Disease transmission models with density-dependent demographics

The models considered for the spread of an infectious disease in a population are of SIRS or SIS type with a standard incidence expression. The varying population size is described by a modification of the logistic differential equation which includes a term for disease-related deaths. The models have density-dependent restricted growth due to a decreasing birth rate and an increasing death rate as the population size increases towards its carrying capacity. Thresholds, equilibria and stability are determined for the systems of ordinary differential equations for each model. The persistence of the infectious disease and disease-related deaths can lead to a new equilibrium population size below the carrying capacity and can even cause the population to become extinct.Research supported in part by Centers for Disease Control contract 200-87-0515     

Two SIS epidemiologic models with delays

 The SIS epidemiologic models have a delay corresponding to the infectious period, and disease-related deaths, so that the population size is variable. The population dynamics structures are either logistic or recruitment with natural deaths. Here the thresholds and equilibria are determined, and stabilities are examined. In a similar SIS model with exponential population dynamics, the delay destabilized the endemic equilibrium and led to periodic solutions. In the model with logistic dynamics, periodic solutions in the infectious fraction can occur as the population approaches extinction for a small set of parameter values. Received: 10 January 1997 / 18 November 1997     

Dynamic models of infectious diseases as regulators of population sizes

Five SIRS epidemiological models for populations of varying size are considered. The incidences of infection are given by mass action terms involving the number of infectives and either the number of susceptibles or the fraction of the population which is susceptible. When the population dynamics are immigration and deaths, thresholds are found which determine whether the disease dies out or approaches an endemic equilibrium. When the population dynamics are unbalanced births and deaths proportional to the population size, thresholds are found which determine whether the disease dies out or remains endemic and whether the population declines to zero, remains finite or grows exponentially. In these models the persistence of the disease and disease-related deaths can reduce the asymptotic population size or change the asymptotic behavior from exponential growth to exponential decay or approach to an equilibrium population size.Research supported by Centers for Disease Control contract 200-87-0515. Support services provided at the University of Iowa Center for Advanced Studies     

Population size dependent incidence in models for diseases without immunity

Epidemiological models of SIS type are analyzed to determine the thresholds, equilibria, and stability. The incidence term in these models has a contact rate which depends on the total population size. The demographic structures considered are recruitment-death, generalized logistic, decay and growth. The persistence of the disease combined with disease-related deaths and reduced reproduction of infectives can greatly affect the population dynamics. For example, it can cause the population size to decrease to zero or to a new size below its carrying capacity or it can decrease the exponential growth rate constant of the population.     

Modeling the dynamics of natural rotifer populations: Phase-parametric analysis

A model of the dynamics of natural rotifer populations is described as a discrete non-linear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of these parameters were investigated by methods of bifurcation theory. A phase-parametric portrait of the model was constructed and domains of population persistence (stable equilibrium, periodic and a-periodic oscillations of population size) as well as population extinction were identified and investigated. The criteria for population persistence and approaches to determining critical parameter values are described. The results identify parameter values that lead to population extinction under various environmental conditions. They further illustrate that the likelihood of extinction can be substantially increased by small changes in environmental quality, which shifts populations into new dynamical regimes.     

Chain flexibility and configurational dimensions of left handed Z- DNA and right handed B-DNA helices

The configurational behaviour of flexible helices of right handed B- and left handed Z-types have been analysed using statistical mechanical procedures. The configuration-dependent parameter, most importantly, the persistence length has been computed, using the heminucleotide scheme of treating polynucleotide chains under the approximation that perturbations in the backbone torsions produce sufficient flexibility in these helices. The values of persistence lengths obtained for Z-helices are very much higher than that of B-helices indicating that former is less flexible compared to the latter. These are in accordance with the results obtained recently on B- and Z-forms of poly(dG-dC). (dG-dC) using light scattering studies. Also the persistence lengths of B_II-DNA helices characterised by a skew 3'-hemiucleotide (ε-270°), and also when they coexist with B-DNA have been computed and the values lie within the range of experimentally reported values on B-helices. It is argued that the decrease in the persistence length values of B-DNA at higher salt concentration is due to additional small fluctuations in sugar residue torsions induced due to neutralisation of electrostatic repulsions between adjacent phosphates of the nucleotide. Noteworthy is that these are correlated to winding angle variations and the consequent bending of the helix. Contribution No. 659.     

