Evolution of dispersal by memory and learning in integrodifference equation models. (English) Zbl 07903463
Summary: In this paper, we develop an integrodifference equation model that incorporates spatial memory and learning so that each year, a fraction of the population use the same dispersal kernel as the previous year, and the remaining individuals return to where they bred or were born. In temporally static environments, the equilibrium of the system corresponds to an ideal free dispersal strategy, which is evolutionarily stable. We prove local stability of this equilibrium in a special case, and we observe convergence towards this equilibrium in numerical computations. When there are periodic or stochastic temporal changes in the environment, the population is less able to match the environment, but is able to do so to some extent depending on the parameters. Overall, the mechanism proposed in this model shows a possible way for the dispersal kernel of a population to evolve towards an ideal free dispersal kernel.
MSC:
| 37N25 | Dynamical systems in biology |
| 92-10 | Mathematical modeling or simulation for problems pertaining to biology |
| 92D40 | Ecology |
Keywords:
integrodifference equation; mathematical biology; evolution of dispersal; ideal free distribution; spatial memory; migrationReferences:
| [1] | Abrahams, M.V., Foraging guppies and the ideal free distribution: the influence of information on patch choice, Ethology82(2) (2010), pp. 116-126. |
| [2] | 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., and Mate, B.R., Memory and resource tracking drive blue whale migrations, Proc. Natl. Acad. Sci.116(12) (2019), pp. 5582-5587. |
| [3] | Averill, I., Lou, Y., and Munther, D., On several conjectures from evolution of dispersal, J. Biol. Dyn.6(2) (2012), pp. 117-130. · Zbl 1444.92132 |
| [4] | BEAUCHAMP, G., Learning rules for social foragers: implications for the producer-scrounger game and ideal free distribution theory, J. Theor. Biol.207(1) (2000), pp. 21-35. |
| [5] | Berestycki, H. and Fang, J., Forced waves of the Fisher-KPP equation in a shifting environment, J. Differ. Equ.264(3) (2018), pp. 2157-2183. · Zbl 1377.35162 |
| [6] | Berestycki, H., Diekmann, O., Nagelkerke, C.J., and Zegeling, P.A., Can a species keep pace with a shifting climate?Bull. Math. Biol.71(2) (2009), pp. 399-429. · Zbl 1169.92043 |
| [7] | Boulinier, T. and Danchin, E., The use of conspecific reproductive success for breeding patch selection in terrestrial migratory species, Evol. Ecol.11(5) (1997), pp. 505-517. |
| [8] | Bracis, C. and Mueller, T., Memory, not just perception, plays an important role in terrestrial mammalian migration, Proc. R. Soc. B: Biol. Sci.284(1855) (2017), pp. 20170449. |
| [9] | Cantrell, R.S., Cosner, C., and Lou, Y., Evolution of dispersal and the ideal free distribution, Math. Biosci. Eng.7(1) (2010), pp. 17-36. · Zbl 1188.35102 |
| [10] | Cantrell, R.S., Cosner, C., Lou, Y., and Schreiber, S.J., Evolution of natal dispersal in spatially heterogenous environments, Math. Biosci.283 (2017), pp. 136-144. · Zbl 1353.92075 |
| [11] | Cantrell, R.S., Cosner, C., and Lam, K.-Y., Ideal free dispersal under general spatial heterogeneity and time periodicity, SIAM. J. Appl. Math.81(3) (2021), pp. 789-813. · Zbl 1468.35210 |
| [12] | Cantrell, R.S., Cosner, C., and Zhou, Y., Ideal free dispersal in integrodifference models, J. Math. Biol.85(1) (2022), pp. 6. · Zbl 1496.92127 |
| [13] | Cosner, C., Reaction-diffusion-advection models for the effects and evolution of dispersal, Discrete Contin. Dyn. Syst.34(5) (2014), pp. 1701-1745. · Zbl 1277.35002 |
| [14] | Cosner, C., Dávila, J., and Martínez, S., Evolutionary stability of ideal free nonlocal dispersal, J. Biol. Dyn.6(2) (2012), pp. 395-405. · Zbl 1447.92275 |
| [15] | Danchin, E., Boulinier, T., and Massot, M., Conspecific reproductive success and breeding habitat selection: implications for the study of coloniality, Ecology79(7) (1998), pp. 2415-2428. |
| [16] | Dockery, J., Hutson, V., Mischaikow, K., and Pernarowski, M., The evolution of slow dispersal rates: a reaction diffusion model, J. Math. Biol.37(1) (1998), pp. 61-83. · Zbl 0921.92021 |
| [17] | Doligez, B., Danchin, E., Clobert, J., and Gustafsson, L., The use of conspecific reproductive success for breeding habitat selection in a non-colonial, hole-nesting species, the collared flycatcher, J. Anim. Ecol.68(6) (1999), pp. 1193-1206. |
| [18] | Doligez, B., Cadet, C., Danchin, E., and Boulinier, T., When to use public information for breeding habitat selection? The role of environmental predictability and density dependence, Anim. Behav.66(5) (2003), pp. 973-988. |
