NCON-D-15-00006 - Research Letters - Supplementary Material
Interrupted time series analysis of water level
An interrupted time series analysis (following Box & Tiao, 1975) was used to test for
a dam effect (i.e., the construction of the Porto Primavera Reservoir on May 1998) on
downstream average water level. This method makes an allowance for serial
correlation and may, therefore, be considered one of the most suitable approaches for
determining whether non-random changes in water level occurred after dam
construction. Following the notation given by Box & Jenkins (1976), our model was
of the form ARIMA (1, 0, 0)(1, 0, 0), which means that it contains one nonseasonal
autoregressive parameter (p) and one seasonal autoregressive parameter (Ps). We
assumed a permanent abrupt impact, implying a shift in average water level after the
construction of the reservoir. This overall shift is denoted by ω, a coefficient that
measures the difference in water level before and after the intervention. To check for
models adequacy, the absence of serial correlation in the residuals was tested using an
autocorrelation function.
The intervention coefficient (ω) was negative and highly significant (Table
S8), indicating that the decrease (ca. -61 cm) in water level (Fig. S4) after reservoir
construction could not be attributed to chance alone. Residuals of the interrupted
ARIMA model were independent (Fig. S5).
REFERENCES
Anderson M.J., Ellingsen K.E., McArdle B.H., 2006. Multivariate dispersion as a
measure of beta diversity. Ecol. Lett. 9, 683–693.
Box, G.E.P., Tiao, G.C. 1975. Intervention analysis with applications to economic and
environmental problems. J. Am. Stat. Assoc. 70, 70–79.
Box, G.E.P., Jenkins G.M. 1976. Time series analysis: Forecasting and control. San
Francisco: Holden-Day.
Table S1 - Mean, minimum and maximum values of the environmental variables
utilized in this study. We obtained the data at the Upper Paraná River floodplain from
2000 to 2011 in 12 sites.
Variables
Temperature (oC)
Dissolved oxygen (mg/L)
pH
Conductivity (μS/cm)
Water transparency - Secchi depth (m)
Turbidity (NTU)
Total suspended material (μg/L)
Alkalinity (mEq/L)
Chlorophyll-a (μg/L)
Total nitrogen (μg/L)
Nitrate (μg/L)
NH4+ (μg/L)
Total phosphorus (μg/L)
Ortho-phosphate (μg/L)
Mean
24.96
5.94
6.61
44.76
1.19
22.12
2.21
282.00
8.62
690.12
63.70
19.46
51.08
9.92
Minimum
16.20
0.11
4.80
15.94
0.10
0.00
0.14
5.60
0.00
73.29
0.00
0.00
3.26
0.00
Maximum
32.30
10.87
8.85
75.00
7.50
198.00
11.00
877.20
109.21
4473.00
621.03
529.60
313.60
92.88
Table S2 - Summary of the 20 models for β-diversity of the whole zooplankton community, including the variables of each model (from column
2 to 5), AIC, delta AIC and Akaike weights (wi). Models are ordered by delta AIC. Water level was calculated using different time lags (10, 20,
30, 40 and 50 days before sampling). The variable time was the same for all models. Two metrics of environmental heterogeneity were tested.
The first (dc) was based on the method proposed by Anderson et al. (2006), while the second (cv) was based on the coefficient of variation (see
main text for details). Two alternative proxies for productivity were used: chlorophyll-a and total phosphorus concentrations.
