What do galaxies and molecular structures have in common? Or trade between countries, communications on the Internet, and trophic relationships within ecosystems? One answer is that they all involve nodes interconnected by flows of mass and energy. In other words, they are networks.
The study of networks has revealed intriguing regularities. For example, it is very common to find networks whose “degree” distribution (i.e., number of connections between nodes) follows power law: most networks have few very connected nodes, but most are poorly connected to each other.
The internet offers an intuitive example: few nodes are very connected, like Google, Facebook, Twitter, Youtube, and most nodes, like my website, are poorly connected. Airport networks follow the same principle. There are few airports that function as high connectivity hubs in an extensive airport network dominated by London (LHR), Chicago (ORD), Frankfurt (FRA), Amsterdam (AMS), Toronto (YYZ) and a few more, followed by a myriad of intermediate and small connectivity airports. Ecosystems are not very different. If we walk into a forest, we will find that trees are connected with most species in the ecosystem, but most species that live there are poorly connected to each other.
The causes for such regularities in network architectures and the exceptions that occasionally occur are the subject of intense investigation. For example, simulations published in Nature by Albert, Jeong and Barabási (2000), entitled “Error and attack tolerance of complex networks”, demonstrated that the architecture of networks can result from the structure of attacks to which they are subject. By exposing virtual networks to simulated attacks, the researchers observed that networks with “degree” distribution following a power law would be more robust to random attacks. On the other hand, networks following a random “degree” distribution, in which most nodes have intermediate connectivity, and few nodes are little or very connected, would tend to be more robust if attacks were directed at certain highly connected nodes.
The conclusions of this study are relevant for the design of policies and infrastructures, and for the planning of security strategies. They are equally relevant to understanding how complex networks in nature and society self-organise. That is, how the dynamics of networks favourably select a particular architecture over another when exposed to different constraints.
Albert et al. (2000) provided a mathematical demonstration of the stated assumptions in a controlled and simplified context. The question remains, however, if empirically, in an uncontrolled and complex reality, the architecture of networks responds in a discernible way to the structure of the attacks.
We decided to investigate this question by analysing the architecture of 351 trophic networks on land, sea, and freshwater. In such networks, species are the nodes and the links between nodes are the trophic relationships between them. We postulated that subject to low human impacts, random attacks prevail as the result of natural stochasticity. In contrast, areas exposed to high human impacts would be additionally exposed to non-random attacks. Such postulate is supported by the observation that human activities generate impacts that target sensitive species, while less sensitive species are more tolerant and, in certain cases, may even benefit from human activities.
If the observations of Albert, Jeong and Barabási were general and predictive, the expectation would be that trophic networks in low human impact environments would have a power law degree distribution, while trophic networks exposed to high human impact would have a random degree distribution. The results of our analysis corroborate the expectation arising from Albert et al. (2020) and were just published in Ecology Letters, in an article by Frederico Mestre, Alejandro Rozenfeld and myself.
Of course, when empirical data from different sampling systems and methods are analyzed, there is noise in the data that sometimes limits the ability to discern clear patterns. Hence the relevance of having revealed patterns, hitherto unknown, in this type of networks.
The consequences of our analysis are potentially substantive. Future investigations will continue to study self-organization of complex networks, identifying patterns and exceptions, but if the generality of the patterns detected is generally demonstrated, we will be in a better position to provide projections on the impacts of human activities on the structure and functioning of ecosystems.
The classical approach consists of modeling individual species. The finding that neglecting biological interactions in models limits their predictive capacity has been addressed by models that include dynamics between small sets of interacting species. Such approach allows building more realistic models for focal species, but that it is not applicable in complex interaction networks across ecosystems. To do so, we will need to understand the emergent properties of networks and our work is a step further in this direction.
The article is available here:
Press release in Spanish here:
Image created by Frederico Mestre.