Extremal events dictate population growth rate inference

Area of Science:

• Quantitative Biology
• Statistical Mechanics
• Cellular Dynamics

Background:

• Single-cell lineage statistics are increasingly used to infer population growth dynamics.
• Existing methods are susceptible to systematic errors due to sampling rare phenotypes from finite data.
• A thorough understanding of these errors, particularly in finite datasets, is lacking.

Purpose of the Study:

• To comprehensively analyze and characterize errors in population growth rate estimation from single-cell lineage data.
• To develop a framework for correcting these systematic biases.
• To improve the reliability of lineage-based growth rate measurements and model inference.

Main Methods:

• Bias-variance decomposition of growth rate estimators.
• Analysis of finite-time and nonlinear averaging biases across different models.
• Application of the Random Energy Model to understand error phase transitions.
• Validation using experimental single-cell lineage data.

Main Results:

• Bias in growth rate estimates can be decomposed into finite-time and nonlinear averaging components.
• Finite-time bias, dominant at short timescales, is reducible by fitting its monotonic behavior.
• Nonlinear averaging bias, dominant at longer timescales, exhibits a phase transition explained by the Random Energy Model.
• Bias correction yields consistent long-term growth rate estimates across methods.

Conclusions:

• A quantitative framework for understanding and correcting errors in lineage-based growth rate estimation is established.
• Corrected methods provide reliable long-term growth rates and enable reverse-engineering of dynamic models.
• Introduces model-free approaches for linking cell physiology to growth dynamics.