Decline of young-of-year walleye (Sander vitreus) growth due to Bythotrephes impacts predicted from bioenergetic principles

Invasive species are a major threat to ecosystem structure and function. For example, Bythotrephes cederströmii (Bythotrephes hereafter) invasions have significantly reduced native zooplankton density and biomass, resulting in competitive interactions with zooplanktivorous fishes. Young of year (YOY) walleye (Sander vitreus) are initially zooplanktivorous and have recently been shown to display reduced growth in Bythotrephes-invaded lakes. Here, we combined a bioenergetics model for larval walleye with changes in the zooplankton community following Bythotrephes invasion and predicted reduced larval walleye growth in the presence of Bythotrephes, supporting field observations. The model predicted greater negative impacts on larval walleye growth in oligotrophic compared with mesotrophic lakes, though reduced growth was only significant under oligotrophic conditions. Under Bythotrephes invasion, net energy available to growth over the simulated period was often observed to be negative (indicating mass loss). These combined results from the model suggest that Bythotrephes invasion could potentially lead to walleye recruitment failure, especially in low nutrient environments. This result was insensitive to differences in annual mean water temperatures ranging from 18.5 to 23.5 °C. As YOY growth, survival, and recruitment are ultimately linked to adult abundance and sustainability of managed stocks, our results highlight the potential impacts of Bythotrephes on the sustainability of walleye populations in boreal lakes.


Introduction
The growth and survival of early life stages of fishes, especially during the first month of life, are major limiting factors to fish recruitment and may determine year-class strength (Venturelli et al. 2010;Grote et al. 2018;May et al. 2020). Mortality is often greatest in early life stages of fish, where factors such as predation, temperature, and prey availability are important predictors of larval fish survival (Hoxmeier et al. 2006). Prey availability is considered to be one of the most critical factors to larval fish survival, as inadequate food supply may lead to death and/ or slower growth rates, along with decreased swimming speed, thus increasing the risk predation (Jonas and Wahl 1998). For predatory fish like walleye (Sander vitreus) which are initially planktivorous, faster growing larvae will reach larger sizes sooner, making ontogenetic diet shifts to benthivory and piscivory earlier. These more rapidly growing individuals, making earlier transitions in diet show selective advantages via increased survival in their first year versus their slower-growing counterparts (Bergenius et al. 2002;May et al. 2020). Larval walleye growth rates (and therefore mortality through to their first year of life) ultimately influence future recruitment of fish populations, and therefore the sustainability of fisheries (Anderson 1988;Post and Evans 1989;Grote et al. 2018). Bioenergetics models can be used to describe the energy and growth budget of fishes, where energetic costs for metabolism, waste loss, and growth can be balanced against the energy consumed from the available prey field (Deslauriers et al. 2017). Understanding how prey availability affects larval growth (and mortality) is therefore critical for identifying recruitment bottlenecks at a particular life stage and represents a critical consideration for informed fisheries management decisions.
Studies have shown that invasive species, particularly Bythotrephes cederströmii (hereafter Bythotrephes), significantly impact the zooplankton communities of lakes they have invaded (Dumitru et al. 2001;Yan et al. 2002;Boudreau and Yan 2003;Pangle et al. 2007). Bythotrephes are a large, predatory cladoceran, and are known to consume zooplankton at higher rates than they are produced, causing rapid decreases in zooplankton diversity and biomass following establishment (Yan et al. 2002; Barbiero and Tuchman 2004;Kerfoot et al. 2016). In some lakes invaded by Bythotrephes, microcrustacean biomass (particularly cladocerans and cyclopoid copepods) was reduced by 40-90%, resulting in decreased prey availability for other zooplanktivores (Yan et al. 2002;Kerfoot et al. 2016;Gillis and Walsh 2017;Rantala et al. 2022). Further, Bythotrephes can consume more zooplankton than some native zooplanktivores, including larval stages of fishes of economically and culturally significance, such as walleye (Bunnell et al. 2011). Reductions in zooplankton prey availability due to Bythotrephes invasion might therefore lead to reductions in the growth, survival, and recruitment rates of other zooplanktivores, including fishes.
