Sequential and continuum bifurcations in degenerate elliptic equations

We examine the bifurcations to positive and sign-changing solutions of degenerate elliptic equations. In the problems we study, which do not represent Fredholm operators, we show that there is a critical parameter value at which an infinity of bifurcations occur from the trivial solution. Moreover, a bifurcation occurs at each point in some unbounded interval in parameter space. We apply our results to non-monotone eigenvalue problems, degenerate semi-linear elliptic equations, boundary value differential-algebraic equations and fully non-linear elliptic equations

Biophysical mechanisms that maintain biodiversity through trade-offs

Published onlineJournal ArticleTrade-offs are thought to arise from inevitable, biophysical limitations that prevent organisms from optimizing multiple traits simultaneously. A leading explanation for biodiversity maintenance is a theory that if the shape, or geometry, of a trade-off is right, then multiple species can coexist. Testing this theory, however, is difficult as trait data is usually too noisy to discern shape, or trade-offs necessary for the theory are not observed in vivo. To address this, we infer geometry directly from the biophysical mechanisms that cause trade-offs, deriving the geometry of two by studying nutrient uptake and metabolic properties common to all living cells. To test for their presence in vivo we isolated Escherichia coli mutants that vary in a nutrient transporter, LamB, and found evidence for both trade-offs. Consistent with data, population genetics models incorporating the trade-offs successfully predict the co-maintenance of three distinct genetic lineages, demonstrating that trade-off geometry can be deduced from fundamental principles of living cells and used to predict stable genetic polymorphisms

The Human Dimensions of Recreational Anglers Targeting Freshwater Species in Coastal Ecosystems, with Implications for Management

Little is known about whether brackish coastal ecosystems attract specific angler types that are characterized by site‐specific preferences and behaviors while targeting freshwater fishes living in a low‐salinity environment. Using the lagoon (“Bodden”) fisheries in northeastern Germany, we compared the human dimensions among anglers fishing in Bodden sites, anglers fishing primarily in freshwater sites, and other, less‐setting‐specialized anglers that use both marine and freshwater fisheries. Data were generated from a 1‐year telephone–mail–diary study involving over 1,000 study participants. The general characteristics, demographics, specialization level, motives, catch orientation, and catch‐and‐release behaviors of the three angler groups were rather similar. However, when targeting specific freshwater fish (i.e., Eurasian Perch Perca fluviatilis, Northern Pike Esox lucius, and Zander [also known as Pikeperch] Sander lucioperca), the motives of anglers choosing the Bodden versus freshwater sites differed. Specifically, Bodden anglers targeting freshwater species in brackish waters were more catch oriented, trophy fish oriented, and challenge seeking compared to freshwater anglers. Bodden anglers were also more likely to fish with friends rather than alone compared to the other angler groups, and they were more likely to use motorboats and to take guides compared to freshwater anglers. Correspondingly, a revealed preference choice model showed that anglers expecting high catch outcomes and social experiences with friends and boat fishing were more likely to select the Bodden waters relative to freshwater sites. Additionally, anglers with a stronger orientation toward the noncatch, experience‐based aspects of fishing were more likely to fish in the Bodden and coastal sites compared to freshwater, suggesting that coastal sites satisfy both catch‐ and non‐catch‐related expectations. We suggest that given their specific preferences and characteristics, Bodden anglers will be particularly sensitive to constraints imposed on using motorboats and to declines in catch rates and trophy sizes in the catch, specifically for Northern Pike.EMFF and State of Mecklenburg‐Vorpommern http://dx.doi.org/10.13039/100014510Peer Reviewe

Metabolic trade-offs and the maintenance of the fittest and the flattest.

