## Introduction

Network analysis is of current and growing importance in diverse fields including ecology and evolutionary biology. Many biological systems consist of interconnected units and can be usefully modelled as networks, which are mathematical constructs describing a set of edges between vertices (Albert & Barabasi 2002; Proulx, Promislow & Phillips 2005; Diestel 2010; Newman 2010). The identity of each varies with the system and question of interest – for example, vertices can be genes, proteins, neurons, individual organisms, species, geographic regions, etc. and edges can represent regulatory interactions, binding affinities, synapses, social associations, predation, gene flow and so on (Dunne, Williams & Martinez 2002; Proulx, Promislow & Phillips 2005; May 2006; Bascompte & Jordano 2007; Wey *et al.* 2008; Sih, Hanser & Mchugh 2009; Bascompte 2010). Network *topology* refers to the structure of edges and vertices and can be quantified with a range of statistics about the pattern of connections among vertices. Processes of *flow* can occur on these edges, representing transfers of resources, disease, information, etc. Network theory provides a basis for analysing outcomes that depend on network topology or flow and is thus a powerful framework for testing hypotheses about biological interactions by measuring and comparing network variation.

Questions of network dynamics are of key interest for many ecological and evolutionary systems, for example, how and why the topology of the network changes over time, how these changes affect the flow of resources (or disease) through the network, and the nature and importance of feedbacks between flow processes and topological change. However, network dynamics can be quantitatively challenging and difficult to address and are largely unaccounted for in most extant network analyses (James, Croft & Krause 2009; Sih, Hanser & Mchugh 2009; Bascompte 2010).

In the current standard framework, networks are usually taken as representations of a system aggregated over a certain limited time interval. It is difficult to ask questions about how and why a system changes over time using this static abstraction, which is based on several critical assumptions. Specifically, this approach assumes that the network’s topology is fixed; processes of flow are at a dynamic steady state; edges represent persistent interactions; interactions are sufficiently stable to address the question of interest; and there is sufficient sampling so that the structure of the network is accurately and completely known. Together, these assumptions imply that the chosen representation of interactions is sufficient to evaluate equilibrium situations, but breaking them, which occurs in many real networks, can lead to a range of serious inferential problems (Box 1). Many networks involve dynamics but have so far been analysed using methods more appropriate for static systems. Thus, while these assumptions permit some simple and fast analyses, an explicitly dynamic approach can be more useful.

Here, we review current approaches that address the need for incorporating temporal dynamics into network analysis of observational data in ecology and evolutionary biology. Our goal is to introduce ecologists and evolutionary biologists interested in network dynamics but that may currently be unfamiliar with the concepts and techniques already available. We survey basic concepts that are important in dynamic network analysis as well as recent advances in a range of disciplines and their applications in ecology and evolutionary biology. Furthermore, we discuss considerations in determining the appropriate network representations for the dynamics of interest and highlight important ecological and evolutionary questions that can be understood as network dynamics questions at different time-scales. These concepts are brought together via the *time-ordered* network framework, which unifies dynamics at multiple time-scales, resolves common inferential problems and enables many new types of analyses. We provide a guide to time-ordered network analysis that includes computational resources, work through an example application and identify research areas where this framework may be valuable.