A competitive coexistence principle?

Competitive exclusion – n species cannot coexist on fewer than n limiting resources in a constant and isolated environment – has been a central ecological principle for the past century. Since empirical studies cannot universally demonstrate exclusion, this principle has mainly relied on mathematical proofs. Here we investigate the predictions of a new approach to derive functional responses in consumer/resource systems. Models usually describe the temporal dynamics of consumer/resource systems at a macroscopic level – i.e. at the population level. Each model may be pictured as one time-dependent macroscopic trajectory. Each macroscopic trajectory is, however, the product of many individual fates and from combinatorial considerations can be realized in many different ways at the microscopic – or individual – level. Recently it has been shown that, in systems with large enough numbers of consumer individuals and resource items, one macroscopic trajectory can be realized in many more ways than any other at the individual – or microscopic – level. Therefore, if the temporal dynamics of an ecosystem are assumed to be the outcome of only statistical mechanics – that is, chance – a single trajectory is near-certain and can be described by deterministic equations. We argue that these equations can serve as a null to model consumer-resource dynamics, and show that any number of species can coexist on a single resource in a constant, isolated environment. Competition may result in relative rarity, which may entail exclusion in finite samples of discrete individuals, but exclusion is not systematic. Beyond the coexistence/exclusion outcome, our model also predicts that the relative abundance of any two species depends simply on the ratio of their competitive abilities as computed from – and only from – their intrinsic kinetic and stoichiometric parameters.     

Differential regulation by the homologous response regulators NarL and NarP of Escherichia coli K-12 depends on DNA binding site arrangement

The NarL and NarP proteins are homologous response regulators of Escherichia coli that control the expression of several operons in response to nitrate and nitrite. A consensus heptameric NarL DNA-binding sequence has been identified, and previous observations suggest that the NarP protein has a similar sequence specificity. However, some operons are regulated by NarL alone, whereas others are controlled by both NarL and NarP. In this study, DNase I footprinting experiments with the fdnG , nirB and nrfA control regions revealed that NarP only binds to heptamer sequences organized as an inverted repeat with a 2 bp spacing (7–2–7 sites). The NarL protein also binds to these 7–2–7 sites but, unlike NarP, also recognizes heptamers in other arrangements. These results provide an explanation for the regulation of some operons by NarL alone and for the different effects of NarL and NarP at common target operons, such as fdnG and nrfA . To investigate this differential DNA binding further, derivatives of the nrfA control region were constructed in which the spacing of the 7–2–7 heptamers was increased (7– n –7 constructs). Increasing the spacing to four or more basepairs abolished NarP binding and significantly reduced NarL binding. The NarL protein also had a reduced binding affinity for heptamers adjacent to the 7– n –7 heptamer pair, suggesting a decrease in cooperative interactions. In conclusion, we propose that 7–2–7 sites are preferred by both NarL and NarP. NarL can also recognize other binding site arrangements, an ability that appears to be lacking in NarP.     

Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model

Population variability and uncertainty are important features of biological systems that must be considered when developing mathematical models for these systems. In this paper we present probability-based parameter estimation methods that account for such variability and uncertainty. Theoretical results that establish well-posedness and stability for these methods are discussed. A probabilistic parameter estimation technique is then applied to a toxicokinetic model for trichloroethylene using several types of simulated data. Comparison with results obtained using a standard, deterministic parameter estimation method suggests that the probabilistic methods are better able to capture population variability and uncertainty in model parameters.     

Uncertainty in life cycle impact assessment of toxic releases practical experiences - arguments for a reductionalistic approach?

