An ecological model was developed to systematically analyze the comprehensive influence of omnivory level and predation intensity of fish on the dynamic state and strength of trophic cascade of a lake ecosystem. Results showed that a higher fish omnivory level reduced the strength of trophic cascade and increased the occurrence of alternative states, while an increase in predation intensity resulted in opposite effects. With the combination of these two factors, the occurrence of alternative states was dependent on the relative increase in the predation intensity. The model was further applied to a subtropical shallow lake in China. Modeling results revealed that the heavy stock of omnivorous fish in the lake increased the occurrence of alternative states and decreased the strength of trophic cascade. Results indicated that the long-term effect of biomanipulation would be significant and therefore high rates of fish removal would be required. The information from this study indicated the importance of understanding the dynamic state and strength of trophic cascade when predicting the long-term effects of biomanipulation.

Introduction

Biomanipulation through the artificial reduction of planktivorous fish biomass is a useful remediation method that has been widely applied to numerous eutrophic lakes (Hansson et al., 1998; Søndergaard et al., 2002). However, the effect of biomanipulation, especially the long-term effect, remains poorly understood. Omnivorous fish have been reported as one of the important factors responsible for the difficulties in biomanipulation, especially in lower latitudes with rich filter-feeding species, such as Gizzard Shad (Dorosoma cepedianum), Silver Carp (Hypophthalmichthys molitrix) and Tilapia (Oreochromis niloticus) (Jeppesen et al., 2010). These fish selectively prey on detritus and planktonic algae besides zooplankton. The complex feeding habit reduces trophic cascade and diminishes water quality improvements that would be obtained by the removal of planktivorous fish (Lazzaro, 1997; Pace et al., 1999). Therefore, the reduced trophic cascade makes biomanipulations less effective.

Nevertheless, at least two aspects need to be considered. First, omnivorous fish biomanipulation is also necessary to release predation pressure (Tátrai et al., 2003; Beklioglu et al., 2007). Attributed to their community structure, life history traits and feeding mode, omnivorous fish often have significant higher predation intensity (Okun et al., 2008; Jeppesen et al., 2010). For example, omnivorous fish in lower-latitude areas are with smaller sizes, substantially higher density, and therefore much higher zooplankton demand per unit of biomass. The strong predation intensity promotes negative cascading effects. Second, the existence of alternative states is another important factor affecting biomanipulation. If a system is monostable, the long-term effect of regime shifts would probably be limited (Hansson et al., 1998). Meanwhile, the alternative states are a possibility of the ecosystem behavior (Schröder et al., 2005). However, in several models incorporating the omnivory factor (Post et al., 2000; Faria and Costa, 2010), the effects of alternative states on biomanipulation have seldom been considered.

The aim of this study was to systematically analyze the comprehensive effects of omnivory and predation intensity of fish on the strength of trophic cascade and alternative states using an ecological model. The model was applied to predict biomanipulation effects through evaluating dynamic states and trophic cascade. Biomanipulation strategies were discussed based on the results.

Material and methods

The ecological model

The model used in the article is a modified version of the Comprehensive Aquatic Simulation Model (CASM) (DeAngelis et al., 1989). It includes three trophic levels and nutrient (phosphorus) circulation from detritus to water, and is able to perform regime shifts triggered by sufficient perturbation under intermediate nutrient loading (Amemiya et al., 2005, 2007). The details of the model are shown in Appendix 1 in the supplementary information. To consider the omnivory habit of fish, we expanded the model by including a prey-switching function (Post et al., 2000; Faria and Costa, 2010):
formula
(1)
where wi (wi ≥ 0) is the food preference degree of fish for zooplankton (i = Z), algae (i = A), and detritus (i = D). For example, if wZ = 1 and wA = wD = 0, fish only prey on zooplankton; if wZ = wA = wD = 1/3, fish feed on zooplankton, algae, and detritus without preference. By incorporating Equation (1), the modified model becomes
formula
(2)
where the definitions and values of all variables and parameters are explained in Table 1. In the model, three growth terms with food preference (θZ, θA, θD) were used to account for the selective consumptions on zooplankton, algae, and detritus. We used Type II equations to reflect fish functional response instead of the type III equations in the original model, because the combination of preference term and type II equation can produce type-III-like functional response (Post et al., 2000; Attayde et al., 2010).

