Disease spread in small-size directed trade networks: the role of hierarchical categories.
Small-size, directed networks are relevant for many biological applications, from meta-populations to food webs, from transport flows to evolutionary trees, from epidemics within households to outbreaks of emerging plant pathogens (e.g. Phytophthora ramorum). However, little attention has been paid to dynamic processes in these networks. In the horticultural trade, structural change in hierarchical categories, i.e. the proportion of producers, wholesalers and retailers, can influence the likelihood that plant epidemics will take place in such systems, but it is unclear how. We model disease spread and establishment in directed networks of 100 nodes at four connectance levels in six network structures [local, small-world, random, and scale-free (SF) networks with positive, no, and negative correlation between in- and out-degree (number of incoming and outgoing links)], and study the role of hierarchical categories. For non-SF networks, the correlation coefficient between number of incoming and outgoing links is negatively correlated with the proportion of producers and retailers, and positively correlated with the proportion of wholesalers. Given the previously reported negative correlation between the in-out degree correlation coefficient and the epidemic threshold, adding producers/retailers and removing wholesalers can contribute to making epidemics more difficult in non-SF networks. For SF networks these associations are not generally present, as in these structures epidemic development is driven by the presence of hubs, rather than the features of the majority of the nodes. Synthesis and applications. Despite the importance of trade movements of plants for plant epidemics and the emergence of new plant pathogens, little is known about the current contact structure of horticultural networks within and among nations, and about how this is changing. Such information is important for risk assessment and management in plant health regulation. This study thus calls for the long-term collection of data on the number and degree distribution of plant producers, wholesalers and retailers. Our results suggest that plant disease management should focus on the middle-tier of the nursery hierarchy. This result is likely to pertain also to other biological applications of small-size directed networks.