Walleye are an important freshwater fish, representing 26% of all fish caught recreationally and 35% of all fish caught commercially in Canada, contributing $7.9 billion to local economies Oceans Canada 2019a, 2019b). For iteroparous species of fishes and other vertebrates, higher rates of larval recruitment success should lead to more sustainable populations (Shelton and Mangel 2011). However, the response of young-of-year (YOY) walleye survival in relation to invasive species impacts on planktivore communities is largely unknown. Bythotrephes is not likely a prey item for YOY walleye during their zooplanktivorous phase, as YOY fishes tend to adopt an aversion behaviour to Bythotrephes due to the difficulty of ingesting their long spine (Barnhisel 1991a, b;Compton and Kerfoot 2004). As zooplanktivores, larval walleye diet typically consists of calanoid copepods, cyclopoid copepods, and Daphnia spp. (Graham and Sprules 1992). In Minnesota lakes, YOY walleye size was reported as smaller in Bythotrephes-invaded lakes compared to non-invaded populations once walleye sizes were corrected for temperature variation that may influence growth (Hansen et al. 2020). As Bythotrephes invasions appear to reduce zooplankton abundance, potentially limiting prey availability to zooplanktivores (Rantala et al. 2022), one might predict a decrease in larval fish (i.e., walleye) prey consumption, leading to slower growth, but this potential link between reduced growth and zooplankton prey abundance has only been speculated (Hansen et al. 2020) and not demonstrated experimentally or theoretically.
Other stressors such as climate change may compound the potential negative impacts of species invasions on fish growth. Temperature plays a critical role in the growth of ectothermic aquatic species, particularly regarding temperature dependent metabolic processes (Kitchell et al. 1977). Walleye metabolic rate, food consumption, and growth are known to increase with temperature up to a thermal optimum (Kitchell et al. 1977;Galarowicz and Wahl 2003). Mean annual water temperature varies between lakes and is predicted to increase by 5 °C for most northern temperate lakes by the end of the twenty-first century due to increased greenhouse gas emissions (Maberly et al. 2020). As food consumption demands vary with temperature, it is important to consider the relationship between Bythotrephes-induced decreases in prey availability and larval walleye growth across latitudes, and in the case of increasing water temperatures due to climate change.
Our overall objective in this study was to use a bioenergetics approach to evaluate whether changes in the zooplankton community expected due to Bythotrephes invasions could provide a mechanistic explanation for observed slower growth of larval walleye in Bythotrephes-invaded lakes as observed elsewhere (Hansen et al. 2020). Specifically, we aimed to combine information from three different sources to determine this linkage: a characterization of key zooplankton taxa known to be consumed by larval walleye in lakes with and without Bythotrephes present, functional response models to predict the consumption of key zooplankton taxa by larval walleye, and a bioenergetics model for larval walleye that uses consumption from the functional response model to predict growth. Using this approach, we sought to determine whether the direction and magnitude of differences in larval walleye growth between lakes with and without Bythotrephes predicted solely by the structure of the zooplankton communities they encounter there, were of similar direction and magnitude to observed differences in larval walleye growth between lakes with and without Bythotrephes as reported elsewhere. In order to account for potential differences in trophic state of lakes subjected to invasion, which is known to affect the species richness and functional diversity of zooplankton (Barnett and Beisner 2007), we compared these predicted impacts in both mesotrophic and oligotrophic lakes, which represents a range of lake productivity, as well as the range of habitats suitable for both walleye and Bythotrephes occupancy (Johnson et al. 1977;Sorensen and Branstrator 2017). Furthermore, metabolic demands are temperature dependent; therefore, we conducted a sensitivity analysis to evaluate the consistency of our findings in both colder, northern lakes as well as in warmer, more southern latitudes.

Zooplankton biomass
To assess how larval walleye growth rate might change due to the impacts of Bythotrephes invasion on zooplankton community structure, we first determined zooplankton densities and basic water chemistry parameters from 265 lakes, both invaded and noninvaded by Bythotrephes, across Northern Ontario and Minnesota. Zooplankton densities were available from four mesotrophic Bythotrephes-invaded lakes in Minnesota (MN DNR Large Lakes Monitoring Program 2020 [Unpublished raw data]), as well as 34 mesotrophic (33 non-invaded and one invaded) and 227 oligotrophic lakes (188 non-invaded and 39 invaded) in Ontario (Arnott 2021 [Unpublished raw data]). These lakes were separated by invasion status and nutrient status/trophic state (categorized as either oligotrophic, 5-12 μg/L total phosphorus [TP], or mesotrophic 12-24 μg/L TP), based on the Trophic State Index (TSI) of Carlson (1977). For the purpose of this study, and to match groupings employed by functional response curves and available energy density estimates for modelling purposes (McDonnell and Roth 2014), we assumed larval walleye consume exclusively preferred zooplankton, classified broadly as Daphnia spp., calanoid and cyclopoid copepods (Houde 1967).