Numerical analysis

A numerical linear stability analysis for the model was carried out with the input rate (IN) being used as a control parameter. Coexisting solutions for same IN values are identified as alternative equilibria. In the study, the IN range assigned for the stability analysis was 0–0.002 g m−2 d−1, slightly larger than that in the original CASM (Amemiya et al., 2005, 2007). Based on the IN range and the parameter values listed in Table 1, algal biomass ranged from 0.8 to 40 g m−2 was obtained, which covered most of possible values in freshwater systems.

In the model, the omnivory level is determined based on phytoplanktivory (wA) and detritivory (wD). Higher wA and/or wD indicated higher omnivory levels. The predation intensity is estimated by the half-saturation constant of zooplankton biomass (kZ) and the feeding rate of fish (fFZ), that is, higher fFZ and/or lower kZ values represents higher predation intensity (Li et al., 2010). To examine the influence of fish ominivory and predation intensity on the dynamic state and trophic cascade of the system, different values of parameters wA, wD, fF and kZ (as listed in Table 1), were selected to perform the stability analysis. Other parameters were set to the default values. Four types of dynamic states were obtained by the analysis. Definitions and characteristics of the four types of dynamic states (S1 to S4) are listed in Table 2. In S2 and S3, regime shifts were most likely triggered by suitable perturbations.

Trophic cascades result in inverse patterns in abundance or biomass across more than one trophic link in a food web (Persson, 1999). For a three-level food chain, abundant top predators (fish) result in lower abundances of mid-level consumers (zooplankton) and higher abundance of basal producers (algae) (Pace et al., 1999). To evaluate the strength of trophic cascade, the tropic cascade index (TCI) was defined:
formula
(3)
where A and F are the algal biomass and fish biomass, and subscripts 1 and 2 denote equilibria with low and high algal biomass, respectively. The stability analysis with the parameter values in Table 1 showed that the A value was ∼0.8 g m−2 with F close to zero and increase (> ∼25 – 40 g m−2) quasi-linearly with high F values. According the sensitivity of TCI values, A1 and A2 were taken 1 and 30 g m−2, respectively, and F1 and F2 were estimated through the stability analysis.

Case study: Wuhan East Lake

A case study was introduced to illustrate how to assess the feasibility of biomanipulation through evaluation of the dynamic states and trophic cascade. Wuhan East Lake (Lake Donghu) is a subtropical urban shallow lake located along the middle reach of Yangtze River in central China (114˚24′E, 30˚32′N). It has an average depth of 2.2 m and a surface area of 27.9 km2. Both acceleration and control of the eutrophication process in the lake are highly associated with commercial fisheries. Since the 1960s, typical omnivorous Asian Carps, Silver Carp (Hypophthalmichthys molitrix) and Bighead Carp (Aristichthys nobilis) have been heavily stocked in the lake. As a result, the community compositions of fish and zooplankton have been heavily altered to small and tolerant species, and nuisance blue-green algal blooms frequently occurred. Dramatically, the blooms have vanished since 1985, as the fish stocking has been intense enough to control the algae since then (Liu and Xie, 1999). However, the lake still has turbid water with low transparency and submerged macrophytes are extinct due to degradation of the ecosystem. Details of the lake's eutrophication are presented in Appendix 2.

