Non‐resource effects of foundation species on meta‐ecosystem stability and function

Ecosystems such as forests and mussel beds, that are driven by foundation species can be characterized by the slow accumulation of matter that affect their structural stability. This non‐resource effect of matter on ecosystems can lead to disturbances and to pulsed release and transport of matter over regional scales. However, non‐resource effects of endogenous pulses of matter on meta‐ecosystem stability and function remain largely unknown. Using a two‐patch meta‐ecosystem model of mussel bed dynamics, we show that non‐resource effects of matter on the structural stability of mussel beds promote pulsed releases of matter and fluctuations in population abundance. These pulsed fluctuations explain the maintenance of meta‐ecosystem heterogeneity in the distribution of abundance and matter through out‐of‐phase synchrony and asynchrony over a broad range of connectivity. These regimes of spatial (a)synchrony explain a tradeoff between the regional retention of matter (ecosystem function) and metapopulation persistence. These results reveal how foundation species can cause local and catastrophic changes that can promote regional asynchrony and stability, even under strong connectivity.     

Convergent ecosystem responses to 23‐year ambient and manipulated warming link advancing snowmelt and shrub encroachment to transient and long‐term climate–soil carbon feedback

Ecosystem responses to climate change can exert positive or negative feedbacks on climate, mediated in part by slow‐moving factors such as shifts in vegetation community composition. Long‐term experimental manipulations can be used to examine such ecosystem responses, but they also present another opportunity: inferring the extent to which contemporary climate change is responsible for slow changes in ecosystems under ambient conditions. Here, using 23 years of data, we document a shift from nonwoody to woody vegetation and a loss of soil carbon in ambient plots and show that these changes track previously shown similar but faster changes under experimental warming. This allows us to infer that climate change is the cause of the observed shifts in ambient vegetation and soil carbon and that the vegetation responses mediate the observed changes in soil carbon. Our findings demonstrate the realism of an experimental manipulation, allow attribution of a climate cause to observed ambient ecosystem changes, and demonstrate how a combination of long‐term study of ambient and experimental responses to warming can identify mechanistic drivers needed for realistic predictions of the conditions under which ecosystems are likely to become carbon sources or sinks over varying timescales.     

Slow variable dominance and phase resetting in phantom bursting

Bursting oscillations are common in neurons and endocrine cells. One type of bursting model with two slow variables has been called ‘phantom bursting’ since the burst period is a blend of the time constants of the slow variables. A phantom bursting model can produce bursting with a wide range of periods: fast (short period), medium, and slow (long period). We describe a measure, which we call the ‘dominance factor’, of the relative contributions of the two slow variables to the bursting produced by a simple phantom bursting model. Using this tool, we demonstrate how the control of different phases of the burst can be shifted from one slow variable to another by changing a model parameter. We then show that the dominance curves obtained as a parameter is varied can be useful in making predictions about the resetting properties of the model cells. Finally, we demonstrate two mechanisms by which phase-independent resetting of a burst can be achieved, as has been shown to occur in the electrical activity of pancreatic islets.     

