The influence of climate on biodiversity is an important ecological question. Various theories try to link climate change to allelic richness and therefore to predict the impact of global warming on genetic diversity. We model the relationship between genetic diversity in the European beech forests and curves of temperature and precipitation reconstructed from pollen databases. Our model links the genetic measure to the climate curves through a linear functional regression. The interaction in climate variables is assumed to be bilinear. Since the data are georeferenced, our methodology accounts for the spatial dependence among the observations. The practical issues of these extensions are discussed.
Deep Dive into Spatio-temporal Functional Regression on Paleo-ecological Data.
The influence of climate on biodiversity is an important ecological question. Various theories try to link climate change to allelic richness and therefore to predict the impact of global warming on genetic diversity. We model the relationship between genetic diversity in the European beech forests and curves of temperature and precipitation reconstructed from pollen databases. Our model links the genetic measure to the climate curves through a linear functional regression. The interaction in climate variables is assumed to be bilinear. Since the data are georeferenced, our methodology accounts for the spatial dependence among the observations. The practical issues of these extensions are discussed.
arXiv:0807.2588v1 [stat.AP] 16 Jul 2008
Spatio-temp
oral
F
un tional
Regression
on
P
aleo-e ologi al
Data
Liliane
Bel ∗
,
UMR
518
A
gr
oParisT
e
h/INRA,16,
rue
Claude
Bernar
d
-
75231
Paris
Ce
dex
05
A
vner
Bar-Hen,
Université
R
ené
Des
artes,
MAP5,
45
rue
des
Saints
Pèr
es,
75270
Paris
e
dex
06
Ra
hid
Cheddadi,
ISEM,
ase
p
ostale
61,
CNRS
UMR
5554,
34095
Montp
el
lier,
F
r
an
e
Rém
y
P
etit,
UMR
1202
INRA
,
69
r
oute
d’A
r
a hon
33612
Cestas
Ce
dex,
F
r
an
e
Abstra t
The
in uen e
of
limate
on
bio
div
ersit
y
is
an
imp
ortan
t
e ologi al
question.
V
ari-
ous
theories
try
to
link
limate
hange
to
alleli
ri
hness
and
therefore
to
predi t
the
impa t
of
global
w
arming
on
geneti
div
ersit
y
.
W
e
mo
del
the
relationship
b
e-
t
w
een
geneti
div
ersit
y
in
the
Europ
ean
b
ee
h
forests
and
urv
es
of
temp
erature
and
pre ipitation
re onstru ted
from
p
ollen
databases.
Our
mo
del
links
the
geneti
measure
to
the
limate
urv
es
through
a
linear
fun tional
regression.
The
in
tera -
tion
in
limate
v
ariables
is
assumed
to
b
e
bilinear.
Sin e
the
data
are
georeferen ed,
our
metho
dology
a oun
ts
for
the
spatial
dep
enden e
among
the
observ
ations.
The
pra ti al
issues
of
these
extensions
are
dis ussed.
Key
wor
ds:
F
un tional
Data
Analysis;
Spatio-temp
oral
mo
deling;
Climate
hange;
Bio
div
ersit
y
Preprin
t
submitted
to
Elsevier
No
v
em
b
er
18,
2018
1
In
tro
du tion
1
Climate
re ords
sho
w
that
the
earth
has
re orded
a
su ession
of
p
erio
ds
of
2
ma
jor
w
arming
and
o
oling
at
dieren
t
time
windo
ws
and
s ales
[5
,
12℄.
During
3
the
last
p
ost-gla ial
p
erio
d
(18000
y
ears
b
efore
the
presen
t),
Europ
e
re orded
4
a
15◦
C
to
20◦
C
w
arming
dep
ending
on
the
area.
A
t
the
same
p
erio
d
there
w
as
5
an
expansion
of
all
forest
biomes
and
an
up
w
ard
mo
v
emen
t
of
the
tree-lines
6
that
rea
hed
an
altitude
300
m
higher
than
to
da
y
.
Although
there
is
a
w
ealth
7
of
paleo
data
and
detailed
limate
re onstru tion
for
the
Holo
ene
p
erio
d,
w
e
8
still
la
k
some
kno
wledge
as
to
ho
w
the
w
arming
w
as
re orded
and
what
the
9
v
egetation
feedba
ks
w
ere
that
ae ted
lo
al
or
regional
past
limates.
