Adaptation is not required to explain the long-term response of axons to molecular gradients

It has been suggested that growth cones navigating through the developing nervous system might display adaptation, so that their response to gradient signals is conserved over wide variations in ligand concentration. Recently however, a new chemotaxis assay that allows the effect of gradient parameters on axonal trajectories to be finely varied has revealed a decline in gradient sensitivity on either side of an optimal concentration. We show that this behavior can be quantitatively reproduced with a computational model of axonal chemotaxis that does not employ explicit adaptation. Two crucial components of this model required to reproduce the observed sensitivity are spatial and temporal averaging. These can be interpreted as corresponding, respectively, to the spatial spread of signaling effects downstream from receptor binding, and to the finite time over which these signaling effects decay. For spatial averaging, the model predicts that an effective range of roughly one-third of the extent of the growth cone is optimal for detecting small gradient signals. For temporal decay, a timescale of about 3 minutes is required for the model to reproduce the experimentally observed sensitivity.

Control of structured populations by harvest

It has long been recognized that demographic structure within a population can significantly affect the likely outcomes of harvest. Many studies have focussed on equilibrium dynamics and maximization of the value of the harvest taken. However, in some cases the management objective is to maintain the population at a abundance that is significantly below the carrying capacity. Achieving such an objective by harvest can be complicated by the presence of significant structure (age or stage) in the target population. in such cases, optimal harvest strategies must account for differences among age- or stage-classes of individuals in their relative contribution to the demography of the population. In addition, structured populations are also characterized by transient non-linear dynamics following perturbation, such that even under an equilibrium harvest, the population may exhibit significant momentum, increasing or decreasing before cessation of growth. Using simple linear time-invariant models, we show that if harvest levels are set dynamically (e.g., annually) then transient effects can be as or more important than equilibrium outcomes. We show that appropriate harvest rates can be complicated by uncertainty about the demographic structure of the population, or limited control over the structure of the harvest taken. (c) 2006 Elsevier B.V. All rights reserved.

Ecological-economic modeling for biodiversity management: Potential, pitfalls, and prospects

Ecologists and economists both use models to help develop strategies for biodiversity management. The practical use of disciplinary models, however, can be limited because ecological models tend not to address the socioeconomic dimension of biodiversity management, whereas economic models tend to neglect the ecological dimension. Given these shortcomings of disciplinary models, there is a necessity to combine ecological and economic knowledge into ecological-economic models. It is insufficient if scientists work separately in their own disciplines and combine their knowledge only when it comes to formulating management recommendations. Such an approach does not capture feedback loops between the ecological and the socioeconomic systems. Furthermore, each discipline poses the management problem in its own way and comes up with its own most appropriate solution. These disciplinary solutions, however are likely to be so different that a combined solution considering aspects of both disciplines cannot be found. Preconditions for a successful model-based integration of ecology and economics include (1) an in-depth knowledge of the two disciplines, (2) the adequate identification and framing of the problem to be investigated, and (3) a common understanding between economists and ecologists of modeling and scale. To further advance ecological-economic modeling the development of common benchmarks, quality controls, and refereeing standards for ecological-economic models is desirable.

Network topology and the evolution of dynamics in an artificial genetic regulatory network model created by whole genome duplication and divergence

Topological measures of large-scale complex networks are applied to a specific artificial regulatory network model created through a whole genome duplication and divergence mechanism. This class of networks share topological features with natural transcriptional regulatory networks. Specifically, these networks display scale-free and small-world topology and possess subgraph distributions similar to those of natural networks. Thus, the topologies inherent in natural networks may be in part due to their method of creation rather than being exclusively shaped by subsequent evolution under selection. The evolvability of the dynamics of these networks is also examined by evolving networks in simulation to obtain three simple types of output dynamics. The networks obtained from this process show a wide variety of topologies and numbers of genes indicating that it is relatively easy to evolve these classes of dynamics in this model. (c) 2006 Elsevier Ireland Ltd. All rights reserved.

