Demographic Rate Variability of Bighead and Silver Carps Along an Invasion Gradient

Within invasion ecology, managers and researchers have recognized that demographic rates, such as growth and mortality, can vary temporally during invasion and spatially from the invasion front (i.e., subpopulations on the leading edge of the invasion range) to more established, colonized subpopulations (i.e., subpopulations behind the invasion front; Rice et al. 2013). For invasive fishes, spatial and temporal changes in demographic rates may influence invasion success and have been observed across a range of invasive species. For example, the demographic rates of Vendace, Coregonus albula, invading the subarctic Pasvik watercourse changed spatially within the invasion range as density increased and the species changed from being a pioneer species to an established species at different locations (Bøhn et al. 2004). Likewise, the demographic rates of Pumpkinseed Lepomis gibbosus varied spatially indicating that subpopulations invading the Iberian Peninsula were more “opportunistic” in their life-history strategy compared with subpopulations in its native range (Fox et al. 2007). Other examples have included the Round Goby Neogobius melanostomus invading the Upper Detroit River, which had decreased generation time compared with subpopulations in their native range in Europe (MacInnis and Corkum 2000) and in the Trent River, where Round Goby exhibited variable demographic rates across different spatial subpopulations within the river (Gutowsky and Fox 2012).

Invasive species demographic rates can change because of phenotypic plasticity in response to intraspecific and environmental conditions (e.g., lower population densities at the invasion front; different habitat conditions), hybridization (Lamer et al. 2019), and genetic bottlenecks (Rice et al. 2013). Understanding spatial heterogeneity in growth, body condition, and length-at-maturity across a species' invaded range provides crucial knowledge for informing management actions even if the mechanism(s) remain unknown. Specifically, management strategies may differ if demographic rates vary across an invasion front and among habitats. For example, growth rates affect the time required for individuals to become vulnerable to size-selective removal efforts, sexual maturation (and generation time), and natural mortality rates (Then et al. 2016).

Different demographic rates may change predicted harvest levels required to reduce and control nonnative species (Tsehaye et al. 2013). Besides growth, spatial heterogeneity in mortality, body condition, and length-at-maturity serve as the basis for determining additive mortality requirements for successful control efforts. Bighead Carp Hypophthalmichthys nobilis and Silver Carp H. molitrix are collectively are referred to as Bigheaded Carp (Garvey 2012), both exist in subpopulations within the Mississippi River Basin. Management may require different control strategies if demographic rates vary across these areas. Bighead and Silver Carp management in the Mississippi River Basin focuses on outreach, prevention, detection, and control with the ultimate goal of preventing invasion into the Laurentian Great Lakes (ACRCC 2018, 2020). Furthermore, population-level models that guide control efforts require demographic rates for model parameterization. Hence, testing for spatial differences in demographic rates may indicate whether subpopulations require different control strategies (Pawson and Jennings 1996; Begg et al. 1999; McBride et al. 2014).

A commercial fish producer in Arkansas imported Bighead and Silver Carp to the United States in 1973, which escaped into downriver portions of the Mississippi River by 1975 (see Kelly et al. 2011 for discussion of the invasion). Both species then spread upriver to other portions of the basin including the Illinois and Ohio rivers (Kolar et al. 2007; Kelly et al. 2011). People first documented Bighead Carp in the Upper Mississippi River Basin in 1981 (USGS Nonindigenous Aquatic Species Database, https://nas.er.usgs.gov/queries/factsheet.aspx?speciesID=549 [February 2021]) and Silver Carp in 1983 (USGS Nonindigenous Aquatic Species Database, https://nas.er.usgs.gov/queries/FactSheet.aspx?speciesID=551 [February 2021]). Bighead and Silver Carp adversely influenced the Upper Mississippi River Basin ecosystems by outcompeting native species, altering habitats, and decreasing water quality (e.g., Irons et al. 2007; Kolar et al. 2007; Sass et al. 2014; DeBoer et al. 2018). Bighead and Silver Carp also negatively affect the economy by decreasing native fisheries and waterfowl production and startled, jumping Silver Carp present a safety hazard to river users (e.g., Irons et al. 2007; Buck et al. 2010; Solomon et al. 2016; Pendleton et al. 2017). Lastly, concern exists if Bighead and Silver Carp enter the Laurentian Great Lakes in that the carps will cause ecological and economic disruptions (Cooke and Hill 2010; Moy et al. 2011; Rasmussen et al. 2011; Roth et al. 2012; Sass et al. 2014).

Environmental conditions (e.g., productivity, habitat availability, intra- and interspecific competition) vary across the Bighead and Silver Carps' invaded range, creating the potential for spatial heterogeneity in demographic rates. Others documented spatial heterogeneity in demographic rates (e.g., growth, survival, immigration) for a wide range of species (e.g., Midway et al. 2015; Seibert et al. 2017) including Bighead and Silver Carp in North America (Hayer et al. 2014; Coulter et al. 2018a; Sullivan et al. 2018). Consequently, we sought to estimate and compare demographic rates of Bighead and Silver Carp across a broad geographic area in the Upper Mississippi River Basin using all data available. Our data set included individual information from fish captured in pools of the Illinois, Ohio, and Mississippi rivers during 1997 to 2018. Specifically, we sought to test whether demographic rates differed across the invasion gradient and among river systems and subpopulations.

