Integral projection models for species with complex demography

Matrix projection models occupy a central role in population and conservation biology. Matrix models divide a population into discrete classes, even if the structuring trait exhibits continuous variation ( e. g., body size). The integral projection model ( IPM) avoids discrete classes and potential artifacts from arbitrary class divisions, facilitates parsimonious modeling based on smooth relationships between individual state and demographic performance, and can be implemented with standard matrix software. Here, we extend the IPM to species with complex demographic attributes, including dormant and active life stages, cross- classification by several attributes ( e. g., size, age, and condition), and changes between discrete and continuous structure over the life cycle. We present a general model encompassing these cases, numerical methods, and theoretical results, including stable population growth and sensitivity/ elasticity analysis for density- independent models, local stability analysis in density- dependent models, and optimal/ evolutionarily stable strategy life- history analysis. Our presentation centers on an IPM for the thistle Onopordum illyricum based on a 6- year field study. Flowering and death probabilities are size and age dependent, and individuals also vary in a latent attribute affecting survival, but a predictively accurate IPM is completely parameterized by fitting a few regression equations. The online edition of the American Naturalist includes a zip archive of R scripts illustrating our suggested methods

Evolutionary tradeoff and equilibrium in an aquatic predator-prey system

Due to the conventional distinction between ecological (rapid) and evolutionary (slow)timescales, ecological and population models to date have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has been recently established and may be critical to understanding how populations adapt to changing environments. In this paper we examine the relationship between ecological and evolutionary dynamics, focusing on a well-studied experimental aquatic predator-prey system (Fussmann et al. 2000; Shertzer et al. 2002; Yoshida et al. 2003). Major properties of predator-prey cycles in this system are determined by ongoing evolutionary dynamics in the prey population. Under some conditions, however, the populations tend to apparently stable steady-state densities. These are the subject of the present paper. We examine a previously developed model for the system, to determine how evolution shapes properties of the equilibria, in particular the number and identity of coexisting prey genotypes. We then apply these results to explore how evolutionary dynamics can shape the responses of the system to "management": externally imposed alterations in conditions. Specifically, we compare the behavior of the system including evolutionary dynamics, with predictions that would be made if the potential for rapid evolutionary change is negelected. Finally, we posit some simple experiments to verify our prediction that evolution can have significant qualitative effects on observed population-level responses to changing conditions.Comment: 30 pages including 8 figures, 2 tables and an Appendix; to appear in Bulletin of Mathematical Biology. Revised three Figures, added references and expanded Section

Charge and spin polarized currents in mesoscopic rings with Rashba spin-orbit interactions coupled to an electron reservoir

The electronic states of a mesoscopic ring are assessed in the presence of Rashba Spin Orbit coupling and a $U(1)$ gauge field. Spin symmetric coupling to an ideal lead is implemented following B\"uttiker's voltage probe. The exact density of states is derived using the reservoir uncoupled eigenstates as basis functions mixed by the reservoir coupling. The decay time of uncoupled electron eigenstates is derived by fitting the broadening profiles. The spin and charge persistent currents are computed in the presence of the SO interaction and the reservoir coupling for two distinct scenarios of the electron filling fraction. The degradation of the persistent currents depends uniformly on the reservoir coupling but nonuniformly in temperature, the latter due to the fact that currents emerge from different depths of the Fermi sea, and thus for some regimes of flux, they are provided with a protective gap. Such flux regimes can be tailored by the SO coupling for both charge and spin currents

Evolution of complex flowering strategies: an age- and size-structured integral projection model

We explore the evolution of delayed age- and size-dependent flowering in the monocarpic perennial Carlina vulgaris, by extending the recently developed integral projection approach to include demographic rates that depend on size and age. The parameterized model has excellent descriptive properties both in terms of the population size and in terms of the distributions of sizes within each age class. In Carlina the probability of flowering depends on both plant size and age. We use the parameterized model to predict this relationship, using the evolutionarily stable strategy (ESS) approach. Despite accurately predicting the mean size of flowering individuals, the model predicts a step-function relationship between the probability of flowering and plant size, which has no age component. When the variance of the flowering-threshold distribution is constrained to the observed value, the ESS flowering function contains an age component, but underpredicts the mean flowering size. An analytical approximation is used to explore the effect of variation in the flowering strategy on the ESS predictions. Elasticity analysis is used to partition the agespecific contributions to the finite rate of increase (u) of the survival-growth and fecundity components of the model. We calculate the adaptive landscape that defines the ESS and generate a fitness landscape for invading phenotypes in the presence of the observed flowering strategy. The implications of these results for the patterns of genetic diversity in the flowering strategy and for testing evolutionary models are discussed. Results proving the existence of a dominant eigenvalue and its associated eigenvectors in general size- and age-dependent integral projection models are presented