Oscillatory regulation of hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Regional climate change and harmful algal blooms in the northeast Atlantic

We investigated long-term spatial variability in a number of Harmful Algal Blooms (HABs) in the northeast Atlantic and North Sea using data from the Continuous Plankton Recorder. Over the last four decades. some dinoflagellate taxa showed pronounced variation in the south and east of the North Sea, with the most significant increases being restricted to the adjacent waters off Norway. There was also a general decrease along the eastern coast of the United Kingdom. The most prominent feature in the interannual bloom frequencies over the last four decades was the anomalously high values recorded in the late 1980s in the northern and central North Sea areas. The only mesoscale area in the northeast Atlantic to show a significant increase in bloom formation over the last decade was the Norwegian coastal region. The changing spatial patterns of HAB taxa and the frequency of bloom formation are discussed in relation to regional climate change, in particular, changes in temperature, salinity, and the North Atlantic Oscillation (NAO). Areas highly vulnerable to the effects of regional climate change on HABs are Norwegian coastal waters and the Skagerrak. Other vulnerable areas include Danish coastal waters, and to a lesser extent, the German and Dutch Bight and the northern Irish Sea. Quite apart from eutrophication, our results give a preview of what might happen to certain HAB genera under changing climatic conditions in temperate environments and their responses to variability of climate oscillations Such as the NAO.

Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the A phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. in this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

A windows program for the derivation of steady-state equations in enzyme systems

Despite the number of computer-assisted methods described for the derivation of steady-state equations of enzyme systems, most of them are focused on strict steady-state conditions or are not able to solve complex reaction mechanisms. Moreover, many of them are based on computer programs that are either not readily available or have limitations. We present here a computer program called WinStes, which derives equations for both strict steady-state systems and those with the assumption of rapid equilibrium, for branched or unbranched mechanisms, containing both reversible and irreversible conversion steps. It solves reaction mechanisms involving up to 255 enzyme species, connected by up to 255 conversion steps. The program provides all the advantages of the Windows programs, such as a user-friendly graphical interface, and has a short computation time. WinStes is available free of charge on request from the authors. (c) 2006 Elsevier Inc. All rights reserved.

Encounter success of free-ranging marine predator movements across a dynamic prey landscape

Movements of wide-ranging top predators can now be studied effectively using satellite and archival telemetry. However, the motivations underlying movements remain difficult to determine because trajectories are seldom related to key biological gradients, such as changing prey distributions. Here, we use a dynamic prey landscape of zooplankton biomass in the north-east Atlantic Ocean to examine active habitat selection in the plankton-feeding basking shark Cetorhinus maximus. The relative success of shark searches across this landscape was examined by comparing prey biomass encountered by sharks with encounters by random-walk simulations of ‘model’ sharks. Movements of transmitter-tagged sharks monitored for 964 days (16754km estimated minimum distance) were concentrated on the European continental shelf in areas characterized by high seasonal productivity and complex prey distributions. We show movements by adult and sub-adult sharks yielded consistently higher prey encounter rates than 90% of random-walk simulations. Behavioural patterns were consistent with basking sharks using search tactics structured across multiple scales to exploit the richest prey areas available in preferred habitats. Simple behavioural rules based on learned responses to previously encountered prey distributions may explain the high performances. This study highlights how dynamic prey landscapes enable active habitat selection in large predators to be investigated from a trophic perspective, an approach that may inform conservation by identifying critical habitat of vulnerable species.

Using continuous plankton recorder data

The continuous plankton recorder (CPR) survey is the largest multi-decadal plankton monitoring programme in the world. It was initiated in 1931 and by the end of 2004 had counted 207,619 samples and identified 437 phyto- and zoo-plankton taxa throughout the North Atlantic. CPR data are used extensively by the research community and in recent years have been used increasingly to underpin marine management. Here, we take a critical look at how best to use CPR data. We first describe the CPR itself, CPR sampling, and plankton counting procedures. We discuss the spatial and temporal biases in the Survey, summarise environmental data that have not previously been available, and describe the new data access policy. We supply information essential to using CPR data, including descriptions of each CPR taxonomic entity., the idiosyncrasies associated with counting many of the taxa, the logic behind taxonomic changes in the Survey, the semi-quantitative nature of CPR sampling, and recommendations on choosing the spatial and temporal scale of study. This forms the basis for a broader discussion on how to use CPR data for deriving ecologically meaningful indices based on size, functional groups and biomass that can be used to support research and management. This contribution should be useful for plankton ecologists, modellers and policy makers that actively use CPR data. (c) 2005 Elsevier Ltd. All rights reserved.

Stochastic delay differential equations for genetic regulatory networks

Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.

Differential Priors for Elastic Nets

The elastic net and related algorithms, such as generative topographic mapping, are key methods for discretized dimension-reduction problems. At their heart are priors that specify the expected topological and geometric properties of the maps. However, up to now, only a very small subset of possible priors has been considered. Here we study a much more general family originating from discrete, high-order derivative operators. We show theoretically that the form of the discrete approximation to the derivative used has a crucial influence on the resulting map. Using a new and more powerful iterative elastic net algorithm, we confirm these results empirically, and illustrate how different priors affect the form of simulated ocular dominance columns.