A biological cell becomes cancerous if a certain set of rare mutations all happen in that same cell before its organism dies. This is quite unlikely to happen in any one cell, but a large organism has enough cells to create a substantial chance of cancer appearing somewhere in it before it dies. If the chances of mutations are independent across time, then the durations between the timing of mutations should be roughly equal, and the chance of cancer in an organism rises as a power law in time, with the power equal to the number of required mutations, usually around six.

A similar process may describe how an advanced civilization like ours arises from a once lifeless planet. Life may need to advance through a number of “hard step” transitions, each of which has a very low chance per unit time of happening. Like evolving photosynthesis or sexual reproduction. But even if the chance of advanced life appearing on any one planet before it becomes inhabitable is quite low, there can be enough planets in the universe to make the chance of life appearing somewhere high.

As with cancer, we can predict that on a planet lucky enough to birth advanced life, the time durations between its step transitions should be roughly equal, and the overall chance of success should rise with time as the power of the number of steps. Looking at the history of life on Earth, many observers have estimated that we went through roughly six (range ~3-12) hard steps.

In our grabby aliens analysis, we say that a power of this magnitude suggests that Earth life has arrived very early in the history of the universe, compared to when it would arrive if the universe would wait empty for it to arrive. Which suggests that grabby aliens are out there, have now filled roughly half the universe, and will soon fill all of it, creating a deadline soon that explains why we are so early. And this power lets us estimate how soon we would meet them: in roughly a billion years.

According to this simple model, the short durations of the periods associated with the first appearance of life, and with the last half billion years of complex life, suggest that at most one hard step was associated with each of these periods. (The steady progress over the last half billion years also suggests this, though our paper describes a “multi-step” process by which the equivalent of many hard steps might be associated with somewhat steady progress.)

In an excellent new paper in the Proceedings of the Royal Society, “Catastrophe risk can accelerate unlikely evolutionary transitions”, Andrew Snyder-Beattie and Michael Bonsall extend this standard model to include set-backs and dead-ends.

Here, we generalize the [standard] model and explore this hypothesis by including catastrophes that can ‘undo’ an evolutionary transition. Introducing catastrophes or evolutionary dead ends can create situations in which critical steps occur rapidly or in clusters, suggesting that past estimates of the number of critical steps could be underestimated. (more)

Their analysis looks solid to me. They consider scenarios where, relative to the transition rate at which a hard step would be achieved, there is a higher rate of a planet “undoing” its last hard step, or of that planet instead switching to a stable “stuck” state from which no further transitions are possible. In this case, advanced life is achieved mainly in scenarios where the hard steps that are vulnerable to these problems are achieved in a shorter time than it takes to undo or stuck them.

As a result, the hard steps which are vulnerable to these set-back or dead-end problems tend to happen together much faster than would other sorts of hard steps. So if life on early Earth was especially fragile amid especially frequent large asteroid impacts, many hard steps might have been achieved then in a short period. And if in the last half billion years advanced life has been especially fragile and vulnerable to astronomical disasters, there might have been more hard steps within that period as well.

Their paper only looks at the durations between steps, and doesn’t ask if these model modifications change the overall power law formula for the chance of success as a function of time. But my math intuition is telling me it feels pretty sure that the power law dependence will remain, where the power now goes as the number of all these steps, including the ones that happen fast. Thus as these scenarios introduce more hard steps into Earth history, the overall power law dependence of our grabby aliens model should remain but become associated with a higher power. Maybe more like twelve instead of six.

With a higher power, we will meet grabby aliens sooner, and each such civilization will control fewer (but still many) galaxies. Many graphs showing how our predictions vary with this power parameter can be found in our grabby aliens paper.