How (co)evolution alters predator responses to increased mortality: extinction thresholds and hydra effects

Infection-induced increases to population size during cycles in a discrete-time epidemic model

One-dimensional discrete-time population models, such as those that involve Logistic or Ricker growth, can exhibit periodic and chaotic dynamics. Expanding the system by one dimension to incorporate epidemiological interactions causes an interesting complexity of new behaviors. Here, we examine a discrete-time two-dimensional susceptible-infectious (SI) model with Ricker growth and show that the introduction of infection can not only produce a distinctly different bifurcation structure than that of the underlying disease-free system but also lead to counter-intuitive increases in population size. We use numerical bifurcation analysis to determine the influence of infection on the location and types of bifurcations. In addition, we examine the appearance and extent of a phenomenon known as the 'hydra effect,' i.e., increases in total population size when factors, such as mortality, that act negatively on a population, are increased. Previous work, primarily focused on dynamics at fixed points, showed that the introduction of infection that reduces fecundity to the SI model can lead to a so-called 'infection-induced hydra effect.' Our work shows that even in such a simple two-dimensional SI model, the introduction of infection that alters fecundity or mortality can produce dynamics can lead to the appearance of a hydra effect, particularly when the disease-free population is at a cycle.

Change in prey genotype frequency rescues predator from extinction

Indirect evolutionary rescue (IER) is a mechanism where a non-evolving species is saved from extinction in an otherwise lethal environment by evolution in an interacting species. This process has been described in a predator-prey model, where extinction of the predator is prevented by a shift in the frequency of defended towards undefended prey when reduced predator densities lower selection for defended prey. We test here how increased mortality and the initial frequencies of the prey types affect IER. Combining the analysis of model simulations and experiments with rotifers feeding on algae we show IER in the presence of increased predator mortality. We found that IER was dependent on the ability of the prey to evolve as well as on the frequency of the defended prey. High initial frequencies of defended prey resulted in predator extinction despite the possibility for prey evolution, as the increase in undefended prey was delayed too much to allow predator rescue. This frequency dependency for IER was more pronounced for higher predator mortalities. Our findings can help informing the development of conservation and management strategies that consider evolutionary responses in communities to environmental changes.

Internal phosphorus recycling promotes rich and complex dynamics in an algae-phosphorus model: Implications for eutrophication management

Internal phosphorus recycling in lakes is an important nutrient source that promotes algal growth. Its persistence impedes the effort to improve water quality and thus poses a challenge to the management of eutrophication in lakes, especially in shallow lakes where the occurrence of internal phosphorus recycling is reportedly more common. This paper aims to provide crucial insights on the effects of internal phosphorus recycling on eutrophication dynamics for effective management of lake eutrophication. For this purpose, a mathematical model for lake eutrophication, comprising two compartments of algae and phosphorus, is first formulated for application to a eutrophic tropical lake named Tasik Harapan in Universiti Sains Malaysia. Numerical bifurcation analysis of the model is then performed to assess the combined influences of internal phosphorus recycling, algal mortality and external phosphorus loading on Tasik Harapan eutrophication dynamics. Specifically, co-dimension one bifurcation analysis of algal mortality rate is carried out by means of XPPAUT for various external phosphorus loading rates. The emergence of limit cycle for a certain range of algal mortality rate could be related to the hydra effect (i.e., algal concentration increases in response to greater algal mortality) and the paradox of enrichment (i.e., destabilization of algae in nutrient rich environment). To trace the locus of co-dimension one bifurcation, co-dimension two bifurcation analysis is performed by means of MatCont. The analysis demonstrated that the inclusion of the internal phosphorus recycling term induces rich and complex dynamics of the model. These dynamics include saddle-node bifurcation, cusp, Bogdanov-Takens bifurcation, Generalized Hopf bifurcation and limit point bifurcation of cycles. The results suggest that high internal phosphorus recycling rate promotes bistability and catastrophic shift in a shallow and tropical lake like Tasik Harapan. Hence, the key to effective management of eutrophication in shallow and tropical lakes is the control of internal phosphorus recycling.

Evolutionary rescue can prevent rate-induced tipping

The transformation of ecosystems proceeds at unprecedented rates. Recent studies suggest that high rates of environmental change can cause rate-induced tipping. In ecological models, the associated rate-induced critical transition manifests during transient dynamics in which populations drop to dangerously low densities. In this work, we study how indirect evolutionary rescue—due to the rapid evolution of a predator’s trait—can save a prey population from the rate-induced collapse. Therefore, we explicitly include the time-dependent dynamics of environmental change and evolutionary adaptation in an eco-evolutionary system. We then examine how fast the evolutionary adaptation needs to be to counteract the response to environmental degradation and express this relationship by means of a critical rate. Based on this critical rate, we conclude that indirect evolutionary rescue is more probable if the predator population possesses a high genetic variation and, simultaneously, the environmental change is slow. Hence, our results strongly emphasize that the maintenance of biodiversity requires a deceleration of the anthropogenic degradation of natural habitats.