

Beau IV Fonta IVa Fre Gord IV

Fre Gord IVb

Fre Gord IVa Join IVNeui IV

Noy IV

Sacy IV

Sev IVWar IV

Fre Gord VFre Noues V

Les V

Neui VVign V a

Vign V bWar V b

War V a

Ann Jab VI

Cha VIFontva VI

Noy VI a

Noy VI e L196

Noy VI d L196

Noy VI c L196

Noy VI b L196

Noy VI a L196Sacy VI a

Sacy VI b

Ver Ch VI

Ver Co VI

Ver Co VI b

Ver Co VI a Vign VI

Ann Beuv VII

Ann Jab VII

Arm VIIFre Noues VII a

Fre Noues VII b

Join VII Les VIINoy VIIa a

Noy VIIa b

Noy VIIa c

Noy VIIb

Ber VIIb

Ber VIIa

Harl VII

Pt St Max VII b

Pt St Max VII a

Ver Ch VIIa

Ver Co VIIa

Ann Beuv VIII

Ann Jab VIII

Arm VIII

Baz VIIIa

Champ VIII

Chat VIII

Fre Noues VIIIb

Fre Gord VIIIa

Cx St Ouen VIIIa

Les VIII

Ber VIIIa

Ber VIII

Harl VIII

Rue VIII a

Rue VIII b

Rue VIII c

Sacy VIIIb

St Pou VIIIa Vig VIII a

Vig VIII b

Baz IX Cant

Beau IXChat IXa

Fre Gord IXb

Houd IX

Jou IX a

Jou IX b

Sacy IXa

Ann Beuv X

Bal Xb

Bal Xa

Beau X

Dou X a

Dou X b

Dou X c

Est X

Fonta X a BEL

Fonta X b BEL

Fonta X c BELFonta X c FRA

Fonta X b FRA

Fonta X a FRA

Fonta X b COU

Fonta X a COU

Fonta X c MAJ

Fonta X b MAJ

Fonta X a MAJ

Fontva XHir X

Jou X

Lai X a

Lai X c

Lai X b

Mou XBran X

Neau X a

Neau X b

Neau X

Ber X

Sen X

Sen X a

Sen X c

Sen X b

Sept Xb

Preboreal IV

Boreal V

Ancient Atlantic VI

Recent Atlantic VII

SubBoreal VIII

Ancient SubAtlantic IX

Recent SubAtlantic X

Until then applied to a single sequence, the Bayesian approach combines 14C dates with a priori informations of

stratigraphic and palynologic type (see dashed arrows), and so to redefine new probability densities (also called distributions)

a posteriori to these dates. The originality of the calculation is to allow the determination of distributions over time for each of

the RPAZ, and also distributions for the begin and the end of these RPAZ.

Bayesian statistics (named after the mathematician Thomas Bayes,

1702-1761) rests on two basic elements:

1 - time series data X (these are the observations: for example 14C

ages with standard deviations) are expressed in the form of random variables

that follow a sampling f(X) depending on parameters ;

2 - parameters (eg calendar time) are unknown but we have prior

knowledge (eg a stratigraphic constraint, or a constraint of belonging to a

period), called a priori, expressed in the form of a probability distribution ().

Bayes' formula allows then to express the probability distribution of ,

called a posteriori, conditionally to the observed data is (X) = f(X) . ().

In our modeling, 14C are encapsulated in Facts (or events) themselves

encapsulated in Phases (or periods). Stratigraphic constraints may exist

between certain facts. Finally, the phases which must be in succession, are

constrained by start and end boundaries that we try to estimate. The

calculation of a posteriori distributions based on numerical methods MCMC

(Markov Chain Monte Carlo), and in this case on the algorithm of Gibbs.

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