This has been the toughest post in the series to write, because the question of how life arose is the most open. A look at the linked article will show a lot of different conjectures. Which one(s) explain how life actually arose on Earth and/or would arise on other planets are still unknown.
Let’s make some guesses about the upper and lower limits on f_l.
The upper limit is, of course, 1. In other words, it might be the case that life arises on every planet where the ingredients are present for a sufficient length of time (estimating from the early Earth, life needs 500-750 million years). This fits with the mediocrity principle, that there’s nothing special about Earth, and so since life arose here, it would arise anywhere.
Even so, let’s bear in mind Clarke’s comment that “the universe is stranger than we can suppose,” and step back from the max. For our purposes, we’ll say the upper limit on f_l is 0.95.
The lower limit depends on which conjecture for the origin of life you subscribe to.
Does the origin of life require sunlight and tidal pools? Then a large moon (for a terrestrial planet) or a large primary (like Jupiter for Europa) would be very important, if not mandatory. (The sun drives only about half of Earth’s tides). For a terrestrial planet to have a large moon probably requires an impact with a [planetary-embryo-sized] body at a particular speed and angle to form that large moon. Though impacts are common in young stellar systems, large moons are not. (See Venus).
Does the origin of life require a step of nucleic acid solutions absorbing UV radiation? Then stars that generate little UV (e.g., the highly numerous stellar class M) are less likely to meet that requirement.
Does the origin of life require deep sea hydrothermal vents? Those vents would be driven by hot planetary cores, which generally would result from the heat of planetary formation and/or radioactive materials. The upshot: small planets (cooling too quickly) or planets around metal-poor stars (not radioactive enough) are unlikely to support life. However, note the moons of gas giants have a third route to core heating—tidal forces from the gas giant and other moons. (That’s the source of Io’s volcanoes and whatever liquid ocean might exist under Europa’s ice.)
(Aside: The further we go in this series, the more I conclude the moons of gas giants would be the most common homeworlds for life).
What, then, is the lower limit for f_l? Who knows. Out of intellectual laziness, we’ll say the lower limit is 0.05 and be done.
Plugging into the Drake equation, we get:
N_upper = 16.03 * f_i * f_c * L
N_lower = 0.84 * f_i * f_c * L
We’re close enough to end of the series to see that, even at the lower limit, if the values of f_i, f_c, and L are relatively high (the first two > 0.90, the last > 100 years), then scores of intelligent civilizations are sending out signals of their existence at all times. If we go closer to the upper limit, and bump up L to 1000 years, then the number of intelligent civilizations is north of 10,000.
Is the explanation for the Fermi Paradox simply that we’re oblivious to their signals? Or is one or more of f_i, f_c, and L very close to 0? My answer is coming up.