Climate change, cyanobacteria blooms and ecological status of lakes: A Bayesian network approach

Abstract

Eutrophication of lakes and the risk of harmful cyanobacterial blooms due is a major challenge for management of aquatic ecosystems, and climate change is expected to reinforce these problems. Modelling of aquatic ecosystems has been widely used to predict effects of altered land use and climate change on water quality, assessed by chemistry and phytoplankton biomass. However, the European Water Framework Directive requires more advanced biological indicators for the assessment of ecological status of water bodies, such as the amount of cyanobacteria. We applied a Bayesian network (BN) modelling approach to link future scenarios of climate change and land-use management to ecological status, incorporating cyanobacteria biomass as one of the indicators. The case study is Lake Vansjø in Norway, which has a history of eutrophication and cyanobacterial blooms. The objective was (i) to assess the combined effect of changes in land use and climate on the ecological status of a lake and (ii) to assess the suitability of the BN modelling approach for this purpose. The BN was able to model effects of climate change and management on ecological status of a lake, by combining scenarios, process-based model output, monitoring data and the national lake assessment system. The results showed that the benefits of better land-use management were partly counteracted by future warming under these scenarios. Most importantly, the BN demonstrated the importance of including more biological indicators in the modelling of lake status: namely, that inclusion of cyanobacteria biomass can lower the ecological status compared to assessment by phytoplankton biomass alone. Thus, the BN approach can be a useful supplement to process-based models for water resource management.

Full text

Ecological
Modelling
337
(2016)
330–347
Contents
lists
available
at
ScienceDirect
Ecological
Modelling
j
ourna
l
h
omepa
ge:
www.elsevier.com/locate/ecolmodel
Climate
change,
cyanobacteria
blooms
and
ecological
status
of
lakes:
A
Bayesian
network
approach
S.
Jannicke
Moea,∗,
Sigrid
Haandea,
Raoul-Marie
Couturea,b
aNorwegian
Institute
for
Water
Research
(NIVA),
Gaustadalléen
21,
0349
Oslo,
Norway
bUniversity
of
Waterloo,
200
University
Ave
W,
Waterloo,
Ontario,
N2L
3G1,
Canada
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
10
July
2015
Received
in
revised
form
21
April
2016
Accepted
7
July
2016
Available
online
1
August
2016
Keywords:
Phytoplankton
Biological
indicators
Eutrophication
Probabilistic
model
Uncertainty
Water
framework
directive
a
b
s
t
r
a
c
t
Eutrophication
of
lakes
and
the
risk
of
harmful
cyanobacterial
blooms
due
is
a
major
challenge
for
man-
agement
of
aquatic
ecosystems,
and
climate
change
is
expected
to
reinforce
these
problems.
Modelling
of
aquatic
ecosystems
has
been
widely
used
to
predict
effects
of
altered
land
use
and
climate
change
on
water
quality,
assessed
by
chemistry
and
phytoplankton
biomass.
However,
the
European
Water
Framework
Directive
requires
more
advanced
biological
indicators
for
the
assessment
of
ecological
status
of
water
bodies,
such
as
the
amount
of
cyanobacteria.
We
applied
a
Bayesian
network
(BN)
modelling
approach
to
link
future
scenarios
of
climate
change
and
land-use
management
to
ecological
status,
incorporating
cyanobacteria
biomass
as
one
of
the
indicators.
The
case
study
is
Lake
Vansjø
in
Norway,
which
has
a
history
of
eutrophication
and
cyanobacterial
blooms.
The
objective
was
(i)
to
assess
the
combined
effect
of
changes
in
land
use
and
climate
on
the
ecological
status
of
a
lake
and
(ii)
to
assess
the
suitability
of
the
BN
modelling
approach
for
this
purpose.
The
BN
was
able
to
model
effects
of
climate
change
and
man-
agement
on
ecological
status
of
a
lake,
by
combining
scenarios,
process-based
model
output,
monitoring
data
and
the
national
lake
assessment
system.
The
results
showed
that
the
benefits
of
better
land-use
management
were
partly
counteracted
by
future
warming
under
these
scenarios.
Most
importantly,
the
BN
demonstrated
the
importance
of
including
more
biological
indicators
in
the
modelling
of
lake
status:
namely,
that
inclusion
of
cyanobacteria
biomass
can
lower
the
ecological
status
compared
to
assessment
by
phytoplankton
biomass
alone.
Thus,
the
BN
approach
can
be
a
useful
supplement
to
process-based
models
for
water
resource
management.1
©
2016
The
Authors.
Published
by
Elsevier
B.V.
This
is
an
open
access
article
under
the
CC
BY-NC-ND
license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
1.
Introduction
Eutrophication
of
lakes
due
to
nutrient
run-off
from
the
catchments
is
a
major
challenge
for
environmental
management
world-wide
(Schindler,
2012).
The
consequences
of
eutrophica-
tion
for
aquatic
ecosystem
include
harmful
cyanobacterial
blooms
(reviewed
by
Merel
et
al.,
2013)
and
altered
fish
communities
(Jeppesen
et
al.,
2010).
Climate
change
is
expected
to
reinforce
the
problems
with
eutrophication
due
to
i.a.
higher
water
tem-
perature
and
increased
nutrient
run-off
(Jeppesen
et
al.,
2009).
In
particular,
altered
conditions
in
lakes
due
to
climate
change
can
favour
cyanobacteria
over
other
phytoplankton
species
(Paerl
and
Huisman,
2008).
Therefore,
climate
change
may
counteract
the
∗Corresponding
author.
E-mail
address:
jmo@niva.no
(S.J.
Moe).
1Abbreviations:
BN
=
Bayesian
network;
Chl-a
=
chlorophyll
a;
WFD
=
Water
Framework
Directive.
effects
of
mitigation
measures
for
nutrient
enrichment,
and
make
it
more
difficult
to
obtain
management
targets
for
lakes.
Modelling
of
aquatic
ecosystems
has
been
used
widely
to
sup-
port
water
management,
and
to
predict
effects
of
altered
land
use
and/or
climate
(Gal
et
al.,
2014;
Mooij
et
al.,
2010;
Recknagel
et
al.,
2014;
Trolle
et
al.,
2012).
Process-based
models
for
catchments
and
lakes
typically
aim
at
predicting
changes
in
water
chem-
istry
(e.g.
phosphorus,
nitrogen
and
oxygen)
or
physical
conditions
(e.g.
transparency,
thermal
stratification)
(e.g.,
Jackson-Blake
et
al.,
2015).
Many
lake
models
also
predict
chlorophyll
a
(chl-a),
which
is
a
proxy
of
phytoplankton
biomass
(e.g.
Saloranta
and
Andersen,
2007),
and
a
traditional
indicator
of
water
quality.
However,
the
European
legislation
for
water
management
(the
Water
Framework
Directive
–
WFD
EC,
2000)
requires
use
of
more
advanced
biological
indicators
for
the
assessment
of
ecological
status
of
water
bod-
ies.
The
key
indicators
of
lake
eutrophication
should
represent
not
only
phytoplankton
biomass,
but
also
other
aspects
of
the
plank-
ton
community.
Many
European
countries
have
therefore
included
intensity
of
cyanobacterial
blooms
as
an
indicator
in
their
assess-
ment
systems
(Poikane
et
al.,
2015).
http://dx.doi.org/10.1016/j.ecolmodel.2016.07.004
0304-3800/©
2016
The
Authors.
Published
by
Elsevier
B.V.
This
is
an
open
access
article
under
the
CC
BY-NC-ND
license
(http://creativecommons.org/licenses/by-nc-nd/4.
0/).

