This paper revisits Solé’s claim that Earth’s atmospheric chemical network is scale-free in nature. Wong and colleagues proceed to show that Earth’s atmospheric system is indeed distinct from the topologies of other Solar System bodies and is the most non-random. They further discuss how planetary assessment of atmospheric networks, using more advanced metrics, could eventually be used as a novel class of biosignatures.

The authors begin their discussion of network-based biosignatures by a basic assessment of traditional biosignatures that motivates the development of novel detection techniques: current biosignatures remain incomplete as we lack a proper theory on the origin of life and how it integrates with the planetary system. A possible way around this problem is to make use of the fact that information plays a central role in living systems, and that this information inevitably flows between living systems and the environment. This coevolution thus makes life a planetary-scale phenomenon that we could detect using network theory.

Solé (2004) was the first to suggest that Earth’s atmospheric chemistry could be structured following a power law. In simple terms, if we were to represent the chemical reactions in Earth’s atmospheric chemistry and quantify the number of chemical species “connected” together via chemical reactions (their “degree”), the distribution of these degrees would follow a power-law organization pattern.

The authors reexamine that claim using astrophysical data and advanced network metrics. They did find that Earth’s atmospheric chemical network can indeed be distinguished from that of other Solar System bodies, which leaves open the possibility of using atmospheric topology as a novel type of biosignature for life detection purposes.

Wong and colleagues used networks from the Caltech-JPL photochemistry-transport model KINETICS, represented as networks (Figure 1). In addition to networks of the various Solar System bodies, they have included that of early Earth, derived from geochemically informed theoretical representations. One key element in these representations is that they used unipartite, unweighted and un-directed graphs so the analysis can directly be compared with that of Solé, even though this limits the amount of information contained in those representations.

In Figure 1, node color represents the degree (i.e., the number of nodes connected to) and node size represents the betweenness centrality, another measure used during analysis that represents the “importance” of each node.

Network theory offers a number of different metrics that can be used to investigate the statistics of a network. These can be classified into three groups: global metrics are derived from the network as a whole, while distributions and centrality metrics are usually based on metrics measured from each node.

The first investigation conducted by Wong et al. is based on four global metrics:

a. Degree assortativity: if the node tends to be connected to nodes of similar degree—a measure of how homogeneous a network is.

b. Clustering coefficient: a global metric that measures how common is node \(u\)’s neighbors (let’s say, \(v\)) to have neighbors (such as \(w\)) connected to \(u\).

c. Transitivity: same as clustering coefficient, but measured locally for each node, then averaged for the whole network.

d. Average shortest path length: the average shortest path between pairs of nodes in the network.

Results are presented in Figure 2. For Earth, Wong et al. have included the network analyzed from “textbook-derived data”, as this was how Solé had based its former analysis on. This data is to be compared to other well-known biological networks representing a metabolic network, a neural network and a marine food web. They also included data derived from a photochemical model of Earth’s atmosphere, this time to be compared to the data derived from models of other planetary bodies.

One preliminary result is that there the metrics calculated using Earth’s model generally stand out compared to other planetary bodies. They deviate from the rest of the planetary networks in a way that is consistent with the network from textbook data in direction, but not in magnitude, which motivates further analysis using more advanced metrics to determine to what extent can it be distinguished statistically.

Before going further, Wong et al. offer a direct comparison between their analysis and that of Solé to verify whether the claim that Earth’s network is structured as a power-law still holds. Degree distribution for the various Solar System bodies is shown on Figure 3.

We can see that the distribution derived from textbook values for Earth could indeed fit a power-law, which agrees with Solé’s initial analysis. But this is no longer the case when considering data derived from Earth’s photochemical model: the distribution now fits a lognormal distribution instead, just like the distribution of other Solar System bodies.

In other words, Solé’s analysis wasn’t wrong when considering data that’s as detailed as what we can find in textbooks for planet Earth. But when considering metrics derives from atmospheric models, in the same way as we consider other (exo)planets, the claim no longer holds, and Earth’s distribution can’t be distinguished anymore from other networks.

This result thus begs the question: can it be distinguished using other metrics than degree distribution?

Wong et al. proceed further in their analysis of reaction networks by considering centrality metrics, that is, measures of the “importance” of each nodes. They considered six of them:

a. Closeness centrality: the reciprocal of the average shortest-path \(d\) between \(u\) and all other nodes.

b. Betweenness centrality: the fraction of shortest paths between other nodes that pass through \(u\).

c. Information centrality: treats nodes as agents communicating through signals, as if information propagates through all paths connecting them (and not only the shortest one)—longer paths having more “noise”.

d. Subgraph centrality: takes into account the relationship between a given node \(u\) and the entire graph structure.

e. Harmonic centrality: uses distance as a measure of importance.

f. Average neighbor degree: represents a node’s proximity to well-connected nodes.

The measured values are represented in Figure 4:

The first two measures (a and b) are mostly “traditional” measures frequently used in network theory. The four remaining ones (c, d, e, and f) are metrics that Wong et al. suggest would be a better fit for chemical networks—something that the distributions on Figure 4 indeed seem to confirm, as they allow us to distinguish the different distributions.

The first two traditional measures—closeness centrality and betweenness centrality—yield similar distribution for all Solar System bodies, including Earth. But when considering the four other ones, we see that the distributions are much more heterogeneous: Mars often stands out, and modern Earth and Jupiter have similar information centrality distributions. Titan and Pluto, the coldest objects, are unsurprisingly pretty similar in their atmospheric chemistry.

Two last analyses were conducted by the authors. The first one is based on “community detection”, which is a way to characterize the relationships among groups of nodes in a network. While global metrics take into account the network as a whole and distributions examine the values derived locally from individual nodes, community detection could be said to determine the mesoscopic properties of network structure. Wong et al. thus used the Louvain community detection method, and found that the networks again differed according to this measure: Mars was found to have three communities, Venus/Titan/Pluto and early Earth/Mars to have four, whereas Jupiter and modern Earth have six.

A second analysis they did was motivated by the fact that their analysis could have been biased simply because the atmospheric chemistry of other planets is less constrained than that of Earth. In other words, could it be that Earth appears different, when analyzed through network theory, only because we have a greater knowledge of its network—hence the number of nodes is higher? They thus proceeded to a reassessment of some of the metrics, this time normalizing each network using an equivalent random network of the same size. Interestingly, this again revealed that Earth and Jupiter’s networks were structurally different from the other networks, and that this result wasn’t simply an artefact due to the varying network sizes.

Wong and colleagues are clear about one point: we should not be expecting their analysis to determine beyond any doubt that atmospheric chemical networks can be used as biosignatures. Models are simplified representations of chemical networks, do not contain every single known molecule or reaction, and there’s still work to do to clarify whether life on Earth really impacted its atmosphere in a unique way.

But one hypothesis would justify using these networks as biosignatures: previous work suggests that life tends to favour some specific types of networks (see e.g., Kim et al, 2019)—structures that are functional, robust and error tolerant. Even if Earth isn’t subjected to Darwinian evolution itself (there’s no reproduction, obviously), these types of networks could still be selected over time solely because of their capacity to persist in time—i.e., through “persistence evolution”.

This is a testable hypothesis that would require the use of more precise representations (e.g., weighted networks) and the derivation of statistical metrics on ensembles of both biotic and abiotic worlds. The authors also suggest that further research avenues can include developing new network-based metrics specifically targeted at characterizing biosignatures, and extracting patterns from chemical reaction networks using multilayer network representations.