SummaryNetworks are ubiquitous in natural, technological and social systems. They are of increasing relevance for improved understanding and control of infectious diseases of plants, animals and humans, given the interconnectedness of today's world. Recent modelling work on disease development in complex networks shows: the relative rapidity of pathogen spread in scale-free compared with random networks, unless there is high local clustering; the theoretical absence of an epidemic threshold in scale-free networks of infinite size, which implies that diseases with low infection rates can spread in them, but the emergence of a threshold when realistic features are added to networks (e.g. finite size, household structure or deactivation of links); and the influence on epidemic dynamics of asymmetrical interactions. Models suggest that control of pathogens spreading in scale-free networks should focus on highly connected individuals rather than on mass random immunization. A growing number of empirical applications of network theory in human medicine and animal disease ecology confirm the potential of the approach, and suggest that network thinking could also benefit plant epidemiology and forest pathology, particularly in human-modified pathosystems linked by commercial transport of plant and disease propagules. Potential consequences for the study and management of plant and tree diseases are discussed. Key words: complex networks, disease management, epiphytotics, landscape pathology, network structure, plant pathogens, small-world, spatial dispersal.
IntroductionMuch scientific work is currently focusing on the properties of networks (see Barabási & Albert, 1999;Newman, 2003; papers cited therein). From a physical point of view, networks may involve transport of energy, matter or information. From a mathematical standpoint, networks are sets of elements and of the relations between them. From both perspectives, networks are models applicable to a wide variety of natural, technological and social systems (e.g. Strogatz, 2001; Albert & Barabási, 2002; Table 1). Networks can be of interest to plant scientists when they are formed by a physical structure, when they refer to abstract relationships between connected entities (e.g. different species), and when they underline processes or flows in a structure. Network types (SF, scale-free; SW, small-world; V, various types; N, none of the previous types) are assigned on the basis of the references provided and do not rule out the possibility that other studies of networks of a similar nature may suggest a different structure. For other references the reader is referred to reviews by, for example, Albert & Barabási (2002), Dorogovtsev & Mendes (2002) andNewman (2003). Network theory (e.g. Bollobás, 1979; Chartrand, 1985; Chen, 1997) has many practical biological applications in plant sciences, for example biochemical networks (Aloy & Russell, 2004; Arita, 2005; De Silva & Stumpf, 2005; Green & Sadedin, 2005;Proulx et al ., 2005;Sweetlove & Fernie, 2005;Uhrig, 20...