Model (2) was applied to simulate the long-term ecological dynamics and evaluate the changes of omnivory level, predation intensity, trophic cascade and dynamic state. Data on total phosphorus concentrations and the biomass of algae, zooplankton and fish from 1980 to 2009 were extracted from published literature (Appendix 2). Essential model parameters, including IN, fZ, wA, wD, kZ and fFZ during every five-year periods were calibrated, among which wA and wD represent the omnivory level, kZ and fFZ represent the predation intensity, and IN and fZ are sensitive to environmental change and algal compositions, respectively. During the calibration process, 1010 sets of parameters (wA, wD, kZ, fF, IN, fF) were randomly generated within their ranges (Table 1) through Latin hypercube sampling to run the model. Other parameters were set to their default values. Simulations (SVsim) and observations (SVobs) were compared by the average error (AE), maximum error (ME), mean sum of standard deviation (SD) and relative error (RE), which are calculated by (Li, 2012):
formula
(4)

For the sets of parameters satisfying AE < 0.1, ME < 0.1 and SD < 0.1 for the state variables, the total relative error (TRE) was obtained by the sum of RE. The optimal parameters should result in the lowest TRE. The model was further used to evaluate the dynamic state and calculate the TCI, as described above.

Results and discussion

Influence of omnivory and predation intensity on trophic cascade and dynamic state

Numerical analysis showed that omnivory reduced the strength of trophic cascade and increased the occurrence of alternative states (Figure 1a), while the increase in predation intensity had opposite effects (Figure 1b) and their combination led to ambiguous influences (Figure 1c). For instance, at a low omnivory level, the dynamic state belonged to S1, where regime shifts were not likely to occur due to the absence of alternative equilibria (Figure 2a). With a higher omnivory level, the dynamic state became S2, where alternative equilibria existed under moderate nutrient loading, implying regime shifts were possible (Figure 2b). With increasing omnivory levels, alternative equilibria coexisted with increasing range of nutrient levels. When the range was wide enough to exclude the monostable equilibrium with high algal biomass, the system entered S3 (Figure 2c). When the omnivory level was high enough, the equilibrium with algal biomass became too high to be captured from our initial condition, and the system entered S4 (Figure 2d). In addition, the slopes of the AF dynamics decreased with the increasing omnivory level (Figure 2h), which revealed that more fish were required to control the same amount of algae, that is, a decrease in trophic cascade. Conversely, with increasing predation intensity, dynamic state changed from S4, S3, S2 to S1, with trophic cascade increasing (Figures 2d–g, and i).

The ecological reasons for the model behavior can be attributed to the alteration of the “biological resistance” (Scheffer et al., 2001). The increase in predation intensity enhances the biological resistance (Beklioglu et al., 2011), which makes the system tend to behave in a monostable manner regime, whereas increased omnivory reduces the resistance by creating horizontal and vertical heterogeneity in food web structure with the potential for bistability (Mylius et al., 2001; Schröder et al., 2005). With respect to the comprehensive influence, Holt and Polis (1997) hypothesized that there was a potential for alternative states if the top predator was relatively inefficient at consuming the intermediate species. Our results support the hypothesis: if the predation intensity is low, the alternative states may exist in wide omnivory ranges; oppositely, the alternative states can only exist at sufficiently high omnivory levels (Figure 1c). In addition, the resistance can be further strengthened by bottom-up input at relative high IN loading levels. The state variables are balanced by a high matter flux and the only source IN decides the matter level of the system. For example, algal biomass increased linearly with IN when the loading level was relatively high (Figures 2a–g), which was also observed in similar models (Scheffer, 1990; Scheffer et al., 2001).

Similar to Lazzaro (1997) and Pace et al. (1999), fish omnivory reduces trophic cascade but increases the occurrence of alternative states (Figure 1a). On the other hand, the increase in predation intensity enhances trophic cascade (Okun et al., 2008) but decreases the occurrence of alternative states (Figure 1b). As the results, omnivorous fish may either increase or decrease the occurrence of alternative states, depending on the relative increase level of predation intensity (Figure 3). The two outcomes compatibly explain the coexistence of the two distinct expectations when applying biomanipulation: one (Outcome 1) queried the unpredictable long-term effect due to the reduced cascading effect (Lazzaro, 1997; Pace et al., 1999), and the other (Outcome 2) emphasized the urgent need to release high predation pressure on zooplankton (Tátrai et al., 2003; Beklioglu et al., 2007).