We tested for differences in spatial demographic rates to inform management decisions. First, Tsehaye et al. (2013) presented a spatially homogenous population-level model in the Illinois River. We sought to test this assumption of no spatial heterogeneity. Second, managers may tailor their actions based upon demographic rates given invasion status (e.g., colonized versus invasion front) and environmental conditions (e.g., productivity of invaded pool). We also used our results to create hypotheses for future investigation regarding plausible mechanisms for observed differences (e.g., does productivity or potential competition explain differences observed among subpopulations?) and the importance of sampling methods on observations and inferences (e.g., do differences in aging techniques affect estimates?). To accomplish our objectives, we estimated von Bertalanffy growth curves to obtain growth coefficients and mortality rates, used logistic curves to obtain the probability of female maturity, and examined length–weight relations to obtain body condition.

The Illinois and Ohio rivers flow into the Mississippi River (Figure 1). The Illinois River, about 439 km long, maintains an artificial connection to the Laurentian Great Lakes Basin through the Chicago Sanitary and Ship Canal (Lian et al. 2011). The Ohio River is about 1,578 km long (Wallus and Simon 2005). Lock and dams and drainage and levee districts alter all three rivers' flow and ecology (Benke and Cushing 2011; Lian et al. 2011). The locks and dams create a series of pools in each river, fragmenting fish subpopulations through physical barriers, as well as changing the hydrology, physiochemical properties, and aquatic vegetation of each pool (Lian et al. 2011). Reforms following The Clean Water Act's enaction improved water quality in these systems by stopping raw sewage from being pumped into these systems (McClelland et al. 2012). These anthropogenic alterations have changed the fish population sizes and aquatic communities (e.g., Koel and Sparks 2002; McClelland et al. 2012; Sass et al. 2014) and are important considerations for fisheries management (Garvey et al. 2010).

Pools in these rivers exhibit different characteristics including their stages of invasion, potentially leading to different demographic rates for Bighead and Silver Carp. For example, different pools contain varying biological attributes and lock-and-dam structures. Within the Illinois River, the Starved Rock Lock and Dam near Oglesby, Illinois, separates the Lower and Upper Illinois River. Each segment possesses different river attributes and Bighead and Silver Carp subpopulations. The lower and longer three pools—Alton, La Grange, and Peoria (each about 130 river km long)—comprise the Lower Illinois River. These pools contain high densities of Bighead and Silver Carp, as well as an abundance of connected backwater lakes, allowing for recruitment to occur within them (Garvey et al. 2007; Sass et al. 2010; McClelland et al. 2012). Wicket dams separate the Lower Illinois River pools, allowing carps movement between pools during high flow (Koel and Sparks 2002; Coulter et al. 2018a).

The shorter, upper three pools—Starved Rock, Marseilles, and Dresden (lengths ranging from 23 to 40 river km)—comprise the Upper Illinois River. These pools lack the abundant, connected backwaters found in the Lower Illinois River and recruitment does not appear to be occurring in these pools (McClelland et al. 2012). Bighead and Silver Carp appear to be maintained in the Upper Illinois River via immigration from the Lower Illinois River (McClelland et al. 2012; Sass et al. 2014; Coulter et al. 2018a). High-head dams separate the pools of the Upper Illinois River, thereby decreasing subpopulation connectivity among the pools compared with the Lower Illinois River (Koel and Sparks 2002; Coulter et al. 2018b). Bighead and Silver Carp contract fishing also occurs within the three upper pools to reduce the risk of range expansion into the Laurentian Great Lakes Basin (Tsehaye et al. 2013; MacNamara et al. 2016; MRWG 2017b).

Environmental and anthropogenic conditions also cause Ohio River pools to have different habitats and Bighead and Silver Carp abundances (Thomas et al. 2005). High-head lock and dams replaced a series of wicket dams and changed the fish communities in the Ohio River (Thomas et al. 2005; Freedman et al. 2014) and restricted fish movements among pools (Bailey et al. 2003). Our Ohio River study area only contained high-head locks and dams. Bighead and Silver Carp recruitment in the Ohio River appears to be limited to major tributaries because of a paucity of backwater habitats based upon otolith microchemistry (Schiller 2018).

Similar lock-and-dam complexes exist for pools on the main stem of the Upper Mississippi River except for Pool 27, which is also known as the Chain of Rocks. The lock-and-dam complexes exist on the downriver end of most pools. The Pool 27 lock-and-dam complex differs because the lock does not directly attach to the dam. Instead, the lock exists on the Chain of Rocks Canal, where a low-head dam with no gates exists on the Mississippi River (U.S. Army Corps of Engineers, [date unknown]). The other pools in our study area (16, 17, 18, 19, 20, 22, 24, and 26) differ from Pool 27 in length (>37 river km compared with 25 river km for Pool 27) and have documented Bighead and Silver Carp reproduction or recruitment (Lohmeyer and Garvey 2009; Norman and Whitledge 2015; Whitledge et al. 2019; Camacho et al. 2020). Generally, the pools of the Upper Mississippi River connect with backwaters, providing Bighead and Silver Carp with juvenile nursery habitat (Kolar et al. 2007). Contract fishing (typically by trammel-netting) primarily occurs in pools above Lock and Dam 19, primarily in pools 17, 18, and 19, to reduce Bighead and Silver Carp abundance and slow and limit the spread to upstream pools.

