3.5 Conclusion

In this chapter, we introduced several evolving network models by focusing on biological networks. The model networks were compared with real data, and they were found to be in good agreement with the real data in terms of structural properties. In particular, the model mentioned in Section 3.2 reproduces several types of biological networks such as gene regulatory networks and metabolic networks. The models in Sections 3.3 and 3.4 do not require parameter tunings, which are necessary in most existing models. Thus, it is easy to estimate the frequency of evolutionary events such as gene duplication and divergences. Our models are expected to provide a platform for the elucidation of formation mechanisms in biological networks. For instance, metabolic networks are believed to shape-shift in response to environmental changes [49,50], and the model in Section 3.3 explains the possible origin of structural differences with respect to growth temperatures (an environmental factor) [27].

In addition to this, our models also serve as a foundation for the prediction of interactions between biomolecules, that is, “link prediction” [51]. It is believed that real networks have several missing links, and the finding of such links is an important challenge in various fields including biology. The statistical and machine-learning techniques are often utilized in link prediction. Network models are particularly useful because they estimate the probability of interactions between nodes.

We use the concepts of network models in biology as well as in society and ecology. As mentioned in Section 3.4, our bipartite network model can also explain the structure of ecological networks in addition to metabolite distributions. The models mentioned in this chapter may be applicable in a wide range of fields.