Mimicking the TYC strategy: Weak Allee effects, and a nonhyperbolic extinction boundary

TL;DR

This paper analyzes a sex-structured population model mimicking the Trojan Y Chromosome strategy, revealing a nonhyperbolic extinction boundary and the role of weak Allee effects in pattern formation, with implications for biocontrol.

Contribution

It introduces the FHMS strategy with weak Allee effects, demonstrating a nonhyperbolic extinction boundary and linking Allee effects to Turing pattern emergence in spatial models.

Findings

Extinction boundary can be nonhyperbolic in sex-structured models.

Weak Allee effect is necessary and sufficient for Turing patterns.

Comparison with strong Allee effects highlights different dynamics.

Abstract

The Trojan Y Chromosome strategy (TYC) is a genetic biocontrol strategy designed to alter the sex ratio of a target invasive population by reducing the number of females over time. Recently an alternative strategy is introduced, that mimics the TYC strategy by harvesting females whilst stocking males . We consider the FHMS strategy, with a weak Allee effect, and show that the extinction boundary need note be hyperbolic. To the best of our knowledge, this is the first example of a non-hyperbolic extinction boundary in mating models, structured by sex. Next, we consider the spatially explicit model and show that the weak Allee effect is both sufficient and necessary for Turing patterns to occur. We discuss the applicability of our results to large scale biocontrol, as well as compare and contrast our results to the case with a strong Allee effect.