Inside Dynamics for Stage-Structured Integrodifference Equations

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dc.contributor.authorNathan G. Marculis
dc.contributor.authorJimmy Garnier
dc.contributor.authorRoger Lui
dc.contributor.authorMark A. Lewis
dc.date.accessioned2025-05-01T22:20:18Z
dc.date.available2025-05-01T22:20:18Z
dc.date.issued2019-05-10
dc.descriptionA stage-structured model of integrodifference equations is used to study the asymptotic neutral genetic structure of populations undergoing range expansion. That is, we study the inside dynamics of solutions to stage-structured integrodifference equations. To analyze the genetic consequences for long term population spread, we decompose the solution into neutral genetic components called neutral fractions. The inside dynamics are then given by the spatiotemporal evolution of these neutral fractions. We show that, under some mild assumptions on the dispersal kernels and population projection matrix, the spread is dominated by individuals at the leading edge of the expansion. This result is consistent with the founder effect. In the case where there are multiple neutral fractions at the leading edge we are able to explicitly calculate the asymptotic proportion of these fractions found in the long-term population spread. This formula is simple and depends only on the right and left eigenvectors of the population projection matrix evaluated at zero and the initial proportion of each neutral fraction at the leading edge of the range expansion. In the absence of a strong Allee effect, multiple neutral fractions can drive the long-term population spread, a situation not possible with the scalar model.
dc.identifier.doihttps://doi.org/10.7939/r3-sag5-2s49
dc.language.isoen
dc.relation.isversionofMarculis, N., Lui, R., Garnier, J., Lewis, M.A. 2020b. Inside Dynamics for Stage-Structured Integrodifference Equations. Journal of Mathematical Biology 80: 157-187. https://doi.org/10.1007/s00285-019-01378-9
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/
dc.subjectIntegrodifference equations
dc.subjectStage-structure
dc.subjectInside dynamics
dc.subjectNeutral genetic structure
dc.subjectFounder effect
dc.titleInside Dynamics for Stage-Structured Integrodifference Equations
dc.typehttp://purl.org/coar/resource_type/c_6501 http://purl.org/coar/version/c_b1a7d7d4d402bcce http://purl.org/coar/version/c_71e4c1898caa6e32
ual.jupiterAccesshttp://terms.library.ualberta.ca/public

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