Stochastic models for the Trojan Y-Chromosome eradication strategy of an invasive species

A Gender-Selective Harvesting Strategy: Weak Allee Effects and a Non-hyperbolic Extinction Boundary

Recently a gender-selective harvesting strategy has been proposed for possible control of aquatic invasive species, wherein females of the invasive species are harvested, whilst stocking the males (abbreviated as FHMS strategy) (Lyu et al. in Nat Resour Model 33(2):e12252, 2020). We consider the FHMS strategy with a weak Allee effect, and show that its extinction boundary need not be hyperbolic. To the best of our knowledge, this is the first example of a non-hyperbolic extinction boundary in two-compartment mating models structured by sex. The model possesses a rich dynamical structure, with several local co-dimension one bifurcations occurring. We also show the occurrence of a global homoclinic bifurcation, which has applicability for large scale strategic bio-control.

On Large and Small Data Blow-Up Solutions in the Trojan Y Chromosome Model

The Trojan Y Chromosome Strategy (TYC) is the only genetic biological control method in practice in North America for controlling invasive populations with an XX–XY sex determinism. Herein a modified organism, that is a supermale or feminised supermale, is introduced into an invasive population to skew the sex ratio over time, causing local extinction. We consider the three species TYC reaction diffusion model, and show that introduction of supermales above certain thresholds, and for certain initial data, solutions can blow-up in finite time. Thus, in order to have biologically meaningful solutions, one needs to restrict parameter and initial data regimes, in TYC type models.

Using YY supermales to destabilize invasive fish populations

A plausible biocontrol strategy for the eradication of invasive species involves augmenting wild populations with genetically modified supermales. Supermales contain double YY chromosomes. When they are augmented into a wild population, destabilization and eventual extinction occurs over time due to a strongly skewed gender ratio towards males. Here, we employ a mathematical model that considers an Allee effect, but we have discovered through simulation that the presence of supermales leads to an increase in the minimal number of females needed for survival at a value higher than the mathematically defined Allee effect. Using this effect, we focus our research on exploring the sensitivity of the optimized supply rate of supermale fish to the initial gender ratio and density of the wild populations. We find that the eradication strategy with optimized supply rate of supermales can be determined with knowledge of reproductive rate and survival fitness of supermale fish.

Sex determination in Neotropical fish: Implications ranging from aquaculture technology to ecological assessment

The high biodiversity of fish in the Neotropical region contrasts with scarce or biased studies on the mechanisms involved in the sex determination in members of this fauna. In this review, we attempted to compile the information available on determination, differentiation, and manipulation of sex for Neotropical species, with special focus on silversides and other two speciose groups, known as characins (Characiformes) and catfishes (Siluriformes). Currently, there is plenty of information available on chromosomal sex determination systems, which includes both male and female heterogamety with many variations, and sex chromosomes evolution at the macro chromosomal level. However, there is hitherto a blank in information at micro, gene/molecule levels and in research related to the effects of environmental cues on sex determination; most of reported studies are limited to silversides and guppies. In view of such a high diversity, it is critically necessary to establish key model species for relevant Neotropical fish taxa and also multi-disciplinary research groups in order to uncover the main patterns and trends that dictate the mechanisms of sex determination and gonadal differentiation in this icthyofauna. By increasing our knowledge on sex determination/differentiation with the identification of sex chromosome-linked markers or sex-determining genes, characterization of the onset timing of morphological gonadal differentiation, and determination of the environmental-hormonal labile period of gonadal sex determination in reference species, it will be possible to use those information as guidelines for application in other related groups. Overall, the strategic advance in this research field will be crucial for the development of biotechnological tools for aquaculture industry and for conservation of fish fauna from the Neotropical Region.