MultiNet: An interactive program for analysing and visualizing complex networks

MultiNet is a Windows-based computer program designed for exploratory data analysis of social and other networks. MultiNet is highly interactive and always provides both textual and visual representations of results. The visualizations are innovative in the use of colour and interaction, and some are unique to MultiNet. MultiNet was designed from the beginning to handle large amounts of data, and uses compact data formats, special storage schemes, and calculation methods that are highly efficient in terms of both space and time. MultiNet was also designed to handle large numbers of variables, both attribute (node) and network (link); it allows easy construction of new variables of either type by means of various operations on existing ones. Hybrid variables are easily constructed: node variables derived fiom networks; link variables derived fiom attributes. These capabilities provide crucial links among other parts of the program. The application of spectral methods to large, sparse networks is both the theoretical and practical centre of the research and development that has gone into MultiNet. Spectral methods provide analytic visualizations of network data: pictures that not only provide understanding, but that provide numerical values that can be used in further analysis. The results of the spectral methods, as well as other attribute and network data, are used together with simple, standard statistical methods such as cross-tabulations, analysis of variance and correlations for testing hypotheses about relationships among the data. MultiNet provides unique methods that allow attributes and networks to be freely mixed in such analyses, and presents results in both textual and interactive visualizations that include two or three discrete or continuous variables. The largest part of this thesis consists of descriptions of the seven main MultiNet program modules. Supplementary sections describe the theoretical background for spectral analysis and provide specific examples of spectral analysis, including a peer-reviewed, published paper that uses most of the parts of MultiNet together. In addition, a separate CDROM provides a working version ofthe program, electronic documentation, sample datasets, software aids and videos showing how the program is used

Partitioning Networks by Eigenvectors

A survey of published methods for partitioning sparse arrays is presented. These include early attempts to describe the partitioning properties of eigenvectors of the adjacency matrix. More direct methods of partitioning are developed by introducing the Laplacian of the adjacency matrix via the directed (signed) edge-vertex incidence matrix. It is shown that the Laplacian solves the minimization of total length of connections between adjacent nodes, which induces clustering of connected nodes by partitioning the underlying graph. Another matrix derived from the adjacency matrix is also introduced via the unsigned edge-vertex matrix. This (the Normal) matrix is not symmetric, and it also is shown to solve the minimization of total length in its own non-Euclidean metric. In this case partitions are induced by clustering the connected nodes. The Normal matrix is closely related to Correspondence Analysis

Networks of Symptoms and Exposures

We present some novel methods for analyzing and visualizing data from medical studies using methods originally developed for the study of social networks. The methods are based on spectral (eigendecomposition) properties of networks, in particular the so-called Normal spectrum. Among the many desirable properties of this spectrum is the natural handling of bipartite (2-mode) networks through negative eigenvalues, the clustering properties related to positive eigenvalues, and the relationship to the chi-squared measure of dependence in contingency tables

Supplementary methods and results for An anchovy ecosystem indicator of marine predator foraging and reproduction

Forage fishes are key energy conduits that transfer primary and secondary productivity to higher trophic levels. As novel environmental conditions caused by climate change alter ecosystems and predator–prey dynamics, there is a critical need to understand how forage fish control bottom-up forcing of food web dynamics. In the northeast Pacific, northern anchovy (Engraulis mordax) is an important forage species with high interannual variability in population size that subsequently impacts the foraging and reproductive ecology of marine predators. Anchovy habitat suitability from a species distribution model (SDM) was assessed as an indicator of the diet, distribution and reproduction of four predator species. Across 22 years (1998–2019), this anchovy ecosystem indicator (AEI) was significantly positively correlated with diet composition of all species and the distribution of common murres (Uria aalge), Brandt's cormorants (Phalacrocorax penicillatus) and California sea lions (Zalophus californianus), but not rhinoceros auklets (Cerorhinca monocerata). The capacity for the AEI to explain variability in predator reproduction varied by species but was strongest with cormorants and sea lions. The AEI demonstrates the utility of forage SDMs in creating ecosystem indicators to guide ecosystem-based management

Recommendations for quantifying and reducing uncertainty in climate projections of species distributions.

Projecting the future distributions of commercially and ecologically important species has become a critical approach for ecosystem managers to strategically anticipate change, but large uncertainties in projections limit climate adaptation planning. Although distribution projections are primarily used to understand the scope of potential change-rather than accurately predict specific outcomes-it is nonetheless essential to understand where and why projections can give implausible results and to identify which processes contribute to uncertainty. Here, we use a series of simulated species distributions, an ensemble of 252 species distribution models, and an ensemble of three regional ocean climate projections, to isolate the influences of uncertainty from earth system model spread and from ecological modeling. The simulations encompass marine species with different functional traits and ecological preferences to more broadly address resource manager and fishery stakeholder needs, and provide a simulated true state with which to evaluate projections. We present our results relative to the degree of environmental extrapolation from historical conditions, which helps facilitate interpretation by ecological modelers working in diverse systems. We found uncertainty associated with species distribution models can exceed uncertainty generated from diverging earth system models (up to 70% of total uncertainty by 2100), and that this result was consistent across species traits. Species distribution model uncertainty increased through time and was primarily related to the degree to which models extrapolated into novel environmental conditions but moderated by how well models captured the underlying dynamics driving species distributions. The predictive power of simulated species distribution models remained relatively high in the first 30 years of projections, in alignment with the time period in which stakeholders make strategic decisions based on climate information. By understanding sources of uncertainty, and how they change at different forecast horizons, we provide recommendations for projecting species distribution models under global climate change