Evaluating the potential role of predation by native fish regulating the abundance of invasive spiny water flea

Abstract Predation by native predators can hinder the success of an invasive species. Bythotrephes, an invasive zooplankton species, established in Trout Lake, Vilas County, Wisconsin, USA, in 2014. However, by 2020, Bythotrephes densities dropped to densities where they were barely detectable. Cisco (Coregonus artedi), a native zooplanktivore, is an abundant fish species in Trout Lake and has been shown to significantly prey on Bythotrephes. Given the decline in Bythotrephes, we asked whether Cisco predation could have played a role in the observed decline in Bythotrephes densities. We modeled Cisco consumption of Bythotrephes using bioenergetic modeling and Bythotrephes production from a production to biomass model. The model results suggested that Cisco consumption was lower than Bythotrephes production during the early years of the invasion, but since 2017 Cisco consumption exceeded Bythotrephes production and has likely played a role in the observed Bythotrephes density declines. Our study provides quantitative context for predation on Bythotrephes, and alongside other studies, suggests native predators can control Bythotrephes densities. Leveraging predation by native species could be an invasive species management tool, so it is important to synthesize and document cases in which predation may control or reduce impacts of invasive species. KEY POLICY HIGHLIGHTS Invasive species can have severe impacts on freshwater ecosystems and will continue to spread across the landscape. When species do invade, invasive species management tools are incredibly important as they can mitigate impacts. However, successful management of invasive species often goes undocumented. Predation by native species can be an invasive species management tool to mitigate impacts of invasions. Leveraging native species to reduce the abundance of an invasive species can be difficult and requires thorough consideration of indirect impacts. There have been some cases where predation by native species has been attributed to controlling the abundances of invasive species. In such cases, promoting native species abundances can reduce the abundance of invasive species. This can be highly advantageous for lake managers, however, natural resource management includes many different stakeholders and therefore decisions regarding invasive species management can be complex.


Introduction
The long-term persistence of an invasive species can depend on the characteristics of the recipient ecosystem (habitat suitability, prey availability, predation pressure, etc.).Of these characteristics, predation by native predators can have a strong impact on the establishment and long term persistence of an invasive species (Elton 1958;Abrams 1987;Mrnak et al. 2022).Many invasive species have or develop defense mechanisms to avoid predation.Further, those defense mechanisms can be strengthened by strong predation pressures (Freeman and Byers 2006).These defense mechanisms can contribute to a lag-time in native predators switching to consuming the novel prey (Carlsson et al. 2009).However, it can be advantageous for native predators to switch to consuming invasive prey, particularly when invasive prey are hyper-abundant.There are many cases where native predators consume invasive prey, and can regulate invasive species abundances (Byers 2002;DeRivera et al. 2005;Carlsson et al. 2011).This can minimize their impacts and such is the primary goal of invasive species management (Prior et al. 2018;Mrnak et al. 2022).Therefore, it is especially important to study cases of native predators regulating invasive species abundances.Yet, it is difficult to study these cases as it requires data collection from the early stages of the invasion.
Bythotrephes cederstoemi (spiny water flea; Bythotrephes hereafter) invaded the Great Lakes in the 1980s and have since spread to many inland lakes and reservoirs (Branstrator et al. 2006;Korovchinsky 2020;Karpowicz et al. 2021).Bythotrephes have a barb ridden caudal spine that can account for over half its total body length (Korovchinsky and Arnott 2019).As a large predatory zooplankton species, predation by Bythotrephes can have rapid and severe impacts on native zooplankton communities, especially cladoceran species (Yan et al. 2002), which in extreme cases has caused ecosystem level trophic cascades (Walsh et al. 2016a;Weidel et al. 2017).Further, by reducing native zooplankton abundances Bythotrephes can create a prey resource bottleneck for gape limited predators and slow the growth of juvenile fishes (Staples et al. 2017;Hansen et al. 2020).Although the defensive barbed caudal spine of Bythotrephes can reduce predation, it mostly guards against gape limited predators, particularly juveniles.Predation on Bythotrephes is size dependent where there is a gape threshold for predators to readily consume Bythotrephes (Barnhisel and Harvey 1995;Jarnagin et al. 2000;Compton and Kerfoot 2004).Studies investigating fish predation on Bythotrephes have found many species prey on Bythotrephes including but not limited to Cisco (Coregonus artedi), alewife (Alosa pseudoharengus), lake whitefish (Coregonus clupeaformis.),rainbow smelt (Osmerus mordax), and yellow perch (Perca flavescens) (Schneeberger 1991;Coulas et al. 1998;Storch et al. 2007;Isaac et al. 2012).The prevalence and diversity of native fish consuming Bythotrephes has further sparked interest into whether native predators could regulate Bythotrephes abundances, which has been supported in some cases (Branstrator et al. 2006;Young et al. 2009;Keeler et al. 2015).
Here, we asked whether predation on Bythotrephes by a native zooplanktivore, Cisco, exceeded Bythotrephes production in a lake where the Bythotrephes population fell to a threshold of very low detection.We used long-term data to inform a Cisco bioenergetics model and Bythotrephes production to biomass (P/B) model to examine the ratio of Cisco consumption to Bythotrephes production.We found that Cisco consumption was lower than Bythotrephes production during the early years of the invasion, but since 2017 Cisco consumption exceeded Bythotrephes production and likely played a role in the major Bythotrephes decline.

