  In ecological systems, be it a garden or a galaxy, populations evolve from
some initial value (say zero) up to a steady state equilibrium, when the mean
number of births and deaths per unit time are equal. This equilibrium point is
a function of the birth and death rates, as well as the carrying capacity of
the ecological system itself. The growth curve is S-shaped, saturating at the
carrying capacity for large birth-to-death rate ratios and tending to zero at
the other end. We argue that our astronomical observations appear inconsistent
with a cosmos saturated with ETIs, and thus SETI optimists are left presuming
that the true population is somewhere along the transitional part of this
S-curve. Since the birth and death rates are a-priori unbounded, we argue that
this presents a fine-tuning problem. Further, we show that if the
birth-to-death rate ratio is assumed to have a log-uniform prior distribution,
then the probability distribution of the ecological filling fraction is
bi-modal - peaking at zero and unity. Indeed, the resulting distribution is
formally the classic Haldane prior, conceived to describe the prior expectation
of a Bernoulli experiment, such as a technological intelligence developing (or
not) on a given world. Our results formally connect the Drake Equation to the
birth-death formalism, the treatment of ecological carrying capacity and their
connection to the Haldane perspective.
