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Harvesting in a resource dependent age structured Leslie type population model.
Rui Dilão1, Tiago Domingos, Elman M Shahverdiev
1Grupo de Dinâmica Não-Linear, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal. rui@sd.ist.utl.pt
Mathematical Biosciences
|April 20, 2004
Summary
Harvesting strategies in age-structured populations can lead to extinction or stable populations. The impact of harvesting depends on fertility, mortality rates, and available resources, influencing population dynamics and yield.
Area of Science:
- Ecology
- Population Dynamics
- Mathematical Biology
Background:
- Resource-dependent population models are crucial for understanding ecological dynamics.
- Harvesting significantly impacts population stability and resource management.
- Age structure is a key factor in population responses to environmental changes.
Purpose of the Study:
- To analyze the effects of harvesting on an age-structured population model dependent on resources.
- To determine conditions for a stable steady state considering fertility, harvesting mortality, and carrying capacity.
- To investigate population extinction risks and harvesting yield patterns under proportional harvesting.
Main Methods:
- Analysis of a resource-dependent, age-structured population model.
- Derivation of conditions for a stable steady state.
- Investigation of population dynamics under proportional harvesting, including extinction conditions.
- Examination of harvesting yield patterns (periodic, quasi-periodic, chaotic).
Main Results:
- A stable steady state exists under specific conditions related to fertility, harvesting mortality, and carrying capacity.
- Proportional harvesting can lead to population extinction, with the harvest magnitude dependent on resource availability.
- Harvesting yield can exhibit complex dynamics, including periodic, quasi-periodic, and chaotic behaviors.
- In populations with high fertility, low harvesting mortality may cause abrupt extinction, while higher mortality can control population size and prevent overconsumption.
Conclusions:
- Harvesting strategies must carefully consider population age structure, fertility, and resource availability to ensure stability.
- Appropriate harvesting levels can prevent overconsumption and stabilize populations, even those with high reproductive rates.
- Harvesting can be a tool to manage and stabilize populations exhibiting periodic or quasi-periodic oscillations, transforming chaotic dynamics into predictable outcomes.