生態文化ニッチモデリングによる分布推定

生態文化ニッチモデリングによる

遺物分布推定

Eco-‐cultural
niche
modelling
近藤康久

東京工業大学大学院情報理工学研究科

日本学術振興会特別研究員(PD)

総括班/A01班/B02班研究協力者

kondo@archaeo.cs.@tech.ac.jp

1
交替劇B01/B02合同班会議

2013.7.22
明治大学中野キャンパス
遺跡と間違え
ましたが...

生態ニッチモデリング

Ecological
niche
modelling
ニッチ
(niche)
とは

•  日本語では「生態的地位」

•  “The
environmental

requirements
(bio@c
or
abio@c)

that
need
to
be
fulﬁlled
for
a

popula@on
to
survive”

(Peterson
et
al.
2011:
276)

•  生息場所（空間）

•  資源利用パターン

2
Peterson
et
al.
2011

ISNN:
978-‐0-‐691-‐13688-‐2

ニッチの定義に２流派あり

Grinnellian
niche
vs.
Eltonian
niche
•  Grinnellian
niche
(Grinnell
1917)

Concept
deﬁned
on
the
basis
of
environmental
space
of

scenopoe@c
(noninterac@ng
and
nonlinking)
environmental

variables
and
focused
on
geographic
scales
and

requirements.

•  Eltonian
niche
(Elton
1927)

Concept
deﬁned
at
small
spa@al
extents
at
which

experimental
manipula@ons
are
feasible,
emphasizing
the

func@onal
role
of
species
in
communi@es,
and
including

models
of
resource
consump@on
and
impacts.

(Peterson
et
al.
2011:
272–273)

3ISBN:
978-‐0-‐691-‐13688-‐2

生態ニッチモデリングの定義

Defini@on
of
ecological
niche
modelling
(ECNM)
“Es@ma@on
of
the
different
niches
(fundamental,

exis@ng,
poten@al,
occupied),
par@cularly
those
defined

using
scenopoe@c
[=noninterac@ng
and
nonlinking]

condi@ons.
In
prac@ce,
carried
out
via
es@ma@on
of

abio@cally
suitable
condi@ons
from
observa@ons
of
the

presence
of
a
species.”
(Peterson
et
al.
2011:
271)

→既知の生息地と環境情報から，機械学習によっ
て生物種のニッチを推定する手法
4ISBN:
978-‐0-‐691-‐13688-‐2

入力変数：位置情報と環境情報

Model
inputs:
occurrence
and
environmental
data
生物の位置

Occurrence
[x,
y]
生態ニッチモデリング

Ecological
niche
modelling
生物群系（植生）

Biome
気候指標（気温&降水量）

Clima@c
indices

標高由来の地形指標

DEM-‐based
topological
indices
5

ヒメゴジュウカラの生態ニッチ

Si#a
pygmaea
predic@ons
in
North
America
6

生態ニッチモデリングの二大アルゴリズム
Two
major
algorithms
of
ecological
niche
modelling
GARP
MaxEnt
遺伝的

アルゴリズム
アルゴリズム

algorithm
最大エントロピー
モデル
在のみ

presence-‐only
サンプリング

sampling
在のみ

presence-‐only
二値
[0,
1]

binary
出力

output
連続的
[0...1]

con@nuous
強い

calibrated
バイアス補正

biased
data
弱い

biased
7どちらもオープンソースのソフトウェアを入手可能

遺伝的アルゴリズム法

Gene@c
Algorithm
for
Rule-‐Set
Produc@on

•  “A
machine-‐learning
gene@c
algorithm
originally

developed
for
determining
the
ecological
niches
of

plant
and
animal
species”

(Stockwell
&
Peters
1999)

•  Desktop
GARP
(open
source
soeware
package)

hfp://www.nhm.ku.edu/desktopgarp/

•  Also
included
in
OpenModeller

hfp://openmodeller.sourceforge.net

8

遺伝的アルゴリズムの実際

Stockwell
1999
in
Machine
Learning
Methods
for
Ecological
Applica9ons
1.  Start
at
ini@al
@me
t
=
0

2.  Ini@alize
a
(usually
random)
popula@on
of
individuals
P(t)

3.  Evaluate
the
ﬁtness
of
all
individuals

4.  Test
for
termina@on
criteria,
while
not
done
do:

5.  Increase
@me
counter

6.  Create
a
new
set
of
individuals
P’(t)

7.  Recombine
the
“genes”
of
selected
individuals

using
heuris@c
operators

8.  Evaluate
new
ﬁtness
of
the
popula@on
P’(t)

9.  Select
the
survivors

10. Go
to
4
9ISBN:
978-‐0-‐412-‐84190-‐3

GARP
parameter
seings
•  1000
replicate
runs

•  0.01
convergence
limit

•  80%
for
training

•  Hard,
0%
omission
error
(i.e.,

failure
to
predict
a
known

presence)