This paper describes the experience with impact assessment of toxic releases in a Substance Flow Analysis (SFA) for PVC in Sweden. For this system, all emissions related to the PVC-chain were inventoried. They have been evaluated making use of the Life Cycle Impact Assessment (LCIA) step from the CMI.-guide, including the new toxicity equivalency factors calculated with the Uniform System for Evaluation of Substances (USES). The application of this method led to the conclusion that I.CA Impact Assessment of toxic releases is still a major bottleneck: the USES-equivalency factors are not to he trusted due to outdated data, inappropriate defaults, etc. in the USES’ substance properties database. Therefore, a second USES-ser of factors was calculated that differed up to factors of 1,000 or more from the old ones. Even these factors probably suffer from unacceptable high structural, in practice not reducible uncertainties. In conclusion, we warn the LCA community not to overestimate the possibility of LCA Impact Assessment to obtain a meaningfull priority setting with regard to toxicity problems. Instead, we propose developing indicator systems for LCIA of toxic releases that genuinely deal with all relevant types of uncertainty: data uncertainty, modelling uncertainty and particularly paradigmatic uncertainty.     

Distribution modelling and statistical phylogeography: an integrative framework for generating and testing alternative biogeographical hypotheses

Statistical phylogeographic studies contribute to our understanding of the factors that influence population divergence and speciation, and that ultimately generate biogeographical patterns. The use of coalescent modelling for analyses of genetic data provides a framework for statistically testing alternative hypotheses about the timing and pattern of divergence. However, the extent to which such approaches contribute to our understanding of biogeography depends on how well the alternative hypotheses chosen capture relevant aspects of species histories. New modelling techniques, which explicitly incorporate spatio-geographic data external to the gene trees themselves, provide a means for generating realistic phylogeographic hypotheses, even for taxa without a detailed fossil record. Here we illustrate how two such techniques – species distribution modelling and its historical extension, palaeodistribution modelling – in conjunction with coalescent simulations can be used to generate and test alternative hypotheses. In doing so, we highlight a few key studies that have creatively integrated both historical geographic and genetic data and argue for the wider incorporation of such explicit integrations in biogeographical studies.     

Does trypsin cut before proline?

Trypsin is the most commonly used enzyme in mass spectrometry for protein digestion with high substrate specificity. Many peptide identification algorithms incorporate these specificity rules as filtering criteria. A generally accepted "Keil rule" is that trypsin cleaves next to arginine or lysine, but not before proline. Since this rule was derived two decades ago based on a small number of experimentally confirmed cleavages, we decided to re-examine it using 14.5 million tandem spectra (2 orders of magnitude increase in the number of observed tryptic cleavages). Our analysis revealed a surprisingly large number of cleavages before proline. We examine several hypotheses to explain these cleavages and argue that trypsin specificity rules used in peptide identification algorithms should be modified to "legitimatize" cleavages before proline. Our approach can be applied to analyze any protease, and we further argue that specificity rules for other enzymes should also be re-evaluated based on statistical evidence derived from large MS/MS data sets.     

Quantifying uncertainty in the potential distribution of an invasive species: climate and the Argentine ant

Maps of a species' potential range make an important contribution to conservation and invasive species risk analysis. Spatial predictions, however, should be accompanied by an assessment of their uncertainty. Here, we use multimodel inference to generate confidence intervals that incorporate both the uncertainty involved in model selection as well as the error associated with model fitting. In the case of the invasive Argentine ant, we found that it was most likely to occur where the mean daily temperature in mid-winter was 7–14 °C and maximum daily temperatures during the hottest month averaged 19–30 °C. Uninvaded regions vulnerable to future establishment include: southern China, Taiwan, Zimbabwe, central Madagascar, Morocco, high-elevation Ethiopia, Yemen and a number of oceanic islands. Greatest uncertainty exists over predictions for China, north-east India, Angola, Bolivia, Lord Howe Island and New Caledonia. Quantifying the costs of different errors (false negatives vs. false positives) was considered central for connecting modelling to decision-making and management processes.     