Study system
Trout Lake is a 1,608 hectare oligotrophic, drainage lake in Vilas County, Wisconsin, USA that is largely undeveloped and reaches a maximum depth of 35 m (Benson et al. 2006).Cisco dominate pelagic zooplanktivory, and their population dynamics in Trout Lake are mediated from the top down by Lake Trout (Parks and Rypel 2018;Martin et al. 2022).The lake's native zooplankton community is comprised of large-bodied grazers (Daphnia and calanoids), and smaller-bodied taxa (cyclopoid, rotifer and copepod nauplii) (Martin et al. 2022).The pelagic food web also has predatory invertebrate taxa including Chaoborus, Mysis, Leptodora, and invasive Bythotrephes (established 2014) (Martin et al. 2022).The Trout Lake food web has undergone multiple ecological regime shifts over the last 40 years, with the most recent occurring from the Bythotrephes invasion (Martin et al. 2022).In Trout Lake, the Bythotrephes invasion coincided with a decline in (1) water clarity, (2) large bodied grazing zooplankton and (3) native predatory invertebrate taxa (Chaoborus, Mysis, and Leptodora) (Martin et al. 2022).However, in 2020 the Bythotrephes densities declined to a very low abundance (almost undetectable), even though frequent monitoring continued as it has since Bythotrephes were first detected.For context, a single zooplankton tow yielded tens to even thousands of Bythotrephes from 2014 to 2019, but in 2020 and 2021, there were only a total of four and one individuals, respectively, captured across monitoring throughout the year.

