To understand how an ecosystem works, ecologists observe the species living alongside one another within it. Over several years, they collect data on the presence or absence of species. How can information be extracted from these sequences of 0s and 1s, particularly to discover which species influence the survival of others through predation, parasitism, mutualism, and so on? This is a far cry from "Big Data," since obtaining such data is costly... They are scarce! The area under study must be monitored for long enough to be (reasonably) sure that each species is present or absent. The idea, then, is to help uncover interactions within a community of species by using graph theory and incorporating "expert" knowledge into a model of species dynamics.
-
Graph theory and probability -----------------------
An ecological interaction graph is a graph-theoretic modeling tool that records, for each species, all the other species whose survival that species influences, positively or negatively, from one time step to the next. Informally, the vertices of this graph represent the species, while a directed edge represents the influence of one species on another. This interaction graph can be used to model changes in the community over time. Its structure is used to construct a particular kind of Bayesian network known as a dynamic Bayesian network (see Tangente 182). This network gives the probability that each species is present at time t, given the list of species present at time t – 1. These probabilities are represented compactly by exploiting conditional independences between certain species: the presence of a species at time t is assumed to depend only on the presence, at the previous time step, of a few other species, conventionally called its parents.
The assumption that each species is influenced by only a few others greatly reduces the resources required, but learning such a model can still be difficult, particularly when little real-world data is available. If each of the n species has k parents, the number of parameters to consider is n × 2k. Unfortunately, it is inconceivable that observations could span that many years—not to mention that the maximum number of parents, k, is not known a priori.