Assessing the suitability of YY males and ZZ females as an invasive species population control method across life histories

Natural resource managers use tools to control invasive species. In theory, stocking YY males or ZZ females would allow managers to skew sex ratios until populations collapse. In combination with other suppression methods, such as removal, this approach could be incorporated into Integrated Pest Management plans. For example, fishery managers have stocked YY males to control isolated non-native brook trout (Salvelinus fontinalis) populations. However, life histories and demographic factors (e.g., lifespans) vary across species and could affect the feasibility of skewing sex ratios as an effective control strategy for a given population. Likewise, some species may have sex determinations that do not allow population control through sex-skewing methods. We compared five representative aquatic invasive species with global invasion ranges for potential control by skewing the sex ratio through closed population simulations: red swamp crayfish (Procambarus clarkii), zebra mussels (Dreissena polymorpha), lake trout (Salvelinus namaycush), silver carp (Hypophthalmichthys molitrix), and Nile tilapia (Oreochromis niloticus). We determined that Nile tilapia, red swamp crayfish, and zebra mussels would be the most suitable to control through skewing the sex ratio assuming appropriate sex determination exists in the species. Lake trout could be eliminated by stocking YY males but would require either long stocking periods or high stocking numbers because of the long lifespan of the species. Silver carp populations were more difficult to crash because they live longer and produce many recruits. Broadly, these patterns demonstrated that short lived species lend themselves to control by skewing the sex ratio.