Ecosystems off track: rate‐induced critical transitions in ecological models

Theory suggests that gradual environmental change may erode the resilience of ecosystems and increase their susceptibility to critical transitions. This notion has received a lot of attention in ecology in recent decades. An important question receiving far less attention is whether ecosystems can cope with the rapid environmental changes currently imposed. The importance of this question was recently highlighted by model studies showing that elevated rates of change may trigger critical transitions, whereas slow environmental change would not. This paper aims to provide a mechanistic understanding of these rate‐induced critical transitions to facilitate identification of rate sensitive ecosystems. Analysis of rate sensitive ecological models is challenging, but we demonstrate how rate‐induced transitions in an elementary model can still be understood. Our analyses reveal that rate‐induced transitions 1) occur if the rate of environmental change is high compared to the response rate of ecosystems, 2) are driven by rates, rather than magnitudes, of change and 3) occur once a critical rate of change is exceeded. Disentangling rate‐induced transitions from classical transitions in observations would be challenging. However, common features of rate‐sensitive models suggest that ecosystems with coupled fast–slow dynamics, exhibiting repetitive catastrophic shifts or displaying periodic spatial patterns are more likely to be rate sensitive. Our findings are supported by experimental studies showing rate‐dependent outcomes. Rate sensitivity of models suggests that the common definition of ecological resilience is not suitable for a subset of real ecosystems and that formulating limits to magnitudes of change may not always safeguard against ecosystem degradation. Synthesis Understanding and predicting ecosystem response to environmental change is one of the key challenges in ecology. Model studies have suggested that slow, gradual environmental change beyond some critical threshold can trigger so‐called critical transitions and abrupt ecosystem degradation. An important question remains however whether ecosystems can cope with the ongoing rapid anthropogenic environmental changes to which they are currently imposed. In this study we demonstrate that in some ecological models elevated rates of change can trigger critical transitions even if slow environmental change of the same magnitude would not. Such rateinduced critical transitions in models suggest that concepts like resilience and planetary boundaries may not always be sufficient to explain and prevent ecosystem degradation.     

Parametric Analysis of a Predator–prey System Stabilized by a Top Predator

We present a complete parametric analysis of a predator–prey system influenced by a top predator. We study ecosystems with abundant nutrient supply for the prey where the prey multiplication can be considered as proportional to its density. The main questions we examine are the following: (1) Can the top predator stabilize such a system at low densities of prey? (2) What possible dynamic behaviors can occur? (3) Under which conditions can the top predation result in the system stabilization? We use a system of two nonlinear ordinary differential equations with the density of the top predator as a parameter. The model is investigated with methods of qualitative theory of ODEs and the theory of bifurcations. The existence of 12 qualitatively different types of dynamics and complex structure of the parametric space are demonstrated. Our studies of phase portraits and parametric diagrams show that a top predator can be an important factor leading to stabilization of the predator-prey system with abundant nutrient supply. Although the model here is applied to the plankton communities with fish (or carnivorous zooplankton) as the top trophic level, the general form of the equations allows applications of our results to other ecological systems.     

Fast activation of a time-dependent outward current in protoplasts derived from coats of developing Phaseolus vulgaris seeds

An outward current that appeared to activate instantaneously in response to depolarising voltage pulses at low sampling frequencies predominated in the plasma membrane of ground-parenchyma protoplasts derived from coats of developing Phaseolus vulgaris L. (cv. Redland Pioneer) seeds. However, the outward current showed time-dependent activation when higher sampling frequencies were used to measure the current. Activation of the current was best described as a double-exponential time course with the fast and slow time constants being 1 and 20 ms, respectively. The current also exhibited a rapid deactivation that followed a double-exponential time course with time constants of approximately 2 and 30 ms, respectively. “Tail-current” analysis allowed us to show that this current exhibited a low selectivity between K⁺ and Cl⁻ (P _K:Cl=1.8). Such a fast-activating current may account for some of the reports of time-independent, instantaneous currents that have been observed in plasma membranes of plant cells digitised at low sampling frequencies. Therefore, when “instantaneous” currents appear it is advisable to characterise these currents using higher sampling frequencies with correspondingly higher filtering frequency cut-offs. Received: 12 May 2000 / Accepted: 26 June 2000     

Periodic orbits arising from Hopf bifurcations in a Volterra prey-predator model

 In this paper we derive a formula which enables the stability of periodic solutions to a Volterra integro-differential system to be determined. This system which has been studied by Cushing [1], models a predator-prey interaction with distributed delays. The results are obtained by using the algorithm developed by Kazarinoff, Wan and van den Driessche [2] based on the centre manifold formulas of Hassard and Wan [3]. We discuss an example of the formula for the case of weak kernels and show that under certain conditions stable periodic solutions arising from Hopf bifurcations at different critical values of the parameters can exist together. Received 30 December 1994; received in revised form 12 December 1995     

