Lake-level invasions of non-indigenous aquatic invasive species (AIS) can disrupt lake ecosystems and lead to catastrophic damages. When presented with the possibility of such an issue, policymakers must first determine whether to invest in strategies to conserve or protect the metapopulations within the ecosystem and then they must decide how much to invest. Historically, policymakers and managers have relied on economic studies to help them allocate scarce funds to invasive species management and, thereby, conservation (e.g., Pimentel et al., 2000, 2005). The investment decisions are often influenced by estimates of economic damages or social welfare implications associated with the invasion that can be used in a benefit-cost analysis (Leung et al., 2002; Finnoff et al., 2005, 2010; Hanley and Roberts, 2019). Yet the usefulness of damage assessments or social welfare estimates can fall short and lead to poor investment decisions if the complex relationships between humans and species across space are overly simplified (see reviews of Perrings et al., 2000; Finnoff et al., 2010; Simberloff et al., 2013; Epanchin-Niell, 2017; Warziniack et al., 2021).

To better understand the consequences of oversimplification of complex relationships in assessments of economic costs, the study herein considers the potential invasion of an AIS in Lake Michigan. Silver Carp, Hypophthalmichthys molitrix, and Bighead Carp, Hypophthalmichthys nobilis, (collectively and henceforth bigheaded¹ carp) are AIS that have been traveling up the Mississippi River and are expected to enter the southern basin of Lake Michigan and spread throughout the lake. Currently, the invasion front is just 76 km away from Lake Michigan (Rutherford et al., 2021). The invasive bigheaded carp are strong competitors that may outcompete larval fish for algae and zooplankton (Solomon et al., 2016; Pendleton et al., 2017; Phelps et al., 2017; DeBoer et al., 2018) or may outcompete forage fish (e.g., alewife, Alosa pseudoharengus or rainbow smelt, Osmerus mordax) – which are primary food for the salmonines (e.g., Chinook salmon, Oncorhynchus tshawytscha, Coho salmon, Oncorhynchus kisutch, lake trout Salvelinus namaycush, or steelhead (rainbow trout), Oncorhynchus mykiss) that are economically important to the recreational sportfishing industry. Young bigheaded carp can be a food source for piscivores that are also important to the sportfishing industry (Wittmann et al., 2015; Anderson, 2016), although rapid growth in body size of juvenile bigheaded carp may limit their positive effects on piscivores predation (Kolar et al., 2007). Further, there is concern that bigheaded carp may disrupt the energy flow from primary producers to fishery species and make the fishery unsustainable (Solomon et al., 2016).

These interactions and any resultant damages will depend on the specific ecological characteristics of different spatial locations in Lake Michigan (Cooke and Hill, 2010; Rutherford et al., 2021). Some studies indicate that bigheaded carp could establish in Lake Michigan (Rutherford et al., 2021) in the nearshore areas and embayment (fish nursery waters) because there are more nutrient resources, and in suitable habitat in the deep chlorophyll layer offshore (Alsip et al., 2019, 2020). Other studies, however, have shown that the productivity in Lake Michigan is too low for bigheaded carp to survive (Cooke et al., 2009; Cooke and Hill, 2010; Rutherford et al., 2021). While it is not clear if bigheaded carp will have the feared detrimental impacts on the recreational fishery and an already fragile lake ecosystem (e.g., Madenjian et al., 2015; Kao et al., 2018; Alsip et al., 2019, 2020; Rutherford et al., 2021), many organizations are actively engaging in research, monitoring, and control including, for example, the U.S. Army Corps of Engineers, the Department of the Interior’s USGS, the Illinois Department of Natural Resources, and the U.S. Fish and Wildlife Service. Approximately $78.5 million has been devoted to prevention of bigheaded carp establishment in the Great Lakes by the federal government (U.S. Fish and Wildlife Service, 2012). The question of whether these funds will be exactly enough to conserve and protect the metapopulations within Lake Michigan is beyond the scope of this analysis, though it points to a more generalizable question that this analysis does seek to answer – can oversimplification of assumptions regarding human interactions, species interactions, and space lead to biased or incomplete assessments of economic damages or social welfare?