Introduction
Resource managers often seek to control aquatic invasive species (AIS) due to their negative consequences on native ecosystems and economies (see reviews such as Havel et al. 2015 on the topic). Some widely used control tools, such as broad-spectrum pesticides and conventional harvest, are non-selective and may affect target and non-target organisms. For example, rotenone treatments for nuisance fish control are generally non-selective and may also adversely affect larval stage amphibians (Billman et al. 2012;Alvarez et al. 2017;Fried et al. 2018), gill-respiring and plastron-respiring aquatic insects (Booth et al. 2015), and general aquatic insect species richness (Woodford et al. 2013). Likewise, harvest tools such as gillnetting may capture, injure, or kill both target and non-target species, even if the non-target species can be released (Zhou et al. 2011). Furthermore, harvest tools may not be able to reasonably target species or individuals due to size limitations such as individuals being too small for nets (Hamley 1975). Resource managers have recognized the limitations of non-selective control methods and are seeking alternative methods to minimize effects on native organisms while maximizing the efficacy to control target species.
Control methods that combine multiple tools to maximize effectiveness and minimize non-target effects offer resource managers opportunities to reduce effects of invasive species while balancing tradeoffs to native species and ecosystems. One such framework for controlling invasive species is Integrated Pest Management (IPM). IPM can help and guide managers with the use of multiple control tools, including the management of AIS (Gaikowski and Kočovský 2021). Briefly, IPM balances the negative (and sometimes positive) effects of a species into management decision frameworks and applies multiple control tools for the overall control effort. IPM considers the ecosystem effects of the species (e.g., tradeoffs that exist when an invasive species is present) and the tradeoffs of the management (e.g., whether the "cure" can be worse than the "disease"). Ultimately, IPM helps managers consider that any action (including the lack of action) presents tradeoffs and, ideally, helps the managers balance these tradeoffs when managing a system. An IPM-based approach for AIS might include one or more types of direct mortality (e.g., pesticides, harvest); the release of pheromones to disrupt spawning, mating, migration, or other key processes; hydrologic actions such as reservoir drawdowns; movement barriers or other deterrents to limit range expansion; release of biocontrol agents; human education such as boater education about removing unwanted aquatic hitchhikers; or release of genetically modified organisms (GMOs) or non-GMOs (e.g., sterile males, YY males for species where males are the heterogametic sex [XY], or neofemales [ZZ females] for species where females are the heterogametic sex [WZ]). All these listed actions may affect target and nontarget species as well as human uses of the systems; hence, frameworks like IPM help managers balance these approaches. In this paper, we focus on the use of sex-skewing methods to cause a population crash of target species, recognizing this approach may work best within an integrated control strategy such as an IPM-based framework. Additionally, sex-skewing methods complement other IPM removal and control tools and may provide benefit in situations where other control tools may not remove enough individuals to crash a population. Lastly, a benefit of stocking organisms like YY males or neofemales, compared to stocking GMOs, is that the YY males avoid the negative perceptions held by some about GMOs (Schliekelman et al. 2005;Thresher et al. 2014).
Skewing sex ratios to cause population crashes has an established history for some taxa of insects (e.g., Knipling 1955), but only more recently has it been applied to aquatic vertebrate species with theorical work by Gutierrez and Teem (2006) and implementation by Schill et al. (2016). Furthermore, the effectiveness of this approach may increase when coupled with other tools such as harvest that do not completely remove a species (e.g., the habitat or fish size prevent harvest) or when the use of other control tools such as pesticide applications is not possible (e.g., a culturally or ecologically sensitive site). Aquaculturists commonly use sex manipulation to select for the sex that grows faster and reaches market or stocking size within the shortest duration. For example, Nile tilapia (Oreochromis niloticus) raised in aquaculture are often sex reversed to all-male progeny because females shift energy resources from growth to producing eggs (Scott et al. 1989). More recently, researchers and managers have applied this technology to control invasive species. Gutierrez and Teem (2006) completed simulations demonstrating how stocking of feminized YY males may be done to produce only male offspring (either normal males or YY males). After stocking, tilapia populations would further produce more male offspring based upon the ratio of normal males to YY males present. The resulting population of Nile tilapia could crash because the sex ratio becomes more skewed through time. Work by Schill and collaborators demonstrated how this approach could be applied for non-native brook trout (Salvelinus fontinalis) populations, including both the biological development of YY males (Schill et al. 2016) and simulations to guide their stocking . Initial assessments of these approaches for brook trout control in Idaho noted that "suppression has not been effective" (Kennedy et al. 2017) or reported mixed results in New Mexico as part of proof-of-concept studies (Armstrong and Caldwell 2021). Researchers have also examined the use of YY males to control other species. For example, McCormick et al. (2021) explored the control of common carp (Cyprinus carpio) with YY males through simulations.
The preceding observations illustrate the challenge for applying the use of YY males and neofemales as a control tool in a management context. First, the population demographics and dynamics of some species do not lend themselves to the use of stocked individuals to skew the sex ratio as a control tool. This lack of feasibility may be for biological reasons, such as species living decades or longer, or societal factors, such as public opposition to releasing a large number of an invasive species that may cause additional damage to ecosystems beyond that of the existing organisms. For example, simulations showed the release of YY males would not likely be a feasible control tool for grass carp (Ctenopharyngodon idella) because of their long lifespan and high fecundity (Erickson et al. 2017). Second, some species with amenable demographic life histories may not be controllable through skewing the sex ratio if the sex determination system is unknown or modified individuals cannot be efficiently produced for release at scale. Identification and assessment of these important life-history characteristics are necessary steps to determine the feasibility of sex skewing as one control method integrated into various AIS IPM programs.
In this study, we compared the suitability of controlling five AIS through sex-skewing methods via the stocking of YY males or ZZ females, depending upon the sex determination of a species. For this comparison, we used a population modeling approach to assess the feasibility of using stocking to skew sex ratios in combination with harvest. We used five representative AIS with different life histories from known nonnative species at various locations throughout the United States: red swamp crayfish (Procambarus clarkii), zebra mussels (Dreissena polymorpha), lake trout (Salvelinus namaycush), silver carp (Hypophthalmichthys molitrix), and Nile tilapia. In addition to representing different life histories, these five species cause ecological and economic damage outside of their native range in North America, the implicit focus of modeling efforts, as well as globally outside of North America (Crossman 1995;Kolar 2007;McLaughlan and Aldridge 2013;Loureiro et al. 2015;Krieg et al. 2020).