We treated each pool as a subpopulation based upon environmental conditions and resource management for our analyses. Environmentally, wicket dams or locks and dams generally fragment pools. The pools also exhibit different characteristics (e.g., unique habitat types, productivities, lock-and-dam structures, hydrology, and connectivity to other pools), which may cause potential differences in Bighead and Silver Carp demographic rates. From a control perspective, monitoring and management actions usually focus on individual pools and management actions may be dictated by interstate agencies in the case of the Mississippi and Ohio rivers. Additionally, the locks and dams between pools may be used as part of barrier systems to deter subpopulation movement between pools.

We used data from research studies, management activities, and monitoring programs to test for spatial patterns in invasive Bighead and Silver Carp demographic rates (i.e., growth, maturity, body condition, mortality) among pools of the Mississippi River Basin and across a gradient of invasion status. Our data set included 42,995 fish from 23 pools throughout the Mississippi River Basin—including the Upper Mississippi, Illinois, and Ohio rivers—collected using a variety of gear types, including boat electrofishing, fyke nets, trammel nets, and gillnets during 1997–2018 (Figure 2). Data sources included fisheries-independent and fisheries-dependent sources from experimental and observational studies conducted by universities, federal and state agencies, and contract commercial fishers (Table 1; Figure 1).

Observers recorded individual fish total length (TL; measured in mm) and weight (measured in g) for all captures. Some observers recorded fish age, sex, and maturation. Observers estimated fish age in whole years using Lapilli otoliths, pectoral fin rays, and postclitherum (Seibert and Phelps 2013). We converted fish age in whole years to fractional age by adding the difference between the birth month and capture month then divided by 12. We assumed all fish had a May birth month because Bighead and Silver Carp spawning generally begins during this month within the Upper Mississippi River (Coulter et al. 2016; Camacho et al. 2020). Observers determined female maturity status using visual macroscopic inspection of the ovaries similar to Hintz et al. (2017), or when available, the gonadosomatic index described in Lamer et al. (2019). Specifically, observers considered females mature if gonadosomatic index exceeded 10% of body mass, following Tsehaye et al. (2013) for data collected during May to August because gonads become small in winter, making maturation determination difficult.

We enumerated the total fish collected using different gears (e.g., nets, electrofishing) and collection types (i.e., fisheries-independent, fisheries-dependent data) prior to analysis. We also calculated the sex ratios for Bighead and Silver Carp. Additionally, we assessed the effects of gear and collection type on fish length and age by visual inspection of plots and linear models (Supplement S1, Supplemental Material). We used these results to inform our hierarchical modeling choices.

We modeled growth, mortality, body condition, and female maturity with hierarchical models (or, synonymously, multilevel models; see chapter 1 of Gelman and Hill (2007) for a discussion of terminology). Royle and Dorazio (2008; see chapter 1) described multiple definitions of “hierarchical modeling” including statistical hierarchies (defined as the nesting of one distribution within a second distribution or mathematical mapping of one distribution to another) and scientific hierarchies (e.g., individual fish nested within pools). Our modeling approach encompasses both definitions. For example, we estimated growth curves for each pool as well as an “average” growth curve based on the growth curves from each pool. The resulting multipool parameters would be hierarchical parameters (or synonymously, hyperparameters).

The use of hierarchical models and their associated hyperparameters provide modeling benefits. First, information can be quantitatively shared across river pools and modeled as knowledge about the system (Tsehaye et al. 2013, 2016). Second, pools with few observations can be modeled drawing information from other pools. Third, the hyperparameters can be used to create predictions for pools without fish observations. We used the results of our hierarchical models to compare demographic rates among rivers and pools within rivers for each species. We did this by examining the 80% and 95% credible intervals (CrIs) from the posterior distribution of the estimated parameter values (Gelman et al. 2013).

We used a hierarchical linear regression for each species to estimate the relation between log₁₀ (length in m) and log₁₀ (weight in kg) as a proxy for body condition. We used log transformations to make the relation linear, a common transformation for fisheries analyses of length–weight data (Ogle 2016). We selected these metric units to improve numerical stability. Increasing numerical stability increases an algorithm's ability to converge to a consistent stationary distribution (Stan Development Team 2020). Numerical stability may also be thought of as the ability of the software to consistently and correctly estimate parameter values and their corresponding distributions.

Conceptually, we fit a regression to the regression coefficients, or synonymously hierarchical modeling. We did not include sex-specific coefficients because no meaningful difference in the length–weight relations were found between sexes during model development (Supplement S1, Supplemental Material). We used the default Stan prior for this model (Stan Development Team 2020). We used this model to compare body condition across rivers and among pools.