Field collected data
Trout Lake has been routinely sampled through the North Temperate Lakes Long Term Ecological Research (NTL-LTER) program since 1981.All sampling methods and data are freely available on their website https://lter.limnology.wisc.edu.For this study, we used the following datasets: pelagic fish density estimates from hydroacoustics, annual predatory zooplankton densities, fish length/weight from vertical gill nets, and daily water temperatures (Magnuson et al. 2020a;2020b, 2021, 2022a, 2022b).
Cisco pelagic abundance was estimated annually in July or August with hydroacoustic surveys, typically within a week of gill net sampling.Hydroacoustic data were collected at night with a BioSonics DTX echosounder and downward facing 70-kHz split-beam transducer mounted 1 m below the water surface.Thresholds for data collection excluded raw echoes below À100 decibel (dB) for S v data and -70dB for target strength data.Transmitted pulse duration was set at 0.4 ms.All hydroacoustic surveys were conducted at least 30 min after nautical twilight and followed a standardized-replicable transect on the south basin of Trout Lake.All acoustic data were analyzed in Echoview software (v5.4) following Mrnak et al. (2021).Post-hoc data analysis followed the Great Lakes Standard Operating Procedures (Parker-Stetter et al. 2009;Mrnak et al. 2021); target strength threshold of À55 dB, 6-dB pulse length determination level, 0.5 minimum and 1.5 maximum normalized pulse length, 6-dB maximum beam compensation, and minorand major-axis angles at 1 .However, 48-hr vertical gillnet sets were used to (1) inform species composition from the hydroacoustic surveys and (2) to inform Cisco size-specific inputs into the bioenergetics model (detailed below).For each set, seven monofilament nets were deployed in the deep hole of Trout Lake from the surface to the bottom ($30 m).Vertical gillnets were 3 Â 30 m with stretched meshes of 19,25,32,38,51,64, or 89 mm.After a 24-hr period, all nets were processed and fish were measured for total length (TL; mm) and weight (g).Species-specific mean total length was then transformed into a target strength (dB) following Love (1971).Species classes were then designated using mean target strength and then assigned a proportion of total biomass (Mrnak et al. 2021).In 2019, a subsample of collected Cisco was further assessed for stomach content composition.Whole stomachs were removed from fish and the contents were emptied into a petri dish and visually assessed to estimate percent by volume of different prey types, with a focus on Bythotrephes.Prey categories included Bythotrephes, unidentifiable zooplankton, macroinvertebrates, Mysis, and plant matter.When Bythotrephes were found in stomach contents, the total number of Bythotrephes individuals was counted, and the life stage of Bythotrephes (instar) was noted.
Since 2014, Bythotrephes density was estimated approximately every two weeks throughout the ice-free season.Each sampling day included two 30 m vertical tows that were taken with a zooplankton net (400 lm mesh and 0.5 m diameter).Entire samples were counted for Bythotrephes individuals to calculate species density.These samples were collected during the daytime.In addition, the broader predatory zooplankton community, i.e.Chaoborus, Leptodora, Mysis, and Bythotrephes, were sampled annually from several depths (10,15,20,25, 32 m) using a zooplankton net (1 mm mesh and 1 m in diameter) since 1983.Three tows were taken at each depth except for at 32 m where five tows were collected.Predatory zooplankton sampling was conducted at night approximately on the same sampling date each year (July/August).Hereafter we will refer to the higher frequency daytime sampling as the "daytime" Bythotrephes sampling and the annual broader predatory zooplankton community sampling as the "nighttime" sampling.Water temperature was measured with a thermistor chain equipped to a buoy that is deployed throughout the ice-free season at the deep hole.Temperature data were collected at 1 m depth intervals and 1 min time intervals.

Cisco consumption
To examine the consumptive effect on Bythotrephes in Trout Lake, we estimated daily consumption rates (g consumed) of Cisco using Fish Bioenergetics 4.0 (Deslauriers et al. 2017) with physiological parameters developed for Coregonus spp.(Rudstam et al. 1994; Table 1).Model inputs included annual size-class specific Cisco starting weights (based on average weight from NTL-LTER vertical gillnet catches), diet composition (Keeler et al. 2015;Gatch et al. 2021), and prey item energy density (Dumont et al. 1975;Garton and Berg 1990).Diet composition was modeled at 10% Bythotrephes and 90% other with energy density values of 1,674 J/g wet weight (Stewart and Binkowski 1986;Bunnell et al. 2011;Walsh et al. 2017) and 3,000 J/g wet weight (Deslauriers et al. 2017), respectively.We estimated the daily thermal experience of Cisco as the daily mean whole water column temperature of Trout Lake's deep hole ($30 m) acquired via a long-term NTL-LTER buoy that records temperature every hour from the surface to bottom at 1 m intervals.Cisco consumption was estimated from one week before the earliest Bythotrephes seasonal detection to the latest that the majority of years had temperature data available (day of year 176-311, June 25-November 7, 135 d) (Figure 1).However, in instances of temperature data limitations, we estimated Cisco consumption during the Bythotrephes availability window only on the range of days where water temperature data existed.In 2016 there were issues with the data collection buoy that severely limited the available data and therefore we did not include 2016 in the models.Models were run by fitting to a specified p-value of 0.3 (Chipps and Wahl 2008;Deslauriers et al. 2017), where the p-value represents the proportion of maximum consumption with 0 representing no feeding and 1 indicating feeding at a maximum rate.To estimate  whole-lake Bythotrephes consumption, daily individual consumption rates of Cisco on Bythotrephes were multiplied by annual size-specific Cisco population estimates derived from hydroacoustic surveys (Magnuson et al. 2020a).