Red swamp crayfish
Red swamp crayfish are crustaceans native to the south-central United States that are commercially raised as a food source. Due to their popularity as an aquaculture species and wide distribution for live food markets, red swamp crayfish infestations now occur globally (Jin 2019; Oficialdegui et al. 2020). Invasive red swamp crayfish exert competitive pressure on native crayfish and cause habitat destruction through burrowing activity and macrophyte consumption (Loureiro et al. 2015). Red swamp crayfish also serve as a disease vector for crayfish plague (Aphanomyces astaci), which causes injury to populations of crayfish species outside of North America (Holdich et al. 2009). Red swamp crayfish readily adapt to a wide range of freshwater habitats, which facilitates successful colonization and expansion outside of their native range and has made control efforts difficult for resource managers.
Resource managers attempting to suppress, contain, or eradicate red swamp crayfish throughout their invaded ranges may choose from several existing options including developing chemical control agents (Schueller et al. 2021), carbon dioxide (Smerud et al. 2022), barriers, dewatering, trapping, harvest, and introducing predator fish (Krieg et al. 2020). However, many control strategies (e.g., trapping, harvest) target the adult life stage, and these efforts generally have not resulted in control of red swamp crayfish due to their short lifespan (2-5 years), rapid sexual maturity (2-5 months), high fecundity (100-500 eggs per female), and ability to disperse overland into new waterbodies (Schueller et al. 2021). Therefore, a combination of techniques may be beneficial to effectively manage red swamp crayfish populations, including controls that target early life stages. For example, researchers are currently investigating methods to skew red swamp crayfish sex ratios through time using neofemales that are modified from heterogametic (WZ) to homogametic (ZZ) at an early life stage and stocked into invaded areas (Savaya et al. 2020). Cross-fertilization of normal males with neofemales produces all male progenies (Ventura and Sagi 2012). Using nonfemales is fairly new to crayfish control, and a first step would be to determine the feasibility of skewing sex ratios as a technique for population control, building upon work by Savaya et al. (2020).

Zebra mussels
Zebra mussels are native to the Ponto-Caspian Seas (Gelembiuk et al. 2006). The species infested Europe in the nineteenth century and the Great Lakes in the late 1980s. The zebra mussel infestation continues to spread across North America (Stoeckel et al. 2004;Gelembiuk et al. 2006;Churchill et al. 2017). The species causes widespread effects such as altered food webs (Grigorovich et al. 2003), altered water quality, and clogged water pipes for electric power generation facilities and drinking water treatment plants (Connelly et al. 2007). Stoeckel et al. (2004) provide a detailed review of zebra mussel life history as part of their empirical study on the species' life history, and Chase and Bailey (1999) provide a review of the species' ecology. Zebra mussel reproduction is similar to that of marine mussels. Zebra mussels are synchronous broadcast spawners whose fertilized eggs develop into planktonic larva (known as a veliger) that, after transformation, settle as benthic-dwelling juveniles. Juvenile mussels mature to sexually mature adults in as little as 12 weeks, depending on water temperature. Zebra mussels have high fecundity, and a single female can produce > 1 million eggs during one spawning event (Sprung 1993). The species lives between 2 and 4+ years in North America (Chase and Bailey 1999). Sex determination in zebra mussels is unknown, and we did not find existing YY male type methods or similar modeling efforts in the literature for the species. For the purpose of this exercise, we will assume that male zebra mussels are heterogametic (XY).

Lake trout
Lake trout are native to parts of the United States and Canada and an invasive species both inside North America and globally (Crossman 1995). Crossman (1995) completed a survey of the species' invaded range and examined introduction efforts globally. Crossman (1995) found introduction efforts to be most successful in areas with similar conditions to the species' native range. Federal and State agencies and anglers introduced the species to lakes outside of their native range as a game fish starting as early as the l880s, both in North America and globally, but lake trout were often detrimental to native species (Halverson 2008). As part of control efforts in the United States, Syslo et al. (2011) developed and parametrized a matrix-based population model for the species that describes the species life history. The maximum age estimate in native habitats varies from 20 to 62 years (Syslo et al. 2011). Female lake trout may produce as many as 17,000 eggs in a year (Eschmeyer 1955). Donaldson and Hunter (1982) reviewed sex control methods for salmonids. Males are the heterogametic sex in lake trout, and conceptually, it should be possible to generate YY males of this species using established methods for other fishes. The topic of sex control in lake trout has received little attention despite a preliminary study completed nearly five decades ago that showed potential as a control measure (Wenstrom 1975). We found no published studies of lake trout control with YY males but did find a U.S. Fish and Wildlife Service newsletter describing future possible work on the topic by the Idaho Department of Fish and Game (U.S. Fish and Wildlife Service 2019).

