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Replicated point processes with application to population dynamics models.

Marco Favretti1

  • 1Dipartimento di Matematica "Tullio Levi-Civita", Università di Padova, Padova, Italy.

Theoretical Population Biology
|April 13, 2019
PubMed
Summary

This study enhances population genetics models by allowing general dispersal kernels, moving beyond simple isolation by distance. This framework improves analysis of spatial genetic structure and variability using advanced statistical estimators.

Keywords:
Dispersal kernelMarkov chainSpatial correlationSpatial point process

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Area of Science:

  • Ecology
  • Population Genetics
  • Spatial Statistics

Background:

  • Traditional models like Malécot's isolation by distance explain spatial genetic structure.
  • Shimatani's neutral model (2010) extended these concepts using point process theory.
  • Previous models often assumed specific dispersal patterns or random migration.

Purpose of the Study:

  • To reformulate Shimatani's neutral model with a general dispersal kernel function.
  • To demonstrate that long dispersal distances can replace the random migration hypothesis.
  • To adapt the framework for spatially explicit statistical estimators of genetic variability.

Main Methods:

  • Utilizing point process theory to model spatially clustered distributions.
  • Reformulating the replicated Neyman-Scott process with a general dispersal kernel.
  • Applying statistical estimators such as the Moran autocorrelation index and Sørensen similarity index.

Main Results:

  • The reformulated model accommodates a broad range of dispersal kernel functions.
  • Long dispersal distances of the kernel effectively substitute the random migration hypothesis.
  • The extended framework is suitable for analyzing spatial genetic variability using specified estimators.

Conclusions:

  • The choice of dispersal kernel is crucial for accurately estimating genetic variability in spatially explicit models.
  • This generalized framework offers a more flexible approach to studying population structure and dynamics.
  • The findings contribute to a deeper understanding of spatial patterns in population genetics theory.