Ecological network inferred from field data elucidates invasion of a freshwater ecosystem by the exotic silver carp

Networks of interspecific interactions drive community structure, dynamics and stability. The ability to infer interspecies interactions from observational field data would open possibilities to apply network models to manage real world ecosystems. Here, we show this is possible for a freshwater fish community in the Illinois River, United States, using long-term data collected through time and space. We solve the challenge of sparsely sampled field data using latent variable regression and constraints imposed by known trophic structure in the fish community. Network analysis indicates that the most abundant 9 fish coexisted thanks to equalizing mechanisms that reduced fitness differences between strong and weak competitors. Importantly, the network sheds light on the ongoing invasion by the exotic silver carp (Hypophthalmichthys molitrix), revealing that the invader outproduces native preys, replacing their contributions to the diets of native predators. Our work shows that field data and constrains imposed by known food webs can improve network inference and produce quantitative insights that could aid in conservation of freshwater ecosystems threatened by invasive species.


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Ecological network theory seeks to understand how the many interactions between species affect dynamics 29 and stability of the ecosystem. In 1972, Robert May questioned a paradigm established at the time by 30 proving that networks with many, highly connected species tend to be less stable (May 1972). May's 31 pioneering work had immense influence and has led to ecological applications of random matrix theory, 32 which assumes that interaction strengths and types are sampled from random distributions.  with the rest of the community members (Fig. 3c). The inferred network is dominated by weak interactions 147 (Fig. 3d), a pattern thought to promote stability and often observed in natural ecosystems (Wootton and 8

Data from another pool validates the interactions inferred in the La Grange pool 151
Data coming from a single source is often biased, which could make the inferred network unreliable. Here 152 we used data from an additional pool to refine the network and improve model predictions. Pool 26-at the 153 confluence of the Upper Mississippi and Illinois Rivers-is the closest pool and had the most similar 154 community to the one in the La Grange pool ( Fig. 1b and Supplementary Fig. 4). Therefore, we assumed 155 that the two communities were similar enough that any pair of species interacting in La Grange pool may 156 interact the same way in Pool 26, if they co-occur.

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We applied the same latent variable approach to the time series of fish population in Pool 26 158 (Supplementary Fig. 6) to infer an independent network (Supplementary Table 4). For both sites, we 159 quantified the uncertainty associated with each interaction coefficient by assigning its own confidence score, 160 defined as the minimum significance level above which the confidence interval does not contain 0, to 161 indicate how likely the coefficient is significantly different than zero. The confidence scores were generally 162 proportional to the absolute values of their corresponding GLV coefficients ( Supplementary Fig. 7). With 163 at least 50% confidence at both sites, we identified 11 negative and 3 positive interspecific interactions (

Fitness equalization maintains species coexistence despite competition 170
The network inferred prompted us to explore the stability of the fish community. The model predicted stable 171 coexistence of all 9 fish species at steady state (Fig. 5a, right). Still, linear stability analysis (see Methods) 172 revealed that 80% of all attainable steady states of the system are stable ( Supplementary Fig. 8), suggesting 173 that the community could stabilize in alternative compositions different than those observed so far.

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To understand the mechanism of species coexistence, we simulated the steady state of two 175 subnetworks consisting of (1) only resource preys and (2) resources preys plus mesopredators. In the 9 absence of any predators, common carp (a strong competitor) is the most competitive resource prey that 177 drives other preys (weak competitors) to extinction in the long run (Fig. 5a, left). This is expected from the 178 competitive exclusion principle. The common carp was an invasive species first introduced to the United 179 States in 1800s that has caused damages to the fish community due to its rapid growth and high tolerance 180 to poor water quality. However, the presence of mesopredators, particularly freshwater drum, can reverse 181 the outcome of competition by preying on common carp (Fig. 5a, middle). The fitness inequality between 182 the strong and weak competitors persists until the addition of top predators, which suppress population of 183 mesopredators and reduce their predation pressure on resource preys (Fig. 5a,

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The simulations indicated that the silver carp integrates stably into the native fish community 208 without causing extinctions (Fig. 6a). Therefore, the invasion impacted the community composition by

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Importantly, our analysis suggested that the silver carp could only invaded when its growth rate 215 exceeded a threshold of 3.33 1/year (Fig. 6c). The need to exceed a threshold growth rate is expected 216 because all native fish species-preys and predators-had a negative impact on the silver carp 217 ( Supplementary Fig. 10); therefore, its population growth rate must be sufficiently high to counterbalance 218 the negative pressure from the native fish network. The estimated population growth rate of silver carp is 11

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Here we demonstrate the feasibility of inferring ecological networks from field data to produce quantitative 223 insights valuable for the management of real world ecosystems. Field data are invaluable for ecology, but

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The parameterized network provided intriguing results that help interpret the ongoing invasion by 244 the exotic silver carp. First, silver carp were predicted to be sufficiently integrated into the local fish 245 community, which suggests they may become "native" eventually. This is not surprising, given that 246 common carp, another invasive carp introduced to United States in the 1800s, have become members of the 12 Illinois River fish community after so many years of establishment and naturalization. Second, the invasion 248 did not seem to cause extinctions and the effects of the prey preference on the population structure of native 249 fish were apparently not drastic. These results could be naïvely interpreted as suggesting that the impact of 250 the silver carp is not detrimental; but the moderate impact may be due to the high productivity and species 251 richness in the Illinois River, which mitigates the effects of interspecific competition for food sources.