Bythotrephes biomass and production
To estimate Bythotrephes biomass, we first compared density estimates from the daytime and nighttime Bythotrephes sampling.Bythotrephes density estimates were generally higher from nighttime sampling than the daytime sampling, which is common for Bythotrephes and other zooplankton species (Supplementary Figures 1 and 2) (Keeler et al. 2015;Armenio et al. 2017;Doubek et al. 2020).However, as the nighttime surveys are only taken once a year, they are less likely to capture the seasonal peaks each year.Therefore, we used daytime sampling estimates to guide Bythotrephes biomass calculations.Given the primary goal of the model was to test if Cisco consumption could exceed Bythotrephes production, we erred on the side of overestimating Bythotrephes production when deciding how to model Bythotrephes production.Therefore, for each year, we applied the highest daytime Bythotrephes density in our biomass calculations to test if Bythotrephes densities could be regulated by Cisco predation.Although it is unlikely that average Bythotrephes densities were actually as high as the highest measured daytime density each year, by using such we are able to ensure we rigorously tested if Cisco consumption could exceed Bythotrephes production.The length-weight regression from Garton and Berg (1990) was used to calculate individual Bythotrephes weights.Bythotrephes biomass was converted from dry weight to wet weight by using a dry: wet weight ratio of 0.12 (Lehman and C aceres 1993).Previously Keeler et al. 2015 multiplied daytime density estimates by 2.06 to account for day/night differences and therefore we did the same to allow for comparisons between our studies (Armenio et al. 2017).Ideally, we would have estimated our own value to account for day/night differences, but the differences in our data were highly variable and limited to only five nighttime sampling events.To summarize, annual Bythotrephes biomass was calculated from the highest measured daytime density within each year, multiplied by 2.06 (Keeler et al. 2015).

Results
The subsample of Cisco that were assessed for stomach content analysis was made up of smaller sized Cisco as they all came from the gillnet panel with the smallest mesh size (139-184mm; average¼ 163.1 mm) (Table 2).Bythotrephes were present in 6/36 Cisco stomachs, which included all stages of Bythotrephes (1 st through 3 rd instar).Among the Cisco that had consumed Bythotrephes, Bythotrephes made up 22.5% by estimated volume of the stomach contents (Table 2).Unidentified zooplankton species was the most abundant prey item in the Cisco diets.Daytime Bythotrephes densities estimates were highly variable within the same sampling day and estimates taken within weeks of sampling also varied (Figure 1).Bythotrephes densities were highest during 2014 and 2015, with a single density estimate in 2017 reaching similar densities to these years (Figure 1).Bythotrephes densities were relatively low for the rest of 2017 (Figure 1).Across all years, the peak densities were spread throughout the icefree season, but were always captured in our modeled date range (days 176-311).
Cisco population density shifted considerably throughout the invasion (Figure 2).Cisco density peaked in 2016 and 2017, and was lowest during 2019 and 2020 (Figure 2).The estimated Cisco density in 2014 was relatively high, however, the limitations in data did not allow for error to be calculated for that year (Figure 2).Modeled individual Cisco consumption of Bythotrephes peaked in the early Fall ($270d) (Figure 3a).Comparing across years, modeled individual Cisco consumption was relatively similar (Figure 3a).At the population level, total Cisco consumption of Bythotrephes peaked in 2017 and was lowest 2019 (Figure 3b).The changes in modeled total Cisco consumption are largely reflective of shifts in annual Cisco population densities (Figures 2 and 3b).The modeled ratio of Cisco consumption of Bythotrephes to Bythotrephes production showed Cisco consumption did not exceed Bythotrephes production during the first two years of the invasion, however, Cisco consumption exceeded Bythotrephes production from 2017-2019 (Table 3 and Figure 4).The ratio of Cisco consumption to Bythotrephes production was highest during 2017, where the ratio peaked at 7.06 (Table 3 and Figure 4).Bythotrephes production was higher than Cisco consumption for all of 2014 and 2015, with 2014 having a lowest average ratio of 0.53 (Table 3).The ratio of Cisco consumption to Bythotrephes production was either higher or lower than 1 for the entirety of all years-in no years did the ratio cross between over and under 1 (Table 3 and Figure 4).

