José D. Flores

Topological plasticity increases robustness of mutualistic networks

1. Earlier studies used static models to evaluate the responses of mutualistic networks to external perturbations. Two classes of dynamics can be distinguished in ecological networks; population dynamics, represented mainly by changes in species abundances, and topological dynamics, represented by changes in the architecture of the web. 2. In this study, we model the temporal evolution of three empirical plant-pollination networks incorporating both population and topological dynamics. We test the hypothesis that topological plasticity, realized through the ability of animals to rewire their connections after depletion of host abundances, enhances tolerance of mutualistic networks to species loss. We also compared the performance of various rewiring rules in affecting robustness. 3. The results show that topological plasticity markedly increased the robustness of mutualistic networks. Our analyses also revealed that network robustness reached maximum levels when animals with less host plant availability were more likely to rewire. Also, preferential attachment to richer host plants, that is, to plants exhibiting higher abundance and few exploiters, enhances robustness more than other rewiring alternatives. 4. Our results highlight the potential role of topological plasticity in the robustness of mutualistic networks to species extinctions and suggest some plausible mechanisms by which the decisions of foragers may shape the collective dynamics of plant-pollinator systems.

Consequences of double Allee effect on the number of limit cycles in a predator-prey model

The main goal of this work is to show a comparative analysis of simple continuous time predator-prey models considering the Allee effect affecting the prey population, also known as depensation in fisheries sciences. This phenomenon may be expressed by different mathematical forms, yielding a distinct number of limit cycles surrounding a positive equilibrium point, when two of these different formalizations are considered in the same system. It is known that the Volterra predation model, using the most usual form to express the Allee effect, has a unique limit cycle. In this work, considering a more complex mathematical expression, the existence of two limit cycles is proved, by means of the Lyapunov quantities. We argue that the second equation explains the existence of two Allee effects affecting the same population, which could justify the difference observed between the models. These results imply that the election of mathematical formulation can have consequences on the fit of the observed data, thus leading to mistakes for ecologists. We conclude that the oscillatory behaviors and overall dynamics depend strongly on the algebraic expression of the Allee effect, making difficult the proposition of general results. Nevertheless, the techniques reviewed in this paper emerge as key tools to analyze the existence of limit cycles in the presence of multiple Allee effects.

Global mortality impact of the 1957-1959 influenza pandemic

Abstract Background. Quantitative estimates of the global burden of the 1957 influenza pandemic are lacking. Here we fill this gap by modeling historical mortality statistics. Methods. We used annual rates of age- and cause-specific deaths to estimate pandemic-related mortality in excess of background levels in 39 countries in Europe, the Asia-Pacific region, and the Americas. We modeled the relationship between excess mortality and development indicators to extrapolate the global burden of the pandemic. Results. The pandemic-associated excess respiratory mortality rate was 1.9/10 000 population (95% confidence interval [CI], 1.2–2.6 cases/10 000 population) on average during 1957–1959. Excess mortality rates varied 70-fold across countries; Europe and Latin America experienced the lowest and highest rates, respectively. Excess mortality was delayed by 1–2 years in 18 countries (46%). Increases in the mortality rate relative to baseline were greatest in school-aged children and young adults, with no evidence that elderly population was spared from excess mortality. Development indicators were moderate predictors of excess mortality, explaining 35%–77% of the variance. Overall, we attribute 1.1 million excess deaths (95% CI, .7 million–1.5 million excess deaths) globally to the 1957–1959 pandemic. Conclusions. The global mortality rate of the 1957–1959 influenza pandemic was moderate relative to that of the 1918 pandemic but was approximately 10-fold greater than that of the 2009 pandemic. The impact of the pandemic on mortality was delayed in several countries, pointing to a window of opportunity for vaccination in a future pandemic.

Vitamin D in multiple sclerosis patients: Not the same risk for everybody.

126 http://msj.sagepub.com 2 Department of Biochemistry, Medical University of Warsaw, Poland 3 Neurodegenerative Diseases Research Group, Medical University of Warsaw, Warsaw, Poland 4 Department of Neurology, Medical University of Warsaw, Poland Correspondence to: Małgorzata Zajda Department of Experimental and Clinical Pharmacology Centre for Preclinical Research and Technology, Medical University of Warsaw, Banacha 1B, 02-091 Warszawa, Poland. malgorzata.e.zajda@gmail.com Visit SAGE journals online http://msj.sagepub.com

Uniqueness of limit cycles and multiple attractors in a Gause-type predator-prey model with nonmonotonic functional response and Allee effect on prey.

The main purpose of this work is to analyze a Gause type predator-prey model in which two ecological phenomena are considered: the Allee effect affecting the prey growth function and the formation of group defence by prey in order to avoid the predation. We prove the existence of a separatrix curves in the phase plane, determined by the stable manifold of the equilibrium point associated to the Allee effect, implying that the solutions are highly sensitive to the initial conditions. Trajectories starting at one side of this separatrix curve have the equilibrium point (0,0) as their ω-limit, while trajectories starting at the other side will approach to one of the following three attractors: a stable limit cycle, a stable coexistence point or the stable equilibrium point (K,0) in which the predators disappear and prey attains their carrying capacity. We obtain conditions on the parameter values for the existence of one or two positive hyperbolic equilibrium points and the existence of a limit cycle surrounding one of them. Both ecological processes under study, namely the nonmonotonic functional response and the Allee effect on prey, exert a strong influence on the system dynamics, resulting in multiple domains of attraction. Using Liapunov quantities we demonstrate the uniqueness of limit cycle, which constitutes one of the main differences with the model where the Allee effect is not considered. Computer simulations are also given in support of the conclusions.