S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
331
The
relationships
between
climatic
variables,
nutrients
and
cyanobacteria
have
been
thoroughly
studied
by
experiments
(e.g.
Davis
et
al.,
2009),
long-term
monitoring
(e.g.
Nõges
et
al.,
2010)
and
analysis
of
time
series
(e.g.
Huber
et
al.,
2012;
Wagner
and
Adrian,
2009)
and
of
multi-lake
data
sets
(Carvalho
et
al.,
2013;
Rigosi
et
al.,
2015).
However,
only
a
few
process-based
lake
mod-
els
have
so
far
incorporated
such
knowledge,
according
to
a
recent
review
(Elliott,
2012).
These
models
are
PROTECH
(Elliott,
2010;
Elliott
and
May,
2008),
PCLake
(Mooij
et
al.,
2007),
DYRESM-
CAEDYM
(Trolle
et
al.,
2011),
CLAMM
(Howard
and
Easthope,
2002),
PROBE
&
BIOLA
(Arheimer
et
al.,
2005)
and
PROTBAS
(Markensten
and
Pierson,
2007).
For
example,
an
application
of
PROTECH
to
Esthwaite
Water
(a
relatively
shallow
English
lake),
predicted
that
under
scenarios
of
increased
water
temperature
and
decreased
flushing
rate,
cyanobacteria
abundance
increased,
comprised
a
higher
proportion
of
the
phytoplankton
and
had
a
longer
duration
(Elliott,
2010).
However,
lake
models
that
comprise
cyanobacteria
have
not
yet
been
used
in
efforts
to
assess
ecological
status
(sensu
WFD),
to
our
knowledge.
In
this
study,
we
apply
a
Bayesian
network
(BN)
modelling
approach
to
link
future
scenarios
of
climate
change
and
land-
use
management
to
ecological
status,
incorporating
cyanobacteria
biomass
as
well
as
other
indicators.
A
BN
provides
a
framework
for
summarising
large
amounts
of
information
(e.g.,
from
process-
based
models)
and
for
integrating
different
types
of
information.
It
also
provides
a
tool
for
displaying
effects
of
different
scenar-
ios,
where
the
change
in
each
component
can
be
easily
visualised.
The
probabilistic
output
can
readily
be
interpreted
as
the
risk
of
failing
a
certain
management
target
and
support
decision
making.
For
these
reasons,
BNs
have
been
increasingly
used
in
environ-
mental
modelling
(reviewed
by
Aguilera
et
al.,
2011),
and
applied
in
the
context
of
e.g.
risk
assessment
(Lecklin
et
al.,
2011;
Moe,
2010),
resource
management
(Barton
et
al.,
2012)
and
ecosystem
services
(Landuyt
et
al.,
2013).
There
are
many
examples
of
BN
mod-
els
addressing
water
resource
management
(Barton
et
al.,
2005;
Borsuk
et
al.,
2004;
Castelletti
and
Soncini-Sessa,
2007;
Keshtkar
et
al.,
2013;
Martín
de
Santa
Olalla
et
al.,
2007;
Molina
et
al.,
2010;
Ticehurst
et
al.,
2007;
Varis
and
Kuikka,
1999).
Here,
we
focus
on
the
assessment
of
ecological
status
classes
of
water
bodies
sensu
WFD
(High,
Good,
Moderate,
Poor
and
Bad).
The
BN
methodology
typi-
cally
predicts
the
probability
of
different
states,
and
can
therefore
be
particularly
suitable
for
this
purpose
(Lehikoinen
et
al.,
2014).
As
a
case
study
for
this
BN
model
we
have
selected
Lake
Vansjø
in
South-East
Norway.
This
lake
has
a
history
of
high
levels
of
phosphorus
and
phytoplankton
biomass,
and
has
experienced
sev-
eral
cyanobacterial
blooms
(Haande
et
al.,
2011).
The
lake
has
been
monitored
since
1980,
and
has
been
subject
to
modelling
by
process-based
models
(Couture
et
al.,
2014;
Saloranta
and
Andersen,
2007)
as
well
as
Bayesian
networks
(Barton
et
al.,
2014
(basin
Vanemfjorden);
Barton
et
al.,
2008
(basin
Storefjorden)).
However,
this
is
the
first
effort
to
incorporate
cyanobacteria
in
a
model
for
Lake
Vansjø,
and
to
link
the
model
to
climate
change
scenarios.
The
objective
of
the
study
is
(i)
to
assess
the
combined
effect
of
changes
in
land
use
and
climate
on
the
ecological
status
of
a
lake,
considering
both
physico-chemical
indicators
and
phy-
toplankton,
including
cyanobacterial
blooms,
and
(ii)
to
assess
the
suitability
of
the
BN
modelling
approach
for
this
purpose.
2.
Material
and
methods
2.1.
Study
site
The
Vansjø-Hobøl
catchment
(area
690
km2),
also
referred
to
as
the
Morsa
catchment,
is
located
in
south-eastern
Norway.
The
Hobøl
River
drains
a
sub-catchment
of
ca.
440
km2into
Lake
Vansjø,
which
is
the
catchment’s
main
lake.
Lake
Vansjø
has
a
surface
area
of
36
km2and
consists
of
several
sub-basins,
the
two
largest
being
the
deeper,
siliceous
basin
Storefjorden
(eastern
basin)
and
the
shallower,
calcareous
basin
Vanemfjorden
(western
basin).
In
addition,
there
are
six
smaller
sub-basins
which
together
represent
less
than
15%
of
the
lake
surface
area.
The
Storefjorden
basin
water
flows
into
the
Vanemfjorden
basin
through
a
shallow
channel.
In
this
study
we
have
used
data
from
the
most
impacted
basin,
Vanem-
fjorden
(national
water
body
code
003-291-L,
59.443◦N,
10.755◦E).
This
basin
is
shallow
(mean
depth
is
3.8
m
and
maximum
depth
is
19.0
m)
and
the
water
column
does
not
stratify
stably.
The
sur-
face
area
is
12
km2,
the
residence
time
is
0.21
year
and
the
water
body
is
humic.
The
phytoplankton
growth
in
this
system
is
proba-
bly
limited
by
light,
because
of
the
high
humic
content
in
the
lake
and
hence
low
transparency
in
the
water
column
(Skarbøvik
et
al.,
2014).
The
current
physico-chemical
and
ecological
status
of
Vanem-
fjorden
are
moderate
(Haande
et
al.,
2011),
hence
it
fails
the
WFD’s
requirement
of
good
ecological
status
(EC,
2000).
However,
the
WFD
also
requires
that
the
current
status
of
a
water
body
should
not
be
worsened.
We
are
therefore
also
interested
in
the
risk
of
deterioration
from
moderate
to
poor
status
of
Vanemfjorden.
2.2.
Data
and
other
information
2.2.1.
Scenarios
The
future
scenarios
apply
for
the
period
2030–2052
(i.e.,
40
years
after
the
reference
period
1990–2012)
and
are
described
in
detail
by
Couture
et
al.
(2014).
In
this
study
we
have
used
the
outcome
of
a
climate
scenario,
“Had”:
The
global
climate
model
HADCM3
combined
with
the
regional
climate
model
(RCM)
HADRM3.
This
scenario
predicts
changes
in
both
yearly
mean
air
temperature
(+1.6 ◦C)
and
yearly
precipitation
(+78.8
mm).
Daily
resolution
scenario
data
for
surface
air
temperature
and
pre-
cipitation
were
derived
from
a
sub-set
of
the
RCM
simulations
and
implemented
by
scaling
the
observed
weather
(1990–2012).
The
observed
temperatures
were
changed
to
reflect
the
increase
in
both
median
and
variance
predicted
by
the
climate
models.
Precipitation
was
scaled
using
a
ratio
of
change
approach,
mul-
tiplying
observation
by
the
ratio
of
observed
(1990–2012)
over
predicted
(2030–2052)
precipitation.
Climate
conditions
during
the
reference
period
are
referred
to
as
climate
“Ref”.
The
man-
agement
scenarios
are
referred
to
as
“Ref”
=
reference
(historical
data),
“Best”
=
best
case
(water-quality
focus),
“Worst”
=
“worst
case”
(economic
focus).
The
“Best”
scenario
is
defined
by
four
cri-
teria:
(1)
a
10%
reduction
in
agricultural
land,
which
is
converted
to
forest,
(2)
a
25%
decrease
in
vegetable
production,
which
is
con-
verted
to
grass
production,
(3)
a
25%
decrease
in
P-based
fertilizer
application,
and
(4)
a
90%
improvement
in
the
P-removing
perfor-
mance
of
WWTPs.
Conversely,
the
“Worst”
scenario
is
defined
by
(1)
a
10%
reduction
of
forest
cover,
which
is
converted
to
agricul-
tural
lands,
(2)
a
shift
of
25%
of
the
grass
production
to
vegetable
production,
(3)
an
increase
of
P-based
fertilizer
application
by
25%,
and
(4)
a
25%
increase
in
the
P
load
of
effluents
from
scattered
dwellings
and
WWTPs
throughout
the
catchment.
More
details
on
the
application
of
these
and
other
scenarios
to
the
catchment
and
lake
process-based
models
are
given
by
Couture
et
al.
(2014).
2.2.2.
Process-based
model
output
All
aspects
of
catchment
and
lake
process-based
modelling
are
described
by
Couture
et
al.
(2014).
In
brief,
the
effects
of
the
climate
and
management
scenarios
on
the
river
hydrology
and
chemistry
were
modelled
by
the
catchment
models
PERSiST
(Futter
et
al.,
2013)
and
INCA-P
(Wade
et
al.,
2002),
respectively.
PERSiST
simulated
daily
runoff
in
the
river
system
using
inputs
of
catch-
ment
characteristics
and
daily
temperature
and
precipitation
time

332
S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
Table
1
Overview
of
nodes
in
the
Bayesian
network
model.
Modules
are
defined
in
Fig.
2.
Module
Node
name
Unit
No.
of
values
Node
states
1
2
3
4
5
6
1
Management
Ref
Worst
Best
1
Climate
Ref
Had
1
Year
1990–1995
1996–2001
2002–2007
2008–2012
1
Month
May
Jun
Jul
Aug
Sep
Oct
1
Season
May–Jun
Jul–Aug
Sep–Oct
2
Irradiance
␮mol/m2s
251,280a0–100
100–150
150–200
200–300
2
Secchi
(pred.)
m
251,280
0–2
2–2.6
2.6–5
2
Total
P
(pred.)
␮g/L
251,280
0–20
20–25
25–30
30–39
39–50
50–80
2
Chl-a
(pred.)
␮g/L
251,280
0–5
5–10.5
10.5–15
15–20
20–25
25–60
2
Temp.
(pred.) ◦C 251,280
0–10 10–15 15–19 19–30
3
Secchi
(obs.) m
191
0–2
2–2.6
2.6–5
3
Total
P
(obs.)
␮g/L
250
0–20
20–39
39–80
3
Chl-a
(obs.)
␮g/L
250
0–10.5
10.5–20
20–60
3
Temp.
(obs.) ◦C
195
0–19
19–30
3
Cyano
␮g/L
103
0–1000
1000–2000
2000–6000
3
CyanoMax
␮g/L
103b0–1000
1000–2000
2000–6000
4
Status
Secchi
HG
M
PB
4
Status
Total
P
HG
M
PB
4
Status
Chl-a HG
M
PB
4
Status
Cyano
HG
M
PB
4
Status
Phys-chem.
HG
M
PB
4
Status
Phytoplankton
HG
M
PB
4
Status
of
lake
HG
M
PB
aThe
number
of
values
in
Module
2
is
generated
by
simulation
of
weekly
values
during
May-Oct
for
23
years
with
60
different
parameter
sets
for
6
scenarios.
bCyanoMax
has
only
9
unique
values
(one
for
each
year
of
observation).
series.
INCA-P
produced
daily
predictions
of
discharge
and
material
transport
in
the
river
(concentration
of
suspended
solids,
soluble
reactive
P
and
total
P
(TP)),
which
were
then
passed
to
the
lake
model.
The
successive
effects
of
the
scenarios
on
the
physical
con-
ditions
and
the
concentration
of
different
P
fractions
in
the
lake
were
modelled
by
the
process-based
model
MyLake
(Saloranta
and
Andersen,
2007).
In
MyLake,
phytoplankton
has
a
constant
C:P
ratio
of
106:1
and
an
organic-P:Chl-a
ratio
of
1:1,
such
that
particu-
late
organic
P
is
a
proxy
for
Chl-a
(Saloranta
and
Andersen,
2007).
The
MyLake
model
was
automatically
calibrated
against
monitor-
ing
data
from
the
years
2005–2012,
using
a
probabilistic
Bayesian
inference
calibration
scheme.
In
this
scheme
each
parameter
was
given
a
prior
and
a
posterior
distribution,
within
the
framework
of
a
self-adaptive
differential
evolution
learning
scheme
(DREAM),
implemented
in
Matlab
(Starrfelt
and
Kaste,
2014).
The
MCMC
algo-
rithm
was
run
along
eight
chains
until
convergence,
monitored
visually,
was
obtained.
Four
hundred
iterations
were
saved
and
used
to
determine
posterior
parameter
distribution.
An
envelope
of
60
parameter
sets
of
equal
likelihood
was
sampled
to
gener-
ate
a
set
of
60
model
realisations
with
daily
resolution
for
23
years
(1990–2012).
The
variability
among
these
sets
(median
and
interquartile
space)
was
discussed
by
Couture
et
al.
(2014).
For
the
BN
model,
all
60
realisations
of
the
process-based
models
are
used
as
input
and
considered
a
source
of
uncertainty.
Specifically,
the
following
outcome
of
the
lake
model
was
used
as
nodes
in
the
BN
model
(see
Table
1):
surface
water
temperature
(hence-
forth
referred
to
as
“temperature”),
Secchi
depth,
total
P
(TP)
and
Chl-a.
Secchi
depth
(SD)
was
calculated
using
the
light
extinc-
tion
coefficient
(␩)
calculated
by
MyLake
and
the
relationship
␩
=
1.7/SD
(French
et
al.,
1982).
Temperature
and
concentrations
were
averaged
for
depths
0–4
m
(to
match
the
monitoring
data).
In
addition
we
included
surface
irradiance
at
noon
(an
input
variable
for
MyLake),
to
represent
seasonal
change
in
addition
to
tempera-
ture.
For
each
variable,
values
for
one
day
per
week
were
selected
(to
match
the
sampling
frequency
of
the
monitoring
data).
2.2.3.
Lake
monitoring
data
The
main
data
source
for
this
study
was
the
data
series
from
Lake
Vansjø,
the
basin
Vanemfjorden
(see
Table
1
and
Fig.
1).
All
data
were
downloaded
from
NIVA’s
monitoring
database
(http://
www.aquamonitor.no).
The
following
data
were
included
in
this
study:
water
temperature
(years
1993–1996,
2005–2012),
Sec-
chi
depth
(2000–2001,
2005–2012),
total
P
(1990–2012),
Chl-a
(1990–2012)
and
biomass
of
cyanobacteria
(2004–2012).
Inte-
grated
water
samples
from
0
to
4
m
were
collected
for
the
chemical
and
biological
analyses.
Only
data
from
the
months
of
May
to
October
were
included
(following
the
national
classification
sys-
tem;
section
2.2.4).
From
2005
all
variables
were
measured
weekly,
except
for
cyanobacteria,
which
were
measured
bi-weekly.
In
addition,
the
larger
dataset
EUREGI
was
used
for
evaluation
of
the
model
(as
described
in
section
3.3).
The
EUREGI
lake
dataset
results
from
the
regional
eutrophication
survey
in
Norway
in
1988
(Oredalen
and
Faafeng,
2002).
The
dataset
includes
quantitative
analyses
from
more
than
400
lakes,
sampled
minimum
4
times.
The
locations
are
selected
in
order
to
cover
the
broadest
possible
gradient
of
human
influence.
Parameters
that
typically
represent
eutrophication
(TP
and
Chl-a)
range
over
two
orders
of
magnitude
in
this
dataset.
Eutrophic
lakes
are
overrepresented
regarding
the
proportion
of
area
covered
by
these
lakes;
nevertheless,
the
dataset
contains
more
oligotrophic
than
eutrophic
lakes.
Almost
75%
of
the
lakes
are
clear-water
lakes,
of
which
the
majority
is
calcium-poor
lakes.
The
remaining
25%
are
humic
lakes;
this
group
has
equal
proportions
of
calcium-poor
and
calcium-rich
lakes.
In
total
599
samples
from
EUREGI
were
used
in
this
study;
samples
that
com-
prised
values
for
water
temperature,
Chl-a
and
cyanobacteria.
2.2.4.
National
classification
system
for
lakes
The
status
assessment
in
this
study
is
based
on
the
main
eutrophication
indicators
and
their
combination
rules
in
the
Norwegian
lake
classification
system,2with
status
class
bound-
aries
defined
for
the
lake
type
L-N8
(lowland,
large,
shallow,
siliceous/moderate
alkalinity,
humic).
Three
of
the
indicators
in
the
classification
system
were
obtained
from
MyLake
model
predictions,
and
included
in
this
study:
seasonal
averages
of
2http://www.vannportalen.no/Revidert
klassifiseringsveileder140123
VZIS-.
pdf.file.