Implications for biomanipulation with the case study

The ecological dynamics of Wuhan East Lake from 1980 to 2009 were simulated and the modeling results were quite consistent with the observations, which indicated that the model was capable of reproducing the features and variability of the lake (Figures 4a–d). Furthermore, the results revealed that the heavy stocking of commercial fish had altered the internal properties of the lake system. Silver Carp and Bighead Carp, the main species stocked in the lake, are characterized by omnivorous feeding habit, high predation pressure on zooplankton and high efficacy of nutrient recycling (Datta and Jana, 1998; Zhang et al., 2006). These characteristics were evident in the calibrated parameters, which showed the omnivory level, the predation intensity and nutrient loading were generally increasing during the modeling period (Figures 4e–g). Moreover, these fish are capable of controlling blue-green algae (Datta and Jana, 1998; Chen et al., 2010), which are not good food source for zooplankton. As a result, the proportion of eatable algae for zooplankton increased, which was evident from the increase in feeding rate (Figure 4g). The above changes of internal properties led to the changes of dynamic state and trophic cascade: the dynamic state changed from S1 during 1980 and 1984 to S2 and S3 during 1985 and 1999, and had remained in S3 since 2000, and the trophic cascade continuously decreased (Figure 4h). The results were further confirmed by the stochastic simulations (Appendix 3).

Combined measures of composition manipulations on the fish community and pulse-like fish removals should be effective for lake restoration. Schooling omnivorous fish such as Silver Carp and Bighead Carp is effective for controlling blue-green algae. While an increase in omnivory level used to be regarded as an unfavorable factor for reducing trophic cascade (Lazzaro, 1997; Pace et al., 1999), it is more favorable to drive the system into alternative states (Figures 1a, 4e and h). On the other hand, these fish prey highly on zooplankton (Figure 4f; see also Okun et al., 2008), and are harmful to aquatic vegetation (Miller and Crowl, 2006). Therefore, it is necessary to remove fish to trigger positive regime shifts in the lake (Starling et al., 2002). Here, the mathematical model provides a useful approach to calculate the timing of biomanipulation through evaluating the dynamic state and trophic cascade. Based on the results of Wuhan East Lake, the ecosystem has changed from monostable to bistable, and the lake remained in S3 (alternative states exist in a wide loading range) since 2000 (Figure 4h). This indicated the long-term effects of biomanipulation would become significant. Meanwhile, the fish removal intensity should be sufficiently high, since the strength of trophic cascade has remarkably decreased.

Conclusions

The comprehensive influence of omnivory level and predation intensity on trophic cascade and dynamic state was examined through an ecological model. Biomanipulation strategies of omnivorous fish were discussed based on the model analysis results and a case study. A higher omnivory level increased the occurrence of alternative states and reduced the strength of trophic cascade, while the predation intensity resulted in opposite effects. The combination of the two factors led to more comprehensive outcomes. The results clearly explained the biomanipulation challenge with omnivorous fish. It is essential to evaluate dynamic state and trophic cascade for implementing biomanipulation. A combinative measure of adjusting dynamic state and pulse-like fish removal should be an effective biomanipulation strategy.

Acknowledgements

We thank Dr. Shizhong Wang for his useful comments and suggestions on earlier drafts of the article.

Funding

This study was supported by the Chinese National Natural Science Foundation (51039007, 51179212 and 41406039) and the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA11010203).

Supplemental material

Supplemental data for this article can be accessed on the publisher's website.