Silver carp
Silver carp are native to China and eastern Siberia, and Kolar (2007) provides a detailed history of the species' introduction to North America and brief overview of the species global invasion range. Silver carp change native ecosystems by altering food webs and can comprise as many as 90 percent of the biomass in infested systems (Seibert et al. 2015). In North America, the maximum known age for silver carp is 13 years (Seibert et al. 2015), and the species can reach maturity at age 2 (Williamson and Garvey 2005). Individual females may produce millions of eggs during their lifespans, with individual females observed to produce up to 300,000 eggs per spawning event (Williamson and Garvey 2005). Partial sex reversal was previously achieved in early studies with silver carp (Mirza and Shelton 1988), indicating YY male creation would be viable. The recent clarification of the timing of gonadal sex differentiation in silver carp may warrant additional studies to improve the success rate of sex reversal in this species (Fatima et al. 2017). We found no YY-modeling efforts for silver carp. Previous research by Erickson et al. (2017) used grass carp as a surrogate for silver carp; however, grass carp live longer than silver carp and are therefore not a representative surrogate.

Nile tilapia
Nile tilapia are native to subtropical and tropical Africa and parts of the Middle East (Nico et al. 2022). Tilapia species (Oreochromis spp., Tilapia spp., and Serranochromis spp.) are some of the most commonly cultured species in aquaculture worldwide (Deines et al. 2016). Tilapia have escaped from cultivation and now occur nearly ubiquitously where they have been cultivated. We selected Nile tilapia as a representative tilapia species because of previous work on the species (e.g., Gutierrez and Teem 2006). Globally, Nile tilapia have degraded water quality and clarity, increased the abundance of microalgae, and decreased the abundance of microcrustaceans within their invaded range (Vitule et al. 2009). Tilapia demonstrate precocious sexual maturity (Mair and Little 1991;Mair et al. 1995;Hörstgen-Schwark and Langholz 1998) and high fecundity. The species becomes sexually mature in 5.6 to 10 months (Duponchelle and Panfili 1998).
Aquaculture often uses monosex populations of Nile tilapia because females redirect somatic growth energy into gamete development. In contrast, production of all male populations ensures that most energy resources are used for somatic growth to attain the desired size in the least amount of time. Because of this growth property, techniques exist for creating YY male Nile tilapia. Monosex populations of Nile tilapia can be created by administering sex hormones, either 17α-methyltestosterone or 17α-ethynylestradiol, to embryos (Rougeot et al. 2008a;Gennotte et al. 2014) or to fry to sex reverse males or females. Exposure to higher temperatures as embryos (Rougeot et al. 2008b) in Nile tilapia also results in a greater proportion of males. New methods to create YY males using genetically improved farmed tilapia are also in development and do not require the use of sex hormone treatment (Chen et al. 2019). Thus, given this commercial application of monosex populations, technology readily exists to create YY males for use as a control tool.
As previously noted, Gutierrez and Teem (2006) explored the use of YY males to control invasive Nile tilapia populations by including feminized YY males to control a population of Nile tilapia. They found a one-time release would not be feasible to crash a population and that a population recovered unless YY males were continuously introduced. Mathematically, the nonstable zero equilibrium would be expected because the model does not include an Allee effect (i.e., small population size limits recruitment), demographic stochasticity (i.e., random births or deaths affect population size), or a similar mechanism, so the trivial (population size of zero) equilibrium is unstable (Allen 2007(Allen , 2011.