S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
333
Fig.
1.
Observed
(open
black
circles)
and
predicted
(red
curves)
values
of
(a)
temper-
ature,
(b)
Secchi
depth,
(c)
total
P,
(d)
chl-a
and
(e)
cyanobacteria.
Predicted
values
are
median
values
(with
25
and
75
percentiles)
of
60
runs
of
the
process
model
MyLake
with
different
parameter
combinations
(see
section
2.1.1).
(Predicted
values
for
cyanobacteria
are
not
available
from
this
model).
Blue
triangles
represent
sea-
sonal
mean
values
for
Secchi
depth,
total
P
and
chl-a,
and
seasonal
maximum
value
for
cyanobacteria
(corresponding
to
the
node
CyanoMax).
Horizontal
lines
indicate
the
boundaries
between
ecological
status
classes:
High-Good
(H-G),
Moderate
(M)
and
Poor-Bad
(P-B).
Secchi
depth,
TP
and
Chl-a.
According
to
the
classification
system,
physico-chemical
indicators
(here:
Secchi
depth
and
TP)
should
be
combined
by
averaging.
Phytoplankton
status
should
in
prin-
ciple
be
assessed
by
four
indicators:
Chl-a,
total
phytoplankton
biomass,
PTI
(a
measure
of
sensitive
vs.
tolerant
taxa;
(Ptacnik
et
al.,
2009))
and
the
yearly
maximum
of
cyanobacterial
biomass.
All
four
indices
can
be
calculated
from
the
monitoring
data,
but
they
are
all
correlated,
and
only
one
can
be
predicted
by
MyLake
(Chl-a).
We
therefore
chose
to
include
only
one
additional
phytoplankton
index
in
the
BN,
namely
the
yearly
maximum
of
cyanobacteria
(termed
“CyanoMax”).
Combined
phytoplankton
status
should
be
obtained
as
follows:
if
CyanoMax
have
worse
status
than
chl-a,
then
the
two
indicators
should
be
averaged;
if
CyanoMax
has
equal
or
better
sta-
tus
than
chl-a,
then
CyanoMax
should
be
ignored.
Thus,
including
cyanobacteria
can
only
result
in
worse
or
equal
status
of
phyto-
plankton
compared
to
the
status
determined
by
chl-a
alone.
Finally,
while
the
overall
ecological
status
of
the
lake
is
determined
pri-
marily
by
biology
(here:
phytoplankton),
it
can
be
compromised
by
physico-chemical
elements.
If
the
status
set
by
biology
is
High
or
Good,
and
the
physico-
chemical
status
is
worse
than
the
biological
status,
then
the
overall
ecological
status
should
be
reduced
by
one
class
(i.e.,
from
High
to
Good
or
from
Good
to
Moderate).
(More
details
are
given
in
Appendix
A).
The
full
classification
system
comprises
several
more
indicators
including
both
physico-chemical
quality
elements
(e.g.
Total
N)
and
biological
quality
elements
(BQEs;
macrophytes,
ben-
thic
invertebrates
and
fish).
In
this
study,
however,
we
included
only
the
indicators
that
could
be
predicted
by
MyLake
or
that
could
be
linked
to
MyLake
predictions
with
high
confidence
(i.e.,
cyanobacteria).
2.3.
Bayesian
network
modelling
For
constructing
the
BN
model,
we
followed
recent
guidelines
for
use
of
BN
in
ecological
modelling
(Marcot
et
al.,
2006;
Pollino
and
Henderson,
2010):
(1)
Defining
the
objective
of
the
model
and
its
final
node
(here:
ecological
status
of
the
lake);
(2)
generating
a
conceptual
model
(nodes
and
arrows)
based
on
knowledge
from
the
literature
and
on
expert
knowledge;
(3)
establishing
the
model
states
and
quantifying
the
relationships.
The
BN
model
was
devel-
oped
and
run
in
the
software
Hugin
Expert,
version
8
(http://www.
hugin.com).
2.3.1.
Model
structure
In
a
BN
model,
each
node
(variable)
is
typically
defined
by
a
discrete
probability
distribution
across
a
number
of
alternative
states
(i.e.,
intervals
or
categories).
This
structure
enables
differ-
ent
types
of
information
to
be
linked
by
conditional
probability
tables
(CPT)
(see
Table
2
and
section
3.1).
Although
continuous
variables
may
also
be
included
in
a
BN
with
certain
restrictions,
this
type
of
nodes
are
not
considered
here.
All
nodes
with
outgoing
arrows
are
termed
“parent
nodes”,
while
all
nodes
with
incoming
arrows
are
termed
“child
nodes”.
In
a
CPT,
the
probabilistic
depen-
dencies
between
a
child
node
and
its
parents
are
defined.
When
the
model
is
run,
probability
distribution
of
the
child
node
is
updated
accordingly,
given
the
states
of
the
parent
nodes,
following
the
Bayes’
theorem
for
conditional
probability
calculation
(Koski
and
Noble,
2009).
The
probability
distributions
in
the
CPTs
can
repre-
sent
the
natural
variability
in
the
system
as
well
as
any
other
type
of
uncertainty
concerning
the
relationship
between
the
variables.
In
our
model
the
main
sources
of
variability
are
(1)
the
tempo-
ral
variation
in
the
predicted
and
observed
time
series
(within
the
specified
time
intervals)
and
(2)
uncertainty
in
the
predictions
of
the
process-based
models
that
are
included
in
the
BN.
The
com-
plexity
of
a
BN
grows
exponentially
with
the
number
of
nodes
and
arrows;
therefore
it
is
often
desirable
to
limit
the
number
of
nodes
(Varis
and
Kuikka,
1999).
The
computing
capacity
of
computers
have
increased
to
the
extent
that
even
relatively
complex
and
big
networks
can
be
built
and
run
(Lehikoinen
et
al.,
2013),
but
more
complex
BNs
nevertheless
require
more
data
or
other
information
than
simpler
ones.
In
this
study,
we
aimed
at
including
only
the
nodes
that
were
necessary
to
(i)
run
the
model
according
to
selected
scenarios,
(ii)
represent
particular
processes
that
were
important

334
S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
Table
2
Examples
of
conditional
probability
tables
(CPT)
for
each
module
of
the
BN
model.
Each
column
contains
the
probability
distribution
of
a
child
node
for
a
given
combination
of
states
of
the
parent
nodes.
The
bottom
row
(“Experience”)
contains
the
total
count
of
observations
for
each
combination
of
parent
nodes.
(a)
CPT
(the
first
8
columns)
for
Chl-a
(predicted)
conditional
on
management,
years,
irradiance
and
water
temperature.
The
full
table
contains
3
(management
scenarios)
x
4
(year
intervals)
x
4
(irradiance
intervals)
x
4
(temperature
intervals)
=
192
columns.
Management
Reference
Years
1990–1995
Irradiance
0–100
100–150
Temp.
(pred.)
0–10
10–15
15–19
19–25
0–10
10–15
15–19
19–25
Chl-a
(pred.)
0–5
0.013
0.012
0
0
0.124
0.067
0.004
0
5–10.5 0.104
0.106
0.117
0.117
0.588
0.180
0.065
0.092
10.5–15 0.066
0.020
0.017
0.017
0.148
0.223
0.082
0.042
15–20
0.297
0.085
0.000
0.000
0.036
0.026
0.033
0.000
20–25
0.313
0.264
0.104
0.104
0.050
0.168
0.018
0.000
25–60
0.206
0.512
0.763
0.763
0.055
0.337
0.798
0.867
Experience
3015
2445
540
0a420
1200
1980
480
(b)
CPT
for
Cyanobacteria
conditional
on
Chl-a
(observed)
and
water
temperature
(observed).
Chl-a
(obs.) 0–10.5 10.5–20
20–60
Temp.
(obs)
0–19
19–25
0–19
19–25
0–19
19–25
Cyano
0–1000
1
1
1
0.923
0.333
0.323
1000–2000
0
0
0
0.077
0.333
0.290
2000–6000
0
0
0
0
0.333
0.387
Experience
20
1
22
13
3
31
(c)
CPT
for
CyanoMax
conditional
on
Cyanobacteria
and
Season.
Cyano
0–1000
1000–2000
2000–6000
Season
May–Jun
Jul–Aug
Sep–Oct
May–Jun
Jul–Aug
Sep–Oct
May–Jun
Jul–Aug
Sep–Oct
CyanoMax
0–1000 0.618
0.724
0.667
0
0
0
0
0
0
1000–2000
0.088
0.138
0.111
0.167
0.167
0
0
0
0
2000–6000
0.294
0.138
0.222
0.833
0.833
1
1
1
1
Experience
34
29
27
6
6
2
1
12
2
(d)
CPT
for
Status
of
lake
conditional
on
status
of
phytoplankton
(PP)
and
status
of
physico-chemical
(PC)
variables.
HG
=
High-Good,
M
=
Moderate,
PB
=
Poor-Bad.
Status
PP
HG
M
PB
Status
PC
HG
M
PB
HG
M
PB
HG
M
PB
Status
Lake
HG
1
0
0
0
0
0
0
0
0
M
0
1
1
1
1
0
0
0
0
PB
0
0
0
0
0
1
1
1
1
aAssumed
probability
distributions
inserted
where
no
observations
were
available.
for
the
cyanobacteria
and
other
phytoplankton
and
(iii)
assess
the
effects
of
the
scenarios
on
the
status
indicators.
A
BN
is
usually
not
a
dynamic
model,
meaning
that
it
does
not
have
a
time
dimension.
Instead,
the
predictions
of
a
BN
can
represent
the
probability
of
realising
different
outcomes
during
a
specified
period.
The
BN
in
our
study
represents
the
whole
period
for
which
the
MyLake
model
was
run
(1990–2012).
However,
there
has
been
substantial
changes
in
the
concentrations
of
TP
and
chl-a
during
this
period
(Fig.
1c
and
d),
which
could
be
useful
to
account
for
in
the
BN.
We
therefore
included
a
node
“Year”
that
divided
the
23-year
time
span
into
4
periods
of
5–6
years;
this
way
the
effects
of
the
different
scenarios
on
water
quality
(i.e.,
the
CPTs)
could
be
estimated
separately
for
these
periods,
and
the
BN
could
be
run
for
selected
periods.
(The
default
setting
of
the
Year
node
was
a
uni-
form
probability
distribution,
corresponding
to
running
the
BN
for
the
whole
23-year
period).
Moreover,
a
node
“Month”
was
included
to
account
for
seasonal
changes
in
the
water
quality.
The
BN
model
developed
in
this
study
(Fig.
2)
comprises
four
modules,
corresponding
to
the
four
sources
of
information
described
above.
Module
1
contains
all
the
parent
nodes,
representing
the
cli-
mate
and
management
scenarios,
as
well
as
the
nodes
representing
specific
periods
(years
and
month).
Module
2
links
these
scenarios
to
the
output
from
the
process-
based
models,
i.e.
the
predicted
effects
on
physico-chemistry
in
the
lake.
Module
3
links
these
model
predictions
to
the
observed
time
series
for
a
set
of
physical,
chemical
and
biological
variables,
and
furthermore
provides
a
link
from
two
of
these
variables
(chl-a
and
water
temperature)
to
the
observed
cyanobacterial
biomass.
In
addition,
the
yearly
maximum
of
cyanobacteria
(“CyanoMax”)
is
set
equal
to
the
highest
observed
cyanobacteria
biomass
across
all
samples
in
a
given
year.
Thus,
each
observation
of
Cyano
is
asso-
ciated
with
a
CyanoMax
from
the
same
year,
but
possibly
from
a
different
month.
Module
4
links
each
of
the
physico-chemical
and
biological
indi-
cators
to
the
lake
classification
system.
This
enables
prediction
of
the
probability
of
different
status
classes
for
each
indicator
as
well
as
for
the
overall
ecological
status
of
the
lake.