A spatial bioeconomic model is developed herein for three purposes: to determine whether there will be social welfare costs associated with a bigheaded carp invasion, to address the importance of including interspecies interactions and spatial characteristics in the assessment, and to demonstrate possible failures in policy implementation from simplifications. Social welfare in this model is a measurement of consumer wellbeing; it determines the amount that consumers would need to be compensated to make up for lost wellbeing from the ecological and economic consequences of the invasion. The model is parameterized to a set of representative fishermen in the Lake Michigan regional economy, who make fishing decisions based on their location in space and the composition of fish species in each location under non-invasion and invasion scenarios. The ecological data – type and abundance of fish species by location – is the output of two different ecological modeling approaches. The first is a simplified model that includes spatial characteristics but excludes species interactions and the second is a complex ecological model that includes layers of interactions between species and space: the Atlantis Ecosystem model (Fulton et al., 2011). An aggregation over locations is performed to demonstrate implications of treating locations as spatially homogenous in their ecological characteristics. Total social welfare consequences from the invasion are calculated from the changes in recreational fishing behavior and are compared across four ecological model specifications. The final comparative case evaluates a hypothetical policy designed to establish a single protected area under each of the ecological specifications.

Modeling the interactions of multiple species across a spatially heterogenous landscape in economic models of decision making is a relatively recent advancement in the economic literature. Prior to seminal works of Albers (1996); Brown and Roughgarden (1997), and Sanchirico and Wilen (1999) economists were in the habit of aggregating “spatially disperse data causing artificially sharp intraregional distinctions and unrealistic interregional uniformity” (Bockstael, 1996). Now many bioeconomic studies focus on metapopulations and space (e.g., Costello and Polasky, 2008; Albers et al., 2010; Sanchirico et al., 2010; Epanchin-Niell and Wilen, 2012; Aadland et al., 2015) by taking exceptional care to include the complexities of relationships between species and space. Yet, as the complexity of spatial problems evolve, so too do the computational costs and data demands. Data can be difficult to find or access, reigniting the question among researchers as to whether richer spatial and ecological details are necessary to generate useful results, or if simplifying assumptions (often aggregation over space or species) are sufficient. The analysis herein lends support to the continual inclusion of key interactions and characteristics in bioeconomic models.

The results of the comparative analysis across ecological specifications demonstrate that aggregation or oversimplification of the ecological system may bias estimates associated with welfare and, thereby, lead to improper investment in policy. For this case study, the aggregation over space does not generate significantly different social welfare outcomes. Conversely, the simplifying assumptions related to species interactions leads to markedly different outcomes. Without interactions, the social welfare losses are an order of magnitude less than the social welfare losses with full species interactions. Further, the designation of a protected area for the hypothetical policy analysis differs across ecological specifications and is biased under the specifications with homogenous spatial characteristics, confirming that spillovers of simplifying assumptions have consequences for effective policy.

In the “Materials and Methods” section, the theoretical models are developed, and the data, calibration, and simulation methods are described. It is followed by the “Results” section, presenting the results of the comparative analysis, and the “Discussion” section, synthesizing the implications of the analysis, and the “Conclusion” section, discussing and defining calls for further research.

The full bioeconomic model is constructed to estimate wellbeing and to capture decision making processes of representative recreational fishermen, both of which depend on space, ecology, and economic tradeoffs. More specifically, representative fishermen chose which zones of Lake Michigan to fish in, how much to fish, which species to fish for, and how much to consume of all other goods given a set budget for spending and differential prices associated with species, consumption goods, fishing goods, and travel. These decisions depend on the ecological characteristics of the zones – types of sportfishing species and their abundance – and how those characteristics change if there is an invasion of bigheaded carp.

The lake is split into five ecologically differentiated zones (Figure 1) – zone 1 (southern Green Bay), zone 2 (northern Green Bay and Northern Lake Michigan), zone 3 (northwest Lake Michigan), zone 4 (southwest Lake Michigan), and zone 5 (southeast Lake Michigan) – following the ecological classifications of Riseng et al. (2017) and the Level III Omernick classification of adjacency (EPA NHEERL, 2003). Riseng et al. (2017) use five variables to represent four classification factors: bathymetry, thermal regime, mechanical energy associated with water motion, and tributary influence and identified 77 aquatic ecological units across the entire Great Lakes, which provided a geospatial accounting framework for research and resources management.

