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Assessing Ecological Changes in Freshwaters using Statistical Models
Claire FergusonAdrian Bowman, Marian Scott
Laurence Carvalho (CEH, Edinburgh)http://www.antarcticconnection.com/antarctic/science/images/climate2.jpg
A Case Study of Loch Leven
Loch Leven Dataset
Length of dataset: 1968 - 2002
150 variables measured,
covering…
• Physics
• Lake chemistry
• Lake biology
• Weather
Sampling frequency: weekly to monthly
Gaps in data: 1984, 1986-87
Loch Leven – TrendsLog SRP
Years
Lo
g(S
RP
, m
ug
/l)
1970 1980 1990 2000
-10
12
34
Log TP
Years
Lo
g(T
P,
mu
g/l)
1970 1980 1990 2000
3.5
4.0
4.5
5.0
5.5
Log Chlorophyll
Years
Lo
g(C
hlo
rop
hyl
l, m
ug
/l)
1970 1980 1990 2000
12
34
5
Water Temperature
Years
Wa
ter
Tem
pe
ratu
re,
oC
1970 1980 1990 2000
05
10
15
20
Log Daphnia
Years
Lo
g(D
ap
hn
ia,
ind
/l)
1970 1980 1990 2000
-4-2
02
4Log NO3N
Years
Lo
g(N
O3
N,
mg
/l)1970 1980 1990 2000
-4-2
0
trend – a pattern in the long run average over time
Loch Leven – Seasonality
Log SRP
Month
Lo
g(S
RP
, m
ug
/l)
2 4 6 8 10 12
-10
12
34
Log TP
MonthL
og
(TP
, m
ug
/l)
2 4 6 8 10 12
3.5
4.0
4.5
5.0
5.5
Log Chlorophyll
Month
Lo
g(C
hlo
rop
hyl
l, m
ug
/l)
2 4 6 8 10 12
12
34
5
Water Temperature
Month
Wa
ter
Tem
pe
ratu
re,
oC
2 4 6 8 10 12
05
10
15
20
Log Daphnia
Month
Lo
g(D
ap
hn
ia,
ind
/l)
2 4 6 8 10 12
-4-2
02
4Log NO3N
Month
Lo
g(N
O3
N,
mg
/l)
2 4 6 8 10 12-4
-20
seasonality – a yearly cyclic pattern in monthly data
For each key variable:
Model: )month()year()SRPlog( 21 mm
Correlated Errors (V ) based on AR(1) correlation.
Circular smoother incorporated for month term (month 12 effect joins up smoothly with month 1 effect).
Additive Models
n
jijiji xmy
1)(
),0(~ 2 VN
Log SRP
a) estimate of m1(year)
year
m1
(ye
ar)
1970 1980 1990 2000
-1.0
-0.5
0.0
0.5
1.0
b) estimate of m2(month)
month
m2
(mo
nth
)
2 4 6 8 10 12
-1.0
-0.5
0.0
0.5
1.0
)month()year()SRPlog( 21 mm
p-value = 4.0 x 10-4 p-value = 0
Log NO3-N
a) estimate of m1(year)
year
m1
(ye
ar)
1970 1980 1990 2000
-2-1
01
b) estimate of m2(month)
monthm
2(m
on
th)
2 4 6 8 10 12
-2-1
01
)month()year()N-NOlog( 213 mm
p-value = 0.011 p-value = 0
Log Chlorophylla
a) estimate of m1(year)
year
m1
(ye
ar)
1970 1980 1990 2000
-0.5
0.0
0.5
1.0
1.5
b) estimate of m2(month)
month
m2
(mo
nth
)
2 4 6 8 10 12
-0.5
0.0
0.5
1.0
1.5
)month()year()lchlorophyllog( 21a mm
p-value = 6.0 x 10-5 p-value = 9.5 x 10-7
Log Chlorophylla
)month year,()lchlorophyllog( a m
year
1970
1980
1990
2000
month
2
4
6
8
10
12
m(year,m
onth)
3.6
3.8
4.0
4.2
Log SRP - Seasonally
)year()SRPlog( m
1970 1980 1990 2000
01
23
4
log srp spring
Year
log(
srp,
mug
/l)
1970 1980 1990 2000
01
23
4
log srp summer
Year
log(
srp,
mug
/l)
1970 1980 1990 2000
01
23
4
log srp autumn
Year
log(
srp,
mug
/l)
1970 1980 1990 2000
01
23
4
log srp winter
Year
log(
srp,
mug
/l)
),0(~ 2 N
p-value = 0.05
p-value = 0.09
p-value = 0.04
p-value = 0.05
Conclusions
Additive and nonparametric regression models –
Flexible tools for modelling
Non-parametric trends and seasonality simultaneously with correlated errors.
Changes in seasonality throughout time.
Nonparametric trends within each season.
Methodological modifications are required including circular smoothers and correlated errors.
Other Work
Modelling chlorophylla in terms of nutrients, water temperature and Daphnia.
To explore:
Lagged relationships
Effects of covariates
Changing relationships over time
Modelling multiple responses of chlorophylla and Daphnia to incorporate feedback relationships.
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