Model rank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Water Level
40 days
30 days
20 days
50 days
10 days
40 days
30 days
20 days
50 days
10 days
40 days
30 days
20 days
50 days
10 days
40 days
30 days
20 days
Time
time
time
time
time
time
time
time
time
time
time
time
time
time
time
time
time
time
time
Environmental Heterogeneity
dc
dc
dc
dc
dc
cv
cv
cv
cv
cv
dc
dc
dc
dc
dc
cv
cv
cv
Productivity
chlorophyll-a
chlorophyll-a
chlorophyll-a
chlorophyll-a
chlorophyll-a
chlorophyll-a
chlorophyll-a
chlorophyll-a
chlorophyll-a
chlorophyll-a
total P
total P
total P
total P
total P
total P
total P
total P
AIC
-99.189
-99.104
-98.875
-98.578
-98.447
-98.209
-98.039
-97.713
-97.446
-97.193
-96.377
-96.300
-96.065
-95.707
-95.617
-94.989
-94.864
-94.542
delta AIC
0.000
0.085
0.314
0.611
0.743
0.980
1.150
1.476
1.744
1.996
2.812
2.889
3.124
3.482
3.572
4.200
4.326
4.647
wi
0.122
0.117
0.104
0.090
0.084
0.075
0.069
0.058
0.051
0.045
0.030
0.029
0.026
0.021
0.020
0.015
0.014
0.012
19
20
50 days
10 days
time
time
cv
cv
total P
total P
-94.161
-93.978
5.028
5.211
0.010
0.009
Table S3 - Generalized least squares regression coefficients of the top six models (with a Akaike weight > 0.07; see Table S2) predicting βdiversity of the whole zooplankton community. The variables with significant effect sizes are highlighted in bold.
Models
1
2
3
4
Variables
(Intercept)
Water Level (40 days)
Time
Env. heterogeneity - dc
chlorophyll-a
(Intercept)
Water Level (30 days)
Time
Env. heterogeneity - dc
chlorophyll-a
(Intercept)
Water Level (20 days)
Time
Env. heterogeneity - dc
chlorophyll-a
(Intercept)
Water Level (50 days)
Coefficient
0.65017
0.00006
0.00230
0.00214
-0.00040
0.65544
0.00005
0.00230
0.00052
-0.00032
0.66210
0.00005
0.00230
-0.00116
-0.00028
0.68153
0.00001
SE
0.0705
0.0001
0.0009
0.0188
0.0012
0.0677
0.0001
0.0009
0.0181
0.0013
0.0638
0.0001
0.0009
0.0174
0.0013
0.0678
0.0001
t
9.22
0.71
2.53
0.11
-0.32
9.69
0.69
2.49
0.03
-0.26
10.38
0.65
2.47
-0.07
-0.22
10.06
0.14
P
0.0000
0.4795
0.0157
0.9099
0.7523
0.0000
0.4931
0.0174
0.9773
0.8001
0.0000
0.5189
0.0182
0.9471
0.8255
0.0000
0.8901
5
6
Time
Env. heterogeneity - dc
chlorophyll-a
(Intercept)
Water Level (10 days)
Time
Env. heterogeneity - dc
chlorophyll-a
(Intercept)
Water Level (40 days)
Time
Env. heterogeneity - cv
chlorophyll-a
0.00234
-0.00396
-0.00045
0.67019
0.00003
0.00230
-0.00233
-0.00032
0.59112
0.00007
0.00242
0.00715
-0.00108
0.0009
0.0181
0.0013
0.0623
0.0001
0.0009
0.0174
0.0013
0.05675
0.00007
0.00077
0.00522
0.00128
2.50
-0.22
-0.35
10.76
0.50
2.44
-0.13
-0.25
10.42
1.01
3.13
1.37
-0.85
0.0168
0.8280
0.7273
0.0000
0.6226
0.0194
0.8942
0.8031
0.0000
0.3192
0.0034
0.1791
0.4030
Table S4 - Summary of the 20 models for β-diversity of the microcrustacean community, including the variables of each model (from column 2
to 5), AIC, delta AIC and Akaike weights (wi). Models are ordered by delta AIC. Water level was calculated using different time lags (10, 20,
30, 40 and 50 days before sampling). The variable time was the same for all models. Two metrics of environmental heterogeneity were tested.
The first (dc) was based on the method proposed by Anderson et al. (2006), while the second (cv) was based on the coefficient of variation (see
main text for details). Two alternative proxies for productivity were used: chlorophyll-a and total phosphorus concentrations.