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Indeed, the native predators could even benefit from supplemental prey that they do catch. But caution is 253 still needed when interpreting these results: The overall decrease in native fish abundance caused a 254 measurable shift in the ratio of predator-to-prey which may increase the likelihood of stochastic extinctions 255 with unforeseen-and potentially irreversible-consequences. Our model makes predictions that could be 256 used to reverse the invasion: reducing silver carp's net growth below the critical threshold of 3.33 1/year, 257 for example by targeted harvest, would dramatically curb the invasion.

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We have adopted the simple GLV model to increase the generality of our inference approach and 259 to reveal the core interactions driving population dynamics, but our algorithm can be extended in multiple where " # (%) is the abundance of species 3 at time t and 4 is the total number of species. ) #,+ is referred to 309 as the net population growth rate (birth minus death) of the species 3 while ) #,. , known as the pairwise 310 interaction coefficient, represents the population influence of species 6 on species 3.

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The most commonly used technique to infer GLV parameters is to discretize Eq.  predator. c, Linear-threshold dependence of silver carp's invasion success on its population growth rate.

Ecological interpretations of inferred fish interaction network
• The positive interaction from ERSN to CNCF; the negative interaction from CNCF to ERSN; the positive interaction from GZSD to CNCF. Emerald shiner is a small fish species feeding on a variety of zooplankton, protozoans and diatoms. Gizzard shad is also small, and its diet consist of phytoplankton, zooplankton and detritus 1 . In contrast, channel catfish is an omnivore: although young catfish feed on vegetation and insects, adult channel catfish begin to use other fish as part of the diet 2 .
So abundant gizzard shads and emerald shiners may provide a forage base to support growth of channel catfish 3 .
• The positive interaction from ERSN to WTBS; the negative interaction from CNCF to WTBS.
Similar to channel catfish, young white bass feed on zooplankton and small invertebrates but its adults are piscivorous. Since both white bass and channel catfish consume small fish such as emerald shiner and gizzard shad 4,5 , the two species may have niche overlap and negative impact each other due to competition.
• The negative interaction from BLGL to GZSD. Bluegill is an omnivore and its diet consist of insect larvae, crayfish, leeches, snails and other very small fish. Similar to gizzard shad and emerald shiner, bluegill is prey to many larger predator fish. Gizzard shad is known to compete with bluegill for food resources 6,7 .
• The negative interaction from ERSN to BLGL. The interaction between emerald shiner and bluegill remains to be found. Given that gizzard shad compete with both fish species for food [6][7][8] , it is very likely that emerald shiner and bluegill have niche overlap and compete for similar resources.
• The negative interaction from FWDM to CARP. Freshwater drum generally eat zooplankton when they are young but start to feed on inserts and fish in adult ages 9 . It is very interesting that some people confuse drum with common carp because the drum's underslung mouth makes many people believe it is a bottom feeder, just like the common carp. Although freshwater drum also chase prey in open water, it is likely that both bottom feeders compete for food and space near the bottom of water.
• The negative interaction from FWDM to BKCP. Black crappies mainly eat plankton and crustaceans when they are young and larger individuals are basically piscivorous and primarily feed on small fish.
Since adult black crappie and freshwater drum share common preys such as gizzard shad 10,11 , their competitions for food resources seem to be unavoidable.
• The negative interaction from BKCP to ERSN. Adult black crappies prefer forage fish and minnows such as gizzard shad and emerald shiner. In fact, they can feed on anything that fits into their mouths.
Emerald shiner is a small fish with a typical length of 8.6 cm and the small size makes it a bait used by anglers for fishing crappie.
• The negative interaction from SMBF to GZSD; the negative interaction from ERSN to SMBF.
Smallmouth buffalo is a detritivore and uses its ventral sucker mouth to eat vegetation, insets and other organisms from the bottom of a body of water. The diet of adult smallmouth buffalo contains 55% of zooplankton and 31% phytoplankton 12 . Since gizzard shad and emerald shiner also feed on plankton, they may compete with smallmouth buffalo for diet and habitat due to the diet overlap. It was observed that the diet between smallmouth buffalo and gizzard shad do have certain overlaps, despite the relative proportions of detritus and zooplankton differ 13 . Table 2 Symbolic constraints used to parameterize generalized Lotka-Volterra model for fish community in La Grange pool. The shaded matrix was used to constrain pairwise interaction coefficients and the last column was used to constrain population growth rates. For species interaction coefficients, -1, 0, 1 represent negative, neutral, and positive interaction from the column species to the row species respectively. For population growth rates (the last column), -1 means negative growth rate and 1 means positive growth rate.  Table 3 Optimized coefficients of the generalized Lotka-Volterra model for fish community in La Grange pool. The shaded area gives pairwise interaction coefficients (each cell represents the interaction from column species to row species) and the last column gives population growth rates.