References

Amemiya, T., Enomoto, T., Rossberg, A. G., Takamura, N., and Itoh, K.,
2005
.
Lake restoration in terms of ecological resilience: a numerical study of biomanipulations under bistable conditions
.
Ecol. Soc.
10
,
3
.
Amemiya, T., Enomoto, T., Rossberg, A. G., Yamamoto, T., Inamori, Y., and Itoh, K.,
2007
.
Stability and dynamical behavior in a lake-model and implications for regime shifts in real lakes
.
Ecol. Model.
206
,
54
62
.
Attayde, J. L., van Nes, E., Araujo, A. I. L., Corso, G., and Scheffer, M.,
2010
.
Omnivory by planktivores stabilizes plankton dynamics, but may either promote or reduce algal biomass
.
Ecosystems
13
,
410
420
.
Beklioglu, M., Romo, S., Kagalou, I., Quintana, X., and Bécares, E.,
2007
.
State of the art in the functioning of shallow Mediterranean lakes: workshop conclusions
.
Hydrobiologia
584
,
317
326
.
Beklioglu, M., Meerfhoff, M., Søndergaard, M., and Jeppesen, E.,
2011
.
Eutrophication and restoration of shallow lakes from a cold temperate to a warm mediterranean and a (sub)tropical climate
. In: A.A. Ansari., S. Singh Gill, G.R. Lanza, W. Rast (Eds.),
Eutrophication: causes, consequences and control
, pp.
91
108
.
Springer
,
Netherlands
.
Chen, Y., Li, Z., and Lin, L.,
2010
.
Effects of a small planktivore (Pseudorasbora parva: Cyprinidae) on eutrophication of a shallow eutrophic lake in central China
.
Aquat. Ecosyst. Health Mgmt.
13
(
3
),
328
334
.
Datta, S., Jana, and B. B.,
1998
.
Control of bloom in a tropical lake: grazing efficiency of some herbivorous fishes
.
J. Fish Biol.
53
,
12
24
.
DeAngelis, D. L., Bartell, S. M., and Brenkert, A. L.,
1989
.
Effects of nutrient recycling and food-chain Length on resilience
.
Am. Nat.
134
,
778
805
.
Faria, L. D. B., and Costa, M. I. d. S.,
2010
.
Omnivorous food web, prey preference and allochthonous nutrient input
.
Ecol. Complex.
7
,
107
114
.
Hansson, L.-A., Annadotter, H., Bergman, E., Hamrin, S. F., Jeppesen, E., Kairesalo, T., Luokkanen, E., Nilsson, P.-A., Søndergaard, M., and Strand, J.,
1998
.
Biomanipulation as an application of food-chain theory: constraints, synthesis, and recommendations for temperate lakes
.
Ecosystems
1
,
558
574
.
Holt, R. D., and Polis, G. A.,
1997
.
A Theoretical Framework for Intraguild Predation
.
Am. Nat.
149
,
745
764
.
Jeppesen, E., Meerhoff, M., Holmgren, K., González-Bergonzoni, I., Teixeira-de Mello, F., Declerck, S., De Meester, L., Søndergaard, M., Lauridsen, T., Bjerring, R., Conde-Porcuna, J., Mazzeo, N., Iglesias, C., Reizenstein, M., Malmquist, H., Liu, Z., Balayla, D., and Lazzaro, X.,
2010
.
Impacts of climate warming on lake fish community structure and potential effects on ecosystem function
.
Hydrobiologia
646
,
73
90
.
Lazzaro, X.,
1997
.
Do the trophic cascade hypothesis and classical biomanipulation approaches apply to tropical lakes and reservoirs?
.
Verh Int. Ver. Theor. Angew. Limnol.
26
,
719
730
.
Li, J.,
2012
.
An observation-based uncertainty evaluation coupling automatic calibration approach for ecological model of shallow lake
.
Fresen. Environ. Bull.
21
,
2255
2265
.
Li, J., Huang, P., Zhang, and R.,
2010
.
