  About 2.5 billion years ago, microbes learned to harness plentiful solar
energy to reduce CO$_2$ with H$_2$O, extracting energy and producing O$_2$ as
waste. O$_2$ production from this metabolic process was so vigorous that it
saturated its photochemical sinks, permitting it to reach "runaway" conditions
and rapidly accumulate in the atmosphere despite its reactivity. Here we argue
that O$_2$ may not be unique: diverse gases produced by life may experience a
"runaway" effect similar to O$_2$. This runaway occurs because the ability of
an atmosphere to photochemically cleanse itself of trace gases is generally
finite. If produced at rates exceeding this finite limit, even reactive gases
can rapidly accumulate to high concentrations and become potentially
detectable. Planets orbiting smaller, cooler stars, such as the M dwarfs that
are the prime targets for the James Webb Space Telescope (JWST), are especially
favorable for runaway due to their lower UV emission compared to higher-mass
stars. As an illustrative case study, we show that on a habitable exoplanet
with an H$_2$-N$_2$ atmosphere and net surface production of NH$_3$ orbiting an
M dwarf (the "Cold Haber World" scenario), the reactive biogenic gas NH$_3$ can
enter runaway, whereupon an increase in the surface production flux of one
order of magnitude can increase NH$_3$ concentrations by three orders of
magnitude and render it detectable by JWST in just two transits. Our work on
this and other gases suggests that diverse signs of life on exoplanets may be
readily detectable at biochemically plausible production rates.