S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
335
Fig.
2.
Structure
of
the
Bayesian
Network
(BN)
model
for
ecological
status
of
Lake
Vansjø,
basin
Vanemfjorden.
The
model
consists
of
four
modules:
(1)
Climate
and
management
scenarios
(2),
output
from
the
process-based
lake
model
MyLake;
(3)
monitoring
data
from
Lake
Vansjø
(1990–2012);
(4)
the
national
classification
system
for
ecological
status
of
lakes.
The
prior
probability
distribution
for
each
node
is
displayed
both
as
horizontal
bars
and
by
percentages
(the
first
column
in
each
node),
across
the
states
(the
second
column).
The
set
of
arrows
pointing
to
one
node
represents
the
conditional
probability
table
for
this
node.
Status
classes:
HG
=
High-Good
(required
by
the
WFD),
M
=
moderate,
PB
=
Poor-Bad.
The
causal
links
between
the
nodes
(i.e.,
the
arrows
and
their
directions)
can
be
determined
in
different
ways.
For
nodes
that
are
based
on
data,
it
is
possible
to
let
the
software
estimate
suggest
a
set
of
arrows
and
their
directions
given
specific
criteria.
Neverthe-
less,
we
chose
to
develop
the
structure
based
on
knowledge
and
theory
about
causal
relationships
among
the
nodes.
For
the
nodes
in
Module
2,
regression
tree
analyses
were
performed
to
explore
which
parent
nodes
had
significant
effect
on
the
child
nodes.
The
analyses
were
performed
with
the
packages
rpart
(Therneau
et
al.,
2015)
and
party
(Hothorn
et
al.,
2006)
in
the
software
R
(R
Core
Team,
2015).
All
indicator
nodes
varied
with
year
and
with
month.
The
node
Management
had
significant
effects
on
all
indicator
nodes
predicted
by
MyLake
(Secchi,
TP
and
Chl-a).
Water
temperature
affected
Chl-a,
but
not
Total
P.
The
node
Irradiance
was
included
as
a
parent
for
Chl-a,
because
of
the
particular
importance
for
phytoplankton
growth.
The
purpose
was
to
distinguish
between
effects
of
Irradiance
and
Temperature;
both
variables
varied
dur-
ing
the
year,
but
only
Temperature
was
affected
by
Climate.
TP
and
Chl-a
were
strongly
correlated,
as
is
commonly
observed
in
lakes
(Phillips
et
al.,
2008),
and
therefore
both
variables
could
have
been
a
Fig.
3.
Regression
tree
for
effects
of
temperature
on
the
variable
CyanoMax
(seasonal
maximum
of
cyanobacteria
biomass).
The
numbers
on
the
branches
(18.85
and
20.2)
show
the
significant
breakpoints
along
temperature
gradient.
The
bar
plots
in
each
resulting
node
show
the
probability
distribution
of
CyanoMax
across
the
three
status
classes:
1:
High-Good
(<10.5
␮g/L),
2:
Moderate
(10.5–20
␮g/L),
Poor-Bad
(≥20
␮g/L).
n
=
number
of
observations
in
each
node.

336
S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
suitable
parent
node
for
Cyanobacteria.
We
chose
Chl-a
as
the
par-
ent
node,
because
this
variable
has
lately
been
reported
to
be
a
better
predictor
of
cyanobacteria
biomass
than
the
more
commonly
used
TP
(Ptacnik
et
al.,
2008).
2.3.2.
Node
states
and
prior
probability
distributions
Continuous
variables
must
be
discretised
into
intervals
(states)
for
use
in
discrete
nodes
in
a
BN.
The
number
of
states
for
each
node
is
typically
kept
low,
because
the
model
complexity
also
grows
quickly
with
the
number
of
states.
In
this
study,
therefore,
we
tried
to
minimise
the
number
of
states,
while
still
obtaining
a
model
with
sufficient
sensitivity
to
respond
to
the
scenarios.
An
overview
of
the
states
of
all
nodes
is
given
in
Table
1.
For
all
status
nodes
(Module
4),
the
five
ecological
status
classes
were
lumped
into
three
states
(High-Good,
Moderate
and
Poor-
Bad).
The
corresponding
indicator
nodes
in
Module
3
(Monitoring
data:
Secchi,
Total
P,
Chl-a
and
CyanoMax)
were
discretised
into
three
intervals,
with
borders
determined
by
the
class
boundaries
of
the
national
classification
system
(see
Table
A1a–d).
Observed
tem-
perature
was
divided
into
two
intervals,
determined
by
a
regression
tree
analysis
(Fig.
3):
A
breakpoint
in
the
effect
of
temperature
on
cyanobacteria
was
estimated
at
19 ◦C
(above
which
there
was
a
higher
probability
of
high
cyanobacteria
concentrations).
For
the
corresponding
variables
predicted
by
MyLake
(Module
2),
the
large
amount
of
simulated
data
allowed
discretisation
with
higher
res-
olution:
predicted
Total
P,
Chl-a
and
Temperature
were
given
6,
6,
and
4
states
respectively.
The
states
from
the
corresponding
vari-
ables
in
Module
3
were
used
as
a
starting
point;
then
the
state(s)
with
the
highest
proportion
of
the
observations
were
split
into
two
or
more
intervals
to
obtain
a
more
even
probability
distribution.
For
example,
the
TP
state
30–39
␮g/L
was
split
into
3
intervals
(20–25,
25–30
and
30–39)
while
the
state
39–80
␮g/L
was
split
into
two
intervals
(39–50
and
50–80).
The
years
(Module
1)
were
grouped
into
four
5-
or
6-year
periods
(1990–1995,
1996–2001,
2002–2007
and
2008–2012).
The
months
were
grouped
into
three
2-months
periods
in
a
separate
node
“Season”
(May-June,
July-
August
and
September-October);
the
purpose
to
obtain
a
parent
node
for
CyanoMax
with
fewer
states
than
the
Month
node.
All
prior
probability
distributions
are
displayed
in
Fig.
2
(and
in
Supplementary
data).
The
prior
probability
distributions
were
defined
as
follows.
For
parent
nodes
representing
scenarios
and
time
intervals
(Module
1),
equal
probability
was
assumed
for
each
state.
This
was
simply
a
starting
point
for
running
the
model,
and
is
not
meant
to
represent
our
beliefs
or
knowledge.
For
each
subse-
quent
child
node,
the
prior
probability
distribution
was
determined
by
their
CPT
in
combination
with
the
prior
probability
distributions
of
their
parent
nodes.
Hence,
the
prior
probability
distributions
of
all
child
nodes
throughout
the
BN
represent
all
the
different
sce-
nario
combinations
with
equal
probability.
3.
Calculation
3.1.
Construction
of
conditional
probability
tables
The
discrete
probability
distributions
in
the
CPTs
are
also
obtained
by
different
approaches
in
the
different
BN
modules.
Table
2
contains
examples
of
CPTs
for
each
module,
while
all
CPTs
are
included
in
Supplementary
data.
In
Module
2
(Process-based
model
output),
the
conditional
probability
distribution
of
each
child
node
was
therefore
calcu-
lated
as
the
frequency
distribution
of
this
variable
across
each
of
its
parent
nodes
in
the
reference
scenario
for
both
climate
and
management,
for
all
60
realisations
of
MyLake
pooled
together.
For
example,
for
predicted
chl-a,
the
probability
of
the
lowest
chl-a
interval
(0–5
␮g/L)
under
a
given
combination
of
states
of
the
parent
nodes
(e.g.
Management
=
Reference,
Year
=
1990-1995,
Irradiance
=
0-100
and
Temperature
=
0-10)
was
determined
by
the
count
of
predicted
chl-a
values
obtained
in
this
interval
for
this
par-
ticular
combination
of
states
of
the
parents
nodes
(40)
divided
by
the
total
number
of
observations
for
this
combination
(3015).
I.e.,
the
probability
is
40/3015
=
0.013
(the
upper
left
cell
in
Table
2a).
Thus,
the
probability
distribution
in
this
column
arises
from
the
variability
between
the
60
MyLake
model
realisations
as
well
as
from
the
temporal
variability
during
the
period
1990–1995.
In
cases
where
a
given
combination
of
parents’
states
in
the
refer-
ence
scenario
did
not
occur
in
the
count
data
(Experience
=
0
in
the
CPT),
values
based
on
expert
judgement
were
inserted
to
allow
the
model
to
run.
For
example,
for
Total
P
(obs.),
the
count
was
zero
for
the
lowest
interval
of
Total
P
(pred.)
(Table
B1a);
here
an
assumed
probability
distribution
based
on
the
neighbour
col-
umn
was
inserted.
For
the
nodes
in
module
2,
where
the
CPTs
had
a
high
number
of
columns,
columns
with
Experience
=
0
were
populated
with
probability
distributions
from
the
neighbour
col-
umn
(see
example
in
Table
2a).
(Testing
showed
that
the
assumed
probability
distributions
in
such
cases
had
negligible
effects
on
the
posterior
probability
distributions
of
the
child
nodes).
In
Module
3
(Monitoring
data),
likewise,
the
links
from
the
pre-
dicted
MyLake
outcome
to
the
observed
monitoring
data
were
based
on
the
joint
frequency
distributions
of
the
two
variables.
The
observed
data
were
paired
with
the
corresponding
predicted
data
for
the
same
week,
and
the
concentration
intervals
were
com-
pared
(Table
B1).
The
CPT
for
the
Cyano
node
was
calculated
from
the
observations
of
Temperature,
Chl-a
and
Cyanobacteria
from
the
same
date.
The
CPT
for
CyanoMax
(the
maximum
of
Cyano
for
each
year)
was
obtained
by
counting
the
number
of
observed
Cyano
in
each
concentration
interval
and
each
season,
and
calculating
the
fre-
quency
distribution
across
the
corresponding
CyanoMax
intervals
for
all
of
these
observations.
For
example,
out
of
the
34
observations
of
Cyano
concentration
below
1000
␮g/L
in
the
May-June
season,
10
observations
(probability
0.29)
came
from
a
year
where
the
CyanoMax
in
the
same
year
exceeded
2000
␮g/L.
The
total
number
of
cyanobacteria
samples
(90)
was
relatively
low
for
calculating
the
9
frequency
distributions
in
the
CPT
of
Cyano
(and
of
CyanoMax;
Table
2c
and
d).
We
therefore
complemented
the
temporal
data
for
the
target
lake
with
the
larger
spatial
dataset
from
the
regional
dataset
EUREGI
(described
in
section
2.2.3).
In
Module
4
(Ecological
status),
each
of
the
four
indicators
(Sec-
chi,
TP,
Chl-a
and
Cyano)
has
a
status
node
where
the
three
states
(High-Good,
Moderate
or
Poor-Bad)
correspond
to
the
three
inter-
vals
of
the
parent
node.
For
these
nodes,
the
CPT
is
set
to
1
for
each
cell
with
matching
states
and
0
for
all
other
cells
(Table
A1a–d).
For
the
subsequent
nodes
(Physico-chemical
status,
Phytoplankton
sta-
tus
and
Lake
status),
the
implementation
of
the
combination
rules
into
the
CPTs
is
described
in
Appendix
A.
3.2.
Running
the
BN
model
A
BN
model
can
be
run
by
altering
the
probability
distribution
of
one
or
more
nodes
(e.g.,
selecting
one
management
scenario)
and
thereby
updating
the
probability
distribution
in
all
the
nodes
that
are
linked
by
CPTs
throughout
the
network
(e.g.,
the
status
of
the
lake).
A
common
way
to
run
the
model
is
to
“set
evidence”
for
one
or
more
of
the
parent
nodes,
i.e.
to
select
one
of
the
states
(assign
100%
probability
for
this
state)
(Fig.
4).
In
this
study,
the
main
model
runs
(the
6
scenarios)
were
performed
by
setting
evi-
dence
for
each
combination
of
the
management
and
climate
node
states,
and
recording
the
posterior
probabilities
in
the
child
nodes.
In
addition,
for
the
purpose
of
model
evaluation,
alternative
model