•  50%
commission
error
(i.e.,

areas
of
absence
that
are

incorrectly
predicted
present)

•  10
ﬁnal
“best-‐subset”
models

for
each
complex

10hfp://www.nhm.ku.edu/desktopgarp/

最大エントロピー法
Maximum
Entropy
(Jaynes
1957)

The
best
approxima@on
is
to
ensure
that:

1.  The
approxima@on
sa@sﬁes
any
constraints
on

the
unknown
distribu@on
that
we
are
aware
of;

2.  Subject
to
those
constraints,
the
distribu@on

should
have
maximum
entropy

11
Phillips
et
al.
2006
hfp://dx.doi.org/10.1016/j.ecolmodel.2005.03.026

最大エントロピー原理

Principle
of
maximum
entropy
12
H( ˆπ) = − ˆπ(x)ln ˆπ(x)
x∈X
∑
a
ﬁnite
set
of
points
approxima@on
of
π

(unknown
probability

distribu@on)
to
point
x

entropy


最大エントロピーの推定

Maximum
Entropy
approxima@on
(Phillips
et
al.
2006:
236)
•  Formalize the constraints on the unknown probability
distribution π.
•  Assume a set of known real-valued functions f1 … fn on X,
known as “features” [=environmental variables].
•  Assume that the information we know about is characterized
by the expectations (averages) of the features under π.
•  Each feature fj assigns a real value fj(x) to each point x in X.
•  The expectation of the feature fj under π is
13
π fj
!" #$= π(x) fj (x)
x∈X
∑ (1)


Maximum
Entropy
approxima@on
(Phillips
et
al.
2006:
236)
•  π [fj] can be approximated using a set of sample points x1 … xm
drawn independently from X.
•  The empirical average of fj is
14
π fj
!" #$=
1
m
fj (xi )
i=1
m
∑ (2)
an estimate
of π [fj]
•  By the maximum entropy principle, seek the probability
distribution of subject to the constraint that each has the
same mean under as observed empirically:
ˆπ
ˆπ
ˆπ fj
!" #$= π fj
!" #$ for each feature fj (3)


Maximum
Entropy
approxima@on
(Phillips
et
al.
2006:
236)
•  has an alternative characterization.
•  Convex duality (Delle Pietra et al. 1997) shows that is
exactly equal to the Gibbs probability distribution qλ that
maximizes the likelihood of the m sample points:
15
qλ (x) =
eλ⋅f (x)
Zλ
(4)
where
•  λ is a vector of n real-valued coefficients (feature weights).
•  f denotes the vector of all n features.
•  Zλ is a normalizing constant to ensure qλ sums to 1.
ˆπ
ˆπ


Maximum
Entropy
approxima@on
(Phillips
et
al.
2006:
236)
•  Equivalently, qλ minimizes the negative log likelihood of the
sample points (“log loss”)
16
π[−ln(qλ )]= lnZλ −
1
m
λ ⋅ f (xi )
i=1
m
∑ (5)
•  Maxent tends to over-fit the training data.
•  Therefore, the means under should be close to their
empirical values by relaxing the constraint in (3)
ˆπ
ˆπ fj
!" #$− π fj
!" #$ ≤ βj for each feature fj (6)
for some constants βj.


Maximum
Entropy
approxima@on
(Phillips
et
al.
2006:
236)
•  The Maxent distribution can now be shown to be the Gibbs
distribution that minimizes
17
π[−ln(qλ )]+ βj λj
j
∑ (7)
where
•  The first term is the log loss (5)
•  The second term penalizes the use of large values for the
weights λj.

環境変数 f の調整法は５通り

Five
feature
types

1.  Linear feature
2.  Quadratic feature
3.  Product feature [for two variables]
4.  Threshold feature [not used]
5.  Binary feature [for categorical values v1 … vk]
ith feature is 1 wherever the variable equals vi, otherwise 0.
18
ˆπ[ f ]
ˆπ[ f 2
]− ˆπ[ f ]2
ˆπ[ fg]− ˆπ[ f ] ˆπ[g]
1
0
!
"
#
if above a given threshold

MaxEnt
parameter
seings
19hfp://www.cs.princeton.edu/~schapire/maxent/

生態文化ニッチモデリング

Eco-‐cultural
niche
modelling
(ECNM):
an
applica@on
to
human
•  過去の人類の生活が自然環境の影響を大きく