Models of central pattern generators for quadruped locomotion I. Primary gaits

In this paper we continue the analysis of a network of symmetrically coupled cells modeling central pattern generators for quadruped locomotion proposed by Golubitsky, Stewart, Buono, and Collins. By a cell we mean a system of ordinary differential equations and by a coupled cell system we mean a network of identical cells with coupling terms. We have three main results in this paper. First, we show that the proposed network is the simplest one modeling the common quadruped gaits of walk, trot, and pace. In doing so we prove a general theorem classifying spatio-temporal symmetries of periodic solutions to equivariant systems of differential equations. We also specialize this theorem to coupled cell systems. Second, this paper focuses on primary gaits; that is, gaits that are modeled by output signals from the central pattern generator where each cell emits the same waveform along with exact phase shifts between cells. Our previous work showed that the network is capable of producing six primary gaits. Here, we show that under mild assumptions on the cells and the coupling of the network, primary gaits can be produced from Hopf bifurcation by varying only coupling strengths of the network. Third, we discuss the stability of primary gaits and exhibit these solutions by performing numerical simulations using the dimensionless Morris-Lecar equations for the cell dynamics.     

Measurement of carbonyl chemical shifts of excited protein states by relaxation dispersion NMR spectroscopy: comparison between uniformly and selectively 13C labeled samples

Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion nuclear magnetic resonance (NMR) spectroscopy has emerged as a powerful method for quantifying chemical shifts of excited protein states. For many applications of the technique that involve the measurement of relaxation rates of carbon magnetization it is necessary to prepare samples with isolated (13)C spins so that experiments do not suffer from magnetization transfer between coupled carbon spins that would otherwise occur during the CPMG pulse train. In the case of (13)CO experiments however the large separation between (13)CO and (13)C(alpha) chemical shifts offers hope that robust (13)CO dispersion profiles can be recorded on uniformly (13)C labeled samples, leading to the extraction of accurate (13)CO chemical shifts of the invisible, excited state. Here we compare such chemical shifts recorded on samples that are selectively labeled, prepared using [1-(13)C]-pyruvate and NaH(13)CO(3,) or uniformly labeled, generated from (13)C-glucose. Very similar (13)CO chemical shifts are obtained from analysis of CPMG experiments recorded on both samples, and comparison with chemical shifts measured using a second approach establishes that the shifts measured from relaxation dispersion are very accurate.     

Random binding of dimers to chains

We develop a probabilistic model for the binding of a small linear polymer to a larger chain. We assume that we can approximate the energy of interaction of the two chains by summing the pairwise interactions between subunits. Because the energy of interaction between a pair of subunits can depend on neighboring subunits, which we assume vary along the chain, we assign the pairwise energies of interactions according to a specified probability distribution. Thus we develop a statistical model for the binding of two molecules. While such models may not be appropriate for studying the interaction of a particular pair of molecules, they can provide insight into questions that deal with populations of molecules, such as why do MHC molecules bind peptides of a certain size? Here we analyze in detail the special case of a heterodimer binding to a polymer.     

A Theory for Cyclic Shifts between Alternative States in Shallow Lakes

Some shallow lakes switch repeatedly back and forth between a vegetation dominated clear-water state and a contrasting turbid state. Usually such alternations occur quite irregularly, but in some cases the switches between states are remarkably regular. Here we use data from a well-studied Dutch lake and a set of simple models to explore possible explanations for such cyclic behavior. We first demonstrate from a graphical model that cycles may in theory occur if submerged macrophytes promote water clarity in the short run, but simultaneously cause an increased nutrient retention, implying an accumulation of nutrients in the long run. Thus, although submerged plants create a positive feedback on their own growth by clearing the water, they may in the long run undermine their position by creating a slow “internal eutrophication”. We explore the potential role of two different mechanisms that may play a role in this internal eutrophication process using simulation models: (1) reduction of the P concentration in the water column by macrophytes, leading to less outflow of P, and hence to a higher phosphorus accumulation in the lake sediments and (2) a build-up of organic matter over time resulting in an increased sediment oxygen demand causing anaerobic conditions that boost P release from the sediment. Although the models showed that both mechanisms can produce cyclic behavior, the period of the cycles caused by the build-up of organic material seemed more realistic compared to data of the Dutch Lake Botshol in which regular cycles with a period of approximately 7 years have been observed over the past 17 years.     