We simulated larval walleye growth under four different conditions: non-invaded mesotrophic lakes (NM), non-invaded oligotrophic lakes (NO), invaded mesotrophic lakes (IM), and invaded oligotrophic lakes (IO). Zooplankton biomass (μg/L) was estimated from densities (individuals/L) using taxaspecific length-mass regressions reported elsewhere (McDonnell and Roth 2014). To determine if zooplankton densities differed between treatments, we used a bootstrap procedure with 1000 iterations and compared 95% bootstrapped confidence intervals for mean zooplankton densities for each zooplankton taxa considered (Daphnia spp., calanoid and cyclopoid copepods).

Bioenergetics model
We used a bioenergetics model to determine larval walleye growth rates over the first three weeks (21 days) of life, comparing results from representative zooplankton community composition in Bythotrephes-invaded lakes and non-invaded lakes. We chose a three week model to simulate the period over which a walleye are typically zooplanktivorous and when zooplankton density is especially important for larval walleye survival (Graham and Sprules 1992;Hoxmeier et al. 2004). At first feeding, walleye typically weigh 0.0040-0.0055 g (Mathias and Li 1982;Malison and Held 1996), so each treatment was run at both these weights as the initial masses for a walleye larva to capture a range of initial larvae sizes. Growth (G) was then determined through a daily energy budget equation (Deslauriers et al. 2017) using bioenergetic parameters from Johnston 1999 (Table 1): where growth (G; J·g −1 ·day −1 ) is the difference between realized consumption (C r,t , J·g −1 ·day −1 ) and energy losses (the sum of R t , F t , U t , and SDA t ). Losses are characterized as respiration (R t , J·g −1 ·day −1 ), egestion (F t , J·g −1 ·day −1 ), excretion (U t , J·g −1 ·day −1 ), and specific dynamic action (SDA t, J·g −1 ·day −1 ). Each of these metabolic parameters can be further broken down into functions (Eqs. 4-16) dependent on mass (g), prey density (μg/L wet mass), and temperature (°C). We simulated daily temperature (T) using a water temperature curve in Trudel et al. (2000) from Lake Simcoe, ON based on the Julian day (J) using (2) to represent a typical larval walleye environment in temperate lakes during the first three weeks of their life (Julian day 135 to 155).
The resulting growth (G t ; J·g −1 ·day −1 ) was then applied to the initial mass (M t ) and energy density of a larval walleye (E pred ; 3349 J·g −1 ; Madon and Culver 1993) using Eq. (3) and input as the mass for the proceeding time-step (M t+1 ) for the duration of the simulation, as: The above model was run for the four treatments of prey availability described previously. If at any Daphnia shape parameter 38.033 time step the mass dropped to 0 g, the larva was considered deceased. Final length, and total growth (J) between treatments were compared to determine how changes in prey availability due to Bythotrephes invasion impact larval walleye growth rates.

Consumption
Prey-specific realized consumption, or the energy input contributed to the specific consumption rate (C j,t ; g·g −1 ·day −1 ) of each prey item (j) was based on a multispecies type II functional response model for larval walleye (McDonnell and Roth 2014): where P j,t is the environmental prey density (μg·L −1 wet mass) for prey type j at time t, and D90 j,L is the prey density at which 90% of the maximum consumption rate (C max ) can be achieved for a walleye at length L (in mm). C max (Eq. 5; g of prey·g of fish −1 ·day −1 ) is a function of consumer mass, M t (g), with parameter estimates of the intercept (CA) and slope (CB) from Johnston 1999.
