  Future exoplanet direct imaging missions, such as HabEx and LUVOIR, will
select target stars to maximize the number of Earth-like exoplanets that can
have their atmospheric compositions characterized. Because one of these
missions' aims is to detect biosignatures, they should also consider the
expected biosignature yield of planets around these stars.
  In this work, we develop a method of computing relative biosignature yields
among potential target stars, given a model of habitability and biosignature
genesis, and using a star's habitability history. As an illustration and first
application of this method, we use MESA stellar models to calculate the time
evolution of the habitable zone, and examine three simple models for
biosignature genesis to calculate the relative biosignature yield for different
stars.
  We find that the relative merits of K stars versus F stars depend sensitively
on model choice. In particular, use of the present-day habitable zone as a
proxy for biosignature detectability favors young, luminous stars lacking the
potential for long-term habitability. Biosignature yields are also sensitive to
whether life can arise on Cold Start exoplanets that enter the habitable zone
after formation, an open question deserving of more attention.
  Using the case study of biosignature yields calculated for $\theta$ Cygni and
55 Cancri, we find that robust mission design and target selection for HabEx
and LUVOIR depends on: choosing a specific model of biosignature appearance
with time; the terrestrial planet occurrence rate as a function of orbital
separation; precise knowledge of stellar properties; and accurate stellar
evolutionary histories.