V
arious
10
theories
try
to
link
limate
hange
to
alleli
ri
hness
and
therefore
to
predi t
11
the
impa t
of
global
w
arming
on
geneti
div
ersit
y
.
12
In
the
re en
t
literature
there
ha
v
e
b
een
a
lot
of
theoreti al
results
for
regres-
13
sion
mo
dels
with
fun tional
data.
Based
on
this
framew
ork,
w
e
used
a
linear
14
fun tional
mo
del
to
mo
del
the
relationship
b
et
w
een
geneti
div
ersit
y
in
Euro-
15
p
ean
b
ee
h
forests
(represen
ted
b
y
a
p
ositiv
e
n
um
b
er)
and
urv
es
of
temp
er-
16
ature
and
pre ipitation
re onstru ted
from
the
past.
The
lassi al
fun tional
17
regression
mo
del
has
b
een
extended
in
t
w
o
w
a
ys
to
a oun
t
for
our
sp
e i
18
problem.
First,
as
the
ee ts
of
temp
erature
and
pre ipitation
are
far
from
19
indep
enden
t
w
e
in luded
an
in
tera tion
term
in
our
mo
del.
This
in
tera tion
20
term
app
ears
as
a
bilinear
fun tion
of
the
t
w
o
predi tors.
Se ond,
sin e
w
e
21
ha
v
e
spatial
data
there
is
dep
enden e
among
the
observ
ations.
T
o
tak
e
in
to
22
a oun
t
with
dep
enden e
the
o
v
arian e
matrix
of
the
residuals
is
estimated
23
in
a
spatial
framew
ork
and
plugged
in
to
generalized
least-squares
to
estimate
24
the
parameters
of
the
mo
del.
The
pra ti al
di ulties
of
these
extensions
will
25
b
e
dis ussed.
26
In
Se tion
2,
w
e
presen
t
the
geneti
and
limate
data.
The
fun tional
regression
27
mo
del
is
studied
in
Se tion
3.
Results
are
presen
ted
and
dis ussed
in
Se tion
4
28
∗
Corresp
onding
author.
Email
addr
ess:
Liliane.Bel agropariste h.fr
(Liliane
Bel).
2
and
on luding
remarks
are
giv
en
in
Se tion
5.
1
2
Data
2
P
ollen
re ords
are
imp
ortan
t
pro
xies
for
the
re onstru tion
of
limate
param-
3
eters
sin e
v
ariations
in
the
p
ollen
assem
blages
mainly
resp
ond
to
limate
4
hanges.
Based
on
the
fossil
and
surfa e
p
ollen
data
from
p
ollen
databases,
5
w
e
used
mo
dern
analogue
te
hnique
(MA
T)
to
re onstru t
limate
v
ariables.
6
Climate
re onstru tion
is
a omplished
b
y
mat
hing
fossil
biologi al
assem-
7
blages
to
re en
tly
dep
osited
(mo
dern)
p
ollen
assem
blages
for
whi
h
limate
8
prop
erties
are
kno
wn.
The
relatedness
of
fossil
and
mo
dern
assem
blages
is
usu-
9
ally
measured
using
a
distan e
metri
that
res ales
m
ultidimensional
sp
e ies
10
assem
blages
in
to
a
single
measure
of
dissimilarit
y
.
The
distan e-metri
metho
d
11
is
widely
used
among
paleo
e ologists
and
paleo
eanographers
[8℄.
T
emp
erature
12
and
pre ipitation
w
ere
re onstru ted
at
216
lo
ations
from
the
presen
t
ba
k
13
to
a
v
ariable
date
dep
ending
on
a
v
ailable
data.
The
p
ollen
dataset
w
as
used
14
to
re onstru t
limate
v
ariables,
throughout
Europ
e
for
the
last
15
000
y
ears
15
of
the
Quaternary
.
Due
to
the
metho
dology
,
ea
h
limate
urv
e
is
sampled
at
16
irregular
times
for
ea
h
lo
ation.
17
Geneti
div
ersities
w
ere
measured
from
v
ariation
at
…(Full text truncated)…
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