Model rank
1
2
Water Level
50 days
20 days
Time
time
time
Environmental Heterogeneity
dc
dc
Productivity
chlorophyll-a
chlorophyll-a
AIC
-39.227
-38.210
delta AIC
0.000
1.016
wi
0.216
0.130
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
10 days
30 days
40 days
50 days
20 days
10 days
30 days
50 days
40 days
20 days
30 days
10 days
40 days
50 days
20 days
30 days
10 days
40 days
time
time
time
time
time
time
time
time
time
time
time
time
time
time
time
time
time
time
dc
dc
dc
cv
cv
cv
cv
dc
cv
dc
dc
dc
dc
cv
cv
cv
cv
cv
chlorophyll-a
chlorophyll-a
chlorophyll-a
chlorophyll-a
chlorophyll-a
chlorophyll-a
chlorophyll-a
total P
chlorophyll-a
total P
total P
total P
total P
total P
total P
total P
total P
total P
-37.881
-37.671
-37.105
-36.949
-36.338
-36.025
-35.724
-35.425
-35.179
-34.617
-34.300
-34.249
-33.921
-32.947
-32.493
-32.142
-32.132
-31.785
1.345
1.555
2.122
2.278
2.888
3.201
3.503
3.802
4.048
4.610
4.926
4.978
5.306
6.279
6.733
7.085
7.095
7.441
0.110
0.099
0.075
0.069
0.051
0.044
0.037
0.032
0.029
0.022
0.018
0.018
0.015
0.009
0.007
0.006
0.006
0.005
Table S5 - Generalized least squares regression coefficients of the top five models (with a Akaike weight > 0.07; see Table S4) predicting βdiversity of the microcrustacean community. The variables with significant effect sizes are highlighted in bold.
Models
1
Variables
(Intercept)
Coefficient
0.7139
SE
0.1486
t
4.80
P
0.0000
Water Level (50 days)
Time
Env. heterogeneity - dc
chlorophyll-a
-0.0003
0.0037
-0.0175
-0.0041
0.0002
0.0014
0.0397
0.0029
-1.70
2.56
-0.44
-1.40
0.0978
0.0147
0.6616
0.1688
2
(Intercept)
Water Level (20 days)
Time
Env. heterogeneity - dc
chlorophyll-a
0.6610
-0.0002
0.0036
-0.0069
-0.0038
0.1403
0.0002
0.0014
0.0388
0.0029
4.71
-1.39
2.55
-0.18
-1.31
0.0000
0.1716
0.0150
0.8603
0.1994
3
(Intercept)
Water Level (10 days)
Time
Env. heterogeneity - dc
chlorophyll-a
0.6501
-0.0002
0.0036
-0.0063
-0.0038
0.1364
0.0002
0.0014
0.0388
0.0029
4.77
-1.37
2.56
-0.16
-1.30
0.0000
0.1791
0.0146
0.8711
0.2001
4
(Intercept)
Water Level (30 days)
Time
Env. heterogeneity - dc
chlorophyll-a
0.6496
-0.0002
0.0036
-0.0071
-0.0035
0.1501
0.0002
0.0014
0.0404
0.0029
4.33
-1.10
2.48
-0.18
-1.19
0.0001
0.2783
0.0177
0.8615
0.2428
5
(Intercept)
Water Level (40 days)
Time
Env. heterogeneity - dc
0.6578
-0.0003
0.0037
0.0031
0.1520
0.0002
0.0011
0.0391
4.33
-1.53
3.42
0.08
0.0001
0.1348
0.0015
0.9368
chlorophyll-a
-0.0046
0.0029
-1.59
0.1213
Table S6 - Summary of the 20 models for β-diversity of the rotifer community, including the variables of each model (from column 2 to 5), AIC,
delta AIC and Akaike weights (wi). Models are ordered by delta AIC. Water level was calculated using different time lags (10, 20, 30, 40 and 50
days before sampling). The variable time was the same for all models. Two metrics of environmental heterogeneity were tested. The first (dc)
was based on the method proposed by Anderson et al. (2006), while the second (cv) was based on the coefficient of variation (see main text for
details). Two alternative proxies for productivity were used: chlorophyll-a and total phosphorus concentrations.
