Many new and highly variable data are currently being produced by the many participants in farmed animal productions systems. These data hold the promise of new information with potential value for animal health surveillance. The current analytical paradigm for dealing with these new data is to implement syndromic surveillance systems, which focus mainly on univariate event detection methods applied to individual time series, with the goal of identifying epidemics in the population. This approach is relatively limited in the scope and not well-suited for extracting much of the additional information that is contained within these data. These approaches have value and should not be abandoned. However, an additional, new analytical paradigm will be needed if surveillance and disease control agencies wish to extract additional information from these data. We propose a more holistic analytical approach borrowed from complex system science that considers animal disease to be a product of the complex interactions between the many individuals, organizations and other factors that are involved in, or influence food production systems. We will discuss the characteristics of farmed animal food production systems that make them complex adaptive systems and propose practical applications of methods borrowed from complex system science to help animal health surveillance practitioners extract additional information from these new data.