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Area of Science:

  • Ecology
  • Mathematical Biology
  • Entomology

Background:

  • Understanding insect population dynamics is crucial for predicting species spread.
  • Phenology, or seasonal timing, significantly influences insect life cycles and interactions.
  • Previous models often simplify or omit the complex phenological aspects of insect development.

Purpose of the Study:

  • To develop a reaction-diffusion model that explicitly incorporates insect phenology.
  • To analyze how seasonal timing affects the spatial spread of univoltine insect species.
  • To provide a general framework applicable to various holometabolous insects.

Main Methods:

  • Developed a phenologically explicit reaction-diffusion model with four life stages (adult, two larval, pupa) and an implicit egg stage.
  • Introduced time-dependent phenological functions for adult emergence, oviposition, and larval conversion.
  • Derived the moment-generating function for the linearized system and proved spreading speed equivalence with the nonlinear system.
  • Analyzed limiting cases with impulsive or delayed phenological events and used numerical simulations for broader scenarios.

Main Results:

  • Derived explicit solutions for spreading speed in specific limiting cases (e.g., impulsive emergence/oviposition, constant larval conversion).
  • Demonstrated that the spreading speed of the linearized system matches the nonlinear system.
  • Numerical simulations explored scenarios with finite-width phenological windows and mobile larvae.
  • Quantified the impact of phenological timing on insect spatial expansion rates.

Conclusions:

  • Phenology plays a critical role in determining the spatial spread of insect populations.
  • The developed model provides a robust framework for studying insect range shifts and invasive species dynamics.
  • Findings are relevant for predicting species responses to climate change and its effects on phenology.