2. 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
3. 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
4. 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
5. 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
7. 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
8. 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
9. 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
10. 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/
11. 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
12. 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
hfp://dx.doi.org/10.1016/j.ecolmodel.2005.03.026
13. 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
!" #$= π(x) fj (x)
x∈X
∑ (1)
hfp://dx.doi.org/10.1016/j.ecolmodel.2005.03.026
14. 最大エントロピーの推定
Maximum
Entropy
approxima@on
(Phillips
et
al.
2006:
236)
• π [fj] can be approximated using a set of sample points x1 … xm
drawn independently from X.
• The empirical average of fj is
14
π fj
!" #$=
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)
hfp://dx.doi.org/10.1016/j.ecolmodel.2005.03.026
15. 最大エントロピーの推定
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
hfp://dx.doi.org/10.1016/j.ecolmodel.2005.03.026
16. 最大エントロピーの推定
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.
hfp://dx.doi.org/10.1016/j.ecolmodel.2005.03.026
17. 最大エントロピーの推定
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.
hfp://dx.doi.org/10.1016/j.ecolmodel.2005.03.026
18. 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
hfp://dx.doi.org/10.1016/j.ecolmodel.2005.03.026
20. 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
21. 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
22. 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
23. 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
27. 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
hfp://dx.doi.org/10.1371/journal.pone.0003972
28. Palaeoenvironmental
variables
28
Warmest
month
temperature
Coldest
month
temperature
Mean
annual
precipita@on
(mm
x100)
Mean
annual
temperature
hfp://dx.doi.org/10.1371/journal.pone.0003972
32. 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…
hfp://dx.doi.org/10.1371/journal.pone.0003972
33. 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