S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
337
Fig.
4.
Examples
of
BN
model
predictions
(posterior
probability
distributions)
for
two
scenarios.
(a)
Scenario
with
current
climate
(Ref)
and
reference
management
(Ref).
(b)
Scenario
with
future
climate
(Had)
and
“best
case”
management.
Note
the
shift
to
higher
probability
of
HG
status
for
most
of
the
nodes
under
the
latter
scenario.
For
more
details,
see
Fig.
2.
runs
were
performed
by
setting
evidence
for
other
selected
nodes
in
the
network
(see
next
section).
3.3.
Model
evaluation
Model
evaluation
is
an
important
step
in
good
modelling
prac-
tice,
but
evaluation
of
Bayesian
network
models
is
often
neglected
(Aguilera
et
al.,
2011).
Ideally,
one
part
of
a
dataset
should
be
used
for
“training”
(model
calibration)
while
another
part
is
reserved
for
evaluation
by
comparison
with
model
predictions
(Chen
and
Pollino,
2012).
However,
the
data
on
the
most
crucial
component
of
this
model
–
Cyanobacteria
–
could
not
be
divided
without
com-
promising
the
calibration
(construction
of
CPTs;
see
Table
2b).
Moreover,
predictions
based
on
future
scenarios
could
not
be
compared
to
real
data.
Other,
more
qualitative
forms
of
model
eval-
uation
have
been
suggested
(Chen
and
Pollino,
2012;
Marcot,
2012),
such
as
applying
different
combinations
of
inputs
and
examining
the
resulting
probabilities
throughout
the
network,
to
test
whether
the
behaviour
of
the
model
is
consistent
with
current
understand-
ing
about
the
system.
Here,
we
identified
three
critical
parts
of
the

338
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/
Ecological
Modelling
337
(2016)
330–347
model
and
inspected
the
sensitivity
of
the
model
to
alterations
of
these
parts.
(1)
The
link
from
process-based
model
predictions
to
observed
data.
The
correspondence
between
predicted
and
observed
values
is
captured
in
the
CPTs
for
the
monitoring
data
(Table
B1).
As
a
rough
evaluation
based
on
the
proportions
of
matching
states
in
these
CPTs,
the
goodness-of-fit
of
the
MyLake
model
predic-
tions
can
be
characterised
as
good
(temperature),
intermediate
(chl-a)
and
less
good
(TP),
respectively.
A
detailed
assessment
of
the
MyLake
model
predictions
and
explanations
for
the
devi-
ations
are
given
by
Couture
et
al.
(2014).
To
assess
the
influence
of
the
prediction
vs.
observation
uncertainty
on
the
model
per-
formance,
we
ran
two
versions
of
the
model:
one
version
that
was
based
on
the
process-based
model
predictions
without
accounting
for
the
mismatch
with
observations
(version
1)
and
another
that
incorporated
this
uncertainty
in
the
CPTs
(version
2).
(2)
The
CPT
for
cyanobacteria.
Due
to
the
limited
number
of
cyanobacteria
observations
(Table
2b),
to
reserve
a
subset
of
the
cyanobacteria
data
for
evaluation
purposes
would
not
be
meaningful.
Instead,
we
used
the
independent
EUREGI
dataset
(see
section
2.2.3)
to
construct
an
alternative
CPT
for
cyanobac-
teria
(model
version
3,
based
on
version
1)
and
compared
the
outcome
of
this
version
with
that
of
version
1.
(3)
Effects
of
water
temperature.
A
critical
component
of
this
BN
is
the
effect
of
water
temperature
on
cyanobacteria.
Moreover,
since
the
conditional
probabilities
used
for
calculating
posterior
probabilities
for
cyanobacteria
are
based
on
very
few
obser-
vations
for
some
of
the
parent
state
combinations
(Table
2b),
it
is
important
to
check
that
these
CPTs
do
not
provide
spuri-
ous
results.
We
therefore
inspected
more
closely
relationship
between
temperature,
Chl-a
and
cyanobacteria
by
setting
evi-
dence
(fixating
probabilities)
for
the
nodes
Temperature
and
Chl-a.
In
addition,
the
effect
of
Season
was
checked.
4.
Result
and
discussion
4.1.
Effects
of
management
and
climate
scenarios
on
lake
status
The
results
reported
in
this
section
are
based
on
version
1
of
the
BN
(defined
in
section
3.3;
the
choice
of
the
version
is
explained
in
section
4.2).
The
model
outcome
of
this
version
is
equal
to
the
outcome
of
the
MyLake
model
(TP
and
Chl-a)
as
reported
by
Couture
et
al.
(2014).
The
BN
model
has
achieved
new
results
in
three
main
ways:
(1)
including
the
Cyanobacteria
component
in
the
model,
as
well
as
Secchi
depth,
(2)
assessing
the
probability
distribution
of
status
classes
for
the
four
indicator
variables,
and
(3)
using
the
combination
rules
of
the
national
classification
system
to
assess
the
overall
lake
status.
In
this
study
we
focus
more
on
the
resulting
status
classes
(High-Good,
Moderate
and
Poor-Bad)
than
on
the
exact
values
of
the
indicators.
The
climate
scenario
had
a
limited
effect
of
the
Temperature
node
(see
Fig.
4):
the
probability
of
“a
warm
year”
(>19 ◦C
water
temperature
during
May-October)
increased
from
17%
to
27%.
All
subsequent
climate
change
effects
in
the
BN
are
based
on
this
increase.
Secchi
depth
values,
both
observed
and
predicted
(MyLake),
were
in
the
Poor-Bad
status
during
the
whole
time
series
(Fig.
1a).
Accordingly,
this
indicator
had
a
100%
probability
of
Poor-Bad
sta-
tus,
for
the
references
scenario
as
well
as
for
all
other
scenarios
(Fig.
5a).
Hence,
the
effects
of
the
different
scenarios
on
Secchi
depth
are
not
given
more
attention
here.
Nevertheless,
the
Sec-
chi
depth
status
affected
the
Physico-chemical
status
(Fig.
5c)
and
thereby
potentially
the
overall
lake
status
(Fig.
5g).
Therefore,
inclusion
of
the
Secchi
depth
node
is
important
for
obtaining
a
more
correct
overall
status
assessment.
For
TP,
the
best-case
management
increased
the
probability
of
obtaining
a
better
status
(Fig.
5b
and
d).
The
probability
of
good
or
high
status
was
<0.1%
for
all
scenarios.
The
probability
of
moderate
status,
however,
increased
from
61%
under
reference
management
to
84%
with
the
best-case
management,
and
decreased
to
only
1.5%
with
the
worst-case
management.
In
the
combined
physico-
chemical
status
assessment
(Fig.
5c),
which
included
both
Secchi
depth
and
TP,
the
probability
of
moderate
status
was
halved
com-
pared
to
the
assessment
for
TP
alone.
This
result
reflects
the
fact
that
the
CPT
for
the
physico-chemical
status
node
(Appendix
A)
weighted
the
contributions
from
TP
and
Secchi
equally.
The
status
indicated
by
Chl-a
was
better
than
the
status
of
TP,
with
30%
probability
of
good
(or
high)
status
under
the
reference
scenario.
This
can
be
explained
by
the
poor
light
conditions
in
the
lake:
a
Secchi
depth
of
1–1.5
m
and
no
stable
stratification
is
proba-
bly
causing
the
phytoplankton
to
be
continuously
mixed
to
depths
beyond
the
photic
zone.
Hence,
the
phytoplankton
is
light-limited,
and
not
able
to
utilize
the
available
P
for
optimal
growth.
Chl-
a
status
was
affected
by
the
climate
scenarios
as
well
as
by
the
management
scenarios
(Fig.
5d).
Under
current
climate
conditions,
best-case
management
increased
the
probability
of
obtaining
good
or
high
status
to
35%
with
the
best-case
management,
while
worst-
case
management
decreased
it
to
18%.
Climate
change
slightly
reduced
the
probability
of
good
or
high
status
in
each
case.
The
status
probability
distribution
of
CyanoMax
(Fig.
5e)
dif-
fered
from
the
distribution
of
Chl-a:
CyanoMax
had
high
probability
of
both
the
best
and
the
worst
status
but
a
low
probability
of
the
intermediate
status.
This
strongly
bimodal
distribution
of
CyanoMax
reflects
the
tendency
of
cyanobacteria
to
occur
in
either
very
low
or
very
high
abundance
(blooms)
(Fig.
1e).
Nevertheless,
the
status
of
Cyanobacteria
responded
to
the
management
and
cli-
mate
scenarios
in
a
similar
way
to
Chl-a.
In
other
words,
reducing
nutrient
concentrations
counteracted
the
increased
cyanobacterial
risk
associated
with
higher
temperatures,
in
agreement
with
the
conclusion
of
Rigosi
et
al.
(2015).
The
status
distribution
of
the
combined
Phytoplankton
node
(Fig.
5f)
was
more
affected
by
the
Chl-a
node
than
by
the
Cyanobac-
teria
node,
as
could
be
expected
from
the
combination
rule
(section
2.2.4).
Notably,
the
Phytoplankton
node
had
generally
worse
sta-
tus
than
either
of
its
two
parent
nodes.
The
probabilities
of
good
or
high
status
were
22%,
25%
and
13%
(for
Reference,
Best
and
Worst
management
respectively)
under
current
climate,
and
18%,
21%
and
10%
under
climate
change.
This
result
is
consistent
with
the
combination
rule
for
phytoplankton:
including
Cyanobacteria
in
the
assessment
can
only
worsen
(or
not
affect)
the
combined
Phytoplankton
status.
In
the
overall
lake
status
assessment
(Fig.
5g),
the
best
possible
status
was
Moderate,
due
to
the
influence
of
the
physico-chemical
node.
In
general,
the
probability
of
moderate
(or
better)
status
(e.g.,
32%
in
the
Reference
scenario)
was
closer
to
the
physico-chemical
node
(31%)
than
to
the
phytoplankton
node
(51%);
i.e.
the
lake
sta-
tus
was
worse
than
indicated
by
phytoplankton
alone.
This
result
reflects
the
whole-lake
combination
rule,
which
selected
the
worse
status
(or
a
compromise)
whenever
the
status
of
the
two
par-
ent
nodes
differ.
Nevertheless,
the
whole-lake
status
also
showed
negative
impact
of
climate
change,
which
was
inherited
from
the
Phytoplankton
node
(since
climate
change
impacts
on
physico-
chemistry
were
not
incorporated
in
this
BN).
Hence,
all
of
the
four
indicator
nodes
(Secchi
depth,
TP,
chl-a
and
cyanobacteria)
played
important
roles
in
the
overall
assessment
of
lake
status
under
the
management
and
different
scenarios.
The
ecological
status
of
Vanemfjorden
assessed
by
the
BN
(35%
probability
of
Moderate
and
65%
probability
of
Poor-Bad
for
the
reference
scenario;
Fig.
5g)
was
somewhat
worse
than
the
most

