Mason A Porter | bioRxiv Science

bioRxiv2014

Null Models for Community Detection in Spatially-Embedded, Temporal Networks

In the study of networks, it is often insightful to use algorithms to determine mesoscale features such as \"community structure\", in which densely connected sets of nodes constitute \"communities\" that have sparse connections to other communities. The most popular way of detecting communities algorithmically is to optimize the quality function known as modularity. When optimizing modularity, one compares the actual connections in a (static or time-dependent) network to the connections obtained from a random-graph ensemble that acts as a null model. The communities are then the sets of nodes that are connected to each other densely relative to what is expected from the null model. Clearly, the process of community detection depends fundamentally on the choice of null model, so it is important to develop and analyze novel null models that take into account appropriate features of the system under study. In this paper, we investigate the effects of using null models that take incorporate spatial information, and we propose a novel null model based on the radiation model of population spread. We also develop novel synthetic spatial benchmark networks in which the connections between entities are based on distance or flux between nodes, and we compare the performance of both static and time-dependent radiation null models to the standard (\"Newman-Girvan\") null model for modularity optimization and a recently-proposed gravity null model. In our comparisons, we use both the above synthetic benchmarks and time-dependent correlation networks that we construct using countrywide dengue fever incidence data for Peru. We also evaluate a recently-proposed correlation null model, which was developed specifically for correlation networks that are constructed from time series, on the epidemic-correlation data. Our findings underscore the need to use appropriate generative models for the development of spatial null models for community detection.\n\nPACS numbers87.19.Xx,89.20.-a,89.75.Fb,05.45.Tp

Biophysics↗

bioRxiv2014

Mesoscale analyses of fungal networks as an approach for quantifying phenotypic traits

We investigate the application of mesoscopic response functions (MRFs) to characterize a large set of networks of fungi and slime moulds grown under a wide variety of different experimental treatments, including inter-species competition and attack by fungivores. We construct structural networks by estimating cord conductances (which yield edge weights) from the experimental data, and we construct functional networks by calculating edge weights based on how much nutrient traffic is predicted to occur along each edge. Both types of networks have the same topology, and we compute MRFs for both families of networks to illustrate two different ways of constructing taxonomies to group the networks into clusters of related fungi and slime moulds. Although both network taxonomies generate intuitively sensible groupings of networks across species, treatments, and laboratories, we find that clustering using the functional-network measure appears to give groups with lower intra-group variation in species or treatments. We argue that MRFs provide a useful quantitative analysis of network behaviour that can (1) help summarize an expanding set of increasingly complex biological networks and (2) help extract information that captures subtle changes in intra-specific and inter-specific phenotypic traits that are integral to a mechanistic understanding of fungal behaviour and ecology. As an accompaniment to our paper, we also make a large data set of fungal networks available in the public domain.

Plant Biology↗