We fit a hierarchical logistic regression to model length and the probability of female maturity in each pool for each species. We formulated the model similar to the hierarchical logistic model, but used a logit link function as described in the fishStan documentation (Erickson 2020). We had data from enough pools to estimate curves for multiple pools, but did not have enough pools to estimate river-level parameters. We used the default Stan priors for the model other than for the hyperparameter where a Normal([8, 10], 5) prior was used (Stan Development Team 2020). The nonzero priors followed the guidance of Gelman and Hill (2007) and Gelman et al. (2013) and were necessary for the hyperparameter because these estimates were far from zero and there were few pools to inform the estimation process.

We did not include a length at age zero parameter, t₀, because we were interested in using this parameterization in a population-level model that assumed t₀ was zero. We based our priors upon the Stan manual's suggestions for numerical stability (Stan Development Team 2020) and the FishBase entries for Bighead Carp and Silver (Froese and Pauly 2021). We fit six hierarchical von Bertalanffy growth models, specifically, a model for each of the two species in three river systems. We used subpopulations within each river as a grouping variable. We used this model to compare mortality rates and the von Bertalanffy growth relations across rivers, between species, and among pools. During initial model development, we explored fitting models for each sex, but the parameter estimates did not indicate sexually dimorphic growth.

We used Program R version 4.0.2 for our analyses (R Core Team 2020) including the fishStan version 1.0 package (Erickson 2020) to fit the three models. The fishStan package uses the Stan language (Gelman et al. 2015) as called through the RStan package version 2.21. We ran 5,000 warmup and 5,000 sampling iterations to ensure numerical convergence, which was checked using diagnostics and traceplots (Gelman and Rubin 1992; Gelman et al. 2015). We used the tidyverse version 1.3.0 to manipulate data, including ggplot2 version 3.2.1 for plotting results (Wickham 2009; Wickham et al. 2019). We have released our data (Erickson et al. 2021) and code (Erickson and Kallis 2021).

We used 42,995 fish in these analyses, including 10,444 Bighead Carp and 32,551 Silver Carp. Collection types differed by river (Figure 2), but these methods generally caught similar length fish (Supplement S1, Supplemental Material). Observed fish lengths were similar when collected using the same methods within each pool for each species (Supplement S1, Supplemental Material). Likewise, we estimated similar lengths for fish collected from commercial and noncommercial harvest (e.g., commercial netting and noncommercial netting caught similar length fish; Supplement S1, Supplemental Material). Observers did not record the sex for most Bighead Carp (7,632, 73.1%). Observers recorded sex for more female Bighead Carp (1,464, 52.1%) than males (1,346 47.9%). Observers classified few Bighead Carp as immature as a result of difficulties of sexing immature fish (44, 0.4%). Observers did not record sex for many Silver Carp (14,996; 46.1%), and of the fish with sex recorded (17,529), observers captured slightly fewer females (8,411, 48.0%) than males (9,118, 52.0%). Observers classified few Silver Carp as immature as a result of difficulties of sexing immature fish (214, 0.2%). Bighead Carp females were 37 mm longer than males on average (95% confidence interval [CI] = 27–48 mm) and 144 mm longer, on average, than unknown sex fish (95% CI = 106–182 mm; Supplement S1: Figure S7, Supplemental Material). Likewise, female Silver Carp were 23 mm longer, on average, than males (95% CI = 16–29 mm) and 287 mm longer, on average, than unknown sex fish (95% CI = 278–296 mm; Supplement S1: Figure S7, Supplemental Material).

We estimated similar body condition for both species in the Mississippi and Ohio rivers using length–weight relations estimated for subpopulations in 23 pools; however, we estimated body condition differences among subpopulations of Bighead Carp in the Illinois River (Supplement S2: Figure S3, Supplemental Material). We estimated similar site-specific intercept parameters (γ-level parameters) across the three river systems for both species (all coefficients ranged from 1.00 to 1.07 and included overlapping 95% CrI; Supplement S2: Figures, Supplemental Material). This similarity indicates the slope (condition) estimates may be compared with each other. The site-specific slope (i.e., condition) parameters were generally similar, but included one noteworthy difference. The Bighead and Silver Carp slopes overlapped for the Ohio River (Bighead Carp 2.89, 95% CrI = 2.56–3.23; Silver Carp 3.02, 95% CrI = 2.79–3.25) and the Mississippi River (Bighead Carp 2.98, 95% CrI = 2.82–3.13; Silver Carp 3.00, 95% CrI = 2.86–3.09). The slope for the Illinois River Silver Carp estimate (2.89, 95 CrI = 2.71–3.01) also overlapped the estimates from the other rivers. The slope estimate for Illinois River Bighead Carp (2.62, 95% CrI = 2.44–2.80) did not overlap with the estimates from the other rivers.

Trends emerged within rivers at the pool-level (or β-level coefficients), (Supplement S2: Figures, Supplemental Material). The Illinois River pool-specific intercepts had tight CrIs for both species. Silver Carp intercept estimates were >1.05 in the upper pools (i.e., Starved Rock, Marseilles, Dresden Island) and <1.05 in the lower pools (i.e., Alton, LaGrange, Peoria). A similar pattern was found for Bighead Carp, with one exception—the Starved Rock Pool was among the pools with intercept estimates <1.05. The slope estimates of Silver Carp in the Illinois River, other than Dresden Island, were >3.0 and did not include 3.0 in the 95% CrI. Estimates for Dresden Island Pool included 3.0 in the 95% and 80% CrI. The value of 3.0 is noteworthy because a value of 3 corresponds to isometric growth, a value >3 corresponds to positive allometry, and a value <3 corresponds to negative allometry (Pope and Kruse 2007). The Bighead Carp slope estimates in the Illinois River were >3.25 in the upper two pools and the lower four pools were all <3.25, with two pools <2.8.

