The Drake Equation
Ward and Brownlee provide an alternative version of the
Drake Equation, modified to estimate the number of planets in this galaxy currently inhabited by complex multi-cellular (metazoan) life.
Their modified equation is as follows:
"N* x fp x fpm x ne x ng x fi x fc x fl x fm x fj x fme = N
where:
N* = stars in the Milky Way galaxy
fp = fraction of stars with planets
fpm = fraction of metal-rich planets
ne = planets in a star's habitable zone
ng = stars in a galactic habitable zone
fi = fraction of habitable planets where life does arise
fc = fraction of planets where complex metazoans arize
fl = percentage of a lifetime of a planet that is marked by the presence of complex metazoans
fm = fraction of planets with a large moon
fj = fraction of solar systems with Jupiter-sized planets
fme = fraction of planets with a critically low number of mass extinction events"
First of all, this equation contains numerous errors and redundancies in its terms. For example, "stars in a galactic habitable zone" should be a fraction, and it should be something like "fraction of those planets orbiting stars in a galactic habitable zone". Each term needs to reference all of the terms before it in some way, like the terms given in the original Drake Equation. Even after these errors are corrected, there is still an additional logical error.
The authors state that "as any term in such an equation approaches zero, so too does the final product." But this is only valid as far as each condition specified is absolutely necessary for complex life. In reality, each term should be modified by the chance that complex life can form without that feature. For example, "fm = fraction of planets with a large moon" should be replaced by something like:
(fm + fm' x (1 - fm))
where fm' = the fraction of planets without a large moon that can develop complex metazoans. Since fm and fm' must always be between zero and one, this term can never be less than fm' even if fm approaches zero.
The equation with each term modified in this way now takes into account the chance that the authors' proposed requirements for complex life are not absolute. Now it is more than a simple matter of proving that one of the terms approaches zero in order to claim that complex life is rare.