We model the population dynamics of two host species attacked by a common parasitoid using a discrete-time formalism that captures their population densities from year to year. It is well known starting from the seminal work of Nicholson and Bailey that a constant parasitoid attack rate leads to an unstable host-parasitoid interaction. However, a Type III functional response, where the parasitoid attack rate accelerates with increasing host density stabilizes the population dynamics. We first consider a scenario where both host species are attacked by a parasitoid with the same Type III functional response. Our results show that sufficient fast acceleration of the parasitoid attack rate stabilizes the population dynamics of all three species. For two symmetric host species, the extent of acceleration needed to stabilize the three-species equilibrium is exactly the same as that needed for a single host-parasitoid interaction. However, asymmetry can lead to scenarios where the removal of a host species from a stable interaction destabilizes the interaction between the remaining host species and the parasitoid. Next, we consider a situation where one of the host species is attacked at a constant rate (i.e., Type I functional response), and the other species is attacked via a Type III functional response. We identify parameter regimes where a Type III functional response to just one of the host species stabilizes the three species interaction. In summary, our results show that a generalist parasitoid with a Type III functional response to one or many host species can play a key role in stabilizing population dynamics of host-parasitoid communities in apparent competition.

A major open question in microbial community ecology is whether we can predict how the components of a diet collectively determine the taxonomic composition of microbial communities. Motivated by this challenge, we investigate whether communities assembled in pairs of nutrients can be predicted from those assembled in every single nutrient alone. We find that although the null, naturally additive model generally predicts well the family-level community composition, there exist systematic deviations from the additive predictions that reflect generic patterns of nutrient dominance at the family level. Pairs of more-similar nutrients (e.g. two sugars) are on average more additive than pairs of more dissimilar nutrients (one sugar-one organic acid). Furthermore, sugar-acid communities are generally more similar to the sugar than the acid community, which may be explained by family-level asymmetries in nutrient benefits. Overall, our results suggest that regularities in how nutrients interact may help predict community responses to dietary changes.

Plant-animal mutualistic networks sustain terrestrial biodiversity and human food security. Global environmental changes threaten these networks, underscoring the urgency for developing a predictive theory on how networks respond to perturbations. Here, I synthesise theoretical advances towards predicting network structure, dynamics, interaction strengths and responses to perturbations. I find that mathematical models incorporating biological mechanisms of mutualistic interactions provide better predictions of network dynamics. Those mechanisms include trait matching, adaptive foraging, and the dynamic consumption and production of both resources and services provided by mutualisms. Models incorporating species traits better predict the potential structure of networks (fundamental niche), while theory based on the dynamics of species abundances, rewards, foraging preferences and reproductive services can predict the extremely dynamic realised structures of networks, and may successfully predict network responses to perturbations. From a theoretician\'s standpoint, model development must more realistically represent empirical data on interaction strengths, population dynamics and how these vary with perturbations from global change. From an empiricist\'s standpoint, theory needs to make specific predictions that can be tested by observation or experiments. Developing models using short-term empirical data allows models to make longer term predictions of community dynamics. As more longer term data become available, rigorous tests of model predictions will improve.