This is the post print version of the article, deposited in accordance with SHERPA RoMEO guidelines. The final definitive version is available from: http://www.nature.com/nature/journal/v472/n7343/full/nature09905.htmlHow is diversity maintained? Environmental heterogeneity is considered to be important, yet diversity in seemingly homogeneous environments is nonetheless observed. This, it is assumed, must either be owing to weak selection, mutational input or a fitness advantage to genotypes when rare. Here we demonstrate the possibility of a new general mechanism of stable diversity maintenance, one that stems from metabolic and physiological trade-offs. The model requires that such trade-offs translate into a fitness landscape in which the most fit has unfit near-mutational neighbours, and a lower fitness peak also exists that is more mutationally robust. The 'survival of the fittest' applies at low mutation rates, giving way to 'survival of the flattest' at high mutation rates. However, as a consequence of quasispecies-level negative frequency-dependent selection and differences in mutational robustness we observe a transition zone in which both fittest and flattest coexist. Although diversity maintenance is possible for simple organisms in simple environments, the more trade-offs there are, the wider the maintenance zone becomes. The principle may be applied to lineages within a species or species within a community, potentially explaining why competitive exclusion need not be observed in homogeneous environments. This principle predicts the enigmatic richness of metabolic strategies in clonal bacteria and questions the safety of lethal mutagenesis as an antimicrobial treatment

When the most potent combination of antibiotics selects for the greatest bacterial load: the Smile-Frown transition

Final published PDF version of article deposited in accordance with SHERPA RoMEO guidelinesConventional wisdom holds that the best way to treat infection with antibiotics is to ‘hit early and hit hard’. A favoured strategy is to deploy two antibiotics that produce a stronger effect in combination than if either drug were used alone. But are such synergistic combinations necessarily optimal? We combine mathematical modelling, evolution experiments, whole genome sequencing and genetic manipulation of a resistance mechanism to demonstrate that deploying synergistic antibiotics can, in practice, be the worst strategy if bacterial clearance is not achieved after the first treatment phase. As treatment proceeds, it is only to be expected that the strength of antibiotic synergy will diminish as the frequency of drug-resistant bacteria increases. Indeed, antibiotic efficacy decays exponentially in our five-day evolution experiments. However, as the theory of competitive release predicts, drug-resistant bacteria replicate fastest when their drug-susceptible competitors are eliminated by overly-aggressive treatment. Here, synergy exerts such strong selection for resistance that an antagonism consistently emerges by day 1 and the initially most aggressive treatment produces the greatest bacterial load, a fortiori greater than if just one drug were given. Whole genome sequencing reveals that such rapid evolution is the result of the amplification of a genomic region containing four drug-resistance mechanisms, including the acrAB efflux operon. When this operon is deleted in genetically manipulated mutants and the evolution experiment repeated, antagonism fails to emerge in five days and antibiotic synergy is maintained for longer. We therefore conclude that unless super-inhibitory doses are achieved and maintained until the pathogen is successfully cleared, synergistic antibiotics can have the opposite effect to that intended by helping to increase pathogen load where, and when, the drugs are found at sub-inhibitory concentrations

Feasibility randomised controlled trial of online group Acceptance and Commitment Therapy for Functional Cognitive Disorder (ACT4FCD)

INTRODUCTION: Functional cognitive disorder (FCD) is seen increasingly in clinics commissioned to assess cognitive disorders. Patients report frequent cognitive, especially memory, failures. The diagnosis can be made clinically, and unnecessary investigations avoided. While there is some evidence that psychological treatments can be helpful, they are not routinely available. Therefore, we have developed a brief psychological intervention using the principles of acceptance and commitment therapy (ACT) that can be delivered in groups and online. We are conducting a feasibility study to assess whether the intervention can be delivered within a randomised controlled trial. We aim to study the feasibility of recruitment, willingness to be randomised to intervention or control condition, adherence to the intervention, completion of outcome measures and acceptability of treatment. METHODS AND ANALYSIS: We aim to recruit 48 participants randomised 50:50 to either the ACT intervention and treatment as usual (TAU), or TAU alone. ACT will be provided to participants in the treatment arm following completion of baseline outcome measures. Completion of these outcome measures will be repeated at 8, 16 and 26 weeks. The measures will assess several domains including psychological flexibility, subjective cognitive symptoms, mood and anxiety, health-related quality of life and functioning, healthcare utilisation, and satisfaction with care and participant-rated improvement. Fifteen participants will be selected for in-depth qualitative interviews about their experiences of living with FCD and of the ACT intervention. ETHICS AND DISSEMINATION: The study received a favourable opinion from the South East Scotland Research Ethics Committee 02 on 30 September 2022 (REC reference: 22/SS/0059). HRA approval was received on 1 November 2022 (IRAS 313730). The results will be published in full in an open-access journal. TRIAL REGISTRATION NUMBER: ISRCTN12939037

