Memory-driven movement model for periodic migrations. (English) Zbl 1457.92199
Summary: We propose a model for memory-based movement of an individual. The dynamics are modeled by a stochastic differential equation, coupled with an eikonal equation, whose potential depends on the individual’s memory and perception. Under a simple periodic environment, we discover that both long and short-term memory with appropriate time scales are essential for producing expected periodic migrations.
MSC:
| 92D50 | Animal behavior |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
References:
| [1] | Abrahms, B.; Hazen, E. L.; Aikens, E. O.; Savoca, M. S.; Goldbogen, J. A.; Bograd, S. J.; Jacox, M. G.; Irvine, L. M.; Palacios, D. M.; Mate, B. R., Memory and resource tracking drive blue whale migrations, Proceedings of the National Academy of Sciences, 116, 12, 5582-5587 (2019) |
| [2] | Amadori, D.; Goatin, P.; Rosini, M. D., Existence results for Hughes’ model for pedestrian flows, Journal of Mathematical Analysis and Applications, 420, 1, 387-406 (2014) · Zbl 1310.35163 |
| [3] | Bardi, M.; Capuzzo-Dolcetta, I., Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations (2008), Springer Science & Business Media · Zbl 1134.49022 |
| [4] | Bartlam-Brooks, H. L.; Beck, P. S.; Bohrer, G.; Harris, S., In search of greener pastures: Using satellite images to predict the effects of environmental change on zebra migration, Journal of Geophysical Research: Biogeosciences, 118, 4, 1427-1437 (2013) |
| [5] | Bennett, D. A.; Tang, W., Modelling adaptive, spatially aware, and mobile agents: Elk migration in yellowstone, International Journal of Geographical Information Science, 20, 9, 1039-1066 (2006) |
| [6] | Berbert, J. M.; Fagan, W. F., How the interplay between individual spatial memory and landscape persistence can generate population distribution patterns, Ecological Complexity, 12, 1-12 (2012) |
| [7] | Bracis, C.; Mueller, T., Memory, not just perception, plays an important role in terrestrial mammalian migration, Proceedings of the Royal Society B: Biological Sciences, 20170449 (2017) |
| [8] | Cantrell, R. S.; Cosner, C.; Lou, Y., Evolution of dispersal and the ideal free distribution, Mathematical Biosciences and Engineering, 7, 1, 17-36 (2010) · Zbl 1188.35102 |
| [9] | Cartee, E., Vladimirsky, A., 2018. Anisotropic challenges in pedestrian flow modeling, arXiv preprint arXiv:1706.06217. · Zbl 1404.35283 |
| [10] | Chacon, A.; Vladimirsky, A., Fast two-scale methods for eikonal equations, SIAM Journal on Scientific Computing, 34, 2, A547-A578 (2012) · Zbl 1244.49047 |
| [11] | Di Francesco, M.; Markowich, P. A.; Pietschmann, J.-F.; Wolfram, M.-T., On the hughes’ model for pedestrian flow: The one-dimensional case, Journal of Differential Equations, 250, 3, 1334-1362 (2011) · Zbl 1229.35139 |
| [12] | Fagan, W. F., Migrating whales depend on memory to exploit reliable resources, Proceedings of the National Academy of Sciences, 116, 12, 5217-5219 (2019) |
| [13] | Fagan, W. F.; Lewis, M. A.; Auger-Méthé, M.; Avgar, T.; Benhamou, S.; Breed, G.; LaDage, L.; Schlägel, U. E.; Tang, W.-W.; Papastamatiou, Y. P., Spatial memory and animal movement, Ecology Letters, 16, 10, 1316-1329 (2013) |
| [14] | Fagan, W. F.; Gurarie, E.; Bewick, S.; Howard, A.; Cantrell, R. S.; Cosner, C., Perceptual ranges, information gathering, and foraging success in dynamic landscapes, The American Naturalist, 189, 5, 474-489 (2017) |
| [15] | Gill, F. B., Trapline foraging by hermit hummingbirds: competition for an undefended, renewable resource, Ecology, 69, 6, 1933-1942 (1988) |
| [16] | Hughes, R. L., A continuum theory for the flow of pedestrians, Transportation Research Part B: Methodological, 36, 6, 507-535 (2002) |
| [17] | Hughes, R. L., The flow of human crowds, Annual Review of Fluid Mechanics, 35, 1, 169-182 (2003) · Zbl 1125.92324 |
| [18] | Jesmer, B. R.; Merkle, J. A.; Goheen, J. R.; Aikens, E. O.; Beck, J. L.; Courtemanch, A. B.; Hurley, M. A.; McWhirter, D. E.; Miyasaki, H. M.; Monteith, K. L.; Kauffman, M. J., Is ungulate migration culturally transmitted? evidence of social learning from translocated animals, Science, 361, 6406, 1023-1025 (2018) |
| [19] | Kitchin, R., Blades, M., 2002. The Cognition of Geographic Space, vol. 4, Ib Tauris. |
| [20] | Lam, K.-Y.; Lou, Y., Evolution of conditional dispersal: evolutionarily stable strategies in spatial models, Journal of Mathematical Biology, 68, 4, 851-877 (2014) · Zbl 1293.35140 |
| [21] | Martínez-García, R.; Calabrese, J. M.; Mueller, T.; Olson, K. A.; López, C., Optimizing the search for resources by sharing information: Mongolian gazelles as a case study, Physical Review Letters, 110, 24, Article 248106 pp. (2013) |
| [22] | Osborne, J.; Clark, S.; Morris, R.; Williams, I.; Riley, J.; Smith, A.; Reynolds, D.; Edwards, A., A landscape-scale study of bumble bee foraging range and constancy, using harmonic radar, Journal of Applied Ecology, 36, 4, 519-533 (1999) |
| [23] | Schlägel, U. E.; Lewis, M. A., Detecting effects of spatial memory and dynamic information on animal movement decisions, Methods in Ecology and Evolution, 5, 11, 1236-1246 (2014) |
| [24] | Schlägel, U. E.; Merrill, E. H.; Lewis, M. A., Territory surveillance and prey management: Wolves keep track of space and time, Ecology and Evolution, 7, 20, 8388-8405 (2017) |
| [25] | Sethian, J. A., A fast marching level set method for monotonically advancing fronts, Proceedings of the National Academy of Sciences, 93, 4, 1591-1595 (1996) · Zbl 0852.65055 |
| [26] | Teitelbaum, C. S.; Converse, S. J.; Fagan, W. F.; Böhning-Gaese, K.; O’Hara, R. B.; Lacy, A. E.; Mueller, T., Experience drives innovation of new migration patterns of whooping cranes in response to global change, Nature Communications, 7, 1, 1-7 (2016) |
| [27] | Twarogowska, M.; Goatin, P.; Duvigneau, R., Macroscopic modeling and simulations of room evacuation, Applied Mathematical Modelling, 38, 24, 5781-5795 (2014) · Zbl 1428.90038 |
| [28] | Xia, Y.; Wong, S.; Shu, C.-W., Dynamic continuum pedestrian flow model with memory effect, Physical Review E, 79, 6, Article 066113 pp. (2009) |
| [29] | Zhao, H., A fast sweeping method for eikonal equations, Mathematics of Computation, 74, 250, 603-627 (2005) · Zbl 1070.65113 |
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