Lastly, P j,t is multiplied by 9 so that D90 j,L reflects the prey density in which consumption is 90% of C max . We assumed that larval walleye consumed exclusively their preferred prey of calanoid copepods, cyclopoid copepods, and Daphnia spp., whose proportions changed based on larval walleye length (L t ) due to gape limitation (Fig. 1;Houde 1967;Graham and Sprules 1992). The proportions of larvae diet consisted of cyclopoids until they reached 11 mm, then a mix of calanoid and cyclopoids until 16 mm where Daphnia began to be the dominant prey item ( Fig. 1; Graham and Sprules 1992;McDonnell and Roth 2014). We calculated D90 j,L using equations below and parameters (Table 1)  Due to gape-limitation, larval walleye may not be capable of consuming larger zooplankton or benthos until they reach larger sizes (Johnston and Mathias 1994). To account for poor capture success at small body sizes, we used a walleye capture success (K t ) function using constants a v (338.45) and b v (−0.16) derived from laboratory studies on larval walleye are the exclusive prey items along with the prey capture success (red line). Data from Johnston and Mathias (1994) length and zooplankton capture success (Johnston and Mathias 1994): Total realized consumption (C r,t , J·g −1 · day −1 ) for inclusion in Eq. (1) was then calculated by summing the specific consumption rates of each prey item (C j,t , Eq. 4) at each time step using Eq. (10), scaling consumption for capture success (Eq. 9) and converting to units of energy, where E prey,j is the energy density of the respective prey item (E copepods = 2100 J·g −1 , E Daphnia = 2600 J·g −1 , McDonnell and Roth 2014):

Metabolic costs
To account for costs associated with metabolism from Eq. 1, we used a respiration function which is a mass and temperature-dependent model with an activity multiplier from Deslauriers et al. (2017): where, where RA is the intercept for maximum standard respiration (g O 2 ·g −1 ·day −1 ), RB is the slope for maximum standard respiration, RQ is the slope for temperature dependent respiration, and RTM and RTO are the maximum and optimal temperatures (°C) for standard respiration. We included an activity multiplier (ACT) to account for energy lost to active metabolism which was set to a constant value of 1 (unitless) to remain consistent with other larval walleye bioenergetic models in the literature (Kitchell et al. 1977;Johnston 1999). Egestion (F t ), excretion (U t ), and assimilated energy (SDA t ) costs from Eq. 1 in this study are equivalent to model 4 from Deslauriers et al. (2017) which are functions of consumption rates and temperature.
As the sample size for lake types were unequal, and that for Bythotrephes-invaded mesotrophic lakes (n = 5) was much smaller than other treatments (i.e., NM n = 33, NO n = 188, and IO n = 39), we used bootstrapping with 1000 iterations to estimate mean larval walleye growth estimates (i.e., length [mm] and growth as units of energy [J]) for the four trophicinvasion treatments (IM, NM, NO, IO). To evaluate the effect of Bythotrephes invasion on the growth of larval walleye, we compared 95% bootstrapped confidence intervals of mean larval walleye length and growth estimates between treatments. We calculated bias-corrected and accelerated bootstrap (BCa) 95% confidence intervals when the distribution of mean growth estimates in a treatment were not normally distributed. Bootstrapping is an appropriate resampling method that allows for a characterization of a population of lakes of each category type, particularly when applied to small sample sizes (Dwivedi et al. 2017), and additionally provides an opportunity to report variation in larval walleye growth across varying zooplankton densities, both among and between treatments.

Temperature sensitivity analysis
To assess the sensitivity of the model to temperature, we simulated two temperature regimes, one using the output of Eq. (2), and another with 5℃ higher mean annual temperature by altering Eq. (2) to become Eq. (17) below (Fig. 2).
The higher daily temperature regime was chosen to represent the projected increase in temperate lake surface water temperatures as predicted by climate change (Maberly et al. 2020), but because it also provides a representation of walleye growth at more southern latitudes. This warmer temperature regime was used an input for separate bioenergetics models using the same zooplankton density estimates, modelling, and bootstrapping methods as above. We (17) T = 4.0 + 23.5⋅e −(J−207) 2 ∕70 2 compared 95% bootstrapped confidence intervals of the mean final length (mm) between warm and cool temperature regimes to evaluate differences.

Zooplankton biomass
Using the entire set of 265 lakes, biomass of the three taxa (Calanoid, cyclopoid and Daphnia) varied both between and within treatments (Fig. 3). Though the bootstrapped means of biomass in invaded mesotrophic lakes appeared lower than in non-invaded mesotrophic lakes, the 95% confidence intervals between treatments overlapped for each of the three taxa, indicating no significant difference of means (Fig. 3). In contrast, mean biomass of each of the three zooplankton taxa was significantly lower in the invaded oligotrophic treatment compared to the noninvaded oligotrophic treatment. There were no significant differences in mean biomass for each of the three taxa between the non-invaded mesotrophic and non-invaded oligotrophic treatments, or between the invaded treatments.

