Appendix 1 – The Comprehensive Aquatic Simulation Model
The Comprehensive Aquatic Simulation Model (CASM) includes three trophic levels and nutrient
(phosphorus) circulation from detritus to water (DeAngelis et al., 1989; Amemiya et al., 2005; 2007),
which satisfies two of seven criteria proposed by Jørgensen (1976) for applying eutrophication models to
lakes. The model consists of five differential equations to describe the dynamics of nutrient (N), algae (A),
zooplankton (Z), fish (F) and detritus (D), respectively:
 dN
 r NA
 I N  rN N  A
  dD D

kN  N
 dt
 dA r AN
f A2 Z
 A
 2Z
  d A  eA  A

2
 dt k N  N k A  A

2
2
 dZ  f Z A Z f F Z F
 2
 2
  d Z  eZ  Z

2
kZ  Z 2
 dt k A  A
 dF
f Z 2F

  FZ
  d F  eF  F
k Z2  Z 2
 dt

2
2
 dD  1    f FZ Z F  1    f Z A Z  d A  d Z  d F   d  e  D
A
Z
F
D
D
 dt
kZ2  Z 2
k A2  A2
 A1
where the definitions, units and default values of all parameters are explained in Table 1 in the main text.
In the model, the nutrient pool is supplied by nutrient input rate (IN). The uptake kinetics of nutrient is
characterized by a Monod function. The consumption of zooplankton on algae and of fish on zooplankton
is described by the type III functional response (Holling, 1959). The representation is appropriate for
situations in which the rate of predation per capita prey becomes smaller with decrease of the biomass.
This type of functional response tends to produce stable food-web dynamics (Nunney, 1980). The
ingested consumptions multiplied by coefficient η are converted into consumers’ growths, while the
indigestible parts are transformed as detritus. A fixed loss rate of algae, zooplankton, fish and detritus due
to respiration, natural mortality or decomposition was used.
The model has been used in many cases for lake management (e. g. Jeppesen et al., 1990; Amemiya et al.,
2005; Amemiya et al., 2007; Fulford et al., 2010). The applications show that the model is capable of
behaving in a bistable manner, where regime shifts are able to be triggered by sufficient perturbation
under intermediate nutrient loading. In addition, the threshold value of phosphorus loading consistent
with field data. For more details about the model, please refer to DeAngelis et al. (1989) and Amemiya et
al. (2005; 2007).
Appendix 2 – Eutrophication and data of Wuhan East Lake
Wuhan East Lake (Lake Donghu) is within Wuhan City along the middle reach of Yangtze River in
central China (114˚09'～114˚39'E, 30˚22'～30˚41'N, Figure A1). The subtropical urban shallow lake is
with a catchment area of 119 km2, an average depth of 2.2 m, and a surface area of 27.9 km2. Before
1960s, the water in the lake was clear, the submerged vegetation was abundant, and the zooplankton
community was dominated by large-body Daphnia species.
In the early 1960s, the lake was cut off from the Yangtze River, and was divided into several sub-lakes for
commercial fishery. Since then commercial omnivorous fish silver carp (Hypophthalmichthys molitrix)
and bighead carp (Aristichthys nobilis) have been heavily stocked in the lake. As results, the fish yield has
been increased from ~160 t/a in 1960 to ~1700 t/a in 2008 (Zhang and Wei, 1998; Liu et al., 2006). The
fish yield in 1985 was 1015 t/a, equivalent to fish yield of 23 g m-3 a-1, a wet-weigh biomass of 46 g m-3
(Tatsukawa et al., 1989; Liu and Xie, 1999), and a dry-weigh biomass of 7.67 g m-3 (Suzuki et al., 2000).
Therefore, the equivalent increase in fish biomass (dry weight) was from 1.2 to 12.4 g m-3 during the
1
nearly 50 years. In addition, the species composition have altered from 18 families 67 species to two
dominant tolerant species (more than 90%) (Liu and Xie, 1999). The high predation intensity of the fish
have resulted in diminution of the size of zooplankton and markedly decreased the species’ numbers of
Cladocera and Copepod (Li and Huang, 1992; Yang et al., 1994). Associated with population growth and
economy development, the lake has suffered serious eutrophication problem. During the 1970s to the
