A logistic two-sex model with mate-finding Allee effect

We consider a ratio-dependent predator-prey system with a mate-finding Allee effect on prey. The stability properties of the equilibria and a complete bifurcation analysis, including the existence of a saddle-node, a Hopf bifurcation, and, a Bogdanov-Takens bifurcations, have been proved theoretically and numerically. The blow-up method has been applied to investigate the structure of a neighborhood of the origin. Our mathematical results show the mate-finding Allee effect can reduce the complexity of system behaviors by making the complicated equilibrium less complicated, and it can be a destabilizing force as well, which makes the system has a high possibility of being threatened with extinction in ecology.

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Evolution of mate-finding Allee effect in prey

Journal of Theoretical Biology ◽

10.1016/j.jtbi.2017.12.024 ◽

2018 ◽

Vol 441 ◽

pp. 9-18 ◽

Cited By ~ 8

Author(s):

Luděk Berec ◽

Veronika Bernhauerová ◽

Barbara Boldin

Keyword(s):

Allee Effect ◽

Mate Finding

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Dynamics of a pest management model with mate‐finding Allee effect induced by sterile release

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.7901 ◽

2021 ◽

Author(s):

Zongmin Yue ◽

Jiao Wang

Keyword(s):

Pest Management ◽

Allee Effect ◽

Management Model ◽

Mate Finding

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Contrasting effects of ecological and evolutionary processes on range expansions and shifts

10.22541/au.161217810.03338053/v1 ◽

2021 ◽

Author(s):

Christopher Weiss-Lehman ◽

Allison Shaw

Keyword(s):

Allee Effect ◽

Extinction Risk ◽

Range Shifts ◽

Evolutionary Processes ◽

Ecological Processes ◽

Mate Finding ◽

Factors Influencing ◽

Spatial Sorting ◽

And Shifts ◽

Dispersal Evolution

Research has conclusively demonstrated the potential for dispersal evolution in range expansions and shifts through a process termed spatial sorting. However, the degree of dispersal evolution observed has varied substantially among organisms. Further, it is unknown how the factors influencing dispersal evolution might impact other ecological processes at play. We use an individual-based model to investigate the effects of the underlying genetics of dispersal and mode of reproduction in range expansions and shifts. Spatial sorting behaves similarly to natural selection in that dispersal evolution increases with sexual selection and loci number. Contrary to our predictions, however, increased dispersal does not always improve a population’s ability to track changing conditions. The mate finding Allee effect inherent to sexual reproduction increases extinction risk during range shifts, counteracting the beneficial effect of increased dispersal evolution. Our results demonstrate the importance of considering both ecological and evolutionary processes for understanding range expansions and shifts.

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