The Mississippi River's slope estimates revealed no spatial patterns for either species. Groups emerged for the pool-specific intercepts for both species with the upper three pools (Pools 19 to 16) and Pools 22 and 24 (which only had Silver Carp data) having similar intercepts ranging from 1.05 to 1.10. The other three pools (Pool 20, 26, and 27) all had similar intercepts ranging from 0.94 to 1.00. The Ohio River showed a large amount of uncertainty around almost all slope estimates for both species and no patterns emerged. The intercept estimates for Bighead Carp contained a large amount of uncertainty. The intercept estimates for Silver Carp generally showed a decreasing gradient with the downriver pools having lower intercept estimates. The three lower pools all had similar intercepts (JT Myers 0.99, 95% CrI = 0.92–1.06; Newburgh 1.00, 95% CrI = 0.97–1.04; and Cannelton 1.00, 95% CrI = 0.996–1.01) with intercepts increasing upriver. McAlpine had an estimate of 1.04 (95% CrI = 1.02–1.05) and Markland had an estimate of 1.08 (95% CrI = 1.05–1.11). Overall, length–weight relations were generally similar within river systems (Figure 3; Supplement S2: Figures S3 and S4, Supplemental Material).

We estimated maturity curves for subpopulations in five pools for Bighead Carp (the La Grange, Peoria pools in the Illinois River and pools 19, 26, and 27 of the Mississippi River) and five pools for Silver Carp (the La Grange, Peoria and Alton pools of the Illinois River and pools 19 and 26 of the Mississippi River), with little difference in maturity curves observed among rivers (Figure 4; Supplement S2: Figure S5, Supplemental Material). The maturity curves' estimated hyperparameters had similar intercept estimates for Bighead Carp (−8.24, 95% CrI = −13.0 to −0.75) and Silver Carp (−7.41 95% CrI = −11.1 to −0.63). The slope estimates for the hyperparameter curves were slightly lower for Bighead Carp (18.4, 95% CrI = 12.8–24.0) than Silver Carp (25.0, 95% CrI = 18.6–29.6). More broadly, we observed similar maturity curves for each species across river systems with more uncertainty in locations with fewer observations (Supplement S2, Supplemental Material). We observed similar maturity curves for both species; however, Silver Carp reached maturity at a shorter length than Bighead Carp. For example, length at 50% maturity was 0.31 m for Silver Carp and 0.48 m for Bighead Carp.

We estimated greater asymptotic lengths (L_∞) for Bighead Carp than Silver Carp with no differences observed in Brody's growth coefficient (K) and natural mortality estimates (M) based on growth curves from subpopulations in 16 pools (Figure 5; Supplement S2, Supplemental Material. We used results from the growth curve analyses (i.e., K, L_∞) to estimate natural mortality (M). We did not have data for immature fish for the growth models (Supplement S2: Figures S13 and S14, Supplemental Material), which caused greater uncertainty around the M and K estimates compared with the L_∞ estimates (Supplement S2; Figures S9 to S11, Supplemental Material). This uncertainty can be seen in the broader width of the 95% CrIs. For example, most L_∞ had relatively narrow 95% CrI widths of <0.05. In contrast, K and M generally had larger 95% CrI widths and 13 of the 95% CrI of K and 11 of the 95% CrI for M were >0.5. Bighead Carp had higher L_∞ estimates than did Silver Carp in most pools and the 95% CrIs did not overlap within rivers (Supplement S2: Figure S9, Supplemental Material). The river-level hyperparameters also had higher estimates for Bighead Carp L_∞ than for Silver Carp, but the 95% CrIs overlapped, indicating uncertainty in the difference of these estimates (Supplement S2: Figure S9, Supplemental Material). For K and M, no general trends emerged either between species or across rivers or pools (Supplement S2: Figurers S10 and S11, Supplemental Material). In summary, we did not observe evidence of river- or pool-level effects on growth for either species with two possible exceptions. Marseilles had different growth curves estimated for each species (i.e., lower K estimates and greater L_∞ estimates than other pools in the Illinois River) and Pool 26 for Silver Carp, which also had lower K and higher L_∞ estimates than other pools in the Mississippi River. Additionally, Bighead and Silver Carp grew at similar rates (similar K estimates); however, Bighead Carp reached greater asymptotic lengths than Silver Carp (different L_∞ estimates).

Spatial differences existed across the Upper Mississippi River Basin, for some, but not all demographic rates examined for Bighead and Silver Carp. Length–weight coefficients differed the most, but some asymptotic length parameters of the growth model differed as well. The downriver pools within each river system generally had lower log₁₀–log₁₀ length–weight intercept estimates and sometimes lower log₁₀–log₁₀ length–weight slopes, which corresponded to lower body condition. The maturity curve estimates were similar across the pools included in our analysis. Asymptotic lengths (L_∞) differed across pools, while Brody's growth coefficients (K) and the L_∞ and K-based natural mortality estimates (M) were similar across pools. The hypercurve plots capture this difference because most growth curves were similar for the increasing, “growth” portion of the curves, but had wider CrIs for around the asymptotic length portion of the curves (Figure 5).