middle 1980s, nuisance blue-green algal blooms occurred every summer and macrophytes declined
considerably.
Dramatically, the bloom problem has disappeared since 1985, attributable to the grazing of the two types
of fishes with high stocking intensity since then (Liu and Xie, 1999). The effects of these filter-feeding
carps on the control of water bloom are documented by increasing reports (Datta and Jana, 1998; Zhang et
al., 2006; Ke et al., 2007). However, the increasing fishery in the lake has led to degradation of the
ecosystem, appearing turbid state with low transparency, extinction of submerged macrophytes and low
density of zooplankton until now. Recent evaluations performed during 2000s show that phosphorus is the
principal factor of the eutrophication and eutrophicated water constitutes 62.21% of the total water area in
the lake (Gan and Guo, 2004; Wang et al., 2010).
Data on ecological components and water quality from 1980 to 2009 were collected from the literature.
As the principal factor of the eutrophication of the lake, total phosphorus was used to represent limited
nutrient (Gan and Guo, 2004). Chlorophyll-a concentration was converted to algal biomass through their
liner correlation (Wang and Wang, 1984). The biomass of zooplankton and fish was converted to dry
weight through the factors proposed by Sagehashi et al. (2000) and Suzuki et al. (2000), respectively.
Variable ranges, sampling locations and data sources during different period are summarized in Table A1.
Table A1. Variable ranges, sampling sites, and source of observed data in typical periods of Wuhan East
Lake.
Variable
(g m-3)
TP concentration
Algal biomass
Zooplankton
biomass
0.51 – 0.76
(I, II)b, c
0.22 – 1.05
(I, II)b, c, e
0.77 – 1.73 (W)j (I,
II, III)k (I, II)c, f
0.36 – 0.83
(W)j
Fish biomass
4.84
4.99 – 6.23
(I, II)a
(W)d, e
0.040 – 0.210
16.9 – 39.0
6.27 – 8.50
1985 – 1989
(I, II)a
(I, II)a, f (II)d
(W)d, e
0.058 – 0.233
10.4 – 31.5
8.69 – 9.52
1990 – 1994
(W)g, h, i, j
(W)g, h, j (I, II)f (II)d
(W)d, e, j
0.060 – 0.085
13.3 – 31.0
11.0 – 12.4
1995 – 1999
(W)h, j (I, II, III)l
(W)h, j (I, II, III)l
(W)d, e, j
0.132 – 0.189
6.73 – 25.7
11.5 – 12.4
–
2000 – 2004
(W)m (I, II, III)l
(W)m (I, II, III)l
(W)e
0.092 – 0.412
4.92 – 14.9
12.8
–
2005 – 2009
(W)n, o (I)p
(W)n, o (I)p
(W)e
Note: the locations of site I, II, III and IV are shown in Figure A1, “W” means the whole lake, i. e., I + II
+ III +IV; aRuan et al. (1988), bLi and Huang (1992), cYang et al. (1994), dLiu and Xie (1999), eLiu et al.
(2006), fXie (1996), gMa et al. (1996), hMa et al. (1997), iZhang and Wei (1998), jYang and Huang
(2002), kYang and Huang (1994), lYan et al. (2005), mGan and Guo (2004), nWang et al. (2010), oYu et al.
(2012), pZhang et al. (2010).
1980 – 1984
–
2
Figure A1. Location and sampling sites (roman numbers) of Wuhan East Lake. In the inset panel, the
black line and circle represent the Yangtze River and the location of Wuhan City, respectively.
Appendix 3 – Results of stochastic simulation
The Monte Carlo simulations were performed to assess the uncertainty of the parameters used. Ten
thousand sets of parameters with the lowest TRE values (Eq. (4)) were extracted from calibrations of the
case study. All sets were used as the model inputs, the simulation results were used to evaluate the
dynamic states and calculate TCI values.
Results showed that the ecosystem was probably monostable with more than 80% probability before 1985,
either monostable or bistable with 50% – 50% probability, and had been bistable with significant higher
chances since 1995 (Figure A2). In addition, the mean value of TCI decreased during the modeling period.
The results were generally agreed with the deterministic simulation (Figure 4 in the main text).
Figure A2. Statistical variations of the proportions of stability types (S1 and S2 + S3) and the mean and
standard deviation (±SD) of TCI, based on the 104 Monte Carlo simulations.
3
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