Model rank
1
2
3
4
5
6
7
8
9
10
11
12
13
Water Level
50 days
50 days
50 days
40 days
30 days
20 days
50 days
40 days
30 days
20 days
10 days
10 days
40 days
Time
time
time
time
time
time
time
time
time
time
time
time
time
time
Environmental Heterogeneity
cv
dc
cv
cv
cv
cv
dc
dc
dc
dc
cv
dc
cv
Productivity
chlorophyll-a
chlorophyll-a
total P
chlorophyll-a
chlorophyll-a
chlorophyll-a
total P
chlorophyll-a
chlorophyll-a
chlorophyll-a
chlorophyll-a
chlorophyll-a
total P
AIC
-106.593
-104.150
-103.570
-102.526
-102.238
-102.083
-101.612
-101.205
-100.910
-100.824
-100.438
-99.068
-98.999
delta AIC
0.000
2.443
3.023
4.067
4.355
4.510
4.981
5.387
5.683
5.768
6.155
7.525
7.594
wi
0.431
0.127
0.095
0.056
0.049
0.045
0.036
0.029
0.025
0.024
0.020
0.010
0.010
14
15
16
17
18
19
20
30 days
20 days
40 days
30 days
20 days
10 days
10 days
time
time
time
time
time
time
time
cv
cv
dc
dc
dc
cv
dc
total P
total P
total P
total P
total P
total P
total P
-98.829
-98.760
-98.438
-98.207
-98.141
-96.868
-96.311
7.763
7.833
8.155
8.386
8.451
9.725
10.282
0.009
0.009
0.007
0.007
0.006
0.003
0.003
Table S7 - Generalized least squares regression coefficients of the top three models (with a Akaike weight > 0.07; see Table S6) predicting βdiversity of the rotifer community. The variables with significant effect sizes are highlighted in bold.
Models
1
2
3
Variables
(Intercept)
Water Level (50 days)
Time
Env. heterogeneity - cv
chlorophyll-a
(Intercept)
Water Level (50 days)
Time
Env. heterogeneity - dc
chlorophyll-a
(Intercept)
Water Level (50 days)
Coefficient
0.49493
0.00017
0.00284
0.01507
-0.00057
0.53830
0.00017
0.00258
0.03036
0.00015
0.49688
0.00018
SE
0.05171
0.00006
0.00075
0.00468
0.00115
0.06271
0.00007
0.00100
0.01658
0.00117
0.05211
0.00006
t
9.57
2.67
3.78
3.22
-0.50
8.58
2.53
2.58
1.83
0.13
9.54
2.914
P
0.0000
0.0111
0.0006
0.0027
0.6201
0.0000
0.0159
0.0139
0.0752
0.8965
0.0000
0.0060
Time
Env. heterogeneity - cv
total-P
0.00285
0.01384
0.00002
0.00077
0.00465
0.00029
3.68
2.97
0.08
Table S8 - Result of the intervention analysis applied to water level.
Constant
p
Ps
ω
Coefficients
366.46
0.69
0.12
-61.25
Standard Error
15.99
0.04
0.05
23.85
t
22.91
18.07
2.32
-2.57
P
0.0000
0.0000
0.0207
0.0106
0.0007
0.0052
0.9373
Fig. S1 - Temporal trends in species occupancy as evaluated by the Mann-Kendall
test. The horizontal line represents a correlation equal to zero. The vertical red line
separates the species with negative and positive trends.
Fig. S2 - Minimum and maximum dissimilarity values (Simpson’s index) for (a) the
whole zooplankton community, (b) rotifers and (c) microcrustaceans.
Fig. S3 - Matrix correlation coefficients between compositional dissimilarities and
geographic distances.
Fig. S4 - Time-series of water level in the Upper Paraná River. The red line indicates
the month when the filling of the Porto Primavera Reservoir was completed.
Fig. S5 - Autocorrelation function of water level in the Upper Paraná River. Analyses
were performed for the original values and for the residuals from an ARIMA model.