An integrodifference model for vegetation patterns in semi-arid environments with seasonality
Vegetation patterns are a characteristic feature of semi-deserts occurring on all continents except Antarctica. In some semi-arid regions, the climate is characterised by seasonality, which yields a synchronisation of seed dispersal with the dry season or the beginning of the wet season. We reformul...
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Online Access: | https://discovery.dundee.ac.uk/en/publications/45890d0f-f423-4ff2-ba00-fb692ea54db2 https://doi.org/10.1007/s00285-020-01530-w https://discovery.dundee.ac.uk/ws/files/51539442/Eigentler_Sherratt2020_Article_AnIntegrodifferenceModelForVeg.pdf http://www.scopus.com/inward/record.url?scp=85090198535&partnerID=8YFLogxK |
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ftunivdundeepure:oai:discovery.dundee.ac.uk:publications/45890d0f-f423-4ff2-ba00-fb692ea54db2 2024-04-28T07:56:17+00:00 An integrodifference model for vegetation patterns in semi-arid environments with seasonality Eigentler, L. Sherratt, Jonathan A. 2020-09 application/pdf https://discovery.dundee.ac.uk/en/publications/45890d0f-f423-4ff2-ba00-fb692ea54db2 https://doi.org/10.1007/s00285-020-01530-w https://discovery.dundee.ac.uk/ws/files/51539442/Eigentler_Sherratt2020_Article_AnIntegrodifferenceModelForVeg.pdf http://www.scopus.com/inward/record.url?scp=85090198535&partnerID=8YFLogxK eng eng https://discovery.dundee.ac.uk/en/publications/45890d0f-f423-4ff2-ba00-fb692ea54db2 info:eu-repo/semantics/openAccess Eigentler , L & Sherratt , J A 2020 , ' An integrodifference model for vegetation patterns in semi-arid environments with seasonality ' , Journal of Mathematical Biology , vol. 81 , no. 3 , pp. 875-904 . https://doi.org/10.1007/s00285-020-01530-w Integrodifference model Nonlocal dispersal Pattern formation Seasonal environments Semi-arid landscapes /dk/atira/pure/subjectarea/asjc/2600/2611 name=Modelling and Simulation /dk/atira/pure/subjectarea/asjc/1100/1101 name=Agricultural and Biological Sciences (miscellaneous) /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics article 2020 ftunivdundeepure https://doi.org/10.1007/s00285-020-01530-w 2024-04-10T00:39:29Z Vegetation patterns are a characteristic feature of semi-deserts occurring on all continents except Antarctica. In some semi-arid regions, the climate is characterised by seasonality, which yields a synchronisation of seed dispersal with the dry season or the beginning of the wet season. We reformulate the Klausmeier model, a reaction–advection–diffusion system that describes the plant–water dynamics in semi-arid environments, as an integrodifference model to account for the temporal separation of plant growth processes during the wet season and seed dispersal processes during the dry season. The model further accounts for nonlocal processes involved in the dispersal of seeds. Our analysis focusses on the onset of spatial patterns. The Klausmeier partial differential equations (PDE) model is linked to the integrodifference model in an appropriate limit, which yields a control parameter for the temporal separation of seed dispersal events. We find that the conditions for pattern onset in the integrodifference model are equivalent to those for the continuous PDE model and hence independent of the time between seed dispersal events. We thus conclude that in the context of seed dispersal, a PDE model provides a sufficiently accurate description, even if the environment is seasonal. This emphasises the validity of results that have previously been obtained for the PDE model. Further, we numerically investigate the effects of changes to seed dispersal behaviour on the onset of patterns. We find that long-range seed dispersal inhibits the formation of spatial patterns and that the seed dispersal kernel’s decay at infinity is a significant regulator of patterning. Article in Journal/Newspaper Antarc* Antarctica Discovery - University of Dundee Online Publications Journal of Mathematical Biology 81 3 875 904 |
institution |
Open Polar |
collection |
Discovery - University of Dundee Online Publications |
op_collection_id |
ftunivdundeepure |
language |
English |
topic |
Integrodifference model Nonlocal dispersal Pattern formation Seasonal environments Semi-arid landscapes /dk/atira/pure/subjectarea/asjc/2600/2611 name=Modelling and Simulation /dk/atira/pure/subjectarea/asjc/1100/1101 name=Agricultural and Biological Sciences (miscellaneous) /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics |
