Carl T. Bergstrom

Maps of random walks on complex networks reveal community structure

To comprehend the multipartite organization of large-scale biological and social systems, we introduce an information theoretic approach that reveals community structure in weighted and directed networks. We use the probability flow of random walks on a network as a proxy for information flows in the real system and decompose the network into modules by compressing a description of the probability flow. The result is a map that both simplifies and highlights the regularities in the structure and their relationships. We illustrate the method by making a map of scientific communication as captured in the citation patterns of >6,000 journals. We discover a multicentric organization with fields that vary dramatically in size and degree of integration into the network of science. Along the backbone of the network—including physics, chemistry, molecular biology, and medicine—information flows bidirectionally, but the map reveals a directional pattern of citation from the applied fields to the basic sciences.

An information-theoretic framework for resolving community structure in complex networks

To understand the structure of a large-scale biological, social, or technological network, it can be helpful to decompose the network into smaller subunits or modules. In this article, we develop an information-theoretic foundation for the concept of modularity in networks. We identify the modules of which the network is composed by finding an optimal compression of its topology, capitalizing on regularities in its structure. We explain the advantages of this approach and illustrate them by partitioning a number of real-world and model networks.

The role of evolution in the emergence of infectious diseases

It is unclear when, where and how novel pathogens such as human immunodeficiency virus (HIV), monkeypox and severe acute respiratory syndrome (SARS) will cross the barriers that separate their natural reservoirs from human populations and ignite the epidemic spread of novel infectious diseases. New pathogens are believed to emerge from animal reservoirs when ecological changes increase the pathogens opportunities to enter the human population and to generate subsequent human-to-human transmission. Effective human-to-human transmission requires that the pathogens basic reproductive number, R0, should exceed one, where R0 is the average number of secondary infections arising from one infected individual in a completely susceptible population. However, an increase in R0, even when insufficient to generate an epidemic, nonetheless increases the number of subsequently infected individuals. Here we show that, as a consequence of this, the probability of pathogen evolution to R0 > 1 and subsequent disease emergence can increase markedly.

Mapping change in large networks

Change is a fundamental ingredient of interaction patterns in biology, technology, the economy, and science itself: Interactions within and between organisms change; transportation patterns by air, land, and sea all change; the global financial flow changes; and the frontiers of scientific research change. Networks and clustering methods have become important tools to comprehend instances of these large-scale structures, but without methods to distinguish between real trends and noisy data, these approaches are not useful for studying how networks change. Only if we can assign significance to the partitioning of single networks can we distinguish meaningful structural changes from random fluctuations. Here we show that bootstrap resampling accompanied by significance clustering provides a solution to this problem. To connect changing structures with the changing function of networks, we highlight and summarize the significant structural changes with alluvial diagrams and realize de Solla Prices vision of mapping change in science: studying the citation pattern between about 7000 scientific journals over the past decade, we find that neuroscience has transformed from an interdisciplinary specialty to a mature and stand-alone discipline.

The Eigenfactor™ Metrics

Quantitative metrics are poor choices for assessing the research output of an individual scholar. Summing impact factors, counting citations, tallying an h-index, or looking at Eigenfactor™ Scores (described below)—none of these methods are adequate compared with what should be the gold standard

The map equation

Abstract Many real-world networks are so large that we must simplify their structure before we can extract useful information about the systems they represent. As the tools for doing these simplifications proliferate within the network literature, researchers would benefit from some guidelines about which of the so-called community detection algorithms are most appropriate for the structures they are studying and the questions they are asking. Here we show that different methods highlight different aspects of a networks structure and that the the sort of information that we seek to extract about the system must guide us in our decision. For example, many community detection algorithms, including the popular modularity maximization approach, infer module assignments from an underlying model of the network formation process. However, we are not always as interested in how a systems network structure was formed, as we are in how a networks extant structure influences the systems behavior. To see how structure influences current behavior, we will recognize that links in a network induce movement across the network and result in system-wide interdependence. In doing so, we explicitly acknowledge that most networks carry flow. To highlight and simplify the network structure with respect to this flow, we use the map equation. We present an intuitive derivation of this flow-based and information-theoretic method and provide an interactive on-line application that anyone can use to explore the mechanics of the map equation. The differences between the map equation and the modularity maximization approach are not merely conceptual. Because the map equation attends to patterns of flow on the network and the modularity maximization approach does not, the two methods can yield dramatically different results for some network structures. To illustrate this and build our understanding of each method, we partition several sample networks. We also describe an algorithm and provide source code to efficiently decompose large weighted and directed networks based on the map equation.

