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In order to grow, reproduce and evolve life requires a supply of energy and nutrients. Astrobiology has the challenge of studying life on Earth in environments which are poorly characterized or extreme, usually both, and predicting the habitability of extraterrestrial environments. We have developed a general astrobiological model for assessing the energetic and nutrient availability of poorly characterized environments to predict their potential biological productivity. NutMEG (nutrients, maintenance, energy and growth) can be used to estimate how much biomass an environment could host, and how that life might affect the local chemistry. It requires only an overall catabolic reaction and some knowledge of the local environment to begin making estimations, with many more customizable parameters, such as microbial adaptation. In this study, the model was configured to replicate laboratory data on the growth of methanogens. It was used to predict the effect of temperature and energy/nutrient limitation on their microbial growth rates, total biomass levels, and total biosignature production in laboratory-like conditions to explore how it could be applied to astrobiological problems. As temperature rises from 280 to 330 K, NutMEG predicts exponential drops in final biomass ( 10 9 − 10 6   cells   l − 1 ) and total methane production ( 62 − 3   μ M ) despite an increase in peak growth rates ( 0.007 − 0.14   h − 1 ) for a typical methanogen in ideal conditions. This is caused by the increasing cost of microbial maintenance diverting energy away from growth processes. Restricting energy and nutrients exacerbates this trend. With minimal assumptions NutMEG can reliably replicate microbial growth behaviour, but better understanding of the synthesis and maintenance costs life must overcome in different extremes is required to improve its results further. NutMEG can help us assess the theoretical habitability of extraterrestrial environments and predict potential biomass and biosignature production, for example on exoplanets using minimum input parameters to guide observations.

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The relative rank rank(S : A) of a subset A of a semigroup S is the minimum cardinality of a set B such that A ∪ B = S. It follows from a result of Sierpiński that, if X is infinite, the relative rank of a subset of the full transformation semigroup T X is either uncountable or at most 2. A similar result holds for the semigroup B X of binary relations on X.A subset S of T N is dominated (by U ) if there exists a countable subset U of T N with the property that for each σ in S there exists µ in U such that iσ iµ for all i in N. It is shown that every dominated subset of T N is of uncountable relative rank. As a consequence, the monoid of all contractions in T N (mappings α with the property that |iα − jα| |i − j| for all i and j) is of uncountable relative rank.It is shown (among other results) that rank(B X : T X ) = 1 and that rank(B X : I X ) = 1 (where I X is the symmetric inverse semigroup on X). By contrast, if S X is the symmetric group, rank(B X : S X ) = 2.

Enceladus is a unique and important target for astrobiology in the solar system. The icy moon has a large subsurface ocean (Iess et al., 2014;Thomas et al., 2016), and analysis of measurements by the Cassini mission show the existence of CO 2 , H 2 , and CH 4 -the reactants and products of the hydrogenotrophic methanogenesis metabolism-as well as salts, silica and organics (e.g.,