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Migration is a tactic used across taxa to access resources in temporally heterogenous landscapes. Populations that migrate can attain higher abundances because such movements allow access to higher quality resources, or reduction in predation risk resulting in increased fitness. However, most migratory species occur in partially migratory populations, a mix of migratory and non-migratory individuals. It is thought that the portion of migrants in a partial migration population is maintained either through (1) a population-level evolutionary stable state where counteracting density-dependent vital rates act on migrants and residents to balance fitness or (2) conditional migration, where the propensity to migrate is influenced by the individual's state. However, in many respects, migration is also a form of habitat selection and the proportion of migrants and residents may be the result of density-dependent habitat selection. Here, we test whether the theory of Ideal Free Distribution (IFD) can explain the coexistence of different migratory tactics in a partially migratory population. IFD predicts individuals exhibit density-dependent vital rates and select different migratory tactics to maximize individual fitness resulting in equal fitness (λ) between tactics. We tested the predictions of IFD in a partially migratory elk population that declined by 70% with 19 years of demographic data and migratory tactic switching rates from >300 individuals. We found evidence of density dependence for resident pregnancy and adult female survival providing a fitness incentive to switch tactics. Despite differences in vital rates between migratory tactics, mean λ (fitness) was equal. However, as predicted by the IFD, individuals switched tactics toward those of higher fitness. Our analysis reveals that partial migration may be driven by tactic selection that follows the ideal free distribution. These findings reinforce that migration across taxa may be a polymorphic behavior in large herbivores where migratory tactic selection is determined by differential costs and benefits, mediated by density dependence.
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Mean Field Games and Ideal Free Distribution
Abstract The ideal free distribution in ecology was introduced by Fretwell and Lucas to model the habitat selection of animal populations. In this paper, we revisit the concept via a mean field game system with local coupling, which models a dynamic version of the habitat selection game in ecology. We establish the existence of classical solution of the ergodic mean field game system, including the case of heterogeneous diffusion when the underlying domain is one-dimensional and further show that the population density of agents converges to the ideal free distribution of the underlying habitat selection game, as the cost of control tends to zero. Our analysis provides a derivation of ideal free distribution in a dynamical context.
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- Award ID(s):
- 2325195
- PAR ID:
- 10636786
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Journal of Mathematical Biology
- Volume:
- 91
- Issue:
- 4
- ISSN:
- 0303-6812
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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