Three-dimensional random walk models of individual animal movement and their application to trap counts modelling.

BACKGROUND: Random walks (RWs) have proved to be a powerful modelling tool in ecology, particularly in the study of animal movement. An application of RW concerns trapping which is the predominant sampling method to date in insect ecology and agricultural pest management. A lot of research effort has been directed towards modelling ground-dwelling insects by simulating their movement in 2D, and computing pitfall trap counts, but comparatively very little for flying insects with 3D elevated traps. METHODS: We introduce the mathematics behind 3D RWs and present key metrics such as the mean squared displacement (MSD) and path sinuosity, which are already well known in 2D. We develop the mathematical theory behind the 3D correlated random walk (CRW) which involves short-term directional persistence and the 3D Biased random walk (BRW) which introduces a long-term directional bias in the movement so that there is an overall preferred movement direction. In this study, we focus on the geometrical aspects of the 3D trap and thus consider three types of shape; a spheroidal trap, a cylindrical trap and a rectangular cuboidal trap. By simulating movement in 3D space, we investigated the effect of 3D trap shapes and sizes and of movement diffusion on trapping efficiency. RESULTS: We found that there is a non-linear dependence of trap counts on the trap surface area or volume, but the effect of volume appeared to be a simple consequence of changes in area. Nevertheless, there is a slight but clear hierarchy of trap shapes in terms of capture efficiency, with the spheroidal trap retaining more counts than a cylinder, followed by the cuboidal type for a given area. We also showed that there is no effect of short-term persistence when diffusion is kept constant, but trap counts significantly decrease with increasing diffusion. CONCLUSION: Our results provide a better understanding of the interplay between the movement pattern, trap geometry and impacts on trapping efficiency, which leads to improved trap count interpretations, and more broadly, has implications for spatial ecology and population dynamics.

Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect.

Traditionally, mathematical modeling in population ecology is mainly focused on asymptotic behavior of the model, i.e. as given by the system attractors. Recently, however, transient regimes and especially long-term transients have been recognized as playing a crucial role in the dynamics of ecosystems. In particular, long-term transients are a potential explanation of ecological regime shifts, when an apparently healthy population suddenly collapses and goes extinct. In this paper, we show that the interplay between delay in maturation and a strong Allee effect can result in long-term transients in a single species system. We first derive a simple 'conceptual' model of the population dynamics that incorporates both a strong Allee effect and maturation delay. Unlike much of the previous work, our approach is not empirical since our model is derived from basic principles. We show that the model exhibits a high complexity in its asymptotic dynamics including multi-periodic and chaotic attractors. We then show the existence of long-term transient dynamics in the system, when the population size oscillates for a long time between locally stable stationary states before it eventually settles either at the persistence equilibrium or goes extinct. The parametric space of the model is found to have a complex structure with the basins of attraction corresponding to the persistence and extinction states being of a complicated shape. This impedes the prediction of the eventual fate of the population, as a small variation in the maturation delay or the initial population size can either bring the population to extinction or ensure its persistence.

[When will the new tuberculosis vaccine appear?].

The problem of tuberculosis prophylaxis remains actual for many countries of the world including Russia. The search of candidates for substitution of the only authorized BCG vaccine has been ongoing for some time, because it does not prevent reactivation of the causative agent in the latent stage and causes generalized BCG-infection in individuals with pronounced immune deficiency. In October 2013 in Lille at the European Congress "World Vaccine 2013" results of multi-year projects and trials of around 40 novel tuberculosis vaccine candidates were presented. The article contains a critical analysis of the materials presented at the congress. 12 vaccines have been developed or are being developed for priming. Among those a live VPM 1002 vaccine based on a genetically modified BCG Mycobacterium bovis (HLY+rBCG) strain and an attenuated vaccine based on Mycobacterium tuberculosis (att. MTB-MTBVAC) have passed phase II clinical trials. 17 candidates are being examined as booster vaccines, among those 6 vaccines have passed phase II clinical trials, and are presented by both modified M. bovis strains and partial proteins of M. tuberculosis. Characteristics of the 3 most perspective vaccines have been presented at the congress: VPM 1002, H &H56 and MVA85A. VPM 1002 is the vaccine closest to introduction. This is a live recombinant anti-tuberculosis vaccine based on the BCG strain, its DNA had genes partially deleted, that code synthesis of listeriolysin. The trials have shown that protective effectiveness of the vaccine is significantly higher than the parent BCG due to better induction of CD4+ and CD8+ cells, as well as IFN-γ, IL-18, 12 and other cytokines responsible for cell immunity function against M. tuberculosis.

Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics.

The dynamics of a simple prey-predator system is described by a system of two reaction- diffusion equations with biologically reasonable non-linearities (logistic growth of the prey, Holling type II functional response of the predator). We show that, when the local kinetics of the system is oscillatory, for a wide class of initial conditions the evolution of the system leads to the formation of a non-stationary irregular pattern corresponding to spatio-temporal chaos. The chaotic pattern first appears inside a sub-domain of the system. This sub-domain then steadily grows with time and, finally, the chaotic pattern invades the whole space, displacing the regular pattern.

Biological factors underlying regularity and chaos in aquatic ecosystems: simple models of complex dynamics.

This work is focused on the processes underlying the dynamics of spatially inhomogeneous plankton communities. We demonstrate that reaction-diffusion mathematical models are an appropriate tool for searching and understanding basic mechanisms of complex spatio-temporal plankton dynamics and fractal properties ofplanktivorous fish school walks

Chaos and regular dynamics in model multi-habitat plankton-fish communities.

This work is focused on the role of diffusive interaction between separate habitats in a patchy environment in plankton pattern formation. We demonstrate that conceptual reaction-diffusion mathematical models constitute an appropriate tool for searching and understanding basic mechanisms of plankton pattern formation and complex spatio-temporal plankton dynamics