Beyond Networks

(Yogi)

We have a new preprint out! It's called "Beyond networks: explaining dynamics in the natural and social sciences", coauthored by James DiFrisco, Andrea Loettgers, and myself.

It presents a broad criticism of network modeling in both the natural & social sciences & a study of where its shortcomings originate historically, following and earlier paper by James and myself. Here, we  extend our earlier argument from the specific discipline of evolutionary-developmental biology (or evo-devo) to a broad range of network models in neuroscience, cell & developmental biology, ecology, and economics.

We trace the origin of network models not only to graph theory but also lattice models (eg the Ising model) in condensed-matter physics in the 1920s, showing that their application to other disciplines follows a complex entangled pattern of model template transfers.

Model templates capture an intertwinement of mathematical structure, computational tools, and theoretical concepts that depict a general mechanism applicable to any field displaying a particular pattern of interactions.

Network models are successful model templates not because they provide accurate representations of the target systems to which they are applied, but because of their generic ontology & associated conceptual framework that can be used to model a wide range of different systems.

We provide extensive examples, starting with connectionist models in (cognitive) neuroscience, arguing that an excessive focus on network structure obscures important phenomena linked to the dynamics of the system.

We then criticize network approaches in cell & developmental biology, focusing on scale-free networks, network motifs, & Davidson's genomic regulatory networks. Again, an excessive focus on structure severely limits our outlook because structure does not determine function. Reverse-engineered networks based on a connectionist formalism may provide a compromise between abstraction of network structure & a focus on dynamical properties of regulatory systems.

Further examples come from ecology, where time-invariant models fail to capture dynamic changes in feeding habits during an organism's life cycle, or the non-discrete dynamics of ecological succession and extinction events.

Finally, we study the fascinating entanglement of Ising's original lattice model of ferromagnetism and Schelling's economic model of segregation in urban environments, showing that template transfer occurs in non-obvious ways, with unexpected feedback between disciplines.

We frame the entire complex of problems that is illustrated by these examples as a mismatch in the possibility spaces generated by static network models & differential-equation models based on dynamical systems theory.

Simply put, the possibility space of static network models is too restricted to capture many relevant phenomena in the domains of application of network models. The restrictions mainly stem from the intrinsic nature of the underlying model templates.

In turn, the possibility space of dynamical models also fails to capture many relevant phenomena that depend on the fact that biological systems (and those based on them) constantly alter their organization based on the intrinsic dynamics of the system.

To conclude: as attractive & versatile as network models are, their power is also their downfall: by abstracting away the dynamics of a system, we are bound to restrict ourselves to small subsets of possible phenomena to be studied & their plausible scientific explanations.