Upriver pools with presumably lower densities generally had greater Bighead and Silver Carp body condition and asymptotic lengths (Sass et al. 2014; MacNamara et al. 2016, Coulter et al. 2018c). For example, the upriver pools of the Illinois River tended to have high values for these estimates and also higher levels of contract commercial harvest (MacNamara et al. 2016). This contract commercial harvest has been documented to decrease density-dependent constraints on growth by reducing Bigheaded Carp densities temporarily and also allowing the zooplankton community to favor Bighead and Silver Carp growth and body condition (Sass et al. 2014; MacNamara et al. 2016; Zalay 2017; Coulter et al. 2018b, c). Lower densities of Bighead and Silver Carp have resulted in higher densities of more energetically favorable cladoceran and copepod prey in contrast to dominance by rotifers (Sass et al. 2014). Upriver pools in all three rivers are the leading edge of the invasion front where Bighead and Silver Carp densities tend to be lower and forage more plentiful and energetically favorable. Species composition, especially in the Illinois River, where Bighead Carp dominate in the upriver pools and Silver Carp dominate in the lower pools, may also be another contributing factor. In the Ohio River, carp have only more recently begun to infest the upriver sites at higher levels.

In contrast to the body condition and asymptotic length parameters, the maturity curves and Brody growth coefficient estimates did not vary as much across pools, suggesting that juveniles grow at similar rates across pools and likewise that fish reach maturity at similar lengths. Indeed, length is often the most important predictor of maturation status in fishes (Froese and Binohlan 2000). Therefore, density-dependent constraints on growth may be more apparent in mature Bighead and Silver Carp as a result of increased metabolic demands, energetic costs of gonad production, and changes in zooplankton community composition (Hanson et al. 1997). Asymptotic length (L_∞) in fishes is often negatively correlates with Brody's growth coefficient (K, early growth). Although K did not vary greatly across pools, asymptotic lengths may have varied as a result of contract commercial harvest in the Upper Illinois River that targets the largest individuals (Tsehaye et al. 2013), differences in river productivities, and variability in Bighead and Silver Carp densities.

Several of the aforementioned potential mechanisms for spatial differences in demographic rates could be formulated into multiple, competing, and overlapping hypotheses used to manage these species based on invasion status. One hypothesis could be habitat-related, where varying quality fish habitats and productivities across rivers and pools cause different demographic rates in the Bigheaded Carp subpopulations (Sass et al. 2017). Testing this hypothesis would require comparing different habitat and river productivity metrics and the demographic rates of the subpopulations among pools. A second hypothesis could be that different hydrological conditions across pools cause disparate demographic rates in the Bigheaded Carp subpopulations. Testing this hypothesis would require comparing different hydrological conditions and the demographic rates of the subpopulations among pools. A third hypothesis could be that contract and commercial harvest is changing the demographic rates of the subpopulations among pools. Testing this hypothesis would require comparing harvest rates and the demographic rates of subpopulations among pools. A fourth hypothesis could be that differences in invasion arrival time caused the observed patterns in demographic rates. A fifth hypothesis could be that differences in Bigheaded Carp densities cause variable demographic rates among pools. This could be related to potential intraspecific and interspecific competition (Coulter et al. 2018b, c). For example, intraspecific competition would occur as the species densities increase. Likewise, interspecific competition may occur because Bighead and Silver Carp diets overlap with other native obligate and facultative planktivorous fishes. Native planktivores with similar diets include Paddlefish Polyodon spathula, Gizzard Shad Dorosoma cepedianum, and Smallmouth Buffalo Ictiobus bubalus (Irons et al. 2007; Sampson et al. 2009). Testing this would require population-level estimates for different pools and the demographics of the subpopulations (Sass et al. 2010; MacNamara et al. 2016). A sixth hypothesis could be that hybridization is influencing demographic rates. Bighead and Silver Carp are known to hybridize in the Upper Mississippi River Basin (Lamer et al. 2015, 2019). Testing this hypothesis would require confirming hybridization through genomic methods and comparing hybridization and demographics rates among the subpopulations. Besides our proposed hypotheses, environmental conditions and the Bigheaded Carp subpopulations could change through time. These two changes are related because Bighead and Silver Carp appear to have the ability to alter their environment to benefit themselves (Williamson and Garvey 2005; Kolar et al. 2007; Sass et al. 2014). Thus, exploring whether the previously proposed hypotheses change through time is also an important consideration. A seventh hypothesis is that gear selection biases are causing observed differences (something we explored in Supplement S1, Supplemental Material). Testing this would either require detailed comparisons within our data set or collection of additional data to empirically compare these collection methods in these systems.

