Stochastic stable population growth in integral projection models: theory and application

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Stochastic matrix projection models are standard for age- or stage-structured populations with fluctuating vital rates.
• Key applications rely on properties like long-term growth rate, asymptotic log-normality, and population structure ergodicity.

Purpose of the Study:

• To demonstrate that a general stochastic integral projection model shares these essential qualitative properties.
• To showcase the parameterization and application of stochastic integral models using field data.
• To explore the evolution of flowering strategy in Onopordum illyricum using an evolutionarily stable strategy (ESS) approach.

Main Methods:

• Extending the approach of Lange and Holmes (1981) using results from Eveson (1991, 1993).
• Utilizing integral projection models capable of handling multiple, changing individual attributes (discrete or continuous).
• Parameterizing a stochastic integral model with a 6-year field study of Onopordum illyricum.

Main Results:

• Stochastic integral projection models exhibit key qualitative properties for population dynamics.
• The model successfully accommodated multiple demographic traits (size, age, quality) in Onopordum illyricum.
• The predicted ESS for flowering strategy closely matched observed behavior, unlike deterministic models.

Conclusions:

• Stochastic integral projection models offer a powerful framework for analyzing complex population dynamics.
• The flowering strategy in Onopordum illyricum is likely an adaptation to random annual variations in vital rates.
• These models are valuable for understanding evolutionary strategies in fluctuating environments.