  We introduce a mathematical framework for statistical exoplanet population
and astrobiology studies that may help directing future observational efforts
and experiments. The approach is based on a set of differential equations and
provides a time-dependent mapping between star formation, metal enrichment, and
the occurrence of exoplanets and potentially life-harboring worlds over the
chemo-population history of the solar neighborhood. Our results are summarized
as follows: 1) the formation of exoplanets in the solar vicinity was episodic,
starting with the emergence of the thick disk about 11 Gyr ago; 2) within 100
pc from the Sun, there are as many as 11,000 (eta/0.24) Earth-size planets in
the habitable zone ("temperate terrestrial planets" or TTPs) of K-type stars.
The solar system is younger than the median TTP, and was created in a star
formation surge that peaked 5.5 Gyr ago and was triggered by an external agent;
3) the metallicity modulation of the giant planet occurrence rate results in a
later typical formation time, with TTPs outnumbering giant planets at early
times; 4) the closest, life-harboring Earth-like planet would be < 20 pc away
if microbial life arose as soon as it did on Earth in > 1 % of the TTPs around
K stars. If simple life is abundant (fast abiogenesis), it is also old, as it
would have emerged more than 8 Gyr ago in about one third of all life-bearing
planets today. Older Earth analogs are more likely to have developed
sufficiently complex life capable of altering the environment and producing
detectable oxygenic biosignatures.