Population model
We used a simple ordinary differential equation (ODE)-based model to capture population dynamics of the species. The model included sex structure and a logistic growth function (Allen 2007). We adapted the YY male model presented by Gutierrez and Teem (2006) and Savaya et al. (2020) for zebra mussels, lake trout, silver carp, and Nile tilapia (Eqs. 1-4). We differed from Gutierrez and Teem (2006) because we used different variable names (based upon Savaya et al. 2020) and did not include YY-females. We also used a weighted average for the sex ratio rather than using a straight multiplicative sex ratio (i.e., we added a denominator to Eqs. 1 and 2). We also thought this last assumption was unreasonable because the number of females, and not males, limits recruitment in populations where females produce many eggs that can be externally fertilized by one male. This model includes typical females ( F xx ) , typical males ( M xy ) , and YY males ( M yy ) as state variables. The model also includes a growth rate ( , B, in Gutierrez and Teem 2006) carrying capacity (K, same as Gutierrez and Teem 2006), natural mortality ( , D in Gutierrez and Teem 2006), and control mortality (e.g., harvest, pesticide; ,not present in Gutierrez and Teem 2006) and assumes half the population is naturally male and the other half naturally female (the same as Gutierrez and Teem 2006). The model also includes stocking for YY males ( W; in Gutierrez and Teem 2006): We used the ZZ female model presented by Savaya et al. (2020) for red swamp crayfish (Eqs. 5-8). The ZZ female model included similar terms as the YY male model (Eqs. 1-4) but included ZZ females rather than YY males; thus, the state variables are typical females ( F wz ) , typical males ( M zz ), and ZZ females ( F zz ). The demographic rate parameters are as previously defined for the YY male model other than the stocking parameter (W), which is of ZZ females rather than YY males:

and
We included four scenarios to demonstrate how each species might be controlled through stocking with individuals to skew the sex ratio: a reference scenario with no control ( = 0 , W = 0 ), a direct mortality only scenario (e.g., harvest, piscicide) ( > 0 , W = 0 ), stocking of YY males or ZZ females ( = 0 , W > 0 ), and both stocking and direct mortality ( > 0 , W > 0 ). We held parameter values for control scenarios (e.g., stocking numbers, years with control) constant within each species. For example, the direct mortality only and both stocking and direct mortality scenarios had the same harvest mortality rates and periods. For all scenarios, initial conditions were set at 100 typical females, 100 typical males, and 0 YY males/ZZ females. We simulated the start of control actions (i.e., stocking, take/mortality) early in the invasion to illustrate how YY males might work as part of an early detection and rapid response framework (Reaser et al. 2020). Our simulation scenarios used example take levels rather than prescriptive harvest levels based upon a specific situation or application.
The model used a constant carrying capacity (K) of 1000 individuals across species and represented a small population that could be controlled by IPM including sex-skewing tools. We found other parameter values from the literature (Table 1). In the control scenarios, direct mortality occurred from years 4 to 6 and stocking occurred from years 5 to 7 for all species. With silver carp, direct mortality occurred from years 4 to 6 with ν = 2 . Stocking With lake trout, direct mortality occurred from years 4 to 6 with = 20 . Stocking occurred from years 5 to 7 with 300 individuals stocked per year. With zebra mussels, direct mortality occurred from years 4 to 6 with = 10 . Stocking occurred from years 5 to 7 with 400 individuals stocked per year. With red swamp crayfish, direct mortality occurred from years 4 to 6 with = 4 . Stocking occurred from years 5 to 7 with 400 individuals stocked per year. Note that, because the model includes constant per capita natural mortality ( ) , in the reference scenario without control mortality or stocking, the total population will approach a population of K(1 − ) individuals, not the carrying capacity, K. We used Python (v 3.10.6; Python Software Foundation) with the solve_ivp function from the SciPy Library to numerically solve our systems of ODEs. We have included a conda environment as part of our software release (Erickson and Thompson 2023) that locked down our environment for reproducible numerical methods (Wilkinson et al. 2016; American Statistical Association 2017; Archmiller et al. 2020). Our software release also includes all code necessary to recreate our results including Jupyter Notebooks that walk the reader through our simulations, allowing people to not only re-create our results but also readily re-use our code. We plotted the number of typical females (i.e., F xx or F wz ) because these individuals would limit the population and their functional extinction would cause the population to crash. We also plotted the total population (P) through time because natural resource managers, as well as stakeholders, may be concerned about the total number of individuals present because of their effects on the natural systems.
A limitation of these proof-of-concept simulations is that the trivial (i.e., all 0) equilibria are unstable with both models (assuming that the natural mortality rate is lower than the growth rate [that is, < ], as would be the case for invasive species of concern). Thus, unless a population reaches numerical zero, the population will rebound even if < 1 female remains in the population. Likewise, these models do not consider other limiting factors such as an Allee effect, where minimal population sizes are required for successful recruitment (Allen 2007), or demographic stochasticity, which is important for small populations where random births and deaths affect a population's survival or extinction (Allen 2011). Likewise, the density term penalizes recruitment of typical males and females but not stocked individuals. If the total population is larger than the carrying capacity, K, this density term becomes negative for typical males and females and acts as a source of mortality for these subpopulations, in addition to natural and harvest mortality. This density dependent mortality does not act on the stocked subpopulation. Depending upon the species, these assumptions may or may not be biologically realistic. For example, stocked YY male brook trout have less favorable demographic rates compared to wild brook trout (Kennedy et al. 2018). We included this assumption to avoid prematurely dismissing YY males as a control tool. Thus, our stocking numbers may be low and required stocking times may be higher. Another assumption of these models is that no lags exist between recruitment and sexual maturity. This assumption was made to simplify models but would need to be assessed for actual species applications.