Larval walleye growth
Our larval walleye model predicted faster growth rates under non-invaded conditions compared to invaded conditions in both mesotrophic and oligotrophic lakes, with the non-invaded mesotrophic conditions providing the fastest larval growth (0.82 mm/day). Based on 95% bootstrapped confidence intervals, mean final larval walleye length under the invadedoligotrophic treatment was significantly smaller than mean larval length under the non-invaded oligotrophic, and the non-invaded mesotrophic treatments for both small (0.0040 g or 9.31 mm) and large (0.0055 g or 10.30 mm) initial larvae sizes (Fig. 4a). However, there was high variation within the mean final length and total growth of both large and small initial sized larvae under the invaded mesotrophic treatment, which did not differ significantly from any of the other treatments (Fig. 4).
The model allowed a diet shift in zooplankton type depending on length in which the first shift occurred from feeding exclusively on cyclopoids to a mix of calanoids and cyclopoids at 11 mm in fish length. In the invaded oligotrophic treatment (both initial sizes), larval walleye on average did not successfully grow above the size with which this Fig. 2 Lake temperature used for temperature dependent functions of the bioenergetic modelling, estimated from a temperature curve of Lake Simcoe water temperatures based on the Julian day (Trudel et al. 2000). A warmer temperature regime (solid yellow line) was used in a sensitivity analysis to represent lake temperatures towards the end of the twentyfirst century as warmer lake surface temperatures are predicted by Maberly et al. (2020). The area highlighted with a red box indicates the Julian days (135-155) and temperatures used for model simulations in this study diet shift could be achieved (≥ 11 mm). Notably, small initial sized larval walleye rarely grew above 11 mm under any treatment (Fig. 4a). Overall, with Bythotrephes present, the final walleye larvae length after 21 days was on average 35.03% and 37.43% shorter than in non-invaded mesotrophic and noninvaded oligotrophic systems, respectively.
Larval walleye successfully grew in all treatments, however in the invaded oligotrophic treatment after 21 days, both initial sized larvae had negligible growth and in some cases a net loss of energy (Fig. 4b). The same was true of small initial sized larvae in the invaded mesotrophic treatment (Fig. 4b). The lower limit of the 95% bootstrapped confidence intervals for total larval growth under the invaded mesotrophic conditions were −8.54 J and −9.80 J for large and small initial sized larvae respectively, and −3.46 J for small initial sized larvae under the invaded oligotrophic treatment. As with final length, energy accumulated as growth in larval walleye in the presence of Bythotrephes was significantly lower than in non-invaded systems for oligotrophic systems only; while the pattern in means was similar in mesotrophic lakes, the large error in walleye growth from invaded systems overlapped with those in non-invaded systems.

Temperature sensitivity analysis
Modelled larval walleye were only slightly sensitive to water temperature; within treatments, 95% bootstrapped confidence intervals overlapped between cool and warm mean temperatures for both initial larval walleye sizes (Fig. 5), As a result, the growth patterns in response to Bythotrephes-induced decreases in prey availability remained the same when exposed to warmer temperatures as under the original temperature regime (Figs. 4, 5). Specifically, both large and small initial sized larvae reached larger final lengths in the non-invaded oligotrophic and non-invaded mesotrophic treatments compared to the invaded oligotrophic treatment under warmer temperatures, but only significantly so in oligotrophic lakes (Fig. 5).

Discussion
Using a simple bioenergetic and functional response modelling framework, we predicted lower growth rates of larval walleye based solely on changes in prey (zooplankton) biomass associated with Bythotrephes invasions. In oligotrophic lakes, our models predicted an average 37% reduction in body length at the end of their first three weeks compared to the noninvaded oligotrophic lakes. For invaded mesotrophic lakes, our models predicted body length to be 35% shorter compared to non-invaded mesotrophic lakes, though predictions were highly variable. These reductions in length relative to invasion status are generally consistent with a recent field study that reported declines in age-0 walleye length at the end of their first summer in lakes invaded by Bythotrephes compared to non-invaded systems (Hansen et al. 2020). The magnitude of our predicted declines were greater than those observed in the field, corrected for GDD (12.8% smaller; Hansen et al. 2020). These differences could be due to the high variation we observed in invaded mesotrophic lakes as well as additional factors that are not accounted for in our model. For example, although we considered lake trophic state, other lake characteristics such as depth and clarity are known to influence the growth of walleye which were not included in this study (Massie et al. 2021). Additionally, predation on YOY walleye may also limit growth, as predation can select against rapid growth (Biro et al. 2006). Furthermore, in invaded oligotrophic lakes, our models predicted larval walleye of Fig. 4 Results of the bioenergetics model in this study showing a final length (mm) of larval walleye (Sander vitreus; initial length of either 10.30 mm or 9.31 mm), and b total growth (J) of larval walleye with consumption varying based on zooplankton abundance treatments for 21 days: Invaded with Bythotrephes and mesotrophic (IM), invaded and oligotrophic (IO), not invaded and mesotrophic (NM), and not invaded and oligotrophic (NO). Error bars represent bootstrapped 95% confidence intervals both initial sizes could not survive on available zooplankton alone, suggesting that lakes below a certain trophic status might be more vulnerable to recruitment failure following Bythotrephes establishment.