Heterogeneity in demographic rates among subpopulations of aquatic invasive species can also influence management decisions and control policies and options. This simply means a subpopulation in one pool may not be the same as a subpopulation in another pool and considerations such as source–sink dynamics and immigration patterns may be important. For example, commercial harvesting fish in a high-density pool might cause a release from density-dependent constraints on growth, which has been observed for Bigheaded Carp (MacNamara et al. 2016; Coulter et al. 2018b; Bouska et al. 2020). Conversely, harvesting fish in less densely populated pools may be less important if these subpopulations are truly sink subpopulations that do not contribute to the net metapopulation through natural recruitment and when recolonization rates after harvest are low (MacNamara et al. 2016). That said, proximity of low-density, sink subpopulations to ecologically and economically sensitive uninvaded habitats (e.g., Laurentian Great Lakes) and new habitats that may have conditions favorable for colonization may be an important consideration for management decisions (Rasmussen et al. 2011; Sass et al. 2014). Lastly, low density subpopulation pools might simply have low abundances because the invasive population has not yet colonized or is limited by river productivity, colonization ease (e.g., barriers), or suitable spawning habitat and juvenile nursery areas. Heterogeneity in demographic rates can also influence the methods by which managers make management and control decisions (Tsehaye et al. 2013; Bouska et al. 2020). Often, fisheries management and invasive species control efforts are informed by tools such as population-level models that make different assumptions about spatial heterogeneity and homogeneity of the population; however, our study is one of the first to explicitly address varying demographic rates among subpopulations of Bigheaded Carps across an invasion gradient and implications for management (Tsehaye et al. 2013; MacNamara et al. 2016; Bouska et al. 2020).

Although we did not explicitly investigate why these demographic rates may have differed among the Bigheaded carp subpopulations and pools in the Upper Mississippi River Basin, many known and confounding reasons exist that may be influencing these patterns. One reason might be the different flow conditions and habitats of these pools, which are known to influence Bigheaded Carp recruitment potential (DeGrandchamp et al. 2007; Camacho 2016; Sullivan et al. 2018). Another possible reason could be density-related, which may change throughout invasion history and is known to change the demographic rates of invasive species (MacInnis and Corkum 2000; Bøhn et al. 2004; Copp and Fox 2007; Fox et al. 2007; Gutowsky and Fox 2012). Additionally, commercial harvest may be reducing subpopulation abundance in certain pools (MacNamara et al. 2016; Coulter et al. 2018b; Bouska et al. 2020), which has been documented to increase zooplankton abundance, particularly for cladocerans and copepods (Sass et al. 2014; Zalay 2017). The interplay between gear and fish length was not explored as part of our study, but may have introduced spatial demographic differences given different gear selectiveness for length (e.g., electrofishing compared with nets; Ickes et al. 2012; Tsehaye et al. 2013). However, commercial compared with noncommercial harvest likely did not influence our observed patterns because commercial harvesters used nets similar to those of noncommercial collectors. Specific gear types used by commercial versus noncommercial collectors may have introduced some biases into model estimates, although our initial explorations did not suggest these were large biases (Supplement S1, Supplemental Material).

The Bighead and Silver Carp infestation in the Illinois River has been highly studied, with fewer fish collected from other more recently invaded sites such as the Ohio River. Given the extremely large number of fish used for our study, where might more data be needed? First, locations with fewer fish such as in the upstream portions of the Ohio or Mississippi rivers could use more observations. Second, more smaller fish, if present, would help to better understand and estimate growth in the subpopulations. These fish may not exist in pools without natural recruitment and suitable juvenile nursery habitat. Collecting more smaller fish would also help to better estimate mortality rates from growth curves. Likewise, these data would be enhanced by the validation of age estimation methods to address concerns such as those raised by Seibert and Phelps (2013). Despite these limitations, we used all age estimates from the three aging structures in our study because Seibert and Phelps (2013) assumed otoliths were the most accurate and precise aging structure but did not validate this assumption through the use of known-age fish. Mortality and other demographic rates could also be estimated using methods such as mark–recapture and multistate modeling (e.g., Coulter et al. 2018a). Fourth, continuing to collect data for the Illinois River would allow for stock assessment using other methods (e.g., Ogle 2016) that may be applicable to other subpopulations because of the well-studied invasion gradient within the Illinois River. However, any applicability or proposed management or control strategies would need to consider several of the aforementioned hypotheses such as difference in river hydrologic, environmental, and productivity conditions.

Our findings suggest that several demographic rates vary for Bighead and Silver Carp within and among the Illinois, Ohio, and Mississippi rivers. This information can be used to inform Bigheaded Carp control efforts. For example, the positive relation between energetic condition and reproductive effort in fishes (Hanson et al. 1997) means that reducing populations that are in better condition—as evidenced by our length–weight analyses—may be a more effective control strategy. However, the exponential population growth exhibited by some aquatic invasive species in responses to harvest efforts may offset this strategy and warrants consideration (Zipkin et al. 2008; Sass et al. 2010; Gaeta et al. 2015). Therefore, invasive species control efforts could likely use multiple approaches to reduce adult abundances and elevate juvenile mortality rates simultaneously (Hein et al. 2007; Gaeta et al. 2015). In contrast to length–weight analyses, we did not detect strong spatial effects on growth (except for asymptotic length) and maturity, suggesting that decision makers may manage different subpopulations of Bigheaded Carp independent of these factors. The exception being Marseilles pool for both species and Pool 26 for Silver Carp, which warrant further investigation. Although growth rates were generally similar across pools, the large variability in our length at age data, which potentially masked spatial patterns in Bighead and Silver Carp growth, exists as a caveat for this conclusion. Lastly, although we did not explicitly test for explanatory covariates of demographic variation, we have presented several explanatory hypotheses to guide future research efforts.

