We use the critical step model to study the major transitions in evolution on Earth. We
find that a total of five steps represents the most plausible estimate, in agreement with previous
studies, and use the fossil record to identify the potential candidates. We apply the model to
Earth-analogs around stars of different masses by incorporating the constraints on habitability
set by stellar physics including the habitable zone lifetime, availability of ultraviolet radiation for
prebiotic chemistry, and atmospheric escape. The critical step model suggests that the habitability
of Earth-analogs around M-dwarfs is significantly suppressed. The total number of stars with
planets containing detectable biosignatures of microbial life is expected to be highest for K-
dwarfs. In contrast, we find that the corresponding value for intelligent life (technosignatures)
should be highest for solar-mass stars. Thus, our work may assist in the identification of suitable
targets in the search for biosignatures and technosignatures.

According to Carter, a hard (or critical) step must be both 1) essential to the evolutionary
emergence of any given trait or organism, and 2) improbable with respect to the externally
allotted time (1, 2). Throughout his publications, Carter variously and interchangeably referred to
the “emergence of civilization” (1), “the emergence of intelligent observers such as ourselves”
(2), and “the evolution of what we recognize as intelligent life” (4) as the evolutionary
innovation whose probability was ultimately in question. While the origin of a “scientific
civilization such as our own” (1) and “the emergence of intelligent life” (4) more generally
represent distinct evolutionary events in the history of life on Earth (that is, the origin of human
civilization vs. the origin of Homo sapiens, respectively), the hard-steps model can be applied
equally – as Carter phrased it – to any given “stage of advancement” (1), including “less
‘advanced’ stages of development” (2). While this language, betraying non-Darwinian notions of
evolution as a linear ‘ascent’ from lower to higher degrees of ‘advancement’ (27), is perhaps too
reminiscent of the Great Chain of Being for most modern evolutionary biologists to accept (28),
Carter nevertheless rejected so-called ‘progressive’ notions of evolution (with humans at the top)
as “unduly anthropocentric?? (1). Indeed, like the anthropic principle itself, the hard-steps model
is applicable to humans and non-human entities alike – notably, extraterrestrial organisms (1), as
well as any organism that has existed or will exist on Earth. In the various applications of the
hard-steps model by other authors, the focus has primarily been on humans or H. sapiens (7, 11),
“intelligent life” (9, 18), and “observerhood” (12). Others adopted a more operational approach
relevant to the field of SETI (the search for extraterrestrial intelligence), defining intelligence as
“the building of radio telescopes” (8) or life capable of manufacturing detectable
“technosignatures” (17). In general, “intelligence” has no standard definition, and arguably
agency (the capacity to deliberately change one's environment) and cognition (knowing how to
perform these changes and reflecting on them) are more relevant traits for SETI (29). For our
purposes, we are concerned with the existence of evolutionary transitions and processes (so-
called “steps”) that were both improbable (relative to 𝜏0) and essential to the evolutionary origin
of H. sapiens on Earth (since we are the self-reflective observers communicating about our own
observations). While this effort concerns SETI, it applies equally to understanding evolutionary
timescales on Earth (30), as well as how life in general may unfold on worlds beyond Earth.