Sexually antagonistic co‐evolution: a model and an empirical test

Models reveal that sexually antagonistic co‐evolution exaggerates female resistance and male persistence traits. Here we adapt an established model by including directional sexual selection acting against persistence. We find similar equilibria to previous models showing that sexually antagonistic co‐evolution can be limited by counteracting sexual, as well as, natural selection. We tested the model using empirical data for the seaweed fly, Coelopa ursina, in which body size acts as a persistence and a resistance trait. Our model can generate continuous co‐evolutionary cycles and stable equilibria, however, all simulations using empirically derived parameter estimates reach stable equilibria. Thus, stable equilibria might be more common in nature than continuous co‐evolutionary cycles, suggesting that sexual conflict is unlikely to promote speciation. The model predicts male biased sexual size dimorphism for C. ursina, comparable with empirically observed values. Male persistence is shown to be more sensitive than female resistance to changes in model parameters.     

Transient dynamics and persistence of ecological systems

Using spatially coupled predator–prey systems as an example of a cyclic ecological system where coexistence depends on oscillations, transient dynamics of models where there are no stable persistent solutions are shown to be a reasonable explanation of persistence over ecological time scales. The parameter values leading to transients within the context of a particular model may be far from parameter values that lead to stable solutions, so transients will need to be explicitly considered in model analysis. Since natural systems with many coupled oscillating species are common, and natural communities are often reset by disturbances or seasonality, transients should play a central role in understanding natural systems.     

Biological control in a disturbed environment

Most ecological and epidemiological models describe systems with continuous uninterrupted interactions between populations. Many systems, though, have ecological disturbances, such as those associated with planting and harvesting of a seasonal crop. In this paper, we introduce host–parasite–hyperparasite systems as models of biological control in a disturbed environment, where the host–parasite interactions are discontinuous. One model is a parasite–hyperparasite system designed to capture the essence of biological control and the other is a host–parasite–hyperparasite system that incorporates many more features of the population dynamics. Two types of discontinuity are included in the models. One corresponds to a pulse of new parasites at harvest and the other reflects the discontinuous presence of the host due to planting and harvesting. Such discontinuities are characteristic of many ecosystems involving parasitism or other interactions with an annual host. The models are tested against data from an experiment investigating the persistent biological control of the fungal plant parasite of lettuce Sclerotinia minor by the fungal hyperparasite Sporidesmium sclerotivorum, over successive crops. Using a combination of mathematical analysis, model fitting and parameter estimation, the factors that contribute the observed persistence of the parasite are examined. Analytical results show that repeated planting and harvesting of the host allows the parasite to persist by maintaining a quantity of host tissue in the system on which the parasite can reproduce. When the host dynamics are not included explicitly in the model, we demonstrate that homogeneous mixing fails to predict the persistence of the parasite population, while incorporating spatial heterogeneity by allowing for heterogeneous mixing prevents fade-out. Including the host''s dynamics lessens the effect of heterogeneous mixing on persistence, though the predicted values for the parasite population are closer to the observed values. An alternative hypothesis for persistence involving a stepped change in rates of infection is also tested and model fitting is used to show that changes in some environmental conditions may contribute to parasite persistence. The importance of disturbances and periodic forcing in models for interacting populations is discussed.     

Structural sensitivity of grazing formulations in nutrient controlled plankton models

Summary Stability and persistence properties of a family of non-spatial plankton models, each differentiated by its herbivore grazing term, are analytically compared. The dynamic persistence function in the model is shown to operate uniformly even though stability configuration characteristics of the model may be topologically distinct. The persistence threshold for each model indicates that total nutrient is a fundamental biological control. In the parameter space, all of the models studied are structurally unstable; however, an important bifurcation mechanism associated with this instability governs persistence. While, topologically, model transfigurement through parameter modulation is non-continuous, the biological populations evolve in a continuous or a lower semicontinuous manner. A basic conclusion of the paper is that fundamental problems for these marine ecological models remain unresolved since each of the models is a structurally unstable system for a fixed dynamically persistent ecology.     

