Presentation Title

Mathematically Modeling the Persistence of Red-Legged Frogs

Faculty Mentor

Courtney Davis

Start Date

23-11-2019 9:00 AM

End Date

23-11-2019 9:15 AM

Location

Markstein 208

Session

oral 1

Type of Presentation

Oral Talk

Subject Area

physical_mathematical_sciences

Abstract

The California red-legged frog is classified as ‘threatened’ by U.S. Fish and Wildlife with factors such as predation by invasive species, drought, and habitat loss contributing to their decline. Some new populations have been established through reintroductions and natural dispersals. One dispersal in the Santa Monica Mountains led to frogs washing downstream and reproducing where invasive red swamp crayfish have previously existed but have been removed via intensive crayfish trapping. This trapping may have been critical in enabling the dispersed frogs to establish in this stream site. We create a discrete stage-structured mathematical model that describes California red-legged frog life history dynamics and includes density-dependent migration. The model is validated against frog field data. We expand the model to consider crayfish predation on the aquatic life stages of the frogs and incorporate invasive crayfish trapping. Using equilibrium and sensitivity analysis as well as numerical simulations, we predict local persistence of the frog population and investigate which crayfish trapping regimes most benefit frog persistence. Modeling results inform conservation efforts.

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Nov 23rd, 9:00 AM Nov 23rd, 9:15 AM

Mathematically Modeling the Persistence of Red-Legged Frogs

Markstein 208

The California red-legged frog is classified as ‘threatened’ by U.S. Fish and Wildlife with factors such as predation by invasive species, drought, and habitat loss contributing to their decline. Some new populations have been established through reintroductions and natural dispersals. One dispersal in the Santa Monica Mountains led to frogs washing downstream and reproducing where invasive red swamp crayfish have previously existed but have been removed via intensive crayfish trapping. This trapping may have been critical in enabling the dispersed frogs to establish in this stream site. We create a discrete stage-structured mathematical model that describes California red-legged frog life history dynamics and includes density-dependent migration. The model is validated against frog field data. We expand the model to consider crayfish predation on the aquatic life stages of the frogs and incorporate invasive crayfish trapping. Using equilibrium and sensitivity analysis as well as numerical simulations, we predict local persistence of the frog population and investigate which crayfish trapping regimes most benefit frog persistence. Modeling results inform conservation efforts.