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Darren P. Croft, Richard James & Jens Krause

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"An important and timely addition to the literature. This book should be readily accessible to researchers who are interested in animal social organization but who have little or no experience in conducting network analysis. The book is well-written in an engaging style and contains a good number of examples drawn from a range of taxonomic groups."--Paul R. Moorcroft, Harvard University

"This book introduces ecologists, behaviorists, and others studying social behavior to the methods of network analysis. It is clearly written and accessible to readers whose primary training is in biology, not physics, mathematics, or sociology--the fields in which network techniques have largely been developed. The book is method oriented, so that it can serve as a practical guide to how readers can analyze their own data."--Stephen C. Pratt, Arizona State University

"No such book of this kind exists, and because it fills a new niche it will be important. New graphical and analytical techniques are emerging that provide insights into how networks form and function. This book is designed as a primer to introduce students, especially graduate students, to these techniques by using and interpreting examples from animal interactions. For anyone interested in networks, this book will be a useful guide."--Daniel I. Rubenstein, Princeton University

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Exploring Animal Social Networks

Princeton University Press

Chapter One

Understanding the link between individual behavior and population-level phenomena is a long-standing challenge in ecology and evolutionary biology (Lima and Zollner 1996; Sutherland 1996). Behavior is expressed as a response to intrinsic and extrinsic factors, including an individual's physical and social environment, the latter made up of nonrandom and heterogeneous social interactions (Krause and Ruxton 2002). That is, individuals are part of a network of inter-individual associations that vary in strength, type, and dynamics. The structure of this social network has far-reaching implications for the ecology and evolution of individuals, populations, and species. For example, the social network supports a diverse array of behaviors that will be influenced by its structure, including: finding and choosing a sexual partner, developing and maintaining cooperative relationships, and engaging in foraging and anti-predator behavior. Such behavior is manifested at the population level in the form of, for example, habitat use, disease transmission, information flow, and mating systems, and forms the basis for evolutionary processes including adapting to changing environments, sexual selection, and speciation. Improving our ability to scale up from the individual to the population by establishing why certain patterns of association develop and how inter-individual association patterns affect population-level structure will revolutionize our understanding of the function, evolution, and implications of social organization.

Across the animal kingdom there is immense diversity in social behavior. Social interactions differ in their type (they might be cooperative, antagonistic, or sexual, for example) as well as their frequency and duration; social bonds may last for years or just minutes or seconds. Which type of interaction occurs and with what frequency and duration will depend on factors such as dominance, body size, sex, age, and parasite load of the participating individuals. This raises the question of how we deal with multiple interactions and complex interaction patterns that can arise even if the number of participants is relatively small. Interestingly, sociologists started addressing this question more than sixty years ago when looking at human interaction patterns, and this literature in combination with recent advances in areas such as statistical physics has provided us with a powerful set of tools for the analysis of animal social networks. These tools make it possible to calculate quantitative metrics describing social structure across different scales of organization, from the individual to the population. The aim of this book is to explore some of the techniques of network analysis that might be applied to a study of animal social structure.

1.1 WHAT IS A NETWORK?

The essential elements of a network are "nodes" and "edges." In a graphical representation of a network, each node is represented by a symbol, and every interaction (of whatever sort) between two nodes is represented by a line (edge) drawn between them. In the context of a social network, each node would normally represent an individual animal (though see later in this chapter for some alternate approaches) and each edge would represent some measured social interaction or association. For example, figure 1.1 represents the social network for a population of bottlenose dolphins, Tursiops truncatus, in New Zealand (Lusseau 2003). In figure 1.1 each filled circle (node) represents an individual dolphin and the connections (edges) between them indicate a certain frequency of social contact over a six-year period. This is the type of network we wish to explore in this book. As we will see as our exploration continues, much of the quantitative analysis of animal social networks is performed not on a graphical representation of interactions but on a matrix of values that conveys the same information. Both the graph and the matrix are representations of the same network.

It should not be a surprise to learn that there are many systems, in many walks of life, that can be thought of as a collection of pair-wise connections between objects. Some types of network are very familiar. Probably all of us regularly tap into a telephone network on which we may simply and quickly be connected to pretty much anywhere in the world without giving it much thought. Other technological systems such as electrical power grids (Xu et al. 2004), transport systems (Sen et al. 2003), and the World Wide Web (Tadic 2001) are all quite naturally considered as a network.

Many people have discovered that network theory may provide novel insight into the local and global properties of a system of interconnected objects that is not possible from considering either the interactions between pairs of agents in isolation or from a study of the average properties of the system as a whole. This has lead to researchers studying networks across a range of systems to gain understanding both of their structure and of some of the consequences of this structure. For example, applications of network theory to technological systems include optimizing the efficiency of telephone communication systems and analyzing the vulnerability of power grids to the loss of a power station.

Mathematicians and statistical physicists have made important contributions to the network literature, providing concrete results on the properties of certain large networks with random assignments of edges to nodes (Erds and Rnyi 1959; Bollobs 1985) and unearthing new paradigms for the characterization of the structure of complex networks and some of the processes that might occur on them (for excellent reviews of the world of networks from a physics perspective, see Albert and Barabsi 2002; Newman 2003a; Boccaletti et al. 2006).

The networks approach has also been embraced by biologists interested in unraveling the interplay between cell function and the intricate web of interactions between genes, proteins, and other molecules involved in the regulation of cell activity. They are developing a general framework in which the biological functions of a cell can be understood by examining the structure of its interacting components (Kollmann et al. 2005), enabling them to move beyond "parts lists" of a system and to understand how its components interact to produce complex patterns and behaviors (Jasny and Ray 2003). For example, networks have been used to understand how selective forces have acted on the function of metabolic pathways (Rausher, Miller, and Tiffin 1999) and how gene regulatory networks shape patterns of development (von Dassow et al. 2000; MacCarthy, Seymour, and Pomiankowski 2003). A similar approach has been applied at other levels of organization (Proulx Promislow, and Phillips 2005; May 2006). For example, biologists have investigated how cells and organs interact by studying neuronal networks (e.g., Laughlin and Sejnowski 2003), and have considered the structure and stability of ecological systems by plotting trophic interactions between species in the form of a food web (Sole and Montoya 2001; Dunne, Williams, and Martinez 2002). By comparison, relatively few biologists have built and analyzed animal social networks. We will of course be discussing their work throughout the book.

All this wealth of interest from various parties is both a good thing and a potentially bad thing for the...