Altogether, the bioeconomic model is built by linking an economic decision model with an ecological model that generates species biomass data for both an invasion of bigheaded carp setting, and a non-invasion setting (Figure 2) for nine sportfishing species. Discussed in the remainder of this section are the theoretical economic and ecological models that when combined form the bioeconomic model, which is calibrated using ecological and economic data. The simulation process is defined following the description of the data and calibration.

This section presents the results of the comparative analyses with respect to species interactions, spatial characteristics, fisherman responsiveness and preferences, and policy assessments. Given the large volume of information across many different dimensions, a set of select species, zones, and economic outcomes are displayed in tables and figures in the main body to support the underlying result, all other figures or relevance are included in the Supplementary Material.

There are two main drivers of the difference between the social welfare estimates when comparing the ecological specifications using the Atlantis model (with layers of species interactions) and the non-Atlantis model (without species interactions). First, the specifications that use the Atlantis model have a wider distribution of possible species biomass outcomes from the invasion because there are compounding or competing bigheaded carp effects for each species and dynamic interactions between species. Throughout the time frame of the invasion, most of the species experience at least some oscillations between periods of growth and decline. However, on net nearly all sportfishing species are negatively impacted by the Asian carp invasion. The magnitude of the implications differ depending on the ecological food web interactions. For fish species that spawn nearshore (i.e., lake whitefish, walleye, and yellow perch), the decreases in population biomass are significant and driven by direct food competition between bigheaded carp and larval fish of these species. Rainbow smelt are also significantly impacted by the invasion, because both they and bigheaded carp feed on zooplankters, compete for food, and share predations. Conversely, piscivorous fish species, such as burbot, Chinook salmon, Coho salmon, lake trout, and steelhead, are negatively impacted less across the time frame. Though the larval fish of these piscivorous species have minor food competition with bigheaded carp, this competition is offset by the fact that bigheaded carp become an extra food source for these species. This offsetting effect is dependent on the growth of the bigheaded carp, which in this simulation is slow due to food limitations and thus it took bigheaded carp longer to outgrow predators’ gape sizes.

Without these interactions, the non-Atlantis model predicts that each species either converges to a lower (or higher) steady state that simply depends on the magnitude of the bigheaded carp impact and whether the species is negatively (or positively) impacted (Figures 3, 7). Second, the magnitude of the ecological implications on each species are starkly different across settings. In the non-Atlantis setting, the bigheaded carp effects are rather small, so the changes in species biomass are also small (e.g., Figure 3, bottom panel), whereas the variation in impacts can be almost 20 times larger (e.g., Figure 3, rainbow smelt) when using the Atlantis model. Further, the biomass values from the bigheaded carp invasion differ greatly for species that hold high value to the fishermen across Atlantis and non-Atlantis specifications (e.g., Coho salmon, Chinook salmon, and steelhead). The representative fishermen cannot substitute as easily to the higher valued species in the Atlantis specifications because of the significant invasion implications on all the other species as well. In the non-Atlantis specification, however, the representative fishermen can make more tradeoffs because there are some species that increase in population biomass as a result of the invasion; the representative fisherman are able to use what they save on those species and spend it on the others.

In comparing spatially heterogenous zones to spatially homogenous zones, the results are understated when using the non-Atlantis model and overstated when using the Atlantis model. This is somewhat surprising as one might expect a similar aggregation to result in similar directions of divergence – either both overstated or both understated¹⁰. Note, however, that in making the assumption that all zones are the same ecologically some species will be present in zones where they would ecologically not exist in any significant volume of biomass (e.g., steelhead in zone 1). An implication of erroneous existence is overstated benefits associated with “greater” abundance of the species. If these existence benefits outweigh the aggregate costs of the invasion, the welfare losses will be understated and vice versa. For this specific analysis, when using the Atlantis model, the negative impacts of the bigheaded carp exacerbate the poor ecological condition in the zones and outweigh the benefit of additional existence. The reverse is true for the non-Atlantis specification. Although the differences in welfare estimates are small and the results of neither the Atlantis model, nor the non-Atlantis model are not significantly different in terms of the biomass for many species across space, the difference in social welfare calculations is a direct bias from aggregating and then assuming the average (Figure 7), implying that modeling the spatial ecological characteristics is important. In this specific analysis, the similarities across zones is caused by a lack of zone-specific spatial data for the non-Atlantis model, and by a predefined seasonal spatial distribution of fish species across zones that aggregates and redistributes species based on a set proportion over four seasons for the Atlantis model. Therefore, though the Atlantis model has different absolute biomass values for both bigheaded carp and the fishery species, based on the different productivities and food web interactions in the nearshore and offshore for each zone, the percent changes across the different zones will be similar.

