The performance of modularity maximization in practical contexts

Although widely used in practice, the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts. Here, we present a broad characterization of its performance in such situations. First, we revisit and clarify the resolution limit phenomenon for modularity maximization. Second, we show that the modularity function Q exhibits extreme degeneracies: it typically admits an exponential number of distinct high-scoring solutions and typically lacks a clear global maximum. Third, we derive the limiting behavior of the maximum modularity Q_max for one model of infinitely modular networks, showing that it depends strongly both on the size of the network and on the number of modules it contains. Finally, using three real-world metabolic networks as examples, we show that the degenerate solutions can fundamentally disagree on many, but not all, partition properties such as the composition of the largest modules and the distribution of module sizes. These results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts. They also explain why many heuristics are often successful at finding high-scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network. We conclude by discussing avenues for mitigating some of these behaviors, such as combining information from many degenerate solutions or using generative models.Comment: 20 pages, 14 figures, 6 appendices; code available at http://www.santafe.edu/~aaronc/modularity

Thinking through the implications of neural reuse for the additive factors method

One method for uncovering the subprocesses of mental processes is the “Additive Factors Method” (AFM). The AFM uses reaction time data from factorial experiments to infer the presence of separate processing stages. This paper investigates the conceptual status of the AFM. It argues that one of the AFM’s underlying assumptions is problematic in light of recent developments in cognitive neuroscience. Discussion begins by laying out the basic logic of the AFM, followed by an analysis of the challenge presented by neural reuse. Following this, implications are analysed and avenues of response considered

Development of modularity in the neural activity of children's brains

We study how modularity of the human brain changes as children develop into adults. Theory suggests that modularity can enhance the response function of a networked system subject to changing external stimuli. Thus, greater cognitive performance might be achieved for more modular neural activity, and modularity might likely increase as children develop. The value of modularity calculated from fMRI data is observed to increase during childhood development and peak in young adulthood. Head motion is deconvolved from the fMRI data, and it is shown that the dependence of modularity on age is independent of the magnitude of head motion. A model is presented to illustrate how modularity can provide greater cognitive performance at short times, i.e.\ task switching. A fitness function is extracted from the model. Quasispecies theory is used to predict how the average modularity evolves with age, illustrating the increase of modularity during development from children to adults that arises from selection for rapid cognitive function in young adults. Experiments exploring the effect of modularity on cognitive performance are suggested. Modularity may be a potential biomarker for injury, rehabilitation, or disease.Comment: 29 pages, 11 figure

Modularity Enhances the Rate of Evolution in a Rugged Fitness Landscape

Biological systems are modular, and this modularity affects the evolution of biological systems over time and in different environments. We here develop a theory for the dynamics of evolution in a rugged, modular fitness landscape. We show analytically how horizontal gene transfer couples to the modularity in the system and leads to more rapid rates of evolution at short times. The model, in general, analytically demonstrates a selective pressure for the prevalence of modularity in biology. We use this model to show how the evolution of the influenza virus is affected by the modularity of the proteins that are recognized by the human immune system. Approximately 25\% of the observed rate of fitness increase of the virus could be ascribed to a modular viral landscape.Comment: 45 pages; 7 figure