Evolution of size-dependent flowering in a variable environment: construction and analysis of a stochastic integral projection model

Understanding why individuals delay reproduction is a classic problem in evolutionary biology. In plants, the study of reproductive delays is complicated because growth and survival can be size and age dependent, individuals of the same size can grow by different amounts and there is temporal variation in the environment. We extend the recently developed integral projection approach to include size- and age-dependent demography and temporal variation. The technique is then applied to a long-term individually structured dataset for Carlina vulgaris, a monocarpic thistle. The parameterized model has excellent descriptive properties in terms of both the population size and the distributions of sizes within each age class. In Carlina, the probability of flowering depends on both plant size and age. We use the parameterized model to predict this relationship, using the evolutionarily stable strategy approach. Considering each year separately, we show that both the direction and the magnitude of selection on the flowering strategy vary from year to year. Provided the flowering strategy is constrained, so it cannot be a step function, the model accurately predicts the average size at flowering. Elasticity analysis is used to partition the size- and age-specific contributions to the stochastic growth rate, λs. We use λs to construct fitness landscapes and show how different forms of stochasticity influence its topography. We prove the existence of a unique stochastic growth rate, λs, which is independent of the initial population vector, and show that Tuljapurkar's perturbation analysis for log(λs) can be used to calculate elasticities

Commentary: How Long Do We Need to Follow-Up Our Hernia Patients to Find the Real Recurrence Rate?

A commentary on How long do we need to follow-up our hernia patients to find the real recurrence rate? by Köckerling F, Koch A, Lorenz R, Schug-Pass C, Stechemesser B and Reinpold W. Front Surg (2015) 2 :24 doi: 10.3389/fsurg.2015.00024 It was a pleasure to go through the manuscript by Ferdinand Köckerling focusing on hernia recurrence in Frontiers in Surgery (1). We would like to applaud the authors on two fronts. We had very peripheral awareness of the Herniamed registry, but having read this paper, we believe that the registry is a brilliant initiative by the German surgical society. Such data sharing will most definitely help to evolve and standardize practices in hernia surgery across the board. Second, the results and recommendations of this study are novel in nature. The recurrence rates followed over such a long interval have important implications for managing follow-up care for hernia patients

New and Improved Diagnostics for Detection of Drug-Resistant Pulmonary Tuberculosis.

PURPOSE OF REVIEW: Tuberculosis (TB) remains a global emergency and continues to kill 1.7 million people globally each year. Drug-resistant TB is now well established throughout the world and most TB patients are not being screened for drug resistance due to lack of laboratory resources and rapid accurate point-of-care tests. Accurate and rapid diagnosis of TB and drug-resistant TB is of paramount importance in establishing appropriate clinical management and infection control measures. During the past decade, there have been significant advances in diagnostic technologies for TB and drug-resistant TB. The purpose of this article is to review the current data, recommendations and evidence base for these tests. RECENT FINDINGS: Second-line drug susceptibility testing (DST) is complex and expensive. Automated liquid culture systems and molecular line probe assays are recommended by the WHO as the current 'gold standard' for first-line DST. Liquid culture DST for aminoglycosides, polypeptides and fluoroquinolones has been shown to have relatively good reliability and reproducibility for diagnosis of extensively drug-resistant TB; however, DST for other second-line drugs (ethionamide, prothionamide, cycloserine, terizidone, para-aminosalicylic acid, clofazimine, amoxicillin-clavulanate, clarithromycin, linezolid) is not recommended. Automated liquid culture systems are currently recommended by the WHO as the 'gold standard' for second-line DST. SUMMARY: In this review, we describe the phenotypic and genotypic methods currently available for the diagnosis of TB and drug-resistant forms of Mycobacterium tuberculosis and discuss future prospects for TB diagnostics. Current technologies for the detection of drug resistant M. tuberculosis vary greatly in terms of turnaround time, cost and complexity. Ultimately, the 'holy grail' diagnostic for TB must fulfil all technical specifications for a good point-of-care test, screen for drug resistance concurrently and be adaptable to the various health system levels and to countries with diverse economic status and TB burden. © 2011 Lippincott Williams & Wilkins, Inc