Age-selective harvesting in a delayed predator–prey model with fear effect

In this article, we discussed the dynamic behavior of a delay-induced harvested predator–prey model with fear effects (perceived by the prey). We then considered selective harvesting terms for both species which provide some fixed elapsed time to the prey and for the predator population before they are harvested. In other words, we are limiting the harvesting of species below a certain age so that they can grow to a certain specific size or age and thus protect juvenile populations. Reproduction of the prey population can also be greatly impeded due to the influence of the fear effect. The consideration of selective harvesting together with the effect of fear on the proposed system to show stable coexistence to the oscillatory mode and vice versa via Hopf-bifurcation. For better ecological management of the community, our study reveals the fact that collection delays and intensities should be maintained. Numerical simulations were performed to validate our analytical results.

Mussel memory: bivalves learn to fear parasites

Fear plays a crucial role in predator-prey interactions and can have cascading impacts on the structure of whole ecosystems. Comparable fear effects have recently been described for hosts and their parasites but our understanding of the underlying mechanisms remains limited by the lack of empirical examples. Here, we experimentally tested if bivalves Mytilus edulis can "learn to fear" the infective transmission stages (cercariae) of the trematode Himasthla elongata and if experienced mussels change their parasite-avoidance behaviour accordingly. Our results show that previous experience with parasites, but not infection per se, lead to a reduced filtration activity in mussels in the presence of cercariae compared to parasite-naive conspecifics. This reduction in filtration activity resulted in lower infection rates in mussels. Since parasite avoidance comes at the cost of lower feeding rates, mussels likely benefit from the ability to adjust their defence behaviour when infection risks are high. Overall, these dynamic learning processes of avoidance behaviour can be expected to play a significant role in regulating the bivalves' ecosystem engineering function in coastal habitats.

Qualitative analysis of a diffusive predator–prey model with Allee and fear effects

In this study, we consider a diffusive predator–prey model with multiple Allee effects induced by fear factors. We investigate the existence, boundedness and permanence of the solution of the system. We also discuss the existence and non-existence of non-constant solutions. We derive sufficient conditions for spatially homogeneous (non-homogenous) Hopf bifurcation and steady state bifurcation. Theoretical and numerical simulations show that strong Allee effect and fear effect have great effect on the dynamics of system.

Representing Attitudes Towards Ambiguity in Hilbert Space: Foundations and Applications

We provide here a general mathematical framework to model attitudes towards ambiguity which uses the formalism of quantum theory as a “purely mathematical formalism, detached from any physical interpretation”. We show that the quantum-theoretic framework enables modelling of the Ellsberg paradox, but it also successfully applies to more concrete human decision-making tests involving financial, managerial and medical decisions. In particular, we elaborate a mathematical representation of various empirical studies which reveal that attitudes of managers towards uncertainty shift from ambiguity seeking to ambiguity aversion, and viceversa, thus exhibiting hope effects and fear effects. The present framework provides a promising direction towards the development of a unified theory of decisions in the presence of uncertainty.