Ecological networks describe the interactions between different species, informing us how they rely on one another for food, pollination, and survival. If a species in an ecosystem is under threat of extinction, it can affect other species in the system and possibly result in their secondary extinction as well.

Understanding how (primary) extinctions cause secondary extinctions on ecological networks has been considered previously using computational methods. However, these methods do not provide an explanation for the properties that make ecological networks robust, and they can be computationally expensive.

We develop a new analytic model for predicting secondary extinctions that requires no stochastic simulation. Our model can predict secondary extinctions when primary extinctions occur at random or due to some targeting based on the number of links per species or risk of extinction, and can be applied to an ecological network of any number of layers.

Using our model, we consider how false negatives and positives in network data affect predictions for network robustness. We have also extended the model to predict scenarios in which secondary extinctions occur once species lose a certain percentage of interaction strength, and to model the loss of interactions as opposed to just species extinction.

From our model, it is possible to derive new analytic results such as how ecological networks are most robust when secondary species are of equal degree. Additionally, we show that both specialization and generalization in the distribution of interaction strength can be advantageous for network robustness, depending upon the extinction scenario being considered.

C. Jones, D. Zurell, K. Wiesner, Novel analytic methods for predicting extinctions in ecological networks, Ecological Monographs 94(2) (2024) e1601.