Modelling Cognitive Decline in the Hypertension in the Very Elderly Trial [HYVET] and Proposed Risk Tables for Population Use

Although, on average, cognition declines with age, cognition in older adults is a dynamic process. Hypertension is associated with greater decline in cognition with age, but whether treatment of hypertension affects this is uncertain. Here, we modelled dynamics of cognition in relation to the treatment of hypertension, to see if treatment effects might better be discerned by a model that included baseline measures of cognition and consequent mortalityThis is a secondary analysis of the Hypertension in the Very Elderly Trial (HYVET), a double blind, placebo controlled trial of indapamide, with or without perindopril, in people aged 80+ years at enrollment. Cognitive states were defined in relation to errors on the Mini-Mental State Examination, with more errors signifying worse cognition. Change in cognitive state was evaluated using a dynamic model of cognitive transition. In the model, the probabilities of transitions between cognitive states is represented by a Poisson distribution, with the Poisson mean dependent on the baseline cognitive state. The dynamic model of cognitive transition was good (R(2) = 0.74) both for those on placebo and (0.86) for those on active treatment. The probability of maintaining cognitive function, based on baseline function, was slightly higher in the actively treated group (e.g., for those with the fewest baseline errors, the chance of staying in that state was 63% for those on treatment, compared with 60% for those on placebo). Outcomes at two and four years could be predicted based on the initial state and treatment.A dynamic model of cognition that allows all outcomes (cognitive worsening, stability improvement or death) to be categorized simultaneously detected small but consistent differences between treatment and control groups (in favour of treatment) amongst very elderly people treated for hypertension. The model showed good fit, and suggests that most change in cognition in very elderly people is small, and depends on their baseline state and on treatment. Additional work is needed to understand whether this modelling approach is well suited to the valuation of small effects, especially in the face of mortality differences between treatment groups.ClinicalTrials.gov NCT0012281

Understanding the limits to generalizability of experimental evolutionary models.

Post print version of article deposited in accordance with SHERPA RoMEO guidelines. The final definitive version is available online at: http://www.nature.com/nature/journal/v455/n7210/abs/nature07152.htmlGiven the difficulty of testing evolutionary and ecological theory in situ, in vitro model systems are attractive alternatives; however, can we appraise whether an experimental result is particular to the in vitro model, and, if so, characterize the systems likely to behave differently and understand why? Here we examine these issues using the relationship between phenotypic diversity and resource input in the T7-Escherichia coli co-evolving system as a case history. We establish a mathematical model of this interaction, framed as one instance of a super-class of host-parasite co-evolutionary models, and show that it captures experimental results. By tuning this model, we then ask how diversity as a function of resource input could behave for alternative co-evolving partners (for example, E. coli with lambda bacteriophages). In contrast to populations lacking bacteriophages, variation in diversity with differences in resources is always found for co-evolving populations, supporting the geographic mosaic theory of co-evolution. The form of this variation is not, however, universal. Details of infectivity are pivotal: in T7-E. coli with a modified gene-for-gene interaction, diversity is low at high resource input, whereas, for matching-allele interactions, maximal diversity is found at high resource input. A combination of in vitro systems and appropriately configured mathematical models is an effective means to isolate results particular to the in vitro system, to characterize systems likely to behave differently and to understand the biology underpinning those alternatives