Discussion
Our model results showed predation pressure by native Cisco was substantial and likely limited Bythotrephes densities in Trout Lake, especially given the observed decline in Bythotrephes densities.Predation did not exceed Bythotrephes production during the first two years of the invasion, which is what we would expect given Bythotrephes densities were  Cisco consumption was modeled using bioenergetic modeling and Bythotrephes production was modeled using a production to biomass approach.If the ratio is greater than 1, there is over consumption of Bythotrephes by Cisco.Temperature data was insufficient for modeling in 2016.
highest during these years (Table 3 and Figure 4).Importantly, Cisco population density increased early in the invasion and peaked during 2017, which was the year the model showed Cisco consumption to Bythotrephes production was highest (Figure 2).Excessive Cisco predation continued as our model showed Cisco predation exceeded Bythotrephes production during 2018 and 2019.The Cisco population estimate in 2020 was similar to that of 2019 (Figure 2), so we expect a similar level of Cisco zooplanktivory, however Bythotrephes densities fell to very low densities.In 2021, Bythotrephes densities remained at low densities.Given this invasion timeline, it is likely that Cisco predation was a limiting factor in the abundance of Bythotrephes in Trout Lake.Overall, our model was able to quantify and contextualize the predation pressure Bythotrephes experienced in Trout Lake.
In our study, we found that Cisco consumption of Bythotrephes exceeded Bythotrephes production at certain times, which corroborates several previous studies.A previous study in the nearshore of Lake Michigan showed Alewife (Alosa pseudoharengus), particularly those of larger body length, consumed Bythotrephes in large enough proportion that it exceeded Bythotrephes production (Pothoven et al. 2007).They further noted that Bythotrephes abundances were relatively low, especially in comparison to another invasive predatory zooplankton (Cercopagis pengoi) that was preyed upon less frequently by Alewife (Pothoven et al. 2007).Keeler et al. (2015) showed zooplanktivore consumption of Bythotrephes exceeded Bythotrephes production in Lakes Michigan and Superior.However, the habitats where zooplanktivore consumption of Bythotrephes exceeded Bythotrephes production were different for the two lakes, as were the individual zooplanktivore species.In Lake Michigan, they found that the nearshore habitat, where zooplanktivory was dominated by Alewife, had higher zooplanktivore consumption of Bythotrephes compared to Bythotrephes production, similar to Pothoven et al. (2007).In Lake Superior, the offshore habitat, where zooplanktivory was dominated by Cisco, had higher zooplanktivore consumption of Bythotrephes compared to Bythotrephes production (Keeler et al. 2015).Alongside these other studies, our study supports that Bythotrephes densities may be controlled by predation.
The Cisco population in Trout Lake declined in population density in the years prior to the Bythotrephes invasion, which may have allowed for the initial population irruption of Bythotrephes.In 2007, Lake Trout populations increased substantially, which caused a major decline in Cisco densities (Parks and Rypel 2018;Martin et al. 2022).During this period of low Cisco density, the potential predation pressure on Bythotrephes would have been even lower than the year our model indicated the lowest total Cisco consumption of Bythotrephes (2019).In many Bythotrephes invasions, it has been found that Bythotrephes were present at very low abundances prior to their first detections (Walsh et al. 2016b;DeWeese et al. 2021).During this period, the Bythotrephes population density is where we are unable to detect their presence with typical zooplankton community monitoring efforts.Analyzing sediment cores for Bythotrephes caudal spines has proven to provide insights into early invasion dynamics and if done in Trout Lake we could test this hypothesis and would add to the continued debate on the colonization history of Bythotrephes in North America (DeWeese et al. 2021;Karpowicz et al. 2021).Overall, the historically low Cisco densities in the years prior to the invasion may have played a role in the initial population irruption of Bythotrephes, but then increased Cisco densities in 2016/2017 quickly limited their success.
In our model for Trout Lake, we assumed that Cisco would be preying on Bythotrephes during the first year of establishment, yet that is not often the case for predation on invasive species.There is often a lag time before native predators switch to consuming novel prey (Carlsson et al. 2009), especially when the prey has defense mechanisms like Bythotrephes (Barnhisel 1991a;Straile and Halbich 2000).This lag time in predators adjusting to prey on novel resources has been documented in several cases and has shown predation pressure can increase as predators adjust (Carlsson and Strayer 2009;Carlsson et al. 2009Carlsson et al. , 2011)).The barbed caudal spine of Bythotrephes contributes to significant "handling time" for smaller predators (Barnhisel 1991b;Compton and Kerfoot 2004).However, larger predators are capable of handling Bythotrephes, and preferentially prey on Bythotrephes (Coulas et al. 1998).In many cases Bythotrephes can reach high densities, especially relative to alternative prey items, which promotes native predators switching to Bythotrephes, however given the defense mechanisms this adjustment likely takes time.In our model, we used a constant diet proportion of 10% Bythotrephes, but this likely varied throughout the invasion, as well as seasonally.Our limited diet data confirmed Bythotrephes were incorporated into the diets of even relatively small Cisco in 2019, which was also when Bythotrephes was at relatively low densities (Table 2).Unfortunately, that data is only a single snapshot and does not include larger Cisco that are present in Trout Lake.More diet analysis was completed in 2020, however, Bythotrephes densities had already declined dramatically so there were not any Bythotrephes in the Cisco diets.A diet proportion of 10% is lower than that of many other Cisco and Bythotrephes diet