An integrodifference model for vegetation patterns in semi-arid environments with seasonality
Lukas Eigentler1,2,3, Jonathan A Sherratt4
1Department of Mathematics, Maxwell Institute for Mathematical Sciences, Heriot Watt University, Edinburgh, EH14 4AS, UK. LEigentler001@dundee.ac.uk.
Journal of Mathematical Biology
|September 5, 2020
Summary
Seasonal vegetation patterns in semi-deserts can be accurately modeled using partial differential equations (PDEs), even with distinct wet and dry seasons for plant growth and seed dispersal. The timing of seed dispersal does not affect pattern formation conditions.
Area of Science:
- Ecology
- Mathematical Biology
- Environmental Science
Background:
- Vegetation patterns are key features of semi-deserts globally.
- Seasonality in semi-arid climates synchronizes plant growth and seed dispersal with wet and dry periods.
Purpose of the Study:
- To reformulate the Klausmeier model into an integrodifference model accounting for seasonal plant growth and seed dispersal.
- To analyze the onset of spatial patterns in semi-arid vegetation dynamics.
Main Methods:
- Reformulation of the Klausmeier reaction-advection-diffusion model into an integrodifference equation model.
- Analysis of pattern onset conditions and numerical investigation of seed dispersal effects.
Main Results:
- Conditions for pattern onset in the integrodifference model are equivalent to the continuous PDE model, independent of dispersal timing.
- Long-range seed dispersal inhibits spatial pattern formation.
- The decay rate of the seed dispersal kernel significantly influences patterning.
Conclusions:
- Partial differential equation (PDE) models adequately describe seasonal vegetation pattern formation in semi-deserts, validating previous findings.
- Seed dispersal behavior, particularly long-range dispersal, plays a crucial role in regulating vegetation patterning.
Keywords:
Integrodifference modelNonlocal dispersalPattern formationSeasonal environmentsSemi-arid landscapesMore Related Videos
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