Complex dynamics of ecological systems
Professor Alan Hastings, University of California, Davis and Santa Fe Institute, USA
Many analyses of ecological systems are still based on the idea that natural (or managed) systems are essentially close to stable equilibria of corresponding simple ecological models. Moving away from this paradigm is key for understanding both natural and managed systems and designing management strategies. The presence of strong density dependent interactions, multiple time scales including changing environmental conditions, spatial interactions, and high dimension all contribute to making the inclusion of the potential for complex dynamics key for understanding ecological systems. Here complex dynamics includes all the dynamical features, including chaotic dynamics, complex basin boundaries, consequences of bifurcations, stochasticity, transient dynamics, as well as other aspects. Recent progress in the kinds of analyses that can be used will be reviewed. The results will be applied to various specific examples from a variety of ecological systems.
Dynamical models and comparative biology: homology and analogy of processes
Dr James DiFrisco, Centre for Logic and Philosophy of Science, Leuven, Belgium
This talk explores the role of dynamical models of developmental processes in comparative biology. Dynamical models of processes such as insect segmentation and vertebrate somitogenesis can explain how these processes might plausibly work, or how they actually work, depending on their level of mechanistic detail. As a consequence, these models can inform phylogenetic hypotheses about homology, parallelism, and convergence by determining the probabilities of transformation between character states. An interesting question concerns how dynamical processes themselves should be described and classified in order to function this way. Should they be classified (1) independently of phylogenetic considerations eg, in terms of ahistorical properties such as phase portrait geometries or, (2) in terms of phylogeny? The first option may be useful at certain stages of research, especially when combined with mechanistic research approaches. But ignoring phylogeny threatens to resurrect some of the classic problems with the pre-Darwinian programs of “rational taxonomy” or “idealistic morphology.” Pursuing the second option gives occasion to re-examine the unresolved conceptual issue of “process homology” from the point of view of dynamical modeling, and to assess its relation to the classical criteria of homology, such as topology, complexity, and congruence. The central question concerns how to productively combine formal and historical approaches to understanding developmental processes.
Dynamical process in biology: on the role of mathematical modelling
Professor Nick Monk, University of Sheffield, UK
Biology is fundamentally dynamic, and mathematical modelling plays an increasingly prominent role in understanding dynamical behaviours of living systems. What does a mathematical representation bring to the study of such systems? A quantitative description can enhance the clarity of assumptions made about the constitution of the system, and open up possibilities for more precise prediction. However, can the use of mathematical models do more than this? In addition to providing a precise deductive framework, mathematics also provides a language for abstract reasoning, with logical structures that do not necessarily correspond in any simple way to the physical elements of a system. Given the complexity of biological phenomena, tracing the route from system composition to system behaviour is challenging: the language of dynamical models provides a natural framework for exploring this dynamic process.
Dissecting transcriptional dynamics in development one burst at a time
Dr Hernan Garcia, UC Berkeley, USA
Over the last few decades in vitro and in situ approaches have revealed the identity of the molecular players driving transcription in eukaryotes. Yet, these studies are virtually silent on the precise timing of the recruitment of each of these players to the promoter, and on how this recruitment determines output transcriptional dynamics in vivo. Here, we present a new method for simultaneously measuring local input transcription factor concentration at target loci and the resulting output transcriptional activity of these loci in single living cells. Specifically, we study how the Dorsal activator, a key transcription factor in the development of the fruit fly Drosophila melanogaster, is recruited to the promoter of its target gene snail in order to drive transcriptional bursting. We found that transient surges in Dorsal concentration coincide with, but do not precede, the onset of transcriptional bursts. Interestingly, these surges are not maintained throughout the duration of the bursts and subside before the promoter transitioned back into a transcriptionally inactive state. Instead, we discovered that the amplitude of the transient Dorsal concentration surges at the start of transcriptional burst, and not surge duration, dictates transcriptional burst duration. We speculate that Dorsal delivers a “package” of downstream players to the promoter (eg, a cluster of RNA polymerase molecules) that sustains the transcriptional burst until this package is exhausted. Thus, our tool sets the stage for uncovering the precise timing and ordering of the diverse molecular players that drive the transcriptional process.