studies including Keeler et al. (2015), Coulas et al. (1998), Gamble et al. (2011), Breaker et al. (2020), and Gatch et al. (2021) (Table 2).Therefore, a 10% diet proportion is our best estimate when also aiming to conservatively test if Cisco could regulate Bythotrephes densities (Keeler et al. 2015;Gatch et al. 2021).If there was a lag time in Cisco incorporating Bythotrephes into their diets, then it would push Bythotrephes production to further exceed Cisco predation in the early years of the invasion, likely in 2014 and 2015.However, if Bythotrephes were present at low abundances prior to their irruption in summer of 2014, then it is likely Cisco had already encountered Bythotrephes, albeit at low abundances, and could have readily adapted to preying on Bythotrephes.Importantly, with a reasonable estimate of 10% diet Bythotrephes, our model shows overwhelming consumption by Cisco by 2017, which corresponds with when we begin to see a decline in Bythotrephes densities.Ideally, we would have diet data throughout the invasion, but with only data from one year and on a small size class of fish, we felt it was best to use a constant diet proportion that is relatively low.Therefore, while our model does not incorporate changes in Cisco diet proportions throughout the invasion, a lag time or shift in predation on Bythotrephes is not likely to change the main result from our model.Branstrator et al. (2006) noted two lakes in Minnesota where Bythotrephes were no longer observed, and they proposed the mechanism limiting Bythotrephes densities likely goes beyond simple zooplanktivore abundance.Beyond planktivore abundance, they suggested it is important to consider the presence of "predation refuge" (low-light, warm water, middepth) where Bythotrephes can minimize their risk of predation.The described predation refuge was hypothesized to be thermally incompatible for coldwater zooplanktivores (Cisco), while also being incompatible for low-light limited visual feeding warmwater fishes (Yellow Perch).They quantified light-refuge thickness using the following formula: Refuge thickness ðmÞ ¼ Maximum lake depth ðmÞ -ð2:41ÃSecchi depth ðmÞÞ In the cases where there is thicker light-refugia, it was suggested that zooplanktivore abundances would have a less direct control over Bythotrephes because Bythotrephes could better evade predators in the refuge habitat.For comparison, we have estimated refuge thickness for Trout Lake.Trout Lake's estimated refuge thickness since 2014 would be $24 m (Secchi depth $5 m; maximum depth ¼ 35.7 m), which is much higher than the two Minnesota lakes where Bythotrephes were no longer observed (Boulder Lake ¼ 0.9 m and Fish Lake ¼ 7.9 m).Therefore, according to the predation refuge hypothesis, Bythotrephes in Trout Lake would have substantial habitat that minimizes predation risk.However the ample availability of proposed predation refuge was not enough for Bythotrephes in Trout Lake.The predation refuge hypothesis was not supported by a later study, where Cisco in Harp Lake, Canada occupied the proposed Bythotrephes refuge habitat (metalimnion) (Young et al. 2009).Cisco were also shown to selectively feed on Bythotrephes in Harp Lake (Coulas et al. 1998).Therefore, in addition to the work from Harp Lake, our study indicates predation refuge was not enough for Bythotrephes to overcome excessive predation pressure.
Bythotrephes life history traits make them problematic to model with a traditional modeling approach, which likely underestimates the predation necessary to mediate Bythotrephes densities.The main trait that makes Bythotrephes problematic for modeling is that Bythotrephes can successfully reproduce even after they are consumed by a predator (Jarnagin et al. 2000;Kerfoot et al. 2011).Bythotrephes diapausing eggs are still viable after passing through a predator's intestinal tract and subsequently excreted.The excreted eggs settle into lake sediment and then have the potential to successfully hatch.So, even though a predator removes an individual Bythotrephes from the population, there is still the potential for reproduction by the individual Bythotrephes that was preyed upon.This life history characteristic of Bythotrephes makes them unlike other prey species where an individual that is preyed upon is instantaneously removed from the population without reproductive potential.This predator-prey interaction can be likened to endozoochory, which is a common plant dispersal strategy where predators consume and disperse viable plant seeds.For Bythotrephes, a predator gains nutritional value by consuming Bythotrephes, but also the predator transports and excretes viable diapause eggs.While the diapause eggs do not hatch until the following season, this dynamic makes Bythotrephes complicated to model as a prey item because consumption does not exclude the possibility of successful reproduction from Bythotrephes.Overall, this life history characteristic of Bythotrephes causes traditional modeling to overestimate 'effective' predation rates because some Bythotrephes will successfully reproduce after being preyed upon.Development of a Bythotrephes specific predation model that would include this unique life history trait could greatly improve our ability to more accurately model their population dynamics.
While there may be more factors influencing the Bythotrephes dynamics in Trout Lake, our study highlights a key factor that can limit the abundance of a major invasive species.The shifts in Bythotrephes densities are unlikely to be simply driven by predation, or any other single factor, but our model results give us a sense for the potential impact of predation pressure on Bythotrephes.Boom-bust dynamics are common in species invasions and the invasion of Bythotrephes in Trout Lake is still relatively recent (<10 years) (Strayer et al. 2017).Long-term monitoring will continue for Trout Lake through NTL-LTER, and this will increasingly provide context for the dynamics at play in this invasion.So far, Trout Lake has provided an exceptional opportunity to understand the complex drivers of Bythotrephes population dynamics and impacts, as long-term study has given us 20 years of data prior to the invasion and increased monitoring since the invasion.