Colonization and persistence ability explain the extent to which plant species fill their potential range

Aim How species traits and environmental conditions affect biogeographical dynamics is poorly understood. Here we test whether estimates of a species’ evolutionary age, colonization and persistence ability can explain its current ‘range filling’ (the ratio between realized and potential range size). Location Fynbos biome (Cape Floristic Region, South Africa). Methods For 37 species of woody plants (Proteaceae), we estimate range filling using atlas data and distribution models, evolutionary age using molecular phylogenies, and persistence ability using estimates of individual longevity (which determines the probability of extinction of local populations). Colonization ability is estimated from validated process‐based seed dispersal models, the arrangement of potential habitat, and data on local abundance. To relate interspecific variation in range filling to evolutionary age, colonization and persistence ability, we use two complementary model types: phenomenological linear models and the process‐based metapopulation model of Levins. Results Linear model analyses show that range filling increases with a species’ colonization and persistence ability but is not affected by species age. Moreover, colonization ability is a better predictor of range filling than its component variables (local abundance and dispersal ability). The phylogenetically independent interaction between colonization and persistence ability is significant (P < 0.05) for 97% of 180 alternative phylogenies. While the selected linear model explains 42% of the variance in arcsine transformed range filling, the Levins model performs more poorly. It overestimates range filling for realistic parameter values and produces unrealistic parameter estimates when fitted statistically. Main conclusions Colonization and local extinction seem to shape Proteaceae range dynamics on ecological rather than macroevolutionary time‐scales. Our results suggest that the positive abundance–range size relationship in this group is due primarily to the effect of abundance on colonization. In summary, this study contributes to a process‐based understanding of range dynamics and highlights the importance of colonization for the future survival of Fynbos Proteaceae.     

Stochastic dietary restriction using a Markov-chain feeding protocol elicits complex, life history response in medflies

Lifespan in individually housed medflies (virgins of both sexes) and daily reproduction for females were studied following one of 12 dietary restriction (DR) treatments in which the availability of high-quality food (yeast-sugar mixture) for each fly was based on a Markov chain feeding scheme--a stochastic dietary regime which specifies that the future dietary state depends only on the present dietary state and not on the path by which the present state was achieved. The stochastic treatments consisted of a combination of one of four values of a 'discovery' parameter and one of three values of a 'persistence' parameter. The results supported the hypotheses that: (i) longevity is extended in most medfly cohorts subject to stochastic DR; and (ii) longevity is more affected by the patch discovery than the patch persistence parameter. One of the main conclusions of the study is that, in combination with the results of earlier dietary restriction studies on the medfly, the results reinforce the concept that the details of the dietary restriction protocols have a profound impact on the sign and magnitude of the longevity extension relative to ad libitum cohorts and that a deeper understanding of the effect of food restriction on longevity is not possible without an understanding of its effect on reproduction.     

Effects of network and dynamical model structure on species persistence in large model food webs

Four models of network structure are combined with models of bioenergetic dynamics to study the role of food web topology and nonlinear dynamics on species coexistence in complex ecological networks. Network models range from the highly structured niche model to loosely constrained energetically feasible random networks. Bioenergetic models differ in how they represent primary production, functional responses, and consumption by generalists. Network structure weakly influenced the ability of species to coexist. Species persistence is strongly affected by functional responses and generalists’ consumption rates but weakly affected by models and amounts of primary production. Despite these generalities, specific mechanisms that determine persistence under one dynamical regime, such as top-down control by consumers, may play an insignificant role under different dynamical conditions. Future research is needed to strengthen the weak empirical basis for various functional forms and parameter values that strongly influence whether species can coexist in complex food webs. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Mitophagy in cells with mtDNA mutations

Despite the emergence of autophagy as a key process for mitochondrial quality control, the existence and persistence of pathogenic mtDNA mutations in human disease suggests that the degradation of dysfunctional mitochondria does not occur widely in vivo. During macroautophagy, a double-membraned cup-shaped structure engulfs cytosolic content. This autophagic vesicle then fuses with lysosomes, allowing hydrolytic enzymes to degrade the contents. Mitochondrial autophagy, or mitophagy, is thought to degrade damaged or nonfunctioning mitochondria specifically. The Parkinson disease-related proteins PINK1 (a mitochondrially localized kinase) and PARK2 (PARKIN, a cytosolically-localized E3 ubiquitin ligase) are essential for targeting mitochondria for mitophagy. Upon chemical uncoupling of the mitochondrial transmembrane potential (Δψ_m), PINK1 located in the mitochondrial outer membrane recruits PARK2 from the cytosol to the mitochondria, followed by delivery of the organelle to the autophagic machinery for degradation.     