Red swamp crayfish
Using both direct mortality and the stocking of F zz females, the "Both" scenario was able to cause the functional extinction of red swamp crayfish (Fig. 1). The "Control only" scenario may have caused functional extinction, but the population quickly rebounded. The total maximum population with the "Both" scenario stayed near the carrying capacity of the system (Fig. 1b) when the highest number of F zz females was present. In contrast, the "Stock only" scenario had a maximum population of ~ 1.6 × the carrying capacity. With all scenarios, the population rebounded through time. In the case of the "Both" scenario and possibly the "Control only" scenario, the rebound from zero is a modeling artifact. However, the "Both" scenario stayed functionally extinct for ~ 3 years.

Zebra mussel
Using both direct mortality and the stocking of M YY males, the "Both" scenario was able to cause functional extinction of zebra mussels (Fig. 2). The "Control only" scenario did not cause a crash of the population. The total maximum population with the "Both" scenario stayed well under carrying capacity of the system (Fig. 2) when the highest number of M YY males was present. The "Stock only" scenario had a maximum population of ~ 1.05 × the Fig. 1 Results from four example scenarios for red swamp crayfish. The "Reference" scenario had no treatments. The "Control only" scenario had direct mortality. The "Stock only" scenario only had the stocking of F zz females. The "Both" sce-nario had both direct mortality and stocking of F zz females. a shows the number of typical females (F wz ) through time. b has the total population through time Fig. 2 Results from four example scenarios for zebra mussels. The "Reference" scenario had no treatments. The "Control only" scenario had direct mortality. The "Stock only" scenario only had the stocking of M YY males. The "Both" scenario had both direct mortality and stocking of M YY males. a shows the number of typical females (F wz ) through time. b has the total population through time carrying capacity. With all scenarios, the population rebounded through time. In the case of the "Both" scenario, this recovery from zero is a modeling artifact. However, the "Both" scenario stayed functionally extinct for ~ 8 years.

Lake trout
Using both direct mortality and the stocking of M YY males, the "Both" scenario was able to cause functional extinction of lake trout (Fig. 3). The "Control only" scenario came close to causing a crash of the population. The total maximum population with the "Both" scenario stayed well under carrying capacity of the system (Fig. 3) when the highest number of M YY males was present. The "Stock only" scenario had a maximum population of ~ 1.2 × the carrying capacity. With all scenarios, the population rebounded through time. In the case of the "Both" scenario, this recovery from zero is a modeling artifact. However, the "Both" scenario stayed functionally extinct for ~ 13 years.