Conclusions
Here we have compared Cisco consumption of Bythotrephes and the population production of Bythotrephes.Our results indicate predatory pressure initially was low enough for the success of Bythotrephes, however, Cisco predation exceeded Bythotrephes production starting in 2017 and likely influenced the decline in Bythotrephes densities.The disappearance of Bythotrephes in invaded lakes has been observed in a few instances and our model results suggest that predation can limit Bythotrephes densities.Biological control of Bythotrephes and other invasive species is an important tool to minimize the impacts of invasive species, and this study provides as example of where a native predator may limit the population density of an invasive species.Long term data collection will continue on Trout Lake and we will have the opportunity to closely monitor the invasion and whether Bythotrephes densities will remain low or if they will rise again.The management of invasive species through predation is one of the few tools available for managers; therefore, it is important that cases where invasive species decline are documented and synthesized.These cases can help inform potential management actions like stocking or other food web alterations to mitigate the impacts of invasive species.As invasive species continue to colonize new systems, there will be more opportunities to test the role native predators have in managing invasive prey.

Figure 1 .
Figure 1.Daily Bythotrephes density (individuals/m 2 ) estimates from vertical zooplankton tows in Trout Lake, Vilas County, Wisconsin, USA, from 2014-2019.Each point represents an individual net tow estimate, with the bars showing the maximum estimate for each day.Dashed vertical lines at day 176 and 311 show the start and end of period modeled in subsequent graphs.Note the y-axis scales are adjusted for each year.
Cisco (daily mean column temperature at the deep hole).Daily Bythotrephes production was modeled using P/B daily ¼10 Ã (a þ b ÁT) where P ¼ production (g m À2 day À1 ), B ¼ biomass (g), and T ¼ epilimnetic temperature ( C), a ¼ À1.725 and b ¼ 0.044(Shuter and Ing 1997).Bythotrephes production estimates were calculated on an areal basis (g wet wt.m À2 day À1 ) in order to allow for comparison with Cisco consumption, which was also calculated on an areal basis.Daily Cisco consumption of Bythotrephes was then divided by daily Bythotrephes production.Ratio values >1 indicate Cisco consumption of Bythotrephes exceeded Bythotrephes production, suggesting Cisco predation limitation on Bythotrephes.A ratio <1 indicates Bythotrephes production exceeds Cisco consumption of Bythotrephes.

