Generalized Lotka-Volterra Equations with Random, Nonreciprocal Interactions: The Typical Number of Equilibria.

We compute the typical number of equilibria of the generalized Lotka-Volterra equations describing species-rich ecosystems with random, nonreciprocal interactions using the replicated Kac-Rice method. We characterize the multiple-equilibria phase by determining the average abundance and similarity between equilibria as a function of their diversity (i.e., of the number of coexisting species) and of the variability of the interactions. We show that linearly unstable equilibria are dominant, and that the typical number of equilibria differs with respect to the average number.

Properties of Equilibria and Glassy Phases of the Random Lotka-Volterra Model with Demographic Noise.

We study a reference model in theoretical ecology, the disordered Lotka-Volterra model for ecological communities, in the presence of finite demographic noise. Our theoretical analysis, valid for symmetric interactions, shows that for sufficiently heterogeneous interactions and low demographic noise the system displays a multiple equilibria phase, which we fully characterize. In particular, we show that in this phase the number of locally stable equilibria is exponential in the number of species. Upon further decreasing the demographic noise, we unveil the presence of a second transition like the so-called "Gardner" transition to a marginally stable phase similar to that observed in the jamming of amorphous materials. We confirm and complement our analytical results by numerical simulations. Furthermore, we extend their relevance by showing that they hold for other interacting random dynamical systems such as the random replicant model. Finally, we discuss their extension to the case of asymmetric couplings.

Complex interactions can create persistent fluctuations in high-diversity ecosystems.

When can ecological interactions drive an entire ecosystem into a persistent non-equilibrium state, where many species populations fluctuate without going to extinction? We show that high-diversity spatially heterogeneous systems can exhibit chaotic dynamics which persist for extremely long times. We develop a theoretical framework, based on dynamical mean-field theory, to quantify the conditions under which these fluctuating states exist, and predict their properties. We uncover parallels with the persistence of externally-perturbed ecosystems, such as the role of perturbation strength, synchrony and correlation time. But uniquely to endogenous fluctuations, these properties arise from the species dynamics themselves, creating feedback loops between perturbation and response. A key result is that fluctuation amplitude and species diversity are tightly linked: in particular, fluctuations enable dramatically more species to coexist than at equilibrium in the very same system. Our findings highlight crucial differences between well-mixed and spatially-extended systems, with implications for experiments and their ability to reproduce natural dynamics. They shed light on the maintenance of biodiversity, and the strength and synchrony of fluctuations observed in natural systems.

Impact of intravenous insulin on 18F-FDG PET in diabetic cancer patients.

UNLABELLED: The aims of this study were to evaluate the effectiveness of a standardized insulin protocol in reducing glycemia, review (18)F-FDG biodistribution with such a protocol, and assess its clinical impact. METHODS: Sixty-three patients with glycemia greater than 10 mmol/L received insulin doses intravenously according to a standardized protocol. One hundred six consecutive euglycemic patients (<6.2 mmol/L) served as controls. (18)F-FDG biodistribution was evaluated by 2 experienced PET readers on a 5-point visual scale based on muscular uptake. The 63 patients who received insulin were divided into insulin subgroup A, with adequate biodistribution (score 0, 1, or 2) and insulin subgroup B, with altered biodistribution (score 3 or 4). 18F-FDG biodistribution was also evaluated semiquantitatively by standardized uptake value (SUV) measurements over the liver, gluteal muscles, and myocardium. Clinical impact (complications and diagnostic accuracy) was assessed by follow-up. RESULTS: Glycemia decreased from 13+/-2 to 7+/-2 mmol/L after insulin injection. Images showed significantly more muscular uptake in patients who received insulin than in the control group (scores 1.6+/-1.5 vs. 0.4+/-0.6, P<0.05). Twenty-five percent of insulin patients studied had altered biodistribution (insulin subgroup B). The two most important factors increasing muscular uptake were the time interval between insulin and 18F-FDG injection (mean in insulin subgroup A, 80.2+/-17 min; mean in insulin subgroup B, 65.7+/-10 min; P<0.01) and the glycemia interval decrease after insulin injection (mean in insulin subgroup A, 5.3+/-2.6 mmol/L; mean in insulin subgroup B, 7.6+/-1.8 mmol/L; P<0.01). In insulin subgroup B, mean hepatic SUV was lower (1.3+/-0.4 vs. 2.1+/-0.4, P<0.01) and mean muscular SUV was higher (1.8+/-0.1 vs. 0.9+/-0.01, P<0.01). Of the 63 patients who received insulin, 6 had hypoglycemia, but only 2 were symptomatic. No patient had severe complications causing permanent disability. CONCLUSION: A standardized protocol of intravenous insulin before 18F-FDG injection in diabetic cancer patients was safe and effective in reducing glycemia. Acceptable 18F-FDG biodistribution was obtained in 75% of patients receiving insulin. In addition to visually increased muscular uptake, low hepatic 18F-FDG uptake was a good indicator of altered biodistribution.

Chilaiditi sign on FDG-PET.

A 66-year-old woman with a history of endometrial cancer underwent a F-18 fluorodeoxyglucose positron emission tomography (FDG-PET). Abnormal uptake was noted in the right lower chest. CT scan showed a loop of colon interposed between the liver and the diaphragm, an entity known as the Chilaiditi sign. This case illustrates the importance to correlate abnormal PET findings with CT images. The Chilaiditi sign should be included in the differential diagnosis of lower chest uptake on an FDG-PET study.