S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
339
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
C
li
mat e scen
ario
Worst
Ref
Best
Mana
gemen
t scena
rio
Secc
hi
depth
Probability (%)
(a)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Climat e sc ena
rio
Wors t
Ref
Best
Manage
ment
scena
rio
Total
P
(b)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Cli
ma te sc ena
rio
Wor s t
Ref
Best
Man age
ment
scena
rio
Phys.-chem.
(c)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
C
li
mat e scen
ario
Worst
Ref
Best
Mana
gemen
t scena
rio
Chl a
Probability (%)
(d)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Climat e sc ena
rio
Wors t
Ref
Best
Manage
ment
scena
rio
Cya n oba c te ri a
(e)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Cli
ma te sc ena
rio
Wor s t
Ref
Best
Man age
ment
scena
rio
Phytop
lankton
(f)
Poor-
Bad
Moderate
High-Good
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Cli
ma te sc ena
rio
Wor s t
Ref
Best
Man age
ment
scena
rio
Lake
Probability (%)
(g)
Fig.
5.
Effects
of
climate
and
management
scenarios
on
the
probability
distribution
of
status
classes
for
all
nodes
in
the
module
“Lake
classification
system”
(Fig.
2).
The
climate
scenarios
are
reference
(“Ref”)
and
HadRM3
(“Had);
the
management
scenarios
are
economy
focus
(“Worst”),
reference
(“Ref”)
and
water-quality
focus
(“Best”).
The
distribution
of
status
classes
(High-Good,
Moderate
and
Poor-Bad)
for
Secchi
depth
(a)
and
total
P
(b)
are
combined
in
the
plot
“Physico-chemical”
(c),
while
the
results
for
Chl-a
(b)
and
Cyanobacteria
(e)
are
combined
in
the
plot
“Phytoplankton”
(f).
Finally,
the
results
for
Physico-chemical
and
Phytoplankton
are
combined
in
the
plot
“Lake”
(g).
recent
official
ecological
status
assessment,
which
is
in
the
middle
of
the
Moderate
class
(Haande
et
al.,
2011).
This
can
be
explained
by
differences
in
the
selection
of
data
for
the
assessment
(where
the
data
selected
for
the
BN
were
constrained
by
the
link
to
the
MyLake
output).
Firstly,
the
official
status
is
based
on
data
from
2004
and
2010
only,
while
the
BN
also
includes
data
from
years
prior
to
2004,
during
which
conditions
were
worse
(Fig.
1c–d).
Secondly,
the
previously
published
assessment
did
not
consider
Secchi
depth,
which
imposed
Poor-Bad
status,
but
instead
included
Total
N,
which
was
associated
with
Moderate
status.
Thirdly,
it
did
not
include
cyanobacteria
(which
could
have
reduced
the
phyto-
plankton
status),
but
instead
included
macrophytes
(which
were
associated
with
Moderate
status).
The
effects
of
climate
change
considered
in
this
study
were
lim-
ited
to
water
temperature
and
effects
on
phytoplankton.
Higher
water
temperature
is
likely
to
affect
other
biological
groups
as
well,
especially
fish
(Hering
et
al.,
2013;
Jeppesen
et
al.,
2012),
which
have
so
far
not
been
monitored
in
Vanemfjorden.
The
climate
change
scenario
also
comprised
increased
precipitation,
which
was
included
in
the
process-based
models
for
the
catchment
and
lake
(Couture
et
al.,
2014),
but
precipitation
has
not
yet
been
incorpo-
rated
explicitly
as
a
node
in
the
BN.
Increased
precipitation
has
the
potential
to
influence
ecological
status
in
several
ways.
For
example,
increased
run-off
of
nutrients
from
agriculture
is
likely
to
give
higher
TP
concentrations
(Jeppesen
et
al.,
2009).
On
the
other
hand,
increased
flushing
of
the
lake
may
reduce
the
concentration
of
phytoplankton
and
in
particular
of
cyanobacteria,
which
tend
to
have
slower
growth
rate
than
other
phytoplankton
(Carvalho
et
al.,
2011;
Elliott,
2012).
Such
contrasting
effects
of
altered
precipita-
tion
patterns
could
be
considered
in
a
more
advanced
version
of
this
BN.
4.2.
Model
evaluation
4.2.1.
The
link
from
process-based
model
predictions
to
observed
values
The
accuracy
of
the
MyLake
model
predictions
varied
highly
among
the
different
indicator
variables.
The
model
performance
is
discussed
in
detail
by
Couture
et
al.
(2014);
here
we
only
con-
sider
the
accuracy
at
the
level
of
node
states
(intervals)
and
focus
on
the
implications
for
the
BN
model.
For
Secchi
depth,
the
match
between
prediction
and
observation
was
100%,
because
all
pre-
dictions
and
observations
were
in
the
same
interval
(0–2
m).
For
water
temperature
the
match
was
generally
good
(Table
B1c),
although
the
highest
observed
temperatures
(19–25 ◦C)
were
fre-
quently
underestimated
by
MyLake
(as
15–19 ◦C).
This
negative
bias
in
the
prediction
of
temperature
may
have
contributed
to
the
mismatch
between
predicted
and
observed
Chl-a
(Table
B1b).
Although
the
precision
of
predicted
Chl-a
was
rather
low
(43%
of
the
observed
values
predicted
to
the
correct
interval),
the
accuracy
was
good
in
terms
of
the
balance
between
underestimations
(28%)
and
overestimations
(29%).
TP
was
less
well
predicted:
although
the
precision
(66%)
was
higher
than
for
chl-a,
the
accuracy
was
lower:
10%
underestimations
vs.
23%
overestimations.
The
underestima-
tions
are
mostly
from
the
period
1990
to
1999
(Fig.
1c),
i.e.
before
the
calibration
period
of
MyLake
(2005–2012).
A
better
match
could

340
S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
have
been
obtained
by
using
only
data
from
the
calibration
period,
but
the
range
of
predicted
values
in
this
period
was
narrow
com-
pared
to
the
whole
time
series
(e.g.,
predicted
Total
P
was
only
in
moderate
status).
Moreover,
our
intention
was
to
make
use
of
as
much
data
as
possible
for
filling
in
the
CPTs.
Accounting
for
the
mismatch
between
predicted
and
observed
values
in
the
CPTs
(Table
B1)
had
clear
consequences
for
the
BN
model
predictions
(BN
version
2,
Fig.
B1).
For
TP
(Fig.
B1b),
the
BN
no
longer
predicted
a
positive
effect
of
better
management
on
the
probability
of
moderate
status,
but
instead
a
weak
increase
in
the
probability
of
poor-bad
status.
For
the
combined
physical-chemical
indicator
(Fig.
B1c)
there
was
no
obvious
response
to
the
manage-
ment
scenarios.
The
Chl-a
variable
(Fig.
B1d)
and
thus
the
combined
phytoplankton
indicator
(Fig.
B1f)
displayed
similar
responses
to
the
management
scenarios
as
in
the
default
BN
version
(Fig.
5d
and
f),
but
the
effects
of
the
scenarios
were
much
weaker.
This
is
consistent
with
the
high
accuracy
and
low
precision
of
predicted
Chl-a
from
the
process-based
model.
The
total
lake
assessment
was
most
dominated
by
the
phytoplankton
node
(as
determined
by
the
classification
rules),
but
the
physical-chemical
indicator
con-
tributed
with
additional
uncertainty.
In
the
BN
version
2,
the
overall
lake
assessment
for
the
reference
scenario
(Fig.
B1g)
was
close
to
the
default
version
(Fig.
5g),
but
there
was
almost
no
effect
of
the
management
or
climate
scenarios.
This
is
a
common
problem
for
BN
models
that
incorporate
several
sources
of
uncertainty:
nodes
further
down
the
causal
chain
have
greater
predictive
uncertainty
(Borsuk
et
al.,
2004;
Marcot
et
al.,
2006).
Our
decision
not
to
include
the
mismatch
between
MyLake
predictions
and
observations
in
the
default
BN
version
can
be
jus-
tified
by
the
fact
that
this
uncertainty
should
already
have
been
accounted
for
in
the
calibration
of
MyLake.
The
resulting
60
param-
eter
sets
were
instead
included
as
a
source
of
uncertainty
in
the
BN.
Incorporating
the
prediction
−
observation
mismatch
as
an
addi-
tional
source
of
uncertainty
would
not
only
make
the
BN
model
non-responsive
to
the
scenarios,
but
also
introduce
a
systematic
error
for
TP.
4.2.2.
The
CPT
for
cyanobacteria
A
minority
of
the
EUREGI
observations
were
from
lakes
with
high
degree
of
eutrophication;
only
45
out
of
559
observations
were
in
the
highest
Chl-a
interval
(vs.
34
out
of
90
observations
from
Lake
Vansjø).
Likewise,
the
number
of
cyanobacteria
observations
in
the
highest
interval
was
relatively
low:
22
out
of
559
(vs.
13
out
of
90
from
Lake
Vansjø).
Nevertheless,
the
EUREGI
dataset
gave
similar
probability
distributions
in
the
CPT
for
cyanobacteria
(Table
B2)
to
those
from
Lake
Vansjø
(Table
2b-c).
Consequently,
model
version
3
with
CPT
from
the
EUREGI
dataset
predicted
effects
of
climate
and
management
scenarios
on
ecological
status
of
cyanobacte-
ria
(Fig.
B2e)
that
were
very
similar
to
the
default
model
version
(Fig.
5e).
The
fact
that
an
independent,
large-scale
dataset
gave
similar
CPTs
and
consequently
very
similar
model
predictions
as
the
original
data
from
Lake
Vansjø
strengthened
our
confidence
in
the
cyanobacteria
component
of
the
model.
4.2.3.
Effects
of
water
temperature
Since
the
future
climate
scenario
had
a
limited
effect
of
the
Temperature
node
(probability
of
“a
warm
year”
increased
from
34%
to
44%),
we
investigated
more
closely
how
the
phytoplankton
nodes
responded
to
changes
in
water
temperature
in
the
model.
One
way
to
inspect
the
temperature
effects
in
the
BN
was
to
select
the
warmest
months,
July-August
(“summer”).
The
full
model
is
based
on
all
data
from
May
to
October,
because
this
is
a
criterion
in
the
national
assessment
system
for
ecological
status.
However,
since
there
is
large
seasonal
variation
in
many
of
the
variables,
selecting
only
summer
months
would
reduce
the
temporal
vari-
ation,
and
might
therefore
improve
the
precision
of
the
model
(i.e.,
result
in
narrower
probability
distributions
of
the
indicators).
We
therefore
compared
the
default
model
outcome
(Fig.
5)
with
the
corresponding
results
from
summer
months
(Fig.
B3).
(To
simplify
the
comparison
we
have
displayed
the
result
in
terms
of
status
classes,
although
it
is
not
strictly
correct
to
base
the
status
assess-
ment
of
summer
values
only).
Lower
probability
of
Moderate
or
better
status
can
be
seen
for
all
indicators,
except
cyanobacteria;
this
is
likely
because
Cyanobacteria
status
is
based
on
the
seasonal
maximum,
which
is
less
sensitive
to
the
selection
of
months.
This
result
shows
that
the
model
behaves
as
expected
regarding
sea-
sonal
variation
in
temperature
and
in
indicator
variables.
Further
inspection
of
the
water
temperature
effects
was
per-
formed
by
setting
evidence
for
“a
warm
year”
(100%
probability
of
temperature
≥
19 ◦C)
vs.
“a
cold
year”
(<19 ◦C)
(Fig.
B4).
The
tem-
perature
effect
was
stronger
for
Chl-a
than
for
cyanobacteria:
from
a
cold
to
a
warm
year,
the
probability
of
moderate
or
better
Chl-
a
status
dropped
from
58%
to
24%
(worst
management)
and
from
70%
to
48%
(best
management).
The
corresponding
probabilities
for
cyanobacteria
were
a
drop
from
64%
to
47%
(worst
manage-
ment)
and
from
71%
to
60%
(best
management),
but
this
response
included
both
the
direct
effect
of
the
temperature
node
and
the
indirect
temperature
effect
through
the
Chl-a
node.
Furthermore,
we
fixed
the
Chl-a
node
at
PB,
M
or
HG
status
under
cold
and
warm
year,
respectively
(Fig.
B5a).
The
additional
temperature
effect
on
cyanobacteria
was
most
evident
when
Chl-a
was
in
moderate
sta-
tus
(Fig.
B5b).
This
result
is
in
line
with
the
conclusion
by
Rigosi
et
al.
(2015),
that
the
cyanobacteria
concentrations
of
mesotrophic
lakes
were
particularly
sensitive
to
warming.
This
temperature
effect
on
cyanobacteria
had
a
small,
but
noticeable
effect
on
the
total
phyto-
plankton
status
(Fig.
B5c).
Although
this
effect
was
small,
it
shows
that
the
BN
generated
reasonable
results.
4.3.
Assessment
of
the
BN
approach
for
modelling
of
ecological
status
Overall,
the
BN
model
satisfied
our
objective:
to
integrate
infor-
mation
from
scenarios,
process-based
models,
monitoring
data
–
especially
cyanobacteria,
and
the
lake
classification
system.
The
BN
approach
gives
a
possibility
to
account
for
mismatch
between
process-model
predictions
and
observations
for
certain
variables,
by
incorporating
this
uncertainty
in
their
CPTs
(cf.
Table
B1)
and
evaluating
its
consequences.
Since
the
selected
model
(version
1)
does
not
account
for
the
mismatch
between
MyLake
prediction
and
observations,
the
results
predicted
by
the
BN
should
not
be
interpreted
in
terms
of
absolute
probability
values.
Nevertheless,
the
qualitative
effects
of
the
scenarios
on
the
different
indicators
predicted
by
the
BN
should
be
valid.
The
components
involving
cyanobacteria
gave
reasonable
results,
and
had
importance
to
the
overall
assessment.
Our
con-
fidence
in
these
components
was
strengthened
by
the
comparison
with
an
independent
dataset
(Fig.
B2);
at
the
coarse
scale
of
the
eco-
logical
status
(rather
than
exact
concentrations),
the
results
were
very
similar.
This
implies
that
our
approach
can
be
used
for
other
lakes
that
are
at
risk
of
algal
blooms.
For
lakes
with
more
lim-
ited
data
on
cyanobacteria
than
Lake
Vansjø,
we
show
that
filling
the
data
gaps
using
cyanobacteria
observations
from
other
lakes
in
combination
with
expert
knowledge
on
lake
type,
local
condi-
tions
etc.
is
a
viable
option.
Rigosi
et
al.
(2015)
demonstrated
this
possibility:
using
physicochemical,
biological,
and
meteorological
observations
collated
from
20
lakes
located
at
different
latitudes
and
characterized
by
a
range
of
sizes
and
trophic
states,
they
con-
structed
a
BN
to
analyse
the
sensitivity
of
cyanobacterial
bloom
development
to
different
environmental
factors
and
to
determine
the
probability
that
cyanobacterial
blooms
would
occur.
The
abil-
ity
to
utilize
other
available
datasets
for
answering
management