The conjugate gradient method for solving fredholm integral equations of the second kind

The conjugate gradient method (CG method) is applied to linear integral equations of the second kind. Based on a result from Winther [23] rate of convergence is given for several integral operators considering the smoothness of the kernel function. Numerical examples are included.

ALLEE EFFECT, EMIGRATION AND IMMIGRATION IN A CLASS OF PREDATOR-PREY MODELS

In this work we analyze a predator-prey model proposed by A. Kent et al. in Ecol. Model.162, 233 (2003), in which two aspect of the model are considered: an effect of emigration or immigration on prey population to constant rate and a prey threshold level for predators. We prove that the system when the immigration effect is introduced in the model has a dynamics that is similar to the Rosenzweig-MacArthur model. Also, when emigration is considered in the model, we show that the behavior of the system is strongly dependent on this phenomenon, this due to the fact that trajectories are highly sensitive to the initial conditions, in similar way as when Allee effect is assumed on prey. Furthermore, we determine constraints in the parameters space for which two stable attractor exist, indicating that the extinction of both population is possible in addition with the coexistence of oscillating of populations size in a unique stable limit cycle. We also show that the consideration of a threshold level of prey population for the predator is not essential in the dynamics of the model.

Severe Mortality Impact of the 1957 Influenza Pandemic in Chile.

Epidemiological studies of the 1957 influenza pandemic are scarce, particularly from lower‐income settings.

Presence of the HLADR13 allele among Mexican Mestizos suggests a protective factor against relapsing-remitting multiple sclerosis (RRMS)

BACKGROUND AND OBJECTIVE Multiple sclerosis (MS) is a chronic demyelinating disease that affects the central nervous system. Researchers have looked for an association between relapsing-remitting MS (RRMS) and human leukocyte antigen (HLA) as risk or protective factor associated to ethnicity, which may add a partial explanation to disease heterogeneity and geographical variations. We described the frequency of the HLA-DR alleles in Mexican Mestizo (RRMS) patients. PATIENTS AND METHODS We included 143 RRMS patients and 377 healthy controls, both Mexican Mestizos. Previous signing informed consent, we record demographic and clinical characteristics of the participants. Genetic profile was made, and HLA frequencies in both groups were compared. RESULTS RRMS patients were 39.8% male and 60.2% female, mean age was 35 years. While, controls were 48%male and 52% women, mean age was 38 years. The most frequent allele found in subjects with RRMS was DR 15 (p=0.006, OR=2.2, 95% CI: 1.3-3.6). DR 13 allele was more frequent among healthy subjects than RRMS patients (p=0.050) with a protective OR 2.6, (95% CI: 1.3-5.2, p=0.050). CONCLUSION In our study we found HLA DR 13 was more frequent in healthy controls than in RRMS patients, suggesting a protective factor among Mexican Mestizo population.

Herpes Zoster and Multiple Sclerosis

Multiple sclerosis (MS), a demyelinating disease of the central nervous system, has been considered multifactorial, and viruses may have a role in disease pathogenesis. Evidence suggests that certain viruses may trigger autoimmune neurological processes that lead to MS in genetically susceptible individuals [1, 2]. In this issue of the Journal, Kang et al analyze a database of 349,477 patients who had herpes zoster (experimental group) as a risk factor for MS (study outcome variable) in a region of the world historically considered low risk for MS. The authors compare their data with a randomly selected control group, more than 3 times as large as the initial sample (n 5 1,262,200), of participants who did not have herpes zoster. Their results show that the herpes zoster group had a 3.96 times greater risk of developing MS than did the control group (95% confidence interval [CI], 2.22–7.07, P % .001). This Kang et al study provides clear epidemiological observations suggesting a role for herpes zoster in the development of MS [3]. Previous studies noted that certain herpes viruses may trigger proinflammatory and autoimmune cascades through particles such as the toll-like receptor 4 (TLR-4) [3, 4], and that infectious environmental factors associated with MS may also belong to the herpesviridae family [4, 5]. This study highlights the time elapsed from the event of shingles until the occurrence of MS (approximately 100 d). In addition, evidence suggests that up to 30% of relapses among MS patients are associated with an infectious process [6, 7]. A possible explanation is the reactivation of latent herpes viruses by other infectious agents, and crossrecognition of common viral antigens with antigens found in the myelin sheath, which thereby induces molecular mimicry or superantigens [8–10]. The time lag for the occurrence of MS could be explained by a series of processes required by the immune systems of genetically susceptible individuals to reach a ‘‘threshold’’ and start the disease process. The threshold may also explain, in part, the observation that some patients have higher recurrence rates of MS around certain months of the year [11]. Some viruses of the herpesviridae family cause B cells to express alpha and beta crystal, a small stress protein that is normally absent from lymphoid tissues and has been considered an immunodominant antigen in the central nervous systems of MS patients [12]. Other studies have suggested a role of varicella zoster virus in the genesis of relapse and progression of some patients with chronic-progressive forms of MS [13, 14]. The evidence provided in this study by Kang et al allows us to better understand the role of these viral factors as an MS risk among certain genetically susceptible individuals. These epidemiological findings should be corroborated in other parts of the world to further clarify the role of varicella zoster virus and other herpes viruses in the pathogenesis of multiple sclerosis.