spellingShingle |
Integrodifference model Nonlocal dispersal Pattern formation Seasonal environments Semi-arid landscapes /dk/atira/pure/subjectarea/asjc/2600/2611 name=Modelling and Simulation /dk/atira/pure/subjectarea/asjc/1100/1101 name=Agricultural and Biological Sciences (miscellaneous) /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics Eigentler, L. Sherratt, Jonathan A. An integrodifference model for vegetation patterns in semi-arid environments with seasonality |
topic_facet |
Integrodifference model Nonlocal dispersal Pattern formation Seasonal environments Semi-arid landscapes /dk/atira/pure/subjectarea/asjc/2600/2611 name=Modelling and Simulation /dk/atira/pure/subjectarea/asjc/1100/1101 name=Agricultural and Biological Sciences (miscellaneous) /dk/atira/pure/subjectarea/asjc/2600/2604 name=Applied Mathematics |
description |
Vegetation patterns are a characteristic feature of semi-deserts occurring on all continents except Antarctica. In some semi-arid regions, the climate is characterised by seasonality, which yields a synchronisation of seed dispersal with the dry season or the beginning of the wet season. We reformulate the Klausmeier model, a reaction–advection–diffusion system that describes the plant–water dynamics in semi-arid environments, as an integrodifference model to account for the temporal separation of plant growth processes during the wet season and seed dispersal processes during the dry season. The model further accounts for nonlocal processes involved in the dispersal of seeds. Our analysis focusses on the onset of spatial patterns. The Klausmeier partial differential equations (PDE) model is linked to the integrodifference model in an appropriate limit, which yields a control parameter for the temporal separation of seed dispersal events. We find that the conditions for pattern onset in the integrodifference model are equivalent to those for the continuous PDE model and hence independent of the time between seed dispersal events. We thus conclude that in the context of seed dispersal, a PDE model provides a sufficiently accurate description, even if the environment is seasonal. This emphasises the validity of results that have previously been obtained for the PDE model. Further, we numerically investigate the effects of changes to seed dispersal behaviour on the onset of patterns. We find that long-range seed dispersal inhibits the formation of spatial patterns and that the seed dispersal kernel’s decay at infinity is a significant regulator of patterning. |
format |
Article in Journal/Newspaper |
author |
Eigentler, L. Sherratt, Jonathan A. |
author_facet |
Eigentler, L. Sherratt, Jonathan A. |
author_sort |
Eigentler, L. |
title |
An integrodifference model for vegetation patterns in semi-arid environments with seasonality |
title_short |
An integrodifference model for vegetation patterns in semi-arid environments with seasonality |
title_full |
An integrodifference model for vegetation patterns in semi-arid environments with seasonality |
title_fullStr |
An integrodifference model for vegetation patterns in semi-arid environments with seasonality |
title_full_unstemmed |
An integrodifference model for vegetation patterns in semi-arid environments with seasonality |
title_sort |
integrodifference model for vegetation patterns in semi-arid environments with seasonality |
publishDate |
2020 |
url |
https://discovery.dundee.ac.uk/en/publications/45890d0f-f423-4ff2-ba00-fb692ea54db2 https://doi.org/10.1007/s00285-020-01530-w https://discovery.dundee.ac.uk/ws/files/51539442/Eigentler_Sherratt2020_Article_AnIntegrodifferenceModelForVeg.pdf http://www.scopus.com/inward/record.url?scp=85090198535&partnerID=8YFLogxK |
genre |
Antarc* Antarctica |
genre_facet |
Antarc* Antarctica |
op_source |
Eigentler , L & Sherratt , J A 2020 , ' An integrodifference model for vegetation patterns in semi-arid environments with seasonality ' , Journal of Mathematical Biology , vol. 81 , no. 3 , pp. 875-904 . https://doi.org/10.1007/s00285-020-01530-w |
op_relation |
https://discovery.dundee.ac.uk/en/publications/45890d0f-f423-4ff2-ba00-fb692ea54db2 |
op_rights |
info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/10.1007/s00285-020-01530-w |
container_title |
Journal of Mathematical Biology |
container_volume |
81 |
container_issue |
3 |
container_start_page |
875 |
op_container_end_page |
904 |
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1797582739264765952 |