Silver carp
Unlike the other species, silver carp did not reach their equilibrium population during the duration of the simulation due to the species' long lifespan. Using both direct mortality and the stocking of M YY males, the "Both" scenario was able to cause functional extinction of silver carp, but this extinction took almost 15 years posttreatment (Fig. 4). Unlike the other species, the "Control only" scenario did not come close to causing a crash of the population. The total maximum population with the "Both" scenario and "Stock only" scenario was greater than the reference population when the highest number of M YY males was present (Fig. 4). With all scenarios, the populations continued to grow through time.

Nile tilapia
Using both direct mortality and the stocking of M YY males, the "Both" scenario was able to cause functional extinction of lake trout (Fig. 5). The "Control only" scenario came close to causing a crash of the population, but the population rebounded. The total maximum population with the "Both" scenario stayed well under carrying capacity of the system (Fig. 5) when the highest number of M YY males was present. The "Stock only" scenario had a maximum population of ~ 1.1 × the carrying capacity. Unlike other species, the "Both" scenario caused the population to crash within the model, and both the typical female and total populations stayed extinct for ~ 13 years. Fig. 3 Results from four example scenarios for lake trout. The "Reference" scenario had no treatments. The "Control only" scenario had direct mortality. The "Stock only" scenario only had the stocking of M YY males. The "Both" scenario had both direct mortality and stocking of M YY males. a shows the number of typical females (F wz ) through time. b has the total population through time