受けたという前提に立てば，先史人類にも

生態ニッチモデリングを適用できる。

•  人類は自然環境に対して他の生物とは異なる

ふるまいをする。

•  自然環境を克服するために，技術を容易に進化させる

•  自然環境を改変する（農耕，家畜化，森林伐採etc.）

→
生態ニッチをみずから変える能力をもっている

→
これこそが文化
(culture)
の発現

20

入力変数：遺跡情報と古環境情報

Model
inputs:
archaeological
and
palaeoenvironmental
data
遺跡の位置

archaeological
sites
[x,
y]
生態文化ニッチモデリング

Eco-‐cultural
niche
modelling
生物群系（植生）

biome
古気候指標（気温&降水量）

palaeoclima@c
indices

標高由来の地形指標

DEM-‐based
topological
indices
21

交替劇のECNMは仏チームが先行

Preceding
studies
by
Banks
et
al.
(2008b,
2013)
22
Humaneclimate interaction during the Early Upper Paleolithic: testing the
hypothesis of an adaptive shift between the Proto-Aurignacian and the Early
Aurignacian
William E. Banks a,b,*, Francesco d’Errico a,c
, João Zilhão d
a
CNRS, UMR 5199-PACEA, Université Bordeaux 1, Bâtiment B18, Avenue des Facultés, 33405 Talence, France
b
Biodiversity Institute, University of Kansas, 1345 Jayhawk Blvd, Dyche Hall, Lawrence, KS 66045-7562, USA
c
Department of Archaeology, History, Cultural Studies and Religion, University of Bergen, Øysteinsgate 3, 5007 Bergen, Norway
d
University of Barcelona, Faculty of Geography and History, Department of Prehistory, Ancient History, and Archaeology, C/Montalegre 6, 08001 Barcelona, Spain
a r t i c l e i n f o a b s t r a c t
Contents lists available at SciVerse ScienceDirect
Journal of Human Evolution
journal homepage: www.elsevier.com/locate/jhevol
Journal of Human Evolution 64 (2013) 39e55
PLoS
ONE
3/2:
e3972
64:
39-‐55

Banks
et
al.
2008:
Neanderthal
ex@nc@on

by
compe@@ve
exclusion
23
Predic@ng
the
habitat
of
hunter-‐gatherers

•  Who?
…Neanderthals
vs.
AMHs

•  Where?
…
Europe

•  When?
…
Three
sub-‐stages
in
MIS
3

•  How?
…
ECNM
by
GARP

Pre-‐Heinrich
event
4

(Pre-‐H4)
Heinrich
event
4

(H4)
Greenland
Interstadial
8

(GI8)
43.3
–
40.2
ka
40.2
–
38.6
ka
38.6
–
36.5
ka
hfp://dx.doi.org/10.1371/journal.pone.0003972

Archaeological
data:
Pre-‐H4
24

Archaeological
data:
H4
25

Archaeological
data:
GI8
26

Palaeoenvironmental
variables
27
•  Landscape
aspects
(slope,
aspect,
and
topographic

index)
from
Hydro-‐1K
(USGS)

•  Clima@c
simula@on
by
LMDZ3.3
Atmospheric
Gerenal

Circula@on
Model
(50km
ﬁnal
resolu@on)

•  Ice-‐sheet:
ICE-‐4G
reconstruc@ons
for
14
kyr
BP
(Pel@er
1994)

•  SSTs
for
the
three
sub-‐stages

•  GARP-‐based
simula@ons
of

–  The
coldest
month/warmest
month/annual
temperature

–  Precipita@on

•  GARP
parameters
are
the
same
as
the
previous
study


Palaeoenvironmental
variables
28
Warmest
month
temperature
Coldest
month
temperature
Mean
annual
precipita@on
(mm
x100)
Mean
annual
temperature

Results:
Neanderthal
vs.
AMH
29
Pre-‐H4
(43.3
–
40.2
ka)

Results:
Neanderthal
vs.
AMH
30
H4
(40.2
–
38.6
ka)

Results:
Neanderthal
vs.
AMH
31
GI8
(38.6
–
36.5
ka)

Counterfactual
results
for
Neanderthals
32
If
the
Neanderthals
survived
as
they

did
during
H4
in
the
GI8
clima@c

condi@ons,
their
niche
would
have

been
like
this…


まとめ：生態文化ニッチモデリングの特徴

ECNM:
Data-‐driven
simula@on
of
the
human
past
•  データ駆動型のシミュレーション

•  遺跡の分布のバイアスを低減できる。むしろ，
バイアスも教師データとして分布予測に活用で
きる。

•  各環境変数の寄与度が評価尺度として重要。

•  静態的な分布を予測するツールなので，時系列
のような動態分析には不向き。

•  人類進化の「なぜ」「どのように」に直接答え
るものではないが，問題発見のためのツールと
位置づけることができる。

33

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