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Integrodifference models for evolutionary processes in biological invasions.

Silas Poloni1,2, Frithjof Lutscher3,4

  • 1Institute of Theoretical Physics, São Paulo State University, São Paulo, SP, 01140-070, Brazil. silaspoloni@gmail.com.

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|June 17, 2023
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Summary
This summary is machine-generated.

Evolutionary processes like spatial sorting significantly impact biological invasions. This study uses novel integrodifference equations to model how traits evolve during range expansions, revealing conditions for spatial sorting and anomalous speeds.

Keywords:
Dispersal evolutionDispersal-reproduction trade-offSpatial sortingSpatial spreadTrait-structured populations

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Area of Science:

  • Ecology
  • Evolutionary Biology
  • Mathematical Biology

Background:

  • Individual variation in dispersal and reproduction drives evolutionary processes affecting biological invasions.
  • Spatial sorting and spatial selection are key evolutionary forces altering range expansion dynamics.
  • Existing models often use continuous-time reaction-diffusion equations with Gaussian dispersal.

Purpose of the Study:

  • To develop novel theory for evolution shaping biological invasions using discrete-time integrodifference equations.
  • To model trait evolution, including dispersal ability and growth rates, across generations.
  • To analyze the impact of mutation and trade-offs on invasion dynamics.

Main Methods:

  • Developed integrodifference equation models for discrete time and varied dispersal kernels.
  • Tracked changes in growth rates and dispersal ability distributions over generations.
  • Analyzed traveling wave solutions, asymptotic spreading speeds, and population distributions at invasion fronts.

Main Results:

  • Determined conditions for the emergence and absence of spatial sorting.
  • Established relationships between spreading speeds and mutation probabilities.
  • Identified scenarios leading to anomalous spreading speeds and explored effects of deleterious mutations.

Conclusions:

  • Integrodifference equations provide a flexible framework for studying evolution during invasions.
  • Trait variability and selection pressures critically influence invasion speed and spatial structure.
  • The model offers new insights into the evolutionary dynamics of biological invasions.