Ancestral reproductive bias in branching processes

Area of Science:

• Mathematical Biology
• Population Dynamics
• Genetics

Background:

• Branching processes model cell populations with homogeneous reproduction laws.
• Cellular lineages can exhibit varying mutation rates, particularly in developing organisms.
• Sampling bias can distort observations of population dynamics.

Purpose of the Study:

• To characterize the evolution of reproduction rates and sizes along a sampled ancestral lineage.
• To explain the 'inspection paradox' in branching processes.
• To provide a framework for understanding mutation rate variations in embryonic development.

Main Methods:

• Analysis of a homogeneous branching process with uniform cell sampling.
• Mathematical characterization of the sampled ancestral lineage's reproduction law.
• Modeling the lineage as a mixture of Poisson processes.

Main Results:

• A sampled ancestral lineage exhibits a heterogeneous reproduction law, increasing with time.
• This heterogeneity arises from sampling bias favoring more prolific cells.
• The bias strength depends on population size and sampling time.

Conclusions:

• The inspection paradox in branching processes leads to a biased view of ancestral reproduction.
• This bias offers an explanation for observed mutation rate variations in human embryonic lineages.
• The findings simplify in special cases and relate to Poisson processes.