Cost and conflict in animal signals and human language

The “costly signaling” hypothesis proposes that animal signals are kept honest by appropriate signal costs. We show that to the contrary, signal cost is unnecessary for honest signaling even when interests conflict. We illustrate this principle by constructing examples of cost-free signaling equilibria for the two paradigmatic signaling games of Grafen (1990) and Godfray (1991). Our findings may explain why some animal signals use cost to ensure honesty whereas others do not and suggest that empirical tests of the signaling hypothesis should focus not on equilibrium cost but, rather, on the cost of deviation from equilibrium. We use these results to apply costly signaling theory to the low-cost signals that make up human language. Recent game theoretic models have shown that several key features of language could plausibly arise and be maintained by natural selection when individuals have coincident interests. In real societies, however, individuals do not have fully coincident interests. We show that coincident interests are not a prerequisite for linguistic communication, and find that many of the results derived previously can be expected also under more realistic models of society.

Multilevel Compression of Random Walks on Networks Reveals Hierarchical Organization in Large Integrated Systems

To comprehend the hierarchical organization of large integrated systems, we introduce the hierarchical map equation, which reveals multilevel structures in networks. In this information-theoretic approach, we exploit the duality between compression and pattern detection; by compressing a description of a random walker as a proxy for real flow on a network, we find regularities in the network that induce this system-wide flow. Finding the shortest multilevel description of the random walker therefore gives us the best hierarchical clustering of the network — the optimal number of levels and modular partition at each level — with respect to the dynamics on the network. With a novel search algorithm, we extract and illustrate the rich multilevel organization of several large social and biological networks. For example, from the global air traffic network we uncover countries and continents, and from the pattern of scientific communication we reveal more than 100 scientific fields organized in four major disciplines: life sciences, physical sciences, ecology and earth sciences, and social sciences. In general, we find shallow hierarchical structures in globally interconnected systems, such as neural networks, and rich multilevel organizations in systems with highly separated regions, such as road networks.

The Role of Gender in Scholarly Authorship

Gender disparities appear to be decreasing in academia according to a number of metrics, such as grant funding, hiring, acceptance at scholarly journals, and productivity, and it might be tempting to think that gender inequity will soon be a problem of the past. However, a large-scale analysis based on over eight million papers across the natural sciences, social sciences, and humanities reveals a number of understated and persistent ways in which gender inequities remain. For instance, even where raw publication counts seem to be equal between genders, close inspection reveals that, in certain fields, men predominate in the prestigious first and last author positions. Moreover, women are significantly underrepresented as authors of single-authored papers. Academics should be aware of the subtle ways that gender disparities can occur in scholarly authorship.

Evolutionary principles and their practical application

Evolutionary principles are now routinely incorporated into medicine and agriculture. Examples include the design of treatments that slow the evolution of resistance by weeds, pests, and pathogens, and the design of breeding programs that maximize crop yield or quality. Evolutionary principles are also increasingly incorporated into conservation biology, natural resource management, and environmental science. Examples include the protection of small and isolated populations from inbreeding depression, the identification of key traits involved in adaptation to climate change, the design of harvesting regimes that minimize unwanted life‐history evolution, and the setting of conservation priorities based on populations, species, or communities that harbor the greatest evolutionary diversity and potential. The adoption of evolutionary principles has proceeded somewhat independently in these different fields, even though the underlying fundamental concepts are the same. We explore these fundamental concepts under four main themes: variation, selection, connectivity, and eco‐evolutionary dynamics. Within each theme, we present several key evolutionary principles and illustrate their use in addressing applied problems. We hope that the resulting primer of evolutionary concepts and their practical utility helps to advance a unified multidisciplinary field of applied evolutionary biology.