How Phenological Variation Affects Species Spreading Speeds.

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.