On the dynamics of populations with two age groups

Area of Science:

• Mathematical Biology
• Population Dynamics
• Demography

Background:

• Population dynamics are often complex, involving changing vital rates.
• Existing models may not fully capture population behavior over extended periods.
• Weak ergodic theorems provide some insights but have limitations.

Purpose of the Study:

• To develop a comprehensive method for specifying population dynamics with deterministic vital rate changes.
• To provide explicit mathematical expressions for population projection.
• To derive accurate relative age distributions and reproductive values.

Main Methods:

• Simplifying population structure to two age groups.
• Utilizing continued fractions to model vital rates.
• Deriving explicit expressions for the product of population projection matrices.

Main Results:

• Complete specification of population dynamics at all times.
• Explicit formulas for population projection matrices.
• Accurate calculation of relative age distribution and reproductive values as functions of vital rates.

Conclusions:

• The developed method provides a stronger analytical framework than existing weak ergodic theorems.
• This approach allows for precise, long-term predictions in population dynamics.
• The findings enhance the understanding of how vital rates influence population structure and reproductive value.