Distribution of dry weight between root and shoot in white clover dependent on N2 fixation or utilizing abundant nitrate nitrogen

Summary Plants of white clover var. Blanca were grown singly in pots in controlled environments, or in small swards in a glasshouse, to determine how their distribution of dry weight between root and shoot was influenced when they were dependent on N₂ fixation in their root nodules or when they lacked nodules but utilized an abundant supply of nitrate nitrogen. In single plants and in swards, changes in root/shoot ratio with increasing age and plant development were not influenced by the source of nitrogen, but nodulated plants always displayed a higher root/shoot ratio. When nodulated plants were supplied with nitrate nitrogen, root/shoot ratio declined to values intermediate between those of nodulated and of nitrate plants. The results are discussed in relation to the persistence of white clover, and the general level of productivity, in grass-clover swards. The Grassland Research Institute is financed through the Agricultural Research Council.     

Modeling persistence and mutual interference among subpopulations of ecological communities

A model is proposed of an ecological community where some (or all) of the subpopulations exhibit mutual interference. Mutual interference introduces sublinearities which makes the persistence analysis of the community more complex since the model is no longer a dynamical system. A transformation is introduced which yields a dynamical system, thereby making a persistence analysis more tractable. The results are applied to determining top-predator persistence of a simple food chain and to the question of invasibility of a stable community by a new subpopulation. Research partially supported by the Natural Sciences and Engineering Research Council of Canada.     

Persistence in food webs—I Lotka-Volterra food chains

Persistence-extinction in simple food chains modelled by Lotka-Volterra dynamics is governed by a single parameter which depends upon the interspecific interaction coefficients, the intraspecific interaction coefficients, and the length of the food chain. In persistent systems with nonzero carrying capacity, two new features predominate. Trophic level influence factors relate persistence on different trophic levels and determine, in conjunction with the persistence parameter, the magnitude of persistence. Equilibrium component ordering, which results in persistent systems, mandates once again that systems need to be studied on the complete ecosystem level; static field measurements reflect species location in the food chain, the total length of the food chain and assume characteristics according to these factors.     

An epidemiological model with a delay and a nonlinear incidence rate

An epidemiological model with both a time delay in the removed class and a nonlinear incidence rate is analysed to determine the equilibria and their stability. This model is for diseases where individuals are first susceptible, then infected, then removed with temporary immunity and then susceptible again when they lose their immunity. There are multiple equilibria for some parameter values, and, for certain of these, periodic solutions arise by Hopf bifurcation from the large nontrivial equilibrium state.Research supported in parts by Centers for Disease Control Contract 200-87-0515Research supported in part by NSERC A-8965     

Minding impacting events in a model of stochastic variance

We introduce a generalization of the well-known ARCH process, widely used for generating uncorrelated stochastic time series with long-term non-Gaussian distributions and long-lasting correlations in the (instantaneous) standard deviation exhibiting a clustering profile. Specifically, inspired by the fact that in a variety of systems impacting events are hardly forgot, we split the process into two different regimes: a first one for regular periods where the average volatility of the fluctuations within a certain period of time is below a certain threshold, , and another one when the local standard deviation outnumbers . In the former situation we use standard rules for heteroscedastic processes whereas in the latter case the system starts recalling past values that surpassed the threshold. Our results show that for appropriate parameter values the model is able to provide fat tailed probability density functions and strong persistence of the instantaneous variance characterized by large values of the Hurst exponent (H>0.8), which are ubiquitous features in complex systems.     

Data-Limited Population-Status Evaluation of Two Coastal Fishes in Southern Angola Using Recreational Catch Length-Frequency Data

Excessive truncation of a population’s size structure is often identified as an important deleterious effect of exploitation, yet the effect on population persistence of size-structure truncation caused by exploitation is often not quantified due to data limitations. In this study, we estimate changes in eggs per recruit (EPR) using annual length-frequency samples over a 9 year period to assess persistence of the two most important recreational fishes in southern Angola: west coast dusky kob (Argyrosomus coronus) and leerfish (Lichia amia). Using a length- and age-structured model, we improve on an existing method to fit this type of model to length-frequency data and estimate EPR. The objectives of the methodological changes are to add flexibility and robustness to the approach for assessing population status in data-limited situations. Results indicate that dusky kob presents very low levels of EPR (5%-10% of the per recruit reproductive capacity in the absence of fishing) in 2013, whereas large inter-annual variability in leerfish estimates suggest caution must be applied when drawing conclusions about its exploitation status. Using simulated length frequency data with known parameter values, we demonstrate that recruitment decline due to overexploitation leads to overestimation of EPR values. Considering the low levels of EPR estimated for the study species, recruitment limitation is not impossible and true EPR values may be even lower than our estimates. It is, therefore, likely that management action, such as the creation of Marine Protected Areas, is needed to reconstitute the west coast dusky kob population.