Using YY supermales to destabilize invasive fish populations
Introduction
Invasive aquatic species continue to be an escalating problem throughout the world. Upon successfully establishing themselves in a new environment, they can be difficult to manage and virtually impossible to eradicate and the control costs can become prohibitive. In an effort to find a better method for eradicating invasive fish species, a sex-skewing technique originally described by Scott et al. (1989), might be used as an autocidal biocontrol strategy in the invasive fish population. Gutierrez and Teem (2006) proposed an autocidal biocontrol TrojanY-Chromosome (TYC) strategy to eliminate invasive alien species with an sex-determination system via a constant release of sex-reversed supermales. Many fish species with an sex-determination system have separate sexes throughout life, a condition known as gonochorism. However, some fish species exhibit sequential hermaphroditism (viz., parrotfish, damselfish) or simultaneous hermaphroditism (viz., Serranidae) (Devlin and Nagahama, 2002). Therefore, the TYC eradication strategy is particularly relevant to gonochoristic fish species (which do not exhibit sequential or simultaneous hermaphroditism) with an environmentally reversible genetic sex determination system. Other life-history characteristics important for sex-reversal in captive breeding includes fishes with sexual dimorphism and rapid life-cycles that would allow subsequent generations of fish to spread rapidly.
Exogenous sex hormones are used widely to manipulate gender in aquaculture fishes. Exposure to certain sex hormones can feminize fish (Scott et al., 1989). Since feminization of male fish using sex reversal hormones (viz. estrogen) sometimes becomes inefficient due to the stronger tolerance of some fish species to estrogens (Shelton, 1986, Teem and Gutierrez, 2010), another viable way to produce fertile female fish is by treating male fish using estrogen together with exogenous Flutamide to block the function of endogenous androgen (Jiang et al., 2018). The phenotypic female (neofemale) fish when mated with wild type male fish produce wild-type females, wild-type males and supermales. supermale fish can also be produced by using androgenesis which does not involve in feminization (Jiang et al., 2018). Crossing these homozygous supermales with wild-type females yield male offspring (cf. Fig. 1). The TYC strategy has been used to obtain supermales in a variety of fish, including Nile tilapia (Mair et al., 1997, Vera Cruz et al., 1999), yellow catfish (Liu et al., 2013), and brook trout (Schill et al., 2016). Further, Gutierrez and Teem (2006) proposed to supply feminized supermales into an undesired population that would produce supermales and males only. Since supermales are more resistant to feminization than wild type species (Liu et al., 2013, Mair et al., 1997), by considering the cost-effectiveness of the eradication strategy, a constant rate of injection of non-feminized supermales to the target invasive fish population seems more viable. Under the assumption that our target fish species have an system of sex determination and supermale fish can survive and reproduce successfully, a constant supply of non-feminized supermale fish into the system would generate of wild-type male progeny and wild-type female progeny, skewing the sex ratio towards the dominance of males (cf. Fig. 1) (Wang et al., 2016).
At low population density, the per-capita growth rate can be related positively to the population density, a phenomenon broadly referred to as an Allee effect (Courchamp et al., 1999, Stephens and Sutherland, 1999). In the context of marine fishes, researchers observe that an Allee effect is significant at very low population size and with bias in sex ratio (Perälä and Kuparinen, 2017, Wedekind, 2012). There is strong statistical evidence that the local extinction of Atlantic cod (Gadus morhua) in the southern Gulf of St. Lawrence and the collapse of Atlantic herring (Clupea harengus) population in the North Sea are due to predation-driven Allee effect (Neuenhoff et al., 2018, Perälä and Kuparinen, 2017). A population with the sex ratio biased towards males would lead to difficulty in finding a mate, even if it utilizes powerful sex pheromones. Such biased sex ratios strengthen pre-existing Allee effects due to mating failure, thereby increasing the risk of population extinction. The model developed here considers a constant supply of non-feminized supermale invasive fish as a biocontrol of the invasive fish species. By considering Allee effects in an invasive fish population and a continual injection of non-feminized supermale invasive fish above some critical threshold, the rarity of wild-type females would lead to difficulty in finding mates, and so the invasive fish population would be likely to eventually become locally extinct. However, it is not economically viable to keep introducing supermales indefinitely. The time for terminating the supply of supermales is critical to preventing the wild-type invasive species from recovering in the absence of supermale invasive fish (Wang et al., 2014).
In this paper, our goal is to find the minimum viable supply rate of supermale invasive species together with the minimum window of time required to inject the supermales and successfully get rid of the wild-type invasive fish population. We also determine how the minimum time for supplying the supermales varies with the supply rates above its minimum threshold for eliminating the wild-type population. Researchers (Bayraktarov et al., 2014) observed that there can be a significant variation in the population density of the invasive fish across its non-native ranges. Therefore, we need to analyze how the optimized management strategy might change as a function of initial gender ratio and population density of the wild-type invasive fish population. Since the supermales might not be as reproductively fit as that of the wild-type fishes (Kennedy et al., 2018, Schill et al., 2017), we analyze how the minimum viable supply rate and the minimum continual supply time varies with the reproductive fitness and survival fitness of supermale species.
Section snippets
Model equations
For the model described below, , and represent the population density of wild-type female invasive fish, wild-type male invasive fish and non-feminized supermale invasive fish, respectively, at time . The rate of injection of supermale invasive fish is (time−1 density−1). The reproduction rate of wild-type invasive fish species due to the interactions between male and female wild-type invasive fish species is (time−1 density−2), whereas the reproduction rate of
Results
Discussion
This study is intended to present a theoretical analysis of a biocontrol strategy to eliminate invasive fish from marine protected areas by considering a mathematical model of three genotype/phenotype variants of the invasive fish species with Allee effect. The proposed model is essentially a modified version of the classical TYC model (Gutierrez and Teem, 2006) which satisfies the non-negativity conditions and prevents blow-up of solutions in a finite time (Parshad et al., 2019). The model
Acknowledgments
JB is supported by the grants from Science and Engineering Research Board (SERB), Govt. of India (File No. TAR/2018/000283). SB acknowledges financial support in the form of J C Bose Fellowship by the SERB, Govt. of India , no. SB/S2/JCB-023/2015.
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