Selected topics on reaction-diffusion-advection models from spatial ecology

We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction-diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially heterogeneous environments. Topics include Lokta-Volterra competition models, river models, evolution of biased movement, phytoplankton growth, and spatial spread of epidemic disease. Open problems and conjectures are presented

General relationships between consumer dispersal, resource dispersal and metacommunity diversity

One of the central questions of metacommunity theory is how dispersal of organisms affects species diversity. Here we show that the diversity-dispersal relationship should not be studied in isolation of other abiotic and biotic flows in the metacommunity. We study a mechanistic metacommunity model in which consumer species compete for an abiotic or biotic resource. We consider both consumer species specialized to a habitat patch, and generalist species capable of using the resource throughout the metacommunity. We present analytical results for different limiting values of consumer dispersal and resource dispersal, and complement these results with simulations for intermediate dispersal values. Our analysis reveals generic patterns for the combined effects of consumer and resource dispersal on the metacommunity diversity of consumer species, and shows that hump-shaped relationships between local diversity and dispersal are not universal. Diversity-dispersal relationships can also be monotonically increasing or multimodal. Our work is a new step towards a general theory of metacommunity diversity integrating dispersal at multiple trophic levels.Comment: Main text: 15 pages, 4 figures. Supplement: 25 pages, 12 figure

Population growth and persistence in a heterogeneous environment: the role of diffusion and advection

The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional reaction-diffusion-advection equations, for the growth of a population on a heterogeneous habitat. Considering a number of models of increasing complexity we investigate the often contrary roles of advection and diffusion for the persistence of the population. When it is possible we demonstrate basic mathematical techniques and give the critical conditions providing the survival of a population, in simple systems and in more complex resource-consumer models which describe the dynamics of phytoplankton in a water column.Comment: Introductory review of simple conceptual models. 45 pages, 15 figures v2: minor change

Mathematical Modelling of Mosquito Dispersal in a Heterogeneous Environment.

Mosquito dispersal is a key behavioural factor that affects the persistence and resurgence of several vector-borne diseases. Spatial heterogeneity of mosquito resources, such as hosts and breeding sites, affects mosquito dispersal behaviour and consequently affects mosquito population structures, human exposure to vectors, and the ability to control disease transmission. In this paper, we develop and simulate a discrete-space continuous-time mathematical model to investigate the impact of dispersal and heterogeneous distribution of resources on the distribution and dynamics of mosquito populations. We build an ordinary differential equation model of the mosquito life cycle and replicate it across a hexagonal grid (multi-patch system) that represents two-dimensional space. We use the model to estimate mosquito dispersal distances and to evaluate the effect of spatial repellents as a vector control strategy. We find evidence of association between heterogeneity, dispersal, spatial distribution of resources, and mosquito population dynamics. Random distribution of repellents reduces the distance moved by mosquitoes, offering a promising strategy for disease control

Trivial movements and redistribution of polyphagous insect herbivores in heterogeneous vegetation

The aim of this thesis was to study the interplay between movement patterns of polyphagous insect herbivores and vegetation heterogeneity within agricultural fields. I examined if and how 1) host plant species, 2) host plant quality, 3) vegetation architecture, and 4) trap crop physical design influence movement patterns of individuals and spatial distribution of populations. Foragers may aggregate in profitable areas by tactic movement, or by area-restricted search, i.e. by moving randomly but slowing down movement and increasing rate of turning after encountering a profitable patch. Movement patterns of polyphagous herbivores have a high potential for influencing their distribution among hosts differing in quality. However, information on the role random vs. non-random components in their movement behavior is scarce. The results of this thesis show that both host plant species and within species differences in host plant quality affect movement behavior of a polyphagous herbivore, the European tarnished plant bug nymphs. The host plant induced movement patterns also explained the distribution of nymphs in heterogeneous vegetation. Because redistribution was very fast, it appears that no tactic behavior is needed for the nymphs to locate preferred hosts in heterogeneous vegetation composed of small patches. Instead the nymphs may successfully locate superior hosts merely by random movement coupled with sensitivity to local host quality. The physical structure of environment influences redistribution of populations at several spatial scales. At small scale the architecture of vegetation may influence redistribution of insects that move on the plant surface. At large scale e.g. trap crop physical design may affect redistribution of pests. In this thesis I derive a model for predicting the impact of vegetation architecture on the rate of displacement by insects moving on the plant surface. I also present and explore models of the interplay between pest movement and trap crop physical design. The trap crop models suggest that considerable reduction in pest density may be achieved using small trap crop cover with trap crops that the pest distinctly prefers over the crop. It supports also the idea that trap crop placement may have a dramatic impact on the efficiency of the trap crops