Nonlocal Mechanistic Models in Ecology: Numerical Methods and Parameter Inferences
Animals utilize their surroundings to make decisions on how to navigate and establish their territories. Some species gather information about competing groups by observing them from a distance, detecting scent markings, or relying on memories of encounters with rival populations. Gathering such inf...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/13/19/10598 |
| _version_ | 1797576282309918720 |
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| author | Erin Ellefsen Nancy Rodríguez |
| author_facet | Erin Ellefsen Nancy Rodríguez |
| author_sort | Erin Ellefsen |
| collection | DOAJ |
| description | Animals utilize their surroundings to make decisions on how to navigate and establish their territories. Some species gather information about competing groups by observing them from a distance, detecting scent markings, or relying on memories of encounters with rival populations. Gathering such information involves a nonlocal process, prompting the development of mechanistic models that incorporate nonlocal terms to explore species movement. These models, however, pose analytical and computational challenges. In this study, we focus on a multi-species advection–diffusion model that incorporates nonlocal advection. To efficiently compute solutions for this system involving a large number of interacting species, we introduce a numerical scheme using spectral methods. Additionally, we examine the influence of various parameters and interaction potentials on population densities. Our investigation aims to provide a method to identify the primary factors driving species movements, and we validate our approach using synthetic data. |
| first_indexed | 2024-03-10T21:50:00Z |
| format | Article |
| id | doaj.art-de4adb3ff17741a6a2e10d08fa574d6e |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T21:50:00Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-de4adb3ff17741a6a2e10d08fa574d6e2023-11-19T14:01:38ZengMDPI AGApplied Sciences2076-34172023-09-0113191059810.3390/app131910598Nonlocal Mechanistic Models in Ecology: Numerical Methods and Parameter InferencesErin Ellefsen0Nancy Rodríguez1Earlham College, Richmond, IN 47374, USADepartment of Applied Mathematics, University of Colorado Boulder, Boulder, CO 80309, USAAnimals utilize their surroundings to make decisions on how to navigate and establish their territories. Some species gather information about competing groups by observing them from a distance, detecting scent markings, or relying on memories of encounters with rival populations. Gathering such information involves a nonlocal process, prompting the development of mechanistic models that incorporate nonlocal terms to explore species movement. These models, however, pose analytical and computational challenges. In this study, we focus on a multi-species advection–diffusion model that incorporates nonlocal advection. To efficiently compute solutions for this system involving a large number of interacting species, we introduce a numerical scheme using spectral methods. Additionally, we examine the influence of various parameters and interaction potentials on population densities. Our investigation aims to provide a method to identify the primary factors driving species movements, and we validate our approach using synthetic data.https://www.mdpi.com/2076-3417/13/19/10598animal movementnon-local mechanistic modelsadvection–diffusion models |
| spellingShingle | Erin Ellefsen Nancy Rodríguez Nonlocal Mechanistic Models in Ecology: Numerical Methods and Parameter Inferences Applied Sciences animal movement non-local mechanistic models advection–diffusion models |
| title | Nonlocal Mechanistic Models in Ecology: Numerical Methods and Parameter Inferences |
| title_full | Nonlocal Mechanistic Models in Ecology: Numerical Methods and Parameter Inferences |
| title_fullStr | Nonlocal Mechanistic Models in Ecology: Numerical Methods and Parameter Inferences |
| title_full_unstemmed | Nonlocal Mechanistic Models in Ecology: Numerical Methods and Parameter Inferences |
| title_short | Nonlocal Mechanistic Models in Ecology: Numerical Methods and Parameter Inferences |
| title_sort | nonlocal mechanistic models in ecology numerical methods and parameter inferences |
| topic | animal movement non-local mechanistic models advection–diffusion models |
| url | https://www.mdpi.com/2076-3417/13/19/10598 |
| work_keys_str_mv | AT erinellefsen nonlocalmechanisticmodelsinecologynumericalmethodsandparameterinferences AT nancyrodriguez nonlocalmechanisticmodelsinecologynumericalmethodsandparameterinferences |