Generating functionals and Gaussian approximations for interruptible delay reactions

We develop a generating functional description of the dynamics of non-Markovian individual-based systems, in which delay reactions can be terminated before completion. This generalises previous work in which a path-integral approach was applied to dynamics in which delay reactions complete with certainty. We construct a more widely applicable theory, and from it we derive Gaussian approximations of the dynamics, valid in the limit of large, but finite population sizes. As an application of our theory we study predator-prey models with delay dynamics due to gestation or lag periods to reach the reproductive age. In particular we focus on the effects of delay on noise-induced cycles.Comment: 18 pages, 4 figure

Eco-evolutionary dynamics. Experiments in a model system

Understanding the consequences of environmental change on both long- and short-term ecological and evolutionary dynamics is a basic pre-requisite for any effective conservation or management programme but inherently problematic because of the complex interplay between ecological and evolutionary processes. Components of such complexity have been described in isolation or within conceptual models on numerous occasions. What remains lacking are studies that characterise effectively the coupled ecological and evolutionary dynamics, to demonstrate feedback mechanisms that influence both phenotypic change, and its effects on population demography, in organisms with complex life histories. We present a systems-based approach that brings together multiple effects that 'shape' an organism's life history (e.g. direct and delayed life-history consequences of environmental variation) and the resulting eco-evolutionary population dynamics. Using soil mites in microcosms, we characterise ecological, phenotypic and evolutionary dynamics in replicated populations in response to experimental manipulations of environment (e.g. the competitive environment, female age, male quality). Our results demonstrate that population dynamics are complex and are affected by both plastic and evolved responses to past and present environments, and that the emergent population dynamic itself shaped the landscape for natural selection to act on in subsequent generations. Evolutionary and ecological effects on dynamics can therefore be almost impossible to partition, which needs to be considered and appreciated in research, management and conservation. © 2014 Elsevier Ltd

When less is more: positive population-level effects of mortality

Experimental and theoretical studies show that mortality imposed on a population can counter-intuitively increase the density of a specific life-history stage or total population density. Understanding positive population-level effects of mortality is advancing, illuminating implications for population, community, and applied ecology. Reconciling theory and data, we found that the mathematical models used to study mortality effects vary in the effects predicted and mechanisms proposed. Experiments predominantly demonstrate stage-specific density increases in response to mortality. We argue that the empirical evidence supports theory based on stage-structured population models but not on unstructured models. We conclude that stage-specific positive mortality effects are likely to be common in nature and that accounting for within-population individual variation is essential for developing ecological theory

Chaotic dynamics in a simple predator-prey model with discrete delay

A discrete delay is included to model the time between the capture of the prey and its conversion to viable biomass in the simplest classical Gause type predator-prey model that has equilibrium dynamics without delay. As the delay increases from zero, the coexistence equilibrium undergoes a supercritical Hopf bifurcation, two saddle-node bifurcations of limit cycles, and a cascade of period doublings, eventu1ally leading to chaos. The resulting periodic orbits and the strange attractor resemble their counterparts for the Mackey-Glass equation. Due to the global stability of the system without delay, these complicated dynamics can be solely attributed to the introduction of the delay. Since many models include predator-prey like interactions as submodels, this study emphasizes the importance of understanding the implications of overlooking delay in such models on the reliability of the model-based predictions, especially since the temperature is known to have an effect on the length of certain delays.Comment: This paper has 28 pages, 12 figures and has been accepted to DCDS-B. Please cite the journal version once it is published in DCDS-B. Appreciate tha

Predator-prey dynamics pertaining to structuralizing predator species into three stages coupled with maturation delay owing to juvenile hunting

The predator-prey dynamic appertaining to two species is explored, wherein the predator species is structured into different stages. As evidenced from natural documentation, the immature predators possess the potential to predate albeit not as competently as the adults. Nevertheless, this potentiality is not acquired immediately after their incipience of life, hence, the immature stage is branched off into the infant stage, the stage with extensive reliance on the adults, and the juvenile stage, the stage with the potential to predate but not to procreate. In this paper, this inaugural concept is coupled with injuries in the juvenile stage as the repercussion of their incompetency in predating, thereby ensuing a delay in their maturation. With the incentive to investigate the ascendancy of these refinements over the whole system, stability analyses along with various bifurcation analyses around the equilibrium points of the system are corroborated. In addition to Hopf, transcritical, and saddle node bifurcations, the existence of Bogdanov-Takens point, cusp point, Bautin bifurcation point, bloom phenomenon, twice occurring Hopf bifurcation, and bi-stability phenomenon make the paper appreciably more rich and efficacious

The effects of predator presence on insect behavior: consequences for individual fitness, population growth and pest suppression in agroecosystems

Organisms respond to the presence of foraging predators with a variety of antipredator strategies including escape responses, microhabitat shifts, and the restriction of conspicuous activities such as movement, foraging, and reproduction. Although these effects have been well-documented in aquatic systems, relatively little information is available about their impacts in terrestrial systems. In addition, because conceptual models of predator-prey interactions form the basis of our understanding of pest suppression in agroecosystems, information regarding the impact of predator presence on economically important pest insects may help us to better understand the qualities embodied by successful biological control agents. In this two-part study, I examined the impacts of predator presence on the feeding activity of insects in garden test systems. In the first part, a series of experiments paired pest insects with single, spider species to measure the relative contributions of direct mortality and predator-induced reductions of feeding activity to reductions in crop damage. Direct mortality accounted for approximately 15% of the observed reduction in crop damage while predator-presence effects accounted for an additional 10-40% depending on the system. In the second part of this study, I present a detailed examination of a single system in which predator-presence effects proved to be important. An individual-based computer simulation of the fifth larval instar of the small, white cabbage butterfly, Pieris rapae L. was developed in conjunction with Dr. Gary Huxel of the University of California at Davis. This simulation incorporated experimentally-derived estimates of feeding activity and growth under predation pressure. The simulation was nm at three different predator densities to evaluate the impact of predator-presence effects on population growth. At high densities, predators significantly lengthen the maturation time for fifth-instar P. rapae larvae resulting in probable losses of fitness and slowed population growth. These effects are discussed within the context of their ecological and evolutionary significance, as well as their implications for the biological control of insect pests in agroecosystems