Richards growth model and viability indicators for populations subject to interventions

Area of Science:

• Ecology
• Population Dynamics
• Mathematical Biology

Background:

• Population modeling is crucial for understanding species dynamics and resource management.
• The Richards growth model offers a framework for population dynamics, but its identification can be challenging.
• Interventions like consumption (hunting, farming) significantly impact population trajectories.

Purpose of the Study:

• To develop a robust method for identifying discrete dynamic population models based on the Richards growth model.
• To estimate key population parameters, including the probability and average time to reach specific population sizes.
• To apply the developed identification method to real-world scenarios in animal husbandry and conservation.

Main Methods:

• Utilized a discrete dynamic model derived from the Richards growth model.
• Employed the likelihood profile technique for parameter inference and model identification.
• Applied the method to analyze the Brazilian beef cattle herd population data.

Main Results:

• Successfully identified population models and estimated parameters related to population growth and intervention effects.
• Quantified the probability and average time for the population to reach predefined levels.
• Demonstrated the model's applicability to assess animal husbandry productivity and extinction risk.

Conclusions:

• The developed model identification technique provides a valuable tool for population dynamics research.
• This method enhances the assessment of animal husbandry productivity and the conservation status of wild populations.
• The study successfully applied the technique to Brazilian beef cattle data, offering insights into herd management.