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A Stage-Structured Continuous-/Discrete-Time Population Model: Persistence and Spatial Spread.

Minglong Wang1, Yuxiang Zhang2, Qihua Huang3

  • 1School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China.

Bulletin of Mathematical Biology
|October 13, 2022
PubMed
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This study introduces a new model for species with complex life cycles, revealing how stage structure impacts population spread and persistence. The findings are crucial for understanding invasion dynamics and conservation in spatial ecology.

Keywords:
Critical domain sizeHybrid modelSpreading speedTraveling wave

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Area of Science:

  • Spatial ecology
  • Mathematical biology
  • Population dynamics

Background:

  • Understanding population persistence and spatial spread is vital in ecology.
  • Species with complex life cycles often disperse via early life stages to invade new habitats.

Purpose of the Study:

  • To develop a hybrid model for spatiotemporal dynamics of species with stage structure.
  • To analyze the impact of demography and dispersal on population spread and persistence.

Main Methods:

  • A reaction-diffusion equation models dispersal of early life stages.
  • Difference equations model the demography of sedentary individuals.
  • Analysis of traveling wave solutions to determine spreading speed and critical domain size.

Main Results:

  • A formula for population spreading speed was derived, linked to the slowest traveling wave speed.
  • An explicit formula for critical domain size, determining population persistence vs. extinction, was established.
  • The stage-structured model was shown to simplify to an unstructured model in specific cases.

Conclusions:

  • Stage structure significantly influences spatial dynamics, affecting population spread and persistence.
  • The developed model provides a more nuanced understanding compared to unstructured models.
  • This research underscores the importance of incorporating life-stage complexity in ecological studies.