On incomplete sampling under birth-death models and connections to the sampling-based coalescent

Area of Science:

• Evolutionary biology
• Epidemiology
• Computational biology

Background:

• The constant rate birth-death process is a key stochastic model for phylogenies and disease transmission.
• Biological data are often incomplete, necessitating analysis of incomplete sampling effects.

Purpose of the Study:

• Analyze the constant rate birth-death process with incomplete sampling.
• Derive the density of bifurcation events for trees under this process.
• Compare the birth-death-sampling process with the coalescent model.

Main Methods:

• Derivation of bifurcation event density for n-leaf trees under birth-death-sampling.
• Interpretation of the birth-death-sampling process as a reduced-rate birth-death process with complete sampling.
• Comparison with the coalescent model, focusing on bifurcation time distributions.

Main Results:

• The birth-death-sampling process can be viewed as a complete sampling model with reduced rates.
• Joint inference of birth rate, death rate, and sampling probability is not feasible.
• Significant differences in bifurcation time distributions exist between birth-death-sampling and coalescent models, even for large populations.
• Hepatitis C virus transmission time estimates differ substantially between models, altering statistical interpretations.

Conclusions:

• The birth-death-sampling model provides a framework for analyzing incomplete biological data.
• The impossibility of joint inference highlights limitations in parameter estimation.
• Model choice significantly impacts phylogenetic and epidemiological inference, as demonstrated with Hepatitis C virus data.