  Branching processes model the evolution of populations of agents that
randomly generate offsprings. These processes, more patently Galton-Watson
processes, are widely used to model biological, social, cognitive, and
technological phenomena, such as the diffusion of ideas, knowledge, chain
letters, viruses, and the evolution of humans through their Y-chromosome DNA or
mitochondrial RNA. A practical challenge of modeling real phenomena using a
Galton-Watson process is the offspring distribution, which must be measured
from the population. In most cases, however, directly measuring the offspring
distribution is unrealistic due to lack of resources or the death of agents. So
far, researchers have relied on informed guesses to guide their choice of
offspring distribution. In this work we propose two methods to estimate the
offspring distribution from real sampled data. Using a small sampled fraction
of the agents and instrumented with the identity of the ancestors of the
sampled agents, we show that accurate offspring distribution estimates can be
obtained by sampling as little as 14% of the population.
