In writing this review paper we hoped to stimulate further thinking and research on how complex modular structures emerge and persist. The commentators raised open questions in the field in which we are interested.
One of the most urgent theoretical problems is the development of "general, flexible definitions" [2] for modularity. Currently, the definition of modularity is "very plastic" . There are numerous quantitative definitions of modularity, all of which have some drawbacks. In fact, a perfect general definition of this biological concept, applicable to a vast array of network types and other biological data, may not exist or may be context dependent. Nevertheless, a quantitative understanding of how complex biological features arise requires a quantitative definition of these features. The definitions of modularity for networks and Euclidean spaces reviewed here provide a starting point and will hopefully spur research into a general definition of modularity.
A second point raised by Morava is that there are many different kinds of biological networks, which differ greatly in their topologies and other properties. The pressures on these different kinds of networks to function in changing environments over time may be distinct. A quantitative study of how the structures of these different networks have evolved to cope with their environmental pressures, e.g. perhaps by developing a modular structure, is warranted.
We are often asked why we use a spin glass system to illustrate emergence of modularity. The reason is that we believe evolution is a slow process, with "glassy" dynamics. We use the spin glass to provide the challenging landscape upon which evolution proceeds. The general spin glass provides a good approximation for all possible landscapes. We often describe the spin glass as a model for chemical structure and function. In this setting, emergence of modularity corresponds to the emergence of protein secondary structure from the large space of chemical possibilities.
Finally, Buchman emphasized a point that we mentioned in our paper. The emergence of modules constrains future evolution. It is even possible that "the modules themselves may delimit evolution, evolvability and hierarchy much more than forces subsequently applied" [1]. This brings up a couple points: the identity of the modules may change over time, and modules suitable in one environment may be unsuitable and inhibiting in another environment. One may make the same points about a highly-optimized, non-modular biological structure. In general, we expect the