Our findings provide evidence that food limitation due to zooplankton community changes resulting from the predatory impacts Bythotrephes is a likely mechanism for YOY walleye growth declines observed elsewhere. Our modelling exercise shows that these differences in YOY walleye growth patterns between lakes with and without Bythotrephes result directly from the distribution of zooplankton taxa biomass in lakes where Bythotrephes are established. This supports speculation in the literature that Bythotrephes-related changes in zooplankton abundance and community composition may be responsible for YOY walleye growth; both May et al. (2020) and Hansen et al. (2020) observed reduced walleye growth rate in the presence of Bythotrephes, and concluded these reductions were due to reduced zooplankton abundances over their study period. In this study, we observed reduced larval walleye growth in both oligotrophic conditions and mesotrophic conditions despite the fact that changes in prey biomass among the mesotrophic lakes supporting our modelling efforts were not significant at the 0.05 level (presumably due to small sample sizes of lakes representing the mesotrophic-invaded category); however, it is worth noting that the mean abundance for all three zooplankton taxa were visually lower in mesotrophic invaded lakes, which is supported by findings elsewhere in the literature (Dumitru et al. 2001;Fig. 5 Sensitivity analysis of daily water temperature using either typical/cool water temperatures (blue pattern bars), or mean annual water temperature increased by 5℃ (solid orange bars) on the growth of larval walleye (Sander vitreus) estimated through a bioenergetics model showing the final length (mm) of larval walleye (initial length of either 9.31 mm [a] or 10.3 mm [b]) with consumption varying based on zooplankton biomass treatments (estimated from 265 lakes) for 21 days: non-Bythotrephes-invaded mesotrophic (NM), invaded mesotrophic (IM), noninvaded oligotrophic (NO), and invaded oligotrophic (IO). Error bars represent bootstrapped 95% confidence intervals Decline of young-of-year walleye (Sander vitreus) growth due to Bythotrephes impacts p… Boudreau and Yan 2003;Strecker and Arnott 2008;Kerfoot et al. 2016).
Differences observed in the final size achieved by larval walleye in our simulations likely have significant implications for understanding walleye recruitment and population growth rates in Bythotrephesinvaded lakes, which may ultimately impact the long-term sustainability of these populations. Walleye can grow to ~ 15 to 25 mm within their first three weeks of feeding (Moore et al. 1994;Dabrowski et al. 2000), and this occurred for large initial sized larvae in both non-invaded treatments and the invaded mesotrophic treatment. However, this large final size was never achieved for small initial-sized larvae in any treatment, nor for large or small initial sized larvae in the oligotrophic invaded treatment. Slow larval walleye growth was likely due to an insufficient availability of cyclopoids early in life, resulting in insufficient growth to reach the length-dependent diet shifts to calanoids at 11 mm or the more energy dense Daphnia at 16 mm (McDonnell and Roth 2014). Because gape is dependent on fish length, decreased growth due to low prey availability delays the timing of diet shifts of larval walleye to larger, more energy dense prey. Decreased growth during the first three weeks of life also implies that ontogenetic diet shifts to benthic invertebrates, and ultimately, piscivory later in their first year of growth are also likely to be delayed (Uphoff et al. 2019). Delayed diet shifts are likely energetically detrimental, as larval walleye are confined to consuming less energy-dense prey items (zooplankton) for a longer period, ultimately with negative impacts on growth potential to the end of their first year. Importantly, small end of year size is known to result in greater overwinter mortality (Post and Evans 1989;Grote et al. 2018), suggesting walleye populations that exhibit smaller sizes at first feeding that appear to grow slower in Bythotrephesinvaded lakes are at an even higher risk of overwinter mortality.
