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Inside dynamics for stage-structured integrodifference equations.

Nathan G Marculis1, Jimmy Garnier2, Roger Lui3

  • 1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada. marculis@ualberta.ca.

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|May 12, 2019
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Summary
This summary is machine-generated.

This study models population range expansion using integrodifference equations to analyze genetic structure. It reveals that the leading edge dynamics, akin to the founder effect, dictate long-term spread, especially with multiple neutral fractions.

Keywords:
Founder effectInside dynamicsIntegrodifference equationsNeutral genetic structureStage-structure

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Area of Science:

  • Population genetics
  • Mathematical biology
  • Ecology

Background:

  • Understanding the genetic consequences of population range expansion is crucial for predicting species' long-term spread.
  • Stage-structured models offer a framework to analyze complex population dynamics.

Purpose of the Study:

  • To investigate the asymptotic neutral genetic structure of populations during range expansion using a stage-structured integrodifference equation model.
  • To analyze the spatiotemporal evolution of neutral genetic fractions driving population spread.

Main Methods:

  • Utilizing a stage-structured integrodifference equation model.
  • Decomposing population solutions into neutral genetic components (neutral fractions).
  • Analyzing the dynamics of these neutral fractions to understand genetic structure during expansion.

Main Results:

  • Population spread is primarily driven by individuals at the leading edge, consistent with the founder effect.
  • A simple formula is derived to calculate the asymptotic proportion of multiple neutral fractions at the leading edge.
  • Multiple neutral fractions can collectively drive long-term spread, a phenomenon not observed in scalar models.

Conclusions:

  • The founder effect plays a significant role in shaping the genetic structure of expanding populations.
  • The derived formula provides a quantitative tool to predict the genetic composition of future populations.
  • Stage-structured models reveal complex genetic dynamics in range expansions, allowing for multiple neutral fractions to influence spread.