Spatial modelling of succession-disturbance dynamics in forest ecosystems: Concepts and examples

Over the last few decades it has become increasingly obvious that disturbance, whether natural or anthropogenic in origin, is ubiquitous in ecosystems. Disturbance-related processes are now considered to be important determinants of the composition, structure and function of ecological systems. However, because disturbance and succession processes occur across a wide range of spatio-temporal scales their empirical investigation is difficult. To counter these difficulties much use has been made of spatial modelling to explore the response of ecological systems to disturbance(s) occurring at spatial scales from the individual to the landscape and above, and temporal scales from minutes to centuries. Here we consider such models by contrasting two alternative motivations for their development and use: prediction and exploration, with a focus on forested ecosystems. We consider the two approaches to be complementary rather than competing. Predictive modelling aims to combine knowledge (understanding and data) with the goal of predicting system dynamics; conversely, exploratory models focus on developing understanding in systems where uncertainty is high. Examples of exploratory modelling include model-based explorations of generic issues of criticality in ecological systems, whereas predictive models tend to be more heavily data-driven (e.g. species distribution models). By considering predictive and exploratory modelling alongside each other, we aim to illustrate the range of methods used to model succession and disturbance dynamics and the challenges involved in the model-building and evaluation processes in this arena.     

Spread of Avian Influenza Viruses by Common Teal (Anas crecca) in Europe

Since the recent spread of highly pathogenic (HP) H5N1 subtypes, avian influenza virus (AIV) dispersal has become an increasing focus of research. As for any other bird-borne pathogen, dispersal of these viruses is related to local and migratory movements of their hosts. In this study, we investigated potential AIV spread by Common Teal (Anas crecca) from the Camargue area, in the South of France, across Europe. Based on bird-ring recoveries, local duck population sizes and prevalence of infection with these viruses, we built an individual-based spatially explicit model describing bird movements, both locally (between wintering areas) and at the flyway scale. We investigated the effects of viral excretion duration and inactivation rate in water by simulating AIV spread with varying values for these two parameters. The results indicate that an efficient AIV dispersal in space is possible only for excretion durations longer than 7 days. Virus inactivation rate in the environment appears as a key parameter in the model because it allows local persistence of AIV over several months, the interval between two migratory periods. Virus persistence in water thus represents an important component of contamination risk as ducks migrate along their flyway. Based on the present modelling exercise, we also argue that HP H5N1 AIV is unlikely to be efficiently spread by Common Teal dispersal only.     

The anarchist's guide to ecological theory. Or, we don't need no stinkin' laws

Several ecologists have recently suggested that ecology has several laws. This conclusion contrasts with the views of some philosophers of science, who have suggested that biology cannot have laws. I argue that the debate has been confused because two very different types of law can be recognised: correlative and causal laws. Once we recognise that there is a difference, the argument against causal laws becomes stronger, and instead I suggest that ecologists should recognise that they can and do produce generalisations that are used to build models – nomological machines – that describe the ecological systems they are studying.     

Supporting Fisheries Management by Means of Complex Models: Can We Point out Isles of Robustness in a Sea of Uncertainty?

Ecosystems are usually complex, nonlinear and strongly influenced by poorly known environmental variables. Among these systems, marine ecosystems have high uncertainties: marine populations in general are known to exhibit large levels of natural variability and the intensity of fishing efforts can change rapidly. These uncertainties are a source of risks that threaten the sustainability of both fish populations and fishing fleets targeting them. Appropriate management measures have to be found in order to reduce these risks and decrease sensitivity to uncertainties. Methods have been developed within decision theory that aim at allowing decision making under severe uncertainty. One of these methods is the information-gap decision theory. The info-gap method has started to permeate ecological modelling, with recent applications to conservation. However, these practical applications have so far been restricted to simple models with analytical solutions. Here we implement a deterministic approach based on decision theory in a complex model of the Eastern English Channel. Using the ISIS-Fish modelling platform, we model populations of sole and plaice in this area. We test a wide range of values for ecosystem, fleet and management parameters. From these simulations, we identify management rules controlling fish harvesting that allow reaching management goals recommended by ICES (International Council for the Exploration of the Sea) working groups while providing the highest robustness to uncertainties on ecosystem parameters.     

