Local ecosystem feedbacks and critical transitions in the climate

Global and regional climate models, such as those used in IPCC assessments, are the best tools available for climate predictions. Such models typically account for large-scale land-atmosphere feedbacks. However, these models omit local vegetationenvironment 5 feedbacks that are crucial for critical transitions in ecosystems. Here, we reveal the hypothesis that, if the balance of feedbacks is positive at all scales, local vegetation-environment feedbacks may trigger a cascade of amplifying effects, propagating from local to large scale, possibly leading to critical transitions in the largescale climate. We call for linking local ecosystem feedbacks with large-scale land10 atmosphere feedbacks in global and regional climate models in order to yield climate predictions that we are more confident about

The Clumping Transition in Niche Competition: a Robust Critical Phenomenon

We show analytically and numerically that the appearance of lumps and gaps in the distribution of n competing species along a niche axis is a robust phenomenon whenever the finiteness of the niche space is taken into account. In this case depending if the niche width of the species $\sigma$ is above or below a threshold $\sigma_c$, which for large n coincides with 2/n, there are two different regimes. For $\sigma > sigma_c$ the lumpy pattern emerges directly from the dominant eigenvector of the competition matrix because its corresponding eigenvalue becomes negative. For $\sigma </- sigma_c$ the lumpy pattern disappears. Furthermore, this clumping transition exhibits critical slowing down as $\sigma$ is approached from above. We also find that the number of lumps of species vs. $\sigma$ displays a stair-step structure. The positions of these steps are distributed according to a power-law. It is thus straightforward to predict the number of groups that can be packed along a niche axis and it coincides with field measurements for a wide range of the model parameters.Comment: 16 pages, 7 figures; http://iopscience.iop.org/1742-5468/2010/05/P0500

The impact of loco-regional recurrences on metastatic progression in early-stage breast cancer: a multistate model

To study whether the effects of prognostic factors associated with the occurrence of distant metastases (DM) at primary diagnosis change after the incidence of loco-regional recurrences (LRR) among women treated for invasive stage I or II breast cancer. The study population consisted of 3,601 women, enrolled in EORTC trials 10801, 10854, or 10902 treated for early-stage breast cancer. Data were analysed in a multivariate, multistate model by using multivariate Cox regression models, including a state-dependent covariate. The presence of a LRR in itself is a significant prognostic risk factor (HR: 3.64; 95%-CI: 2.02-6.5) for the occurrence of DM. Main prognostic risk factors for a DM are young age at diagnosis (</=40: HR: 1.79; 95%-CI: 1.28-2.51), larger tumour size (HR: 1.58; 95%-CI: 1.35-1.84) and node positivity (HR: 2.00; 95%-CI: 1.74-2.30). Adjuvant chemotherapy is protective for a DM (HR: 0.66; 95%-CI: 0.55-0.80). After the occurrence of a LRR the latter protective effect has disappeared (P = 0.009). The presence of LRR in itself is a significant risk factor for DM. For patients who are at risk of developing LRR, effective local control should be the main target of therapy

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio

Intraepidermal nerve fiber density and its application in sarcoidosis

Background: Intraepidermal nerve fiber density (IENFD) is considered a good diagnostic tool for small fiber neuropathy (SFN). Objectives: To assess stratified normative values for IENFD and determine the reliability and validity of IENFD in sarcoidosis. Methods: IENFD was assessed in 188 healthy volunteers and 72 patients with sarcoidosis (n = 58 with SFN symptoms, n = 14 without SFN symptoms). Healthy controls were stratified (for age and sex), resulting image groups (20-29, 30-39, ... up to >= 70 years) containing at least 15 men and 15 women. A skin biopsy was taken in each participant 10 cm above the lateral malleolus and analyzed in accordance with the international guidelines using bright-field microscopy. Interobserver/intraobserver reliability of IENFD was examined. In the patients, a symptoms inventory questionnaire (SIQ; assessing SFN symptoms) and the Vickrey Peripheral Neuropathy Quality-of-Life Instrument-97 (PNQoL-97) were assessed to examine the discriminative ability of normative IENFD values. Results: There was a significant age-dependent decrease of IENFD values in healthy controls, with lower densities in men compared with women. Good interobserver/intraobserver reliability scores were obtained (kappa values >= 0.90). A total of 21 patients with sarcoidosis had a reduced IENFD score (<5th percentile; 19 [32.8%] in patients with SFN symptoms, 2 [14.3%] in patients without SFN symptoms). The validity of the normative IENFD values was demonstrated by distinguishing between the SIQ scores and various PNQoL-97 values for the different patient groups. Conclusion: This study provides clinically applicable distal intraepidermal nerve fiber density normative values, showing age-and sex-related differences. Neurology (R) 2009; 73: 1142-114

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Positive Feedbacks in Seagrass Ecosystems – Evidence from Large-Scale Empirical Data

Positive feedbacks cause a nonlinear response of ecosystems to environmental change and may even cause bistability. Even though the importance of feedback mechanisms has been demonstrated for many types of ecosystems, their identification and quantification is still difficult. Here, we investigated whether positive feedbacks between seagrasses and light conditions are likely in seagrass ecosystems dominated by the temperate seagrass Zostera marina. We applied a combination of multiple linear regression and structural equation modeling (SEM) on a dataset containing 83 sites scattered across Western Europe. Results confirmed that a positive feedback between sediment conditions, light conditions and seagrass density is likely to exist in seagrass ecosystems. This feedback indicated that seagrasses are able to trap and stabilize suspended sediments, which in turn improves water clarity and seagrass growth conditions. Furthermore, our analyses demonstrated that effects of eutrophication on light conditions, as indicated by surface water total nitrogen, were on average at least as important as sediment conditions. This suggests that in general, eutrophication might be the most important factor controlling seagrasses in sheltered estuaries, while the seagrass-sediment-light feedback is a dominant mechanism in more exposed areas. Our study demonstrates the potentials of SEM to identify and quantify positive feedbacks mechanisms for ecosystems and other complex systems