Gradual regime shifts in spatially extended ecosystems

Ecosystem regime shifts are regarded as abrupt global transitions from one stable state to an alternative stable state, induced by slow environmental changes or by global disturbances. Spatially extended ecosystems, however, can also respond to local disturbances by the formation of small domains of the alternative state. Such a response can lead to gradual regime shifts involving front propagation and the coalescence of alternative-state domains. When one of the states is spatially patterned, a multitude of intermediate stable states appears, giving rise to step-like gradual shifts with extended pauses at these states. Using a minimal model, we study gradual state transitions and show that they precede abrupt transitions. We propose indicators to probe gradual regime shifts, and suggest that a combination of abrupt-shift indicators and gradual-shift indicators might be needed to unambiguously identify regime shifts. Our results are particularly relevant to desertification in drylands where transitions to bare soil take place from spotted vegetation, and the degradation process appears to involve step-like events of local vegetation mortality caused by repeated droughts.     

Parametric analysis of the ratio-dependent predator–prey model

We present a complete parametric analysis of stability properties and dynamic regimes of an ODE model in which the functional response is a function of the ratio of prey and predator abundances. We show the existence of eight qualitatively different types of system behaviors realized for various parameter values. In particular, there exist areas of coexistence (which may be steady or oscillating), areas in which both populations become extinct, and areas of "conditional coexistence" depending on the initial values. One of the main mathematical features of ratio-dependent models, distinguishing this class from other predator-prey models, is that the Origin is a complicated equilibrium point, whose characteristics crucially determine the main properties of the model. This is the first demonstration of this phenomenon in an ecological model. The model is investigated with methods of the qualitative theory of ODEs and the theory of bifurcations. The biological relevance of the mathematical results is discussed both regarding conservation issues (for which coexistence is desired) and biological control (for which extinction is desired).     

Tracking unstable states: ecosystem dynamics in a changing world

Ecological systems can show complex and sometimes abrupt responses to environmental change, with important implications for their resilience. Theories of alternate stable states have been used to predict regime shifts of ecosystems as equilibrium responses to sufficiently slow environmental change. The actual rate of environmental change is a key factor affecting the response, yet we are still lacking a non-equilibrium theory that explicitly considers the influence of this rate of environmental change. We present a metacommunity model of predator–prey interactions displaying multiple stable states, and we impose an explicit rate of environmental change in habitat quality (carrying capacity) and connectivity (dispersal rate). We study how regime shifts depend on the rate of environmental change and compare the outcome with a stability analysis in the corresponding constant environment. Our results reveal that in a changing environment, the community can track states that are unstable in the constant environment. This tracking can lead to regime shifts, including local extinctions, that are not predicted by alternative stable state theory. In our metacommunity, tracking unstable states also controls the maintenance of spatial heterogeneity and spatial synchrony. Tracking unstable states can also lead to regime shifts that may be reversible or irreversible. Our study extends current regime shift theories to integrate rate-dependent responses to environmental change. It reveals the key role of unstable states for predicting transient dynamics and long-term resilience of ecological systems to climate change.     

Predicting Habitat Utilization and Extent of Ecosystem Disturbance by an Increasing Herbivore Population