Modeling the refuge effect of submerged macrophytes in ecological dynamics of shallow lakes: A new model of fish functional response
.
Ecol. Model.
221
,
2076
2085
.
Liu, J., and Xie, P.,
1999
.
Unraveling the enigma of the disappearance of water bloom from the East Lake (Lake Donghu) of Wuhan. in Chinese
.
Resources and Environment in the Yangtze Basin
8
,
312
319
.
Miller, S. A., and Crowl, T. A.,
2006
.
Effects of common carp (Cyprinus carpio) on macrophytes and invertebrate communities in a shallow lake
.
Freshw. Biol.
51
,
85
94
.
Mylius, S. D., Klumpers, K., Roos, d. A. M., and Persson, L.,
2001
.
Impact of intraguild predation and stage structure on simple communities along a productivity gradient
.
Am. Nat.
158
,
259
276
.
Okun, N., Brasil, J., Attayde, J. L., and Costa, I.A.S.,
2008
.
Omnivory does not prevent trophic cascades in pelagic food webs
.
Freshw. Biol.
53
,
129
138
.
Pace, M. L., Cole, J. J., Carpenter, S. R., and Kitchell, J. F.,
1999
.
Trophic cascades revealed in diverse ecosystems
.
Trends Ecol. Evol.
14
,
483
488
.
Persson, L.,
1999
.
Trophic Cascades: Abiding Heterogeneity and the Trophic Level Concept at the End of the Road
.
Oikos
85
,
385
397
.
Post, D. M., Conners, M. E., and Goldberg, D. S.,
2000
.
Prey preference by a top predator and the stability of linked food chains
.
Ecology
81
,
8
14
.
Sagehashi, M., Sakoda, A., and Suzuki, M.,
2000
.
A predictive model of long-term stability after biomanipulation of shallow lakes
.
Water Res.
34
,
4014
4028
.
Sagehashi, M., Sakoda, A., and Suzuki, M.,
2001
.
A mathematical model of a shallow and Eutrophic Lake (The Keszthely Basin, Lake Balaton) and simulation of restorative manipulations
.
Water Res.
35
,
1675
1686
.
Scheffer, M.,
1990
.
Multiplicity of stable states in freshwater systems
.
Hydrobiologia 200/201
,
475
486
.
Scheffer, M., Carpenter, S., Foley, J. A., Folke, C., and Walker, B.,
2001
.
Catastrophic shifts in ecosystems
.
Nature
413
,
591
596
.
Schröder, A., Persson, L., and De Roos, A. M.,
2005
.
Direct experimental evidence for alternative stable states: a review
.
Oikos
110
,
3
19
.
Søndergaard, M., Jensen, J. P., Jeppesen, E., and Møller, P.H.,
2002
.
Seasonal dynamics in the concentrations and retention of phosphorus in shallow Danish lakes after reduced loading. Aquat. Ecosyst
.
Health
5
(
1
),
19
29
.
Starling, F., Lazzaro, X., Cavalcanti, C., and Moreira, R.,
2002
.
Contribution of omnivorous tilapia to eutrophication of a shallow tropical reservoir: evidence from a fish kill
.
Freshw. Biol.
47
,
2443
2452
.
Suzuki, M., Sagehashi, M., and Sakoda, A.,
2000
.
Modelling the structural dynamics of a shallow and eutrophic water ecosystem based on mesocosm observations
.
Ecol. Model.
128
,
221
243
.
Tátrai, I., Paulovits, G., Mátyás, K., and Korponai, J.,
2003
.
The role of fish communities in water quality management of a large shallow lake
.
Int. Rev. Hydrobiol.
88
,
498
507
.
Zhang, X., Xie, P., Hao, L., Guo, N., Gong, Y., Hu, X., Chen, J., and Liang, G.,
2006
.
Effects of the phytoplanktivorous silver carp (Hypophthalmichthys molitrixon) on plankton and the hepatotoxic microcystins in an enclosure experiment in a eutrophic lake, Lake Shichahai in Beijing
.
Aquaculture
257
,
173
186
.

Supplementary data