Effects of scale-dependent variation in ice cover on the distribution of wintering belted kingfishers Ceryle alcyon

Understanding why species react differently to changing environments requires detailed understanding of the factors that regulate distributions within current ranges These types of investigations require spatially and temporally explicit examination of the scales at which a species responds to environmental factors To obtain this type of information, we analyzed the relationship between ice cover and abundance, distribution, and spacing of belted kingfishers Ceryle alcyon during the autumn/winters of 1993–1994 and 1994–1995 Our results indicate that the effects of ice cover on kingfisher populations are complex and scale dependent At a small spatial scale (0 5 km) the abundance of kingfishers was negatively correlated with ice cover, as we expected At a large spatial scale (15 5 km), however, there was no relationship between these variables We argue this contradiction m our results is due to differences in the patchiness of ice cover at these scales In a year with average winter temperatures (1993–1994) the spatial and temporal autocorrelation of ice cover and kingfisher distribution were similar In a warm year (1994–1995), however, we found no such similarity Neighbor distances were shorter during the cold year than during the warm year and shorter during censuses with extensive ice cover than censuses with sparse ice cover We conclude that ice cover is a key factor regulating the distribution and abundance of belted kingfishers in our study area during cold to average years, but that during warm years other factors are likely to be more important Based on these patterns we think that patterns of ice cover may be important in mediating the response of kingfishers to changes in climate     

Fuzzy knowledge- and data-based models of damage to reeds by grazing of Greylag Geese

This paper describes a fuzzy and neuro-fuzzy approach to modelling feeding intensity of Greylag Geese on reed. As a consequence of the presence of some non-measurable or random factors and the heterogeneity of reed and goose behaviour, the relationships between the model variables are often not well known and the data collected have a high degree of uncertainty. A fuzzy approach was selected which can be applied with vague knowledge and data of high uncertainty. Fuzzy logic can be used to handle inexact reasoning in knowledge-based models with fuzzy rules and fuzzy sets to handle uncertainty in data. The neural network technique was applied to develop the fuzzy data-based models. For training, several dataset combinations of three lakes in North Germany were used. The generalisation capability of these models was checked for other lakes. The performance of these models was compared with the results of the fuzzy knowledge-based model developed in the next step. The knowledge base of this model contains the Mamdani-type rules formulated by a domain expert. All models were implemented using the Fuzzy Logic Toolbox of MATLAB^®.     

An argument for mechanism-based statistical inference in cancer

Cancer is perhaps the prototypical systems disease, and as such has been the focus of extensive study in quantitative systems biology. However, translating these programs into personalized clinical care remains elusive and incomplete. In this perspective, we argue that realizing this agenda—in particular, predicting disease phenotypes, progression and treatment response for individuals—requires going well beyond standard computational and bioinformatics tools and algorithms. It entails designing global mathematical models over network-scale configurations of genomic states and molecular concentrations, and learning the model parameters from limited available samples of high-dimensional and integrative omics data. As such, any plausible design should accommodate: biological mechanism, necessary for both feasible learning and interpretable decision making; stochasticity, to deal with uncertainty and observed variation at many scales; and a capacity for statistical inference at the patient level. This program, which requires a close, sustained collaboration between mathematicians and biologists, is illustrated in several contexts, including learning biomarkers, metabolism, cell signaling, network inference and tumorigenesis.     