Herbivory can lead to shifts in ecosystem state or changes in ecosystem functioning, and recovery from herbivory is particularly slow in disturbance-sensitive ecosystems such as arctic tundra. Herbivore impacts on ecosystems are variable in space and time due to population fluctuations and selective utilization of habitats; thus there is a need to accurately predict herbivore impacts at the landscape scale. The habitat utilization and extent of disturbance caused by increasing populations of pink-footed geese (Anser brachyrhynchus) foraging in the high arctic tundra of Svalbard were assessed using a predictive model of the population’s habitat use. Pink-footed geese arrive in Svalbard in early spring when they forage for belowground plant parts; this foraging (called grubbing) can cause vegetation loss and soil disturbance. Surveys of the extent and intensity of grubbing were carried out to develop predictive models that were subsequently tested against data collected during the following year from different areas. Both habitat type at a particular point and the amount of preferred fen habitat in the surrounding area were powerful predictors of grubbing likelihood and the developed model correctly classified over 69% of validation observations with an AUC of 0.75. Pink-footed geese showed a strong preference for wetter habitats within low-lying landscapes. Extrapolation of the predictive model across the archipelago showed that a maximum potential area of 2300 km² (3.8% of the archipelago) could be disturbed by grubbing. Thus, increasing populations of geese may cause large-scale vegetation loss and soil disturbance in arctic ecosystems.     

Human‐aided admixture may fuel ecosystem transformation during biological invasions: theoretical and experimental evidence

Biological invasions can transform our understanding of how the interplay of historical isolation and contemporary (human‐aided) dispersal affects the structure of intraspecific diversity in functional traits, and in turn, how changes in functional traits affect other scales of biological organization such as communities and ecosystems. Because biological invasions frequently involve the admixture of previously isolated lineages as a result of human‐aided dispersal, studies of invasive populations can reveal how admixture results in novel genotypes and shifts in functional trait variation within populations. Further, because invasive species can be ecosystem engineers within invaded ecosystems, admixture‐induced shifts in the functional traits of invaders can affect the composition of native biodiversity and alter the flow of resources through the system. Thus, invasions represent promising yet under‐investigated examples of how the effects of short‐term evolutionary changes can cascade across biological scales of diversity. Here, we propose a conceptual framework that admixture between divergent source populations during biological invasions can reorganize the genetic variation underlying key functional traits, leading to shifts in the mean and variance of functional traits within invasive populations. Changes in the mean or variance of key traits can initiate new ecological feedback mechanisms that result in a critical transition from a native ecosystem to a novel invasive ecosystem. We illustrate the application of this framework with reference to a well‐studied plant model system in invasion biology and show how a combination of quantitative genetic experiments, functional trait studies, whole ecosystem field studies and modeling can be used to explore the dynamics predicted to trigger these critical transitions.     

Cinnamomin: separation,crystallization and preliminary X-ray diffraction study

Cinnamomin from Cinnamonum camphora seeds, a type II ribosome-inactivating protein that interferes with protein biosynthesis in mammalian cells, can induce the apoptosis of carcinoma cells and be used as an insecticide. A rapid and improved method has been developed for the extraction and purification of cinnamomin from camphora seed. Purification of cinnamomin is achieved with two successive steps of hydrophobic interaction chromatography carried out on a fast protein liquid chromatography (FPLC) system. Crystals suitable for X-ray diffraction analysis were obtained by vapor diffusion method. A complete data set at 2.8 A resolution has been collected. Data indexation and refinement indicate that the crystal is orthorhombic with space group P2(1)2(1)2(1) and unit cell dimensions a = 52.39 A, b = 126.33 A, c = 161.45 A. There are two molecules per asymmetric unit. Initial phasing by molecular replacement method yielded a solution, which will contribute to the structure determination. A molecular model will further the understanding of the mechanism of cinnamomin function. The latter will be combined with bio-informatics to facilitate the medical and other applications of cinnamomin.     

Consequences of range contractions and range shifts on molecular diversity

Due to past and current climatic changes, range contractions and range shifts are essential stages in the history of a species. However, unlike range expansions, the molecular consequences of these processes have been little investigated. In order to fill this gap, we simulated patterns of molecular diversity within and between populations for various types of range contractions and range shifts. We show that range contractions tend to decrease genetic diversity as compared with population with stable ranges but quite counterintuitively fast range contractions preserve higher levels of diversity and induce lower levels of genetic differentiation among refuge areas than slow contractions. Contrastingly, fast range shifts lead to lower levels of diversity than slow range shifts. At odds with our expectations, we find that species actively migrating toward refuge areas can only preserve higher levels of diversity in refugia if the contraction is rapid. Under slow range contraction or slow range shift, active migration toward refugia lead to a larger loss of diversity as compared with scenarios with isotropic migration and may thus not be a good evolutionary strategy. These results suggest that the levels of diversity preserved after a climate change both within and between refuge areas will not only depend on the dispersal abilities of a species but also on the speed of the change. It also implies that a given episode of climatic change will impact differently species with different generation times.     