Please note: The Journal of Fish and Wildlife Management is not responsible for the content or functionality of any supplemental material. Queries should be directed to the corresponding author for the article.

Supplement S1. Exploratory data analysis for Bighead Carp Hypophthalmichthys nobilis and Silver Carp H. molitrix data from the Mississippi, Illinois, and Ohio rivers. Fish were collected between 1997 and 2018.

Available: https://doi.org/10.3996/JFWM-20-070.S1 (1.22 MB PDF)

Supplement S2. Summary of model performance and outputs for length–weight model, growth model, and maturity model for fish Bighead Carp Hypophthalmichthys nobilis and Silver Carp H. molitrix. Observations were from 1997 to 2018.

Available: https://doi.org/10.3996/JFWM-20-070.S2 (2.77 MB PDF)

Reference S1.[ACRCC] Asian Carp Regional Coordinating Committee. 2018. Asian Carp action plan. Asian Carp Regional Coordinating Committee.

Available: https://doi.org/10.3996/JFWM-20-070.S3 (6.45 MB PDF) and http://asiancarp.us/Documents/2018ActionPlan.pdf

Reference S2.[ACRCC] Asian Carp Regional Coordinating Committee. 2020. Asian Carp action plan. Asian Carp Regional Coordinating Committee.

Available: https://doi.org/10.3996/JFWM-20-070.S4 (5.58 MB PDF) and http://asiancarp.us/Documents/2020-Action-Plan.pdf

Reference S3. Bailey SW, Knights BC, Wlosinski JH, Kalas JA. 2003. Upstream fish passage opportunities at Ohio River mainstem dams. La Crosse, Wisconsin: U.S. Geological Survey, Upper Midwest Environmental Sciences Center.

Available: https://doi.org/10.3996/JFWM-20-070.S5 (4.88 MB PDF)

Reference S4. Buck EH, Upton HF, Stern CV, Nicols JE. 2010. Asian carp and the Great Lakes region. Congressional Research Service Reports.

Available: https://doi.org/10.3996/JFWM-20-070.S6 (541 KB PDF) and https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1011&context=crsdocs

Reference S5. Garvey JE, DeGrandchamp KL, Williamson CJ. 2007. Life history attributes of Asian carps in the Upper Mississippi River System. Aquatic Nuisance Species Research Program.

Available: https://doi.org/10.3996/JFWM-20-070.S7 (513 KB PDF) and https://pdfs.semanticscholar.org/529b/016243b140f3ae7e2050784be41efe0c8ea0.pdf

Reference S6. Ickes BS, De Lain S, Bowler BM, Ratcliff E, Gittinger E, Solomon L, Michaels N, Sauer J, Schlifer B, Ridings J. 2012. Quality assurance results UMRR-EMP LTRMP fish component: mapping of the electrical fields on the new fleet of electrofishing rigs. La Crosse, Wisconsin: Upper Midwest Environmental Sciences Center, U.S. Geological Survey.

Available: https://doi.org/10.3996/JFWM-20-070.S8 (414 KB PDF) and https://www.umesc.usgs.gov/ltrmp_fish/sow_2013b13_final_draft.pdf

Reference S7.[MRWG] Monitoring and Response Workgroup. 2017a. 2017 Asian carp monitoring and response plan. Asian Carp Regional Coordinating Committee.

Available: https://doi.org/10.3996/JFWM-20-070.S9 (17.47 MB PDF)

Reference S8.[MRWG] Monitoring and Response Workgroup. 2017b. Interim summary report: Asian carp monitoring and response plan. Asian Carp Regional Coordinating Committee.

Available: https://doi.org/10.3996/JFWM-20-070.S10 (7.77 MB PDF)

Reference S9. Zalay B. 2017. Zooplankton response to Asian carp harvesting in Illinois River backwaters: a natural experiment. Master's thesis. Urbana-Champaign: University of Illinois at Urbana-Champaign.

Available: https://doi.org/10.3996/JFWM-20-070.S11 (674 KB PDF) and http://hdl.handle.net/2142/97291

Data and code: Our supporting data have been published (Erickson et al. 2021) on ScienceBase and our supporting code (Erickson and Kallis 2021) on code.usgs.gov. This includes a README file explaining the organization of the code files and data as well as an XML file with the meta-data.

We thank the people and organizations who collected and shared their Bighead and Silver Carp data. We thank Brent Knights for reading through a draft of this manuscript. We thank Christopher R. Peterson for assistance with our Stan code. We also thank reviewers who provided feedback on this manuscript and Michael J. Hansen for serving as the Associate Editor for this article. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. The authors received funding from the Great Lakes Restoration Initiative (GLRI) for this project.

Any use of trade, product, website, or firm names in this publication is for descriptive purposes only and does not imply endorsement by the U.S. Government.