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Interaction between harvesting intervention and birth perturbation in an age-structured model
Haiyan Xu1, Zhigui Lin2, Carlos Alberto Santos3
1School of Mathematical Science, Yangzhou University, Yangzhou, 225002, China.
Journal of Mathematical Biology
|June 23, 2025
Summary
This study models fish populations with birth and harvesting pulses. Understanding the interplay between these factors is key to managing fishery resources for either species extinction or sustainable development.
Area of Science:
- Ecology
- Population Dynamics
- Fisheries Science
Background:
- Age-structured fish models are crucial for understanding population dynamics.
- Birth and harvesting pulses significantly impact fish population size.
- Sustainable fishery management requires predicting population persistence or extinction.
Purpose of the Study:
- To establish an age-structured fish model incorporating discrete birth and harvesting pulses.
- To investigate the principal eigenvalue as a threshold determining population dynamics.
- To provide conditions for species extinction or persistence in managed fish populations.
Main Methods:
- Development of a mathematical model for age-structured populations.
- Analysis of the principal eigenvalue using three distinct mathematical approaches.
- Numerical simulations to explore population dynamics under various pulse intensities and timings.
Main Results:
- The principal eigenvalue acts as a critical threshold influenced by birth and harvesting intensities.
- Asymptotic population behavior was fully characterized, defining conditions for extinction and persistence.
- Numerical simulations confirmed that the interaction between harvesting and birth pulses dictates species fate.
Conclusions:
- The balance between birth and harvesting pulses determines fish population extinction or persistence.
- Fishery resources can be managed for sustainable development by adjusting pulse intensities and timing.
- This model offers insights into controlling population dynamics for ecological and economic benefits.
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