Fiber-type proportions in mammalian soleus muscle during postnatal development

We analyzed the fiber-type composition of the soleus muscle in rats and mice to determine whether the adult proportion of fiber types is fixed soon after birth or whether it changes during postnatal maturation. We examined muscles from animals varying in age from 1 week to 1 year using monoclonal antibodies that distinguish between fast and slow isoforms of myosin heavy chains. In cross sections of unfixed muscle containing profiles of all myofibers in the muscle, we counted the fibers that stained with antibodies to fast myosin, and in adjacent sections, those that stained positive with an antibody to slow myosin. We also counted the total number of fibers in each section. Rat soleus contained about 2500 myofibers, and mouse about 1000 at all ages studied, suggesting that myogenesis ceases in soleus by 1 week after birth or sooner. In mouse soleus, the relative proportions of fibers staining positive with fast and slow myosin antibodies were similar at all ages studied, about 60%–70% being fast and 30%–40% slow. In rat soleus, however, the proportions of fast antibody-positive and slow antibody-positive fibers changed dramatically during postnatal maturation. At 1 week after birth, about 50% of rat soleus fibers stained with fast myosin antibodies, whereas between 1 and 2 months this value fell to about 10%. In mouse, about 10% of fibers at 1 week, but none at 1 year, reacted with both fast and slow antibodies, whereas in rat, fewer than 3% bound both antibodies to a significant degree at 1 week. It is puzzling why, in rat soleus, the majority of apparently fast fibers present at 1 week is converted to a slow phenotype, whereas in mouse soleus the predominant change appears to be the suppression of fast myosin expression in a subset of fibers that expresses both myosin types at 1 week. It is possible that this may be related to differences in size and the amount of body growth between these two species.     

Period doubling of calcium spike firing in a model of a Purkinje cell dendrite

Recordings from cerebellar Purkinje cell dendrites have revealed that in response to sustained current injection, the cell firing pattern can move from tonic firing of Ca²⁺ spikes to doublet firing and even to quadruplet firing or more complex firing. These firing patterns are not modified substantially if Na⁺ currents are blocked. We show that the experimental results can be viewed as a slow transition of the neuronal dynamics through a period-doubling bifurcation. To further support this conclusion and to understand the underlying mechanism that leads to doublet firing, we develop and study a simple, one-compartment model of Purkinje cell dendrite. The neuron can also exhibit quadruplet and chaotic firing patterns that are similar to the firing patterns that some of the Purkinje cells exhibit experimentally. The effects of parameters such as temperature, applied current, and potassium reversal potential in the model resemble their effects in experiments. The model dynamics involve three time scales. Ca²⁺- dependent K⁺ currents, with intermediate time scales, are responsible for the appearance of doublet firing, whereas a very slow hyperpolarizing current transfers the neuron from tonic to doublet firing. We use the fast-slow analysis to separate the effects of the three time scales. Fast-slow analysis of the neuronal dynamics, with the activation variable of the very slow, hyperpolarizing current considered as a parameter, reveals that the transitions occurs via a cascade of period-doubling bifurcations of the fast and intermediate subsystem as this slow variable increases. We carry out another analysis, with the Ca²⁺ concentration considered as a parameter, to investigate the conditions for the generation of doublet firing in systems with one effective variable with intermediate time scale, in which the rest state of the fast subsystem is terminated by a saddle-node bifurcation. We find that the scenario of period doubling in these systems can occur only if (1) the time scale of the intermediate variable (here, the decay rate of the calcium concentration) is slow enough in comparison with the interspike interval of the tonic firing at the transition but is not too slow and (2) there is a bistability of the fast subsystem of the spike-generating variables.