Beyond overwinter mortality, cascading impacts of delayed YOY growth can impact other life history outcomes, including time to reproduction. Maturity of walleye is typically defined by a length at maturation relationship (Ma et al. 2021), and walleye age at maturation depends on growth rate/time to reach the length at maturity (Venturelli et al. 2010). Delayed maturation can act to reduce the proportion of spawning fish in the population, with negative impacts on future recruitment (Rowe and Thorpe 1990). Future studies that continue building this bioenergetics approach could extend the modelling period to also incorporate length-dependent diet shifts to benthic invertebrates and piscivory, which may ultimately demonstrate how Bythotrephes invasions impact the timing of diet shifts and the total growth of not just larval walleye, but ultimately growth and development into both YOY and juvenile stages.
Although our study found that prey availability in lakes invaded by Bythotrephes results in an energetic deficiency for larval walleye, walleye persist in many invaded oligotrophic lakes such as Lake Michigan (TP = 7-12 μg/L) and Lake Ontario (TP = 5.9 μg/L; Bunnell et al. 2011;Wang et al. 2012;Zorn et al. 2020), and invaded mesotrophic lakes such as Lake Winnipeg (TP = 15-20 μg/L; Bunting et al. 2016;Jansen et al. 2017). The reason our model may predict an such a great energy deficiency for larval walleye in oligotrophic lakes may be due to our inability to account for seasonal variation in zooplankton densities among our lakes. Like many datasets that trade off sampling effort across space against temporal detail, the lakes used in this study were based on one sampling event per lake (excluding the four lakes in Minnesota which were based on monthly events), at some point between May-August (Ross, personal communication). By contrast, first feeding in walleye typically occurs in spring (modelled here during the month of May or on Julian day 135-155). Therefore, our prey availability estimates may not necessarily coincide with the communities present at first larval walleye first feeding (spring) and may reflect densities later in the summer when native zooplankton are more impacted by Bythotrephes (Kerfoot et al. 2016;Stein et al. 2017). A more accurate representation of prey availability would be daily prey density estimates for the month of the simulation (late spring); unfortunately, daily zooplankton density estimates are rare for most lake ecosystems, as are early spring data immediately after ice off for most lakes of the size and region being considered here, due mainly to logistical reasons. Another potential issue may arise from the zooplankton taxa selected for prey availability estimates, as we included only prey preferred by larval walleye. It is possible prey alternatives may be consumed by larval walleye when preferred prey are not readily available. As an example, during their zooplanktivorous phase, larval walleye are known to consume Chaoborus larvae (Mathias and Li 1982), and some small benthic invertebrates such as chironomids (Galarowicz et al. 2006;Hoxmeier et al. 2006), neither of which are typically consumed by Bythotrephes (Foster and Sprules 2010;Jokela et al. 2017). While chironomids and/or Chaoborus could be diet items for larval walleye in Bythotrephes-invaded lakes where native zooplankton may be not readily available, their ability to be included in diets will still be limited by gape, as both are much larger than the zooplankton diet items considered here. Additionally, we made the simplifying assumption in this modelling exercise that activity was negligible (e.g., essentially included in basal metabolism), other studies have shown that this assumption is unrealistic, including for larval walleye (Madon and Culver 1993). Based on our findings, it is reasonable to expect that including increased activity in the metabolic costs of larval walleye would only exacerbate the patterns of growth declines and reduced survival observed here.
Recognizing these potential limitations, we believe our findings are important as they still provide a mechanistic framework through mathematical models, explicitly linking the connection between prey availability and walleye growth in wild populations. Future efforts may be improved by encouraging monitoring agencies to better emphasize early spring zooplankton community characterizations and undertake newer studies evaluating walleye diets from across a broader field of potential prey items. As such data and studies become available, our study can provide an important methodological framework for testing hypotheses linking prey availability to larval walleye growth.