| [19] | Doligez, B., Pärt, T., Danchin, E., Clobert, J., and Gustafsson, L., Availability and use of public information and conspecific density for settlement decisions in the collared flycatcher, J. Anim. Ecol.73(1) (2004), pp. 75-87. |
| [20] | Dreisig, H., Ideal free distributions of nectar foraging bumblebees, Oikos72(2) (1995), pp. 161-172. |
| [21] | Fagan, W.F., Cantrell, R.S., Cosner, C., Mueller, T., and Noble, A.E., Leadership, social learning, and the maintenance (or collapse) of migratory populations, Theor. Ecol.5(2) (2012), pp. 253-264. |
| [22] | 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., and Forester, J., Spatial memory and animal movement, Ecol. Lett.16(10) (2013), pp. 1316-1329. |
| [23] | Fretwell, S.D., Populations in a seasonal environment, Monogr. Pop. Biol.5 (1972), pp. 16-36. |
| [24] | Gerber, B.D, Hooten, M.B., Peck, C.P., Rice, M.B., Gammonley, J.H., Apa, A.D., and Davis, A.J., Extreme site fidelity as an optimal strategy in an unpredictable and homogeneous environment, Funct. Ecol.33(9) (2019), pp. 1695-1707. |
| [25] | Gurarie, E., Potluri, S., Christopher Cosner, G., Cantrell, R.S., and Fagan, W.F., Memories of migrations past: sociality and cognition in dynamic, seasonal environments, Front. Ecol. Evol.1 (2021), pp. 647. |
| [26] | Hastings, A., Can spatial variation alone lead to selection for dispersal?Theor. Popul. Biol.24(3) (1983), pp. 244-251. · Zbl 0526.92025 |
| [27] | Holt, R.D., Population dynamics in two-patch environments: some anomalous consequences of an optimal habitat distribution, Theor. Popul. Biol.28(2) (1985), pp. 181-208. · Zbl 0584.92022 |
| [28] | Korobenko, L. and Braverman, E., On evolutionary stability of carrying capacity driven dispersal in competition with regularly diffusing populations, J. Math. Biol.69(5) (2014), pp. 1181-1206. · Zbl 1309.92070 |
| [29] | Lewis, M.A., Marculis, N.G., and Shen, Z., Integrodifference equations in the presence of climate change: persistence criterion, travelling waves and inside dynamics, J. Math. Biol.77(6-7) (2018), pp. 1649-1687. · Zbl 1404.92156 |
| [30] | Lin, H.-Y, Fagan, W.F., and Jabin, P.-E., Memory-driven movement model for periodic migrations, J. Theor. Biol.508 (2021), pp. 110486. · Zbl 1457.92199 |
| [31] | and H. L. Lucas, S. D. Fretwell, On territorial behavior and other factors influencing habitat distribution in birds. i. theoretical development, Acta. Biotheor.19 (1970), pp. 16-36. |
| [32] | Matsumura, S., Arlinghaus, R., and Dieckmann, U., Foraging on spatially distributed resources with sub-optimal movement, imperfect information, and travelling costs: departures from the ideal free distribution, Oikos119(9) (2010), pp. 1469-1483. |
| [33] | McPeek, M.A. and Holt, R.D., The evolution of dispersal in spatially and temporally varying environments, Am. Nat.140(6) (1992), pp. 1010-1027. |
| [34] | Menezes, J.F.S., Marginal value theorem as a special case of the ideal free distribution, Ecol. Modell.468 (2022), pp. 109933. |
| [35] | Merkle, J.A., Sawyer, H., Monteith, K.L., Dwinnell, S.P.H., Fralick, G.L., and Kauffman, M.J., Spatial memory shapes migration and its benefits: evidence from a large herbivore, Ecol. Lett.22(11) (2019), pp. 1797-1805. |
| [36] | Morrison, T.A., Merkle, J.A., Hopcraft, J.G.C., Aikens, E.O., Beck, J.L., Boone, R.B., Courtemanch, A.B., Dwinnell, S.P., Fairbanks, W.S., Griffith, B., and Middleton, A.D., Drivers of site fidelity in ungulates, J. Anim. Ecol.90(4) (2021), pp. 955-966. |
| [37] | Potapov, A.B. and Lewis, M.A., Climate and competition: the effect of moving range boundaries on habitat invasibility, Bull. Math. Biol.66(5) (2004), pp. 975-1008. · Zbl 1334.92454 |
| [38] | Shi, J., Wang, C., and Wang, H., Diffusive spatial movement with memory and maturation delays, Nonlinearity32(9) (2019), pp. 3188-3208. · Zbl 1419.35114 |
| [39] | Shi, J., Wang, C., Wang, H., and Yan, X., Diffusive spatial movement with memory, J. Dyn. Differ. Equ.32(2) (2020), pp. 979-1002. · Zbl 1439.92215 |
| [40] | Shi, Q., Shi, J., and Wang, H., Spatial movement with distributed memory, J. Math. Biol.82(4) (2021), pp. 33. · Zbl 1461.35034 |
| [41] | Song, Y., Shi, J., and Wang, H., Spatiotemporal dynamics of a diffusive consumer-resource model with explicit spatial memory, Stud. Appl. Math.148(1) (2022), pp. 373-395. · Zbl 1530.92311 |
| [42] | Switzer, P.V., Past reproductive success affects future habitat selection, Behav. Ecol. Sociobiol.40(5) (1997), pp. 307-312. |
| [43] | Zhou, Y., Range shifts under constant-speed and accelerated climate warming, Bull. Math. Biol.84(1) (2022), pp. 1. · Zbl 1478.92256 |
| [44] | Zhou, Y. and Kot, M., Discrete-time growth-dispersal models with shifting species ranges, Theor. Ecol.4(1) (2011), pp. 13-25. |
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