When adapting how easy or difficult it is for the representative fishermen to substitute between species when responding to the invasion, the results are straightforward for most specifications: making it harder (or easier) to substitute makes fishermen worse off (or better off). The exception is for the non-Atlantis, spatially homogenous zones specification (Figure 6, right panel). The main question behind the result becomes, why would constraining substitution make the fishermen better off? The answer is in how social welfare is measured; the social welfare losses are calculated by comparing social wellbeing in the good state (i.e., the non-invasion state) to social wellbeing in the bad state (i.e., the invasion state), which is a relative measure that compares how different the values are. Being able to substitute less does in fact generate lower absolute levels of social welfare in both the non-invasion and invasion states, such that fishermen are in fact worse-off. But because the invasion effects are less severe when the non-Atlantis model is used and the zones are spatially homogenous, the relative difference between the levels of wellbeing in the two states is smaller.

The final point of discussion relates to the simplified and synthetic policy analysis, which considers designating one zone as a protected area that is not impacted from the bigheaded carp invasion. When the zones are treated as spatially homogenous – regardless of whether the Atlantis or non-Atlantis model is used – the model-suggested protected area is zone 4. Because the ecological characteristics are the same across zones, the ecological benefit (or value) of making any zone a protected area should, all else equal, be the same. However, the tradeoff between the ecological quality and the costs of traveling and purchases of quality-enhancing inputs – which are not aggregated – influence this result (Supplementary Table 1). Zone 4 is on average the costliest zone to travel to in terms of distance costs, and by making it the protected area the fishermen can tradeoff higher levels of quality for fewer trips; it becomes comparatively less expensive and generates the greatest benefit in terms of social welfare. This result, though, is biased due to the spatial homogeneity assumption and the issue of species having populations in zones where they ecologically are not well-established. For example, Chinook salmon do not have a well-established biomass in zone 4, yet the assumption that all zones are ecologically homogenous incorrectly assumes that Chinook salmon are established in the zone and overstates the benefits of making zone 4 a protected area (e.g., Supplementary Figure 9), especially in this instance because fishermen assign the highest willingness to pay values to Chinook salmon.

This bias is corrected to some extent when the zones account for spatial heterogeneity, but even still the designated protected area is different across the Atlantis and non-Atlantis models. The best zone to designate as a protected area is zone 3 under the Atlantis model specification. Zone 3 is one of the more ecologically diverse zones (i.e., all sportfishing species are established there) and one of the most impacted zones by the invasion in terms of increased costs of fishing (Figure 4, right column)¹¹. It is also one of the least costly to travel to, which altogether makes it the zone that creates the greatest value to the fishermen as a protected area in terms of bang for the buck. Using the more simplified, non-Atlantis model and maintaining spatial heterogeneity in zones, the best protected area designation is zone 1; under this specification, the population biomass implications are more negatively impacted by the bigheaded carp invasion as compared to the other zones (Figure 7).