Discussion
Our simulations predicted the crash of four of the five species using an IPM method with both skewing the sex and direct control. The taxon that crashed most readily was Nile tilapia, and the model numerically reached a population of zero. Red swamp crayfish and zebra mussels also had a population crash but also a rebound, which was likely a modeling artifact. Compared to other taxa, these three species have short lifespans. Release of sterile males has been successfully used to control mosquito, another short-lived species (Ernst et al. 2015). In contrast, we found lake trout could potentially be controlled with both direct control and YY male stocking, but stock fish persisted for long periods (e.g., decades). Furthermore, stocking with YY males may not be necessary in some locations such as Yellowstone Lake, Wyoming, USA, because intensive harvest is effectively controlling lake trout reproduction (Syslo et al. 2021). Lastly, silver carp were not controllable with our respective scenarios. This lack of control was due to the species' high recruitment and long lifespan. In contrast to most species that follow either a high recruitment ("r") strategy or long lived ("K") strategy (Pianka 1970), silver carp have both high recruitment and long lifespans and are thus both an "r" and "K" species.
The stocking levels necessary to control species also highlight a limitation of sex-skewing methods. Notably, many individuals may need to be released relative to the wild population size. Thus, this release of a large number of individuals for long-lived species like lake trout or silver carp may not be feasible, either from a human dimensions perspective or from an ecological damage perspective due to both real and perceived damages. Thus, consideration of both a species' biology and population dynamics as well as broader ecological and human considerations would likely be important for the use of sex-skewing tools.
Our simulations illustrate the importance of reducing the population either before or concurrently with stocking individuals to skew the sex of the population. An IPM that included harvest or similar control tools could decrease the number of stocked individuals necessary for skewing the population. Furthermore, if harvesting preferentially targeted nonstocked individuals, then fewer stocked individuals would be required to skew the sex ratios. For example, targeted harvest could be done by externally tagging YY males and then releasing these individuals if caught via nets. Likewise, species-specific control tools could also be used as part of IPM such as underwater acoustic deterrent systems or attractants (Cupp et al. 2021). More broadly, our findings demonstrate how skewing the sex ratio of a population as a control tool is not only species specific but also application specific. For example, controlling an isolated release of red swamp crayfish in a farm pond would be different from controlling silver carp in the Mississippi River. YY males might be a feasible control tool for closed systems but may be logistically infeasible for open systems such as large rivers unless the open systems could be closed (e.g., species-specific barriers) or targeting a geographically limited part of a species' range (e.g., fish species with specific spawning areas). Although our paper primarily focused on the demographic life history of potential species in their suitability for control through the stocking of YY males, not all species may be controlled because of sex determination constraints, time to sexual maturity, and lifespan. Lastly, one additional consideration of stocking is to ensure that the spawning of released individuals matches the wild population. For example, if a wild fish species spawns three times per year but the stocked individuals only spawn once per year, then sex-skewing approaches will either require more individuals or may not be feasible as a control tool.
Building upon the simulations we presented, skewing the sex of a population to cause collapse warrants additional consideration before natural resource managers can apply this tool to control invasive species. These limitations have been previously noted by others such as Klein et al. (2022), who noted both the benefits and challenges of YY males that also apply to similar approaches (such as ZZ females). Namely, major factors limiting the use of YY males include the ability to develop broodstock such as unknown sex determination for species, nonbinary sex differentiation, sex reversal, and the ability to produce and scale production of YY males or ZZ females; mathematical limitations such as the number of individuals required to stock or the lifespan of stocked individuals; and managerial limitations such as managers, stakeholders, and the general public's possible limited acceptance of stocking invasive species. Additionally, Klein et al. (2022) noted the approach remains largely untested in the field for fish species, and preliminary results show mixed results for fisheries management (Kennedy et al. 2017;Armstrong and Caldwell 2021). Furthermore, a similar application, the release of sterile males for sea lamprey (Petromyzon marinus) control in the Great Lakes, was halted due to no noticeable effect on sea lamprey population numbers (Ferreira-Martins et al. 2021).
Despite those limitations, skewing the sex ratio of populations to cause population crash has worked with insects and may work with some AIS as well. Lessons learned from mosquito applications could help AIS management, such as those learned in Florida, USA, with mosquito control (Vreysen et al. 2006;Ernst et al. 2015). For managers seeking to use sex-skewing tools, understanding the limitations of YY males and similar tools may be helpful. Besides development challenges, stocking levels may be higher and longer than a manager may realize. Likewise, our results showed that stocking YY males or ZZ females required the use of other removal tools to be effective. We did not include metapopulation dynamics, but these also would affect a real-world application of these tools. Lastly, the stocking of YY males or ZZ females would benefit from an IPM framework. An IPM-based application would help managers articulate their goals, understand management action tradeoffs, use multiple control tools, and include a monitoring and assessment methodology to ensure their management was having the desired, or at least acceptable, outcome.

Conclusion
Life history ultimately determines whether an invasive species can be controlled using YY males, ZZ females, or similar tools. Specifically, mathematical models indicate that controlling long-lived species using YY males or ZZ females would be challenging due to long generation times and corresponding long stocking times. The mathematics of YY male release also dovetail with other factors. First, ecological and sociological factors may limit releases. For example, stocking 1000 YY male tilapia may be perceived more favorably than the release of 1000 YY male silver carp because of risks of the latter to ecosystem services and detrimental effects from leaping silver carp. Second, sex determination mechanisms may limit the creation of YY males or ZZ females in some species. Additionally, using additional control tools to reduce wild populations would be important for sexskewing tools to be effective in controlling invasive populations.
Author contributions RAE and JJA conceived the study. RAE created and programmed the models used for the manuscript, and HMT verified the coding. GMA assisted with running the simulations. GMA and SAK assisted with the literature search for species parameter values. RAE, GMA, and SAK wrote the initial draft of the manuscript. ARC and RP provided simulation context and species expertise. All authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Funding Our funding is internal funding from our agency (USGS).
Data availability Our paper used parameter values from the literature, and we did not generate new empirical data. We have released specific model runs, parameter values, and parameter value sources as a U.S. Geological Survey software release (Erickson and Thompson 2023). We also list key parameter values and sources in Table 1.

Conflict of interest
The authors have no relevant financial or non-financial interests to disclose.
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