S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
341
questions
is
a
strength
of
the
BN
approach,
given
the
financial
con-
straints
of
most
agencies
(Wilson
et
al.,
2008).
A
complete
ecological
status
assessment
should
in
principle
include
three
more
biological
quality
elements
(BQEs),
namely
macrophytes,
benthic
invertebrates
and
fish
(EC,
2000).
Such
an
assessment
is
likely
to
have
resulted
in
even
worse
status,
due
to
the
“one-out,
all-out”
combination
rule
of
the
WFD
(EC,
2005).
This
rule
states
that
the
ecological
status
should
be
determined
by
the
BQE
with
lowest
status,
meaning
that
including
more
BQEs
inevitably
leads
to
a
stricter
or
equally
strict
assessment.
The
more
pessimistic
outcome
of
the
one-out,
all-out
rule
compared
to
other
combina-
tion
rules
was
also
demonstrated
by
Lehikoinen
et
al.
(2014),
who
used
a
BN
for
analysing
the
probability
of
reaching
good
ecologi-
cal
status
of
coastal
waters
in
the
Gulf
of
Finland.
When
there
is
high
uncertainty
associated
with
the
data,
assessments
based
on
this
combination
rule
tend
to
underestimate
the
ecological
status
(Moe
et
al.,
2015).
A
probabilistic
result
such
as
the
outcome
of
a
BN
can
be
helpful,
giving
a
more
nuanced
and
more
informative
result
than
only
a
single
status
class
(Gottardo
et
al.,
2011).
Compared
to
existing
process-based
models
for
ecological
sta-
tus
of
rivers
and
lakes,
the
BN
approach
provides
an
opportunity
to
include
biological
elements,
as
demonstrated
by
our
study.
Even
when
data
are
sparse,
theory
or
expert
knowledge
on
selected
bio-
logical
indicators
can
be
used
as
a
first
step
to
construct
causal
links
(CPTs)
between
abiotic
and
biotic
responses.
Since
the
WFD
requires
that
assessments
are
based
primarily
on
biology
(EC,
2000),
this
is
clearly
an
added
value
for
use
of
models
in
water
management
in
Europe.
Moreover,
the
WFD
requires
that
poten-
tial
impacts
of
climate
change
are
considered
in
the
next
set
of
river
basin
management
plans
(EC,
2009).
Although
much
knowledge
is
available
on
effects
on
climate
change
on
ecosystems,
including
specific
effects
on
biological
quality
elements
in
lakes
(Moe
et
al.,
2014),
incorporating
such
information
in
predictive
models
is
a
challenge.
The
BN
methodology
can
facilitate
the
use
of
such
knowl-
edge,
manifested
as
expert
judgement
of
probabilities
under
given
climatic
scenarios.
Furthermore,
a
BN
model
may
be
relatively
easy
to
understand
for
end
users
who
do
not
have
any
modelling
back-
ground
{Borsuk
et
al.,
2012
#138}.
Therefore,
BNs
are
promising
tools
for
supporting
informed
decision
making
and
thus
the
work
of
water
managers.
There
are
of
course
also
several
limitations
associated
with
the
BN
methodology
in
the
context
of
environmental
manage-
ment.
The
fact
that
the
non-dynamic
network
cannot
contain
loops
puts
constraints
on
the
ecological
processes
that
can
be
modelled;
phosphorus
and
phytoplankton
dynamics
in
lakes
are
typically
dominated
by
feedback
processes
(Saloranta
and
Andersen,
2007).
For
example,
high
phytoplankton
biomass
can
reduce
the
Secchi
depth;
on
the
other
hand,
lower
Secchi
depth
can
limit
further
phytoplankton
growth
due
to
light
limitation.
In
our
study,
such
feedback
loops
were
handled
by
dynamic
models
(INCA-P
and
MyLake),
while
the
BN
summarised
the
outcome
of
the
catchment
and
lake
process.
Moreover,
the
accumulation
of
uncertainty
with
the
length
of
the
network
implies
that
it
can
be
difficult
to
draw
conclusions
from
the
final
output
nodes
(Borsuk
et
al.,
2004).
Other
challenges
associated
with
the
use
of
BNs
have
been
discussed
pre-
viously
(Landuyt
et
al.,
2013;
Uusitalo,
2007;
Varis
and
Kuikka,
1999).
The
current
BN
model
can
be
further
developed
in
several
ways.
An
important
improvement
would
be
to
reduce
the
predictive
uncertainty
of
the
catchment-lake
model
chain
(i.e.
INCA-P
and
MyLake).
A
more
quantitative
sensitivity
analysis
of
the
model,
such
as
calculation
of
entropy
reduction,
can
help
identify
nodes
to
which
the
final
output
is
particularly
sensitive
(Chen
and
Pollino,
2012).
A
more
complete
representation
of
climate
change
in
the
BN
would
include
effects
of
changed
precipitation
patterns
(cf.
Lehikoinen
et
al.,
2014),
and
potentially
other
meteorological
or
hydrological
variables.
Inclusion
of
Total
N
in
the
BN
would
make
the
assessment
of
physico-chemical
status
more
complete.
The
total
N
concentration
also
seems
to
play
a
role
in
favour-
ing
certain
N-fixating
cyanobacteria
taxa
(order
Nostocales,
e.g.
Anabaena),
especially
in
late
summer/autumn
after
N
has
been
depleted.
Effects
of
nutrients
and
other
environmental
variables
on
Anabaena
biomass
in
a
reservoir
were
recently
analysed
by
another
BN
model
(Williams
and
Cole,
2013):
reduced
levels
of
N
and/or
P
had
negligible
impact
on
the
phytoplankton
in
their
study,
while
high
water
temperature
and
stratification
increased
the
risk
of
Anabaena
blooms.
Anyway,
to
model
effects
of
climate
or
management
scenarios
on
Total
N
in
our
BN
would
require
that
this
variable
is
first
incorporated
in
the
process-based
lake
model.
Finally,
a
dynamic
version
of
the
BN
could
be
considered
(Molina
et
al.,
2013;
Nicholson
and
Flores,
2011),
which
might
better
handle
feedback
processes.
In
this
study
we
used
an
external,
larger
dataset
for
evaluation
by
constructing
an
alternative
CPT
for
cyanobacteria
and
compar-
ing
the
results
with
the
default
model
version.
External
datasets
can
also
be
used
in
a
more
integrated
way
for
estimation
of
CPTs.
However,
differences
in
lake
type
factors
such
as
water
colour
and
alkalinity
may
be
even
more
important
than
the
TP
concen-
tration
(Carvalho
et
al.,
2011).
A
hierarchical
Bayesian
regression
model
would
be
a
suitable
method
for
estimating
relationships
for
a
target
lake
while
“borrowing
information”
on
this
type
of
relationship
from
a
larger
set
of
lakes,
and
simultaneously
account-
ing
for
differences
in
lake
type
(Kotamäki
et
al.,
2015).
Inclusion
of
more
biological
quality
elements
would
also
be
desirable;
pri-
marily
macrophytes,
for
which
some
data
exist
(Haande
et
al.,
2011).
Future
monitoring
in
Lake
Vansjø
might
provide
some
more
biological
data
also
for
macrophytes
and
fish.
However,
new
bio-
logical
elements
for
which
few
observations
are
available
will
be
associated
with
high
uncertainty.
The
model
structure
in
its
cur-
rent
version
is
rather
simple
and
general,
and
should
be
feasible
to
adapt
for
other
lakes
or
other
aquatic
ecosystems.
The
model
can
be
considered
over-fitted
to
Lake
Vansjø,
since
the
estimation
of
probability
distributions
is
based
solely
on
data
from
this
case
study.
Application
of
this
model
to
other
ecosystems
should
involve
calibration
and
validation
of
the
model
with
relevant
data.
4.4.
Conclusions
In
summary,
the
Bayesian
network
approach
was
able
to
model
effects
of
climate
change
and
management
on
ecological
status
of
a
lake,
by
combining
scenarios,
process-based
model
output,
monitoring
data
and
the
national
lake
assessment
system.
The
BN
model
showed
that
the
benefits
of
better
land-use
management
were
partly
counteracted
by
future
warming
under
these
scenar-
ios.
Most
importantly,
the
BN
demonstrated
the
importance
of
including
more
biological
elements,
namely
cyanobacteria,
in
the
modelling
of
lake
status.
Thus,
the
BN
modelling
approach
can
be
a
useful
supplement
to
more
traditional
process-based
models
for
lakes,
which
only
rarely
include
cyanobacteria
or
other
biological
groups.
Acknowledgements
We
are
grateful
to
David
Barton,
Andrew
Wade
and
Richard
Skeffington
for
discussions
on
the
model
structure,
Koji
Tominaga
for
providing
output
from
the
MyLake
model,
Anne
Lyche
Sol-
heim
for
information
on
the
national
classification
system
and
Peter
Friis
Hansen
for
technical
help
with
the
Hugin
software.
The
authors
have
received
funding
from
the
projects
REFRESH
(Adaptive
Strategies
to
Mitigate
the
Impacts
of
Climate
Change
on
European
Freshwater
Ecosystems;
EU
FP7,
contract
no.
244121),