Extending, changing, and explaining the brain

This paper addresses concerns raised recently by Datteri (Biol Philos 24:301–324, 2009) and Craver (Philos Sci 77(5):840–851, 2010) about the use of brain-extending prosthetics in experimental neuroscience. Since the operation of the implant induces plastic changes in neural circuits, it is reasonable to worry that operational knowledge of the hybrid system will not be an accurate basis for generalisation when modelling the unextended brain. I argue, however, that Datteri’s no-plasticity constraint unwittingly rules out numerous experimental paradigms in behavioural and systems neuroscience which also elicit neural plasticity. Furthermore, I propose that Datteri and Craver’s arguments concerning the limitations of prosthetic modelling in basic neuroscience, as opposed to neuroengineering, rests on too narrow a view of the ways models in neuroscience should be evaluated, and that a more pluralist approach is needed. I distinguish organisational validity of models from mechanistic validity. I argue that while prosthetic models may be deficient in the latter of these explanatory virtues because of neuroplasticity, they excel in the former since organisational validity tracks the extent to which a model captures coding principles that are invariant with plasticity. Changing the brain, I conclude, is one viable route towards explaining the brain.     

Empirical perspectives on species borders: from traditional biogeography to global change

In this paper we will outline several empirical approaches to developing and testing hypotheses about the determinants of species borders. We highlight environmental change as an important opportunity – arguing that these unplanned, large-scale manipulations can be used to study mechanisms which limit species distributions. Our discussion will emphasize three main ideas. First, we review the traditional biogeographic approach. We show how modern analytical and computer techniques have improved this approach and generated important new hypotheses concerning species' range determinants. However, abilities to test those hypotheses continue to be limited. Next we look at how the additions of temporal data, field and lab experimentation, biological details and replication, when applied to systems that have been the subject of classical biogeographic studies, have been used to support or refute hypotheses on range determinants. Such a multi-faceted approach adds rigor, consistency and plausible mechanisms to the study of species ranges, and has been especially fruitful in the study of climate and species' ranges. Lastly, we present an alternative avenue for exploration of range-limiting mechanisms which has been under-utilized. We argue that carefully designed comparisons and contrasts between groups of species or systems provide a powerful tool for examining hypotheses on species' borders. The seasonality hypothesis as an explanation for Rapoport's rule serves as a model of this approach. A test is constructed by comparing patterns of seasonality and range size among marine and terrestrial systems. The seasonality hypothesis is not supported.     

Catastrophes,connectivity and Allee effects in the design of marine reserve networks

Catastrophic events, like oil spills and hurricanes, occur in many marine systems. One potential role of marine reserves is buffering populations against disturbances, including the potential for disturbance-driven population collapses under Allee effects. This buffering capacity depends on reserves in a network providing rescue effects, setting up a tradeoff where reserves need to be connected to facilitate rescue, but also distributed in space to prevent simultaneous extinction. We use a set of population models to examine how dispersal ability and the disturbance regime interact to determine the optimal reserve spacing. We incorporate fishing in a spatially-explicit model to understand the effect of objective choice (e.g. conservation versus fisheries yield) on the optimal reserve spacing. We show that the optimal spacing between reserves increases when accounting for catastrophes with larger spacing needed when Allee effects interact with catastrophes to increase the probability of extinction. We also show that classic tradeoffs between conservation and fishing objectives disappear in the presence of catastrophes. Specifically, we found that at intermediate levels of disturbance, it is optimal to spread out reserves in order to increase both population persistence and to maximize spillover into non-reserve areas.     

A framework for mapping,visualisation and automatic model creation of signal‐transduction networks

Intracellular signalling systems are highly complex. This complexity makes handling, analysis and visualisation of available knowledge a major challenge in current signalling research. Here, we present a novel framework for mapping signal‐transduction networks that avoids the combinatorial explosion by breaking down the network in reaction and contingency information. It provides two new visualisation methods and automatic export to mathematical models. We use this framework to compile the presently most comprehensive map of the yeast MAP kinase network. Our method improves previous strategies by combining (I) more concise mapping adapted to empirical data, (II) individual referencing for each piece of information, (III) visualisation without simplifications or added uncertainty, (IV) automatic visualisation in multiple formats, (V) automatic export to mathematical models and (VI) compatibility with established formats. The framework is supported by an open source software tool that facilitates integration of the three levels of network analysis: definition, visualisation and mathematical modelling. The framework is species independent and we expect that it will have wider impact in signalling research on any system.