The bioeconomic model presented in this paper assesses the potential social welfare losses associated with a bigheaded carp invasion and illustrates the biases that might result in those estimates if spatial characteristics or species-interactions are aggregated or excluded from the model and the implications of those biases on designing policy. Several key characteristics drive the results: the composition of the species in each lake zone, the relative economic importance or value of the species, and the compounding or competing effects of the interactions in levels of species biomass. When full ecological system and food web interactions are accounted for under the Atlantis model specification, the welfare losses are an order of magnitude larger than when the interactions are excluded in the non-Atlantis specification. This has important implications for policy. When using the social welfare estimates as a guide for how much or whether to invest in mitigation or conservation of metapopulations, incorrect estimates could lead to significant underfunding or overfunding by tens of millions of dollars. Further errors in policymaking were demonstrated through the simplified policy analysis, in which a designated protected area – lake zone – was selected based on the criteria of which zone reduced social welfare losses the most. When aggregating out spatially explicit ecological characteristics and treating all zones as spatially homogenous, the selection of the protected area was inherently biased. Though this bias is clear from this analysis because of the nature of the simplifying assumptions, the result tells a cautionary tale regarding aggregation and homogeneity assumptions. Altogether, the analysis reinforces the importance of including relevant species specifics and spatially explicit characteristics and supports the adage that the devil is in the details (e.g., Finnoff et al., 2005, 2019; Settle and Shogren, 2006; Wainger et al., 2010).

There are some caveats, which serve as motivation for future work. First, it is not clear that excluding species interactions – using the non-Atlantis model – will always understate the welfare outcome. Here, the effect of bigheaded carp on sportfishing species appears relatively minor (Zhang et al., 2016), but had the impact been much more severe, the results of the two ecological approaches could be starkly different. The simpler non-Atlantis model may predict species extinction while the more complex Atlantis model may show some attenuation of the impacts, further justifying the need to consider the spatial ecology surrounding the metapopulation. Similarly, the results across ecological regions may be much more distinct than those predicted by the Atlantis and non-Atlantis models. Because of data constraints and predefined seasonal distributions of fish data that is always proportional to the total population for the zones, the spatial implications across zones were very similar in this analysis, which leads to the next point. The model assumptions are not innocuous and should be thoughtfully considered, especially at the point of connection between the economic and ecological systems. There were further limitations on the availability of data, specifically related to fishing behavior. As a consideration for future research, data on differences in fishing behavior across representative fishermen and zones would improve the accuracy of welfare estimates. In addition, this analysis considers the implications of the invasion primarily on recreational fisherman, yet invasive species often impact additional segments of society (e.g., infrastructure, commercial fishing industries, transportation industries, labor markets and employment, or trade relationships). To understand full society-wide implications of the invasion, a complete economic model of the regional economy – firms, governments, trade, all consumer types, and market linkages – should be considered in general equilibrium setting.

Finally, from this analysis, a major underlying result is that a bigheaded carp invasion is likely to lead to social welfare loss. Regardless of whether the Atlantis or non-Atlantis model is used, most sportfishing species are on net negatively impacted by the invasion which increases the costs of fishing for each species across all zones for each recreational fisherman. The fishermen respond by reducing trips, quality purchases, and fishing across all zones due to budget limitations, and it is these lost fishing experiences that generate the social welfare losses. Therefore, the natural next step is to expand on this framework to address the above caveats and to begin assessing the ecological and economic efficacy of policy options being currently considered, rather than the synthetic and simplified analysis used herein for demonstrative purposes. The current policy recommendations, which are outside the scope of this analysis, include: (1) stocking economically important species that are impacted by the invasion to mitigate the effects of the invasion (Kao et al., 2018), (2) constructing barriers to keep bigheaded carp out of the lake (U.S. Geological Services, 2018; U.S. Army Corps of Engineers, 2019) or (3) developing a for profit market for bigheaded carp through commercial fishing or recreational tournaments (Illinois Department of Natural Resources, 2021; Kentucky Department of Fish and Wildlife Resources, 2021). Using a more comprehensive model to assess these policies would illustrate how the full economy would respond and if social welfare losses would indeed improve.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

SB developed the economic model and simplified ecological model, calibrated the bioeconomic model, wrote the first draft of the manuscript, designed the comparative analysis, and generated figures and tables. HZ, DM, and ER collected the data used for the ecological models, developed and calibrated the Atlantis ecosystem model, and supplied the parameters for the simplified ecosystem model. HZ wrote on the ecological and spatial details of the invasion, the ecological Atlantis model section, and the Atlantis results. DM and ER provided feedback, clarifications, and edited and revised the latest manuscript. All authors contributed to the article and approved the submitted version.

HZ was employed by the company Eureka Aquatic Research, LLC. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.