Figure 2 .
Figure 2. Cisco density estimates (# per hectare) from 2014-2020 for Trout Lake, Vilas County, Wisconsin, USA.Standard error is shown for each density estimate except for 2014 due to data limitations.

Figure 3 .
Figure 3. Modeled (a) individual and (b) total population daily Cisco consumption of Bythotrephes (g wet wt.) by day of year (176-311) in Trout Lake, Vilas County, WI, USA, from 2014-2019.Each year is displayed in a different color.2016 is not shown because of insufficient temperature data for the model.

Figure 4 .
Figure 4. Ratio of modeled Cisco consumption of Bythotrephes to Bythotrephes production by day of year (176-311) in Trout Lake, Vilas County, WI, USA, from 2014-2019.The dashed horizontal line shows where Cisco consumption and Bythotrephes production are equal (1).Each year is displayed in a different color.2016 is not shown because of insufficient temperature data for the model.

Table 1 .
Rudstam et al. 1994.ns and values for the Coregonus species bioenergetics model fromRudstam et al. 1994.

Table 2 .
Coulas et al. 1998 that report Cisco (Coregonus artedi) diet proportions containing Bythotrephes.The sample size (n), and total length range (mm) are shown for Cisco from each study.Bythotrephes proportion is the average proportion across each study.A dash signifies the sample size or total length range applies to both size categories of Cisco reported.ForCoulas et al. 1998, a size range was not reported so the average (standard deviation) is provided.A second diet proportion with an asterisk has been provided for the present study, which is calculated as the average Bythotrephes proportion from only fish that contained any Bythotrephes.
Bythotrephes biomass was modeled as a constant biomass each year, again to rigorously test if Bythotrephes densities could be regulated by Cisco predation.While Bythotrephes densities fluctuate throughout the season, our model is intended to test if Cisco predation could exceed production when Bythotrephes are at the highest densities we can reasonably expect.Daily thermal experience was modeled the same for Bythotrephes as

Table 3 .
Minimum, maximum, and average daily Cisco consumption (g wet weight) versus Bythotrephes production ratio from 2014-2019 for Trout Lake, Vilas County, WI, USA.