Making sense of transient dynamics: Ecological systems can switch between alternative dynamic states. For example, the species composition of the community can change or nutrient dynamics can shift, even if there is little or no change in underlying environmental conditions. Such switches can be abrupt or more gradual, and a growing number of studies examine the transient dynamics between one state and another—particularly in the context of anthropogenic global change. Hastings et al. review current knowledge of transient dynamics, showing that hitherto idiosyncratic and individual patterns can be classified into a coherent framework, with important general lessons and directions for future study. Science , this issue p. eaat6412

There is a growing recognition that ecological systems can spend extended periods of time far away from an asymptotic state, and that ecological understanding will therefore require a deeper appreciation for how long ecological transients arise. Recent work has defined classes of deterministic mechanisms that can lead to long transients. Given the ubiquity of stochasticity in ecological systems, a similar systematic treatment of transients that includes the influence of stochasticity is important. Stochasticity can of course promote the appearance of transient dynamics by preventing systems from settling permanently near their asymptotic state, but stochasticity also interacts with deterministic features to create qualitatively new dynamics. As such, stochasticity may shorten, extend or fundamentally change a system’s transient dynamics. Here, we describe a general framework that is developing for understanding the range of possible outcomes when random processes impact the dynamics of ecological systems over realistic time scales. We emphasize that we can understand the ways in which stochasticity can either extend or reduce the lifetime of transients by studying the interactions between the stochastic and deterministic processes present, and we summarize both the current state of knowledge and avenues for future advances.

The use of predator–prey models in theoretical ecology has a long history, and the model equations have largely evolved since the original Lotka–Volterra system towards more realistic descriptions of the processes of predation, reproduction and mortality. One important aspect is the recognition of the fact that the growth of a population can be subject to an Allee effect, where the per capita growth rate increases with the population density. Including an Allee effect has been shown to fundamentally change predator–prey dynamics and strongly impact species persistence, but previous studies mostly focused on scenarios of an Allee effect in the prey population. Here we explore a predator–prey model with an ecologically important case of the Allee effect in the predator population where it occurs in the numerical response of predator without affecting its functional response. Biologically, this can result from various scenarios such as a lack of mating partners, sperm limitation and cooperative breeding mechanisms, among others. Unlike previous studies, we consider here a generic mathematical formulation of the Allee effect without specifying a concrete parameterisation of the functional form, and analyse the possible local bifurcations in the system. Further, we explore the global bifurcation structure of the model and its possible dynamical regimes for three different concrete parameterisations of the Allee effect. The model possesses a complex bifurcation structure: there can be multiple coexistence states including two stable limit cycles. Inclusion of the Allee effect in the predator generally has a destabilising effect on the coexistence equilibrium. We also show that regardless of the parametrisation of the Allee effect, enrichment of the environment will eventually result in extinction of the predator population.

It is well recognized that models in the life sciences can be sensitive to small variations in their model functions, a phenomenon known as ‘structural sensitivity’. Conventionally, modellers test for sensitivity by varying parameters for a specific formulation of the model functions, but models can show structural sensitivity to the choice of functional representations used: a particularly concerning problem when system processes are too complex, or insufficiently understood, to theoretically justify specific parameterizations. Here we propose a rigorous test for the detection of structural sensitivity in a system with respect to the local stability of equilibria, the main idea being to project infinite dimensional function space onto a finite dimensional space by considering the local properties of the model functions. As an illustrative example, we use our test to demonstrate structural sensitivity in the seminal Rosenzweig–MacArthur predator–prey model, and show that the conventional parameter-based approach can fail to do so. We also consider some implications that structural sensitivity has for ecological modelling: we argue that when the model exhibits structural sensitivity but experimental results remain consistent it may indicate that there is a problem with the model construction, and that in some cases trying to find an ‘optimal’ parameterization of a model function may simply be impossible when the model exhibits structural sensitivity. Finally, we suggest that the phenomenon of structural sensitivity in biological models may help explain the irregular oscillations often observed in real ecosystems.

Understanding of complex trophic interactions in ecosystems requires correct descriptions of the rate at which predators consume a variety of different prey species. Field and laboratory data on multispecies communities are rarely sufficient and usually cannot provide an unambiguous test for the theory. As a result, the conventional way of constructing a multi-prey functional response is speculative, and often based on assumptions that are difficult to verify. Predator responses allowing for prey selectivity and active switching are thought to be more biologically relevant compared to the standard proportion-based consumption. However, here we argue that the functional responses with switching may not be applicable to communities with a broad spectrum of resource types. We formulate a set of general rules that a biologically sound parameterization of a predator functional response should satisfy, and show that all existing formulations for the multispecies response with prey selectivity and switching fail to do so. Finally, we propose a universal framework for parameterization of a multi-prey functional response by combining patterns of food selectivity and proportion-based feeding.

Self-regulation of population dynamics in nutrient-rich (eutrophic) ecosystems has been a fascinating topic for decades in ecological literature. Simple theoretical models predict population oscillations of large amplitudes in such systems, those predictions often being at odds with reality. Plankton communities possess a particular combination of two important properties, making them unique among ecosystems with eutrophication. These are: (i) the existence of a pronounced spatial gradient of the prey growth rate (through light attenuation with depth) and (ii) the presence of fast-moving predator (zooplankton) capable of quick adjustment of grazing load in vertical direction throughout the whole habitat. Surprisingly, the interplay of those factors is rarely taken into account while analysing stability of nutrient-rich plankton communities. In this paper, we construct generic plankton models (based on integro-differential equations) incorporating the light attenuation in the water column as well as food-searching behaviour of zooplankton. We found that the interplay between the two factors would stabilize a system at low species densities even for an ‘unlimited’ nutrient stock (infinite system's carrying capacity). Different possible scenarios of stabilization have been found. Since both the vertical gradient of light and the active food search by zooplankton in the column are common characteristics of real plankton communities, we suggest that the obtained mechanism of self-regulation is rather generic in nature. We argue that taking into account this mechanism would be important for understanding the dynamics of nutrient-rich low-chlorophyll ocean systems as well as major causes of non-seasonal plankton blooms.