The impact of Bythotrephes on larval walleye growth was greatest in oligotrophic lakes in our study, identifying them as potentially most vulnerable to Bythotrephes invasion. To determine the management implications of this finding, we examined publicly available survey data from lakes across the province of Ontario, Canada (Ontario Biodiversity Council 2021), and classified them according to trophic state as described previously using reported TP data (see methods). This lake database was then cross-referenced for lakes that had been sampled for walleye presence using the Broad Scale Monitoring (BSM) program, intended to represent the state of sport fisheries in Ontario (Ontario Ministry of Natural Resources and Forestry 2020a). Across 524 surveyed lakes which had been evaluated by both programs, we found that most lakes were classified as either oligotrophic (61.6%) or mesotrophic (19.3%). Of those lakes, walleye were present in 36.8% of oligotrophic lakes surveyed and 64.4% of mesotrophic lakes surveyed (Fig. 6). For lakes that support walleye, 91% fall into the mesotrophic to oligotrophic categories. Based on these survey data, our results suggest that among lakes identified and surveyed as important sport fisheries for provincial monitoring, the majority (91%) of walleye populations across Ontario may be vulnerable to reduced growth, and, in the case of oligotrophic Fig. 6 Distribution of walleye (Sander vitreus) among 524 surveyed lakes in Ontario, Canada, classified by lake trophic state based on the total phosphorus of the trophic state index (Carlson 1977). Walleye presence data are from Ontario Ministry of Natural Resources and Forestry (2020), and TP data are from the Ontario Biodiversity Council (2021) lakes, potentially recruitment failure, if invaded by Bythotrephes.
The compounding effects of both climate change and invasive species have been predicted to be the key drivers in biodiversity loss (Mainka and Howard 2010). Our temperature sensitivity analysis results suggest that the impacts of Bythotrephes invasion were similar under contemporary and warming climates. The response to temperature may have been insensitive because although the warmer temperature regime had an average annual temperature 5 °C higher than the contemporary regime, the average daily temperature among the 21-day simulation differed by only 2.33 °C between the two temperature regimes. Another important caveat of this simulation under warmer temperatures is that we do not have zooplankton data available from lakes with and without Bythotrephes at latitudes that experience a gaussian maximum of 23.5 °C. As such, our results should be interpreted primarily on the basis of how changes in temperature affect the scaling of maximum consumption and metabolism in the larval bioenergetics model.
As surface water temperatures are predicted to increase by 5 °C by the end of the twenty-first century (Maberly et al. 2020), YOY walleye that have previously been observed to have slower growth (Hansen et al. 2020) may be at higher risk of mortality with increasing temperature due to additional factors we could not account for in our model. Increased water temperatures due to climate change will influence not just zooplankton community composition, but also influence the phenological timing of plankton in lakes and optical thermal habitat for all aquatic species (Kraemer et al. 2021;Matsuzaki et al. 2021), a factor known to be important in walleye yield (Lester et al. 2004;Geisler et al. 2016). Although the number of waterbodies within the habitable temperature range for Bythotrephes are predicted to decrease with temperature in the next few decades (Walsh et al. 2020), climate change may shift some waterbodies into a suitable temperature range which could trigger "sleeper populations" of Bythotrephes to become highly abundant, likely impacting the prey availability for zooplanktivores in those systems (Walsh et al. 2016;Spear et al. 2021). As demonstrated here, predicting the impacts of Bythotrephes on the growth of fishes requires a holistic approach given that temperature strongly influences ecological processes, including planktonic community composition. Further research is suggested to expand on this study by evaluating the impacts of Bythotrephes on the growth of larval walleye under a broader range of climate scenarios that consider Bythotrephes densities and prey availability (community composition) as they fluctuate with temperature (Walsh et al. 2016).
This study aimed to determine if a change in zooplankton biomass due to Bythotrephes invasion could impact the growth rates of larval walleye. Our results suggest that walleye in less productive/oligotrophic lakes may be particularly at risk to Bythotrephes invasion, where zooplankton biomass post-invasion may be insufficient to sustain larval walleye growth. In more productive/mesotrophic lakes, larval walleye growth was slower in invaded lakes, but not significantly. Bioenergetics models have been used in the past to determine changes in fish growth due to invasive species (Johnston 1999;McDonnell and Roth 2014), but this is the first we know of to apply bioenergetics models in the evaluation of the impacts of Bythotrephes invasions on larval walleye specifically. Importantly, we have linked observed decreases in growth rate of YOY walleye found in Hansen et al. (2020) to the decreased prey availability in Bythotrephes-invaded lakes, expanding our knowledge on the impacts of invasive species to freshwater fisheries. and bioenergetic model output data are available from the Knowledge Network for Biocomplexity (https:// knb. ecoin forma tics. org/ view/ urn% 3Auuid% 3Aea6 8a408-8a33-4f2d-a0a3-8b0d8 48d11 b6). All other data and parameters used in models are available in the source literature referenced in the body text of the manuscript.

Declarations
Conflict of interest The authors declare that they have no competing interests.