Evolution of predator dispersal in relation to spatio-temporal prey dynamics : how not to get stuck in the wrong place!

Peer reviewedPublisher PD

Partial differential equations for self-organization in cellular and developmental biology

Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field

Evolution-based modelling of complex airport networks

Copyright @ 2011 Society for Electronics, Telecommunications, Automation, and InformaticsThis paper presents a time-series model of the United States Airport Network as a directed, weighted network, with the weight representing the total number of passengers flying from an origin to a destination airport, in a two month time period. Six independent networks are built for a given year, in order to capture the seasonal variation of passengers. To explore the evolution of the network over the past two decades, three specific years are investigated: 1990, 2000, and 2010. The results highlight the growth of the network in terms of airports and connections, and suggest a scale-free, small-world topology. In addition, the ranked passenger distribution appears to follow a logarithmic trend, implying high heterogeneity in passengers on different connections.This project was funded by te Brunel Research Support and Development Office

On the foundations of cancer modelling: selected topics, speculations, & perspectives

This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some of the novel mathematical problems in the field. This review attempts to capture, from the appropriate literature, the main issues involved in the modelling of phenomena related to cancer dynamics at all scales which characterise this highly complex system: from the molecular scale up to that of tissue. The last part of the paper discusses the challenge of developing a mathematical biological theory of tumour onset and evolution

A Computational Approach for Designing Tiger Corridors in India

Wildlife corridors are components of landscapes, which facilitate the movement of organisms and processes between intact habitat areas, and thus provide connectivity between the habitats within the landscapes. Corridors are thus regions within a given landscape that connect fragmented habitat patches within the landscape. The major concern of designing corridors as a conservation strategy is primarily to counter, and to the extent possible, mitigate the effects of habitat fragmentation and loss on the biodiversity of the landscape, as well as support continuance of land use for essential local and global economic activities in the region of reference. In this paper, we use game theory, graph theory, membership functions and chain code algorithm to model and design a set of wildlife corridors with tiger (Panthera tigris tigris) as the focal species. We identify the parameters which would affect the tiger population in a landscape complex and using the presence of these identified parameters construct a graph using the habitat patches supporting tiger presence in the landscape complex as vertices and the possible paths between them as edges. The passage of tigers through the possible paths have been modelled as an Assurance game, with tigers as an individual player. The game is played recursively as the tiger passes through each grid considered for the model. The iteration causes the tiger to choose the most suitable path signifying the emergence of adaptability. As a formal explanation of the game, we model this interaction of tiger with the parameters as deterministic finite automata, whose transition function is obtained by the game payoff.Comment: 12 pages, 5 figures, 6 tables, NGCT conference 201