342
S.J.
Moe
et
al.
/
Ecological
Modelling
337
(2016)
330–347
MARS
(Managing
Aquatic
ecosystems
and
water
Resources
under
multiple
Stress;
EU
FP7,
contract
no.
603378),
Climate
effects
from
mountains
to
fjords
(Research
Council
of
Norway
project
no.
208279)
and
Lakes
in
Transition
(Research
Council
of
Norway
project
no.
244558/E50).
We
also
thank
two
anonymous
reviewers
for
their
many
helpful
comments.
Appendix
A.
Implementation
of
combination
rules
of
the
national
classification
system
Implementation
of
combination
rules
of
the
national
classification
system
For
the
combined
Physico-Chemical
status,
the
classification
system
requires
averaging
of
the
two
variables
Secchi
and
TP,
which
is
not
straight-forward
in
a
probabilistic
model.
When
both
indica-
tors
had
the
same
status,
the
combined
status
was
the
same
with
100%
probability.
The
averaging
was
implemented
by
assigning
50%
probability
of
both
High-Good
and
Moderate
status
when
one
indicator
was
in
High-Good
status
and
the
other
was
in
Moderate
status,
and
likewise
for
Moderate
and
Poor-Bad
status
(Table
A1e).
When
one
indicator
was
High-Good
and
the
other
Poor-Bad,
the
combined
status
was
Moderate
with
100%
probability.
For
the
com-
bined
Phytoplankton
status,
a
similar
solution
was
used,
with
some
exceptions:
when
the
status
of
Cyano
was
better
than
or
equal
to
the
status
of
Chl-a,
the
combined
status
was
set
equal
to
the
status
of
Chl-a
(Table
A1f).
The
overall
lake
status
(Table
2d)
was
set
equal
to
the
phytoplankton
status
when
the
physico-chemical
status
was
equal
or
better,
and
to
one
lower
state
when
the
physico-chemical
status
was
worse.
Appendix
B
Figs.
B1–B5
.
Tables
B1
and
B2.
Table
A1
Conditional
probability
tables
for
the
national
classification
system
for
ecological
status
of
lakes
(see
Fig.
2,
Module
4).
(a)
Status
Secchi,
(b)
Status
Total
P,
(c)
Status
Chl-a,
(d)
Status
Cyano,
(e)
Status
Phys-Chem,
(f)
Status
Phytoplankton.
(For
the
node
Status
of
Lake,
see
Table
1e).
HG
=
High-Good,
M
=
Moderate,
PB
=
Poor-Bad.
(a)
Secchi
0–2
2–2.6
2.6–5
Status
Secchi
HG
0
0
1
M
0
1
0
PB
1
0
0
(b)
Total
P
0–20
20–39
39–80
Status
Total
P
HG
1
0
0
M
0
1
0
PB
0
0
1
(c)
Chl-a
0–10.5
10.5–20
20–60
Status
Chl-a
HG
1
0
0
M
0
1
0
PB
0
0
1
(d)
CyanoMax
0–1000
1000–2000
2000–6000
Status
Cyano
HG
1
0
0
M
0
1
0
PB
0
0
1
(e)
Status
Total
P
HG
M
PB
Status
Secchi
HG
M
PB
HG
M
PB
HG
M
PB
Status
Phys-chem.
HG
1
0.5
0
0.5
0
0
0
0
0
M
0
0.5
1
0.5
1
0.5
1
0.5
0
PB
0
0
0
0
0
0.5
0
0.5
1
(f)
Status
Chl-a
HG
M
PB
Status
Cyano
HG
M
PB
HG
M
PB
HG
M
PB
Status
Phytoplankton
HG
1
0.5
0
0
0
0
0
0
0
M
0
0.5
1
1
1
0.5
0
0
0
PB
0
0
0
0
0
0.5
1
1
1

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Ecological
Modelling
337
(2016)
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343
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
C
li
mat e scen
ario
Worst
Ref
Best
Mana
gemen
t scena
rio
Secc
hi
depth
Probability (%)
(a)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Climat e sc ena
rio
Wors t
Ref
Best
Manage
ment
scena
rio
Total
P
(b)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Cli
ma te sc ena
rio
Wor s t
Ref
Best
Man age
ment
scena
rio
Phys.-chem.
(c)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
C
li
mat e scen
ario
Worst
Ref
Best
Mana
gemen
t scena
rio
Chl a
Probability (%)
(d)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Climat e sc ena
rio
Wors t
Ref
Best
Manage
ment
scena
rio
Cya n oba c te ri a
(e)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Cli
ma te sc ena
rio
Wor s t
Ref
Best
Man age
ment
scena
rio
Phytop
lankton
(f)
Poor-
Bad
Moderate
High-Good
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Cli
ma te sc ena
rio
Wor s t
Ref
Best
Man age
ment
scena
rio
Lake
Probability (%)
(g)
Fig.
B1.
Effects
of
climate
and
management
scenarios
on
the
probability
distribution
of
status
classes
for
all
indicator
nodes,
when
the
mismatch
between
process-based
model
predictions
and
observations
is
accounted
for
by
the
conditional
probability
tables
(Table
B1).
For
more
details
and
for
comparison
with
the
default
model,
see
Fig.
5.
Table
B1
Conditional
probability
table
for
the
nodes
that
link
predicted
to
observed
data:
(a)
Total
P,
(b)
Chl-a,
(c)
(water)
temperature.
Asterisk
indicates
a
match
between
predicted
and
observed
values.
For
Secchi
depth,
all
predicted
and
observed
values
were
in
the
same
state
(0–2
m).
For
more
explanation,
see
Table
2.
(a)
Total
P
(pred.)
0–20
20–25
25–30
30–39
39–50
50–80
Total
P
(obs.)
0–20
*0.800
0.075
0.022
0.039
0.053
0.044
20–39
0.200
*0.717
*0.887
*0.838
0.887
0.923
39–80
0
0.209
0.091
0.123
*0.060
*0.033
Experience
0a254
1977
10689
2701
879
(b)
Chl-a
(pred.)
0–5
5–10.5
10.5–15
15–20
20–25
25–60
Chl-a
(obs.)
0–10.5
*0.492
*0.281
0.327
0.164
0.098
0.126
10.5–20
0.389
0.486
*0.344
*0.480
0.402
0.415
20–60
0.119
0.232
0.329
0.356
*0.501
*0.459
Experience
1652
3017
1729
2779
4455
2868
(c)
Temp.
(pred.)
0–10
10–15
15–19
19–30
Temp.
(obs.)
0–19
*1
*1
*0.513
0
19–30
0
0
0.487
*1
Experience
775
3596
4933
2636
aAssumed
probability
distributions
inserted
where
no
observations
were
available.

344
S.J.
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al.
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Ecological
Modelling
337
(2016)
330–347
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
C
li
mat e scen
ario
Worst
Ref
Best
Mana
gemen
t scena
rio
Secc
hi
depth
Probability (%)
(a)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Climat e sc ena
rio
Wors t
Ref
Best
Manage
ment
scena
rio
Total
P
(b)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Cli
ma te sc ena
rio
Wor s t
Ref
Best
Man age
ment
scena
rio
Phys.-chem.
(c)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
C
li
mat e scen
ario
Worst
Ref
Best
Mana
gemen
t scena
rio
Chl a
Probability (%)
(d)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Climat e sc ena
rio
Wors t
Ref
Best
Manage
ment
scena
rio
Cya n oba c te ri a
(e)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Cli
ma te sc ena
rio
Wor s t
Ref
Best
Man age
ment
scena
rio
Phytop
lankton
(f)
Poor-
Bad
Moderate
High-Good
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Cli
ma te sc ena
rio
Wor s t
Ref
Best
Man age
ment
scena
rio
Lake
Probability (%)
(g)
Fig.
B2.
Effects
of
climate
and
management
scenarios
on
the
probability
distribution
of
status
classes
for
all
indicator
nodes,
when
the
conditional
probability
table
for
Cyanobacteria
is
based
on
the
alternative
larger
dataset
EUREGI
(see
section
2.2.3).
For
more
details
and
for
comparison
with
the
default
model,
see
Fig.
5.
Table
B2
Conditional
probability
table
for
the
two
cyanobacteria
nodes
based
on
the
alternative,
larger
dataset
(EUREGI,
see
section
2.2.3):
(a)
Cyano,
(b)
CyanoMax
(corresponding
to
Table
2c
and
d,
respectively).
For
more
information,
see
Table
2.
(a)
Chl-a
(obs.)
0–10.5
10.5–20
20–60
Temp.
(obs.) 0–19 19–30
0–19
19–30
0–19
19–30
Cyano
0–1000
0.993
1
0.949
1
0.444
0.111
1000–2000
0.007
0
0.051
0
0.111
0.222
2000–6000
0
0
0
0
0.444
0.667
Experience
454
19
39
2
36
9
(b)
Cyano
0–1000
1000–2000
2000–6000
Season
May–Jun
Jul–Aug
Sep–Oct
May–Jun
Jul–Aug
Sep–Oct
May–Jun
Jul–Aug
Sep–Oct
CyanoMax
0–1000
0.882
0.964
0.870
0
0
0
0
0
0
1000–2000
0.076
0.034
0.087
0.5
0.889
0
0
0
0
2000–6000
0.042
0.003
0.043
0.5
0.111
0
1
1
1
Experience
119
384
23
2
9
0
5
16
1

S.J.
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/
Ecological
Modelling
337
(2016)
330–347
345
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
C
li
mat e scen
ario
Worst
Ref
Best
Mana
gemen
t scena
rio
Secc
hi
depth
Probability (%)
(a)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Climat e sc ena
rio
Wors t
Ref
Best
Manage
ment
scena
rio
Total
P
(b)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Cli
mate scena
rio
Wor s t
Ref
Best
Man age
ment
scena
rio
Phys.-chem.
(c)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
C
li
mat e scen
ario
Worst
Ref
Best
Mana
gemen
t scena
rio
Chl a
Probability (%)
(d)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Climat e sc ena
rio
Wors t
Ref
Best
Manage
ment
scena
rio
Cya n oba c te ri a
(e)
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Cli
mate scena
rio
Wor s t
Ref
Best
Man age
ment
scena
rio
Phytop
lankton
(f)
Poor-
Bad
Moderate
High-Good
0
20
40
60
80
100
Ref
Had
Ref
Had
Ref
Had
Cli
mate scena
rio
Wor s t
Ref
Best
Man age
ment
scena
rio
Lake
Probability (%)
(g)
Fig.
B3.
Effects
of
climate
and
management
scenarios
on
the
probability
distribution
of
status
classes
for
all
indicator
nodes,
when
the
model
is
run
only
for
the
warmest
months
(July–August).
For
more
details
and
for
comparison
with
the
default
model,
see
Fig.
5.
0
20
40
60
80
100
Cold
Warm
Cold
Warm
Cold vs.
w
arm yea
r
Wor st
Bes t
Man age
ment
scena
rio
Chla
Probability (%)
(a)
0
20
40
60
80
100
Cold
Warm
Cold
Warm
Cold vs .
w
arm yea
r
Wor st
Bes t
Man age
men t
scena
rio
Cyanob
acteria
(b)
0
20
40
60
80
100
Cold
Warm
Cold
Warm
Cold vs .
w
arm yea
r
Wor s t
Bes t
Man age
men t
scena
rio
Phytoplankton
(c)
Poor-
Bad
Moderate
High-Good
Fig.
B4.
Effects
of
high
vs.
low
water
temperature
(above
vs.
below
19 ◦C,
respectively)
under
different
management
scenarios
(worst
vs.
best)
on
the
probability
distribution
of
status
classes
for
Chl-a
(a),
Cyanobacteria
(b)
and
Phytoplankton
(c).
For
more
details
and
for
comparison
with
the
default
model,
see
Fig.
5.

346
S.J.
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et
al.
/
Ecological
Modelling
337
(2016)
330–347
0
20
40
60
80
100
C
W
C
W
C
W
Cold vs.
w
arm yea
r
PB M HG
Chla st atus
Chla
(a)
Probability (%)
0
20
40
60
80
100
C
W
C
W
C
W
Cold vs .
w
arm yea
r
PB M HG
Chla st atus
Cyanobacteria
(b)
0
20
40
60
80
100
C
W
C
W
C
W
Cold vs .
w
arm yea
r
PB M H G
Chla st atus
Phytoplankton
(c)
Poor-
Bad
Moderate
High-Good
Fig.
B5.
Effects
of
high
vs.
low
water
temperature
(above
vs.
below
19 ◦C,
respectively)
under
different
scenarios
of
chl-a
status
(Poor-Bad,
Moderate
or
Good-High)
on
the
probability
distribution
of
status
classes
for
Chl-a
(a),
Cyanobacteria
(b)
and
Phytoplankton
(c).
For
more
details
and
for
comparison
with
the
default
model,
see
Fig.
5.
Appendix
C.
Supplementary
data
The
file
Supplementary
Data.pdf
contains
tables
with
prior
prob-
ability
distributions
for
all
parent
nodes
and
conditional
probability
distributions
for
all
child
nodes.
The
probability
distributions
are
given
as
counts
rather
than
proportions.
The
file
is
generated
from
the
BN
model
by
the
software
Hugin.
Supplementary
data
associated
with
this
article
can
be
found,
in
the
online
version,
at
http://dx.doi.org/10.1016/j.ecolmodel.2016.
07.004.
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using
a
Bayesian
probabilistic
model.
Ecol.
Model.
214,
210–218.