Lifesaving explains mortality decline with time

Mortality rates of human populations in developed countries are declining with time. We show that this effect can be explained via a 'lifesaving' methodology. Our approach is based on considering a non-homogeneous Poisson process of potentially harmful events. Each of these events can be 'cured' with a given probability or can result in a termination of the Poisson process (death) with a complementary probability. A lifesaving ratio, defining the corresponding relative increase in life expectancy for homogeneous and heterogeneous populations is analyzed. Some generalizations are discussed. Several simple examples are considered.     

On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations

The expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is mathematically defined as the dominant eigenvalue of a positive linear operator. It is shown that in certain special cases one can easily compute or estimate this eigenvalue. Several examples involving various structuring variables like age, sexual disposition and activity are presented.     

On the spread of epidemics in a closed heterogeneous population

Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective-removed) model is formulated and analyzed when susceptibility to or infectivity of a particular disease is distributed. It is shown that a heterogeneous model can be reduced to a homogeneous model with a nonlinear transmission function, which is given in explicit form. The widely used power transmission function is deduced from the model with distributed susceptibility and infectivity with the initial gamma-distribution of the disease parameters. Therefore, a mechanistic derivation of the phenomenological model, which is believed to mimic reality with high accuracy, is provided. The equation for the final size of an epidemic for an arbitrary initial distribution of susceptibility is found. The implications of population heterogeneity are discussed, in particular, it is pointed out that usual moment-closure methods can lead to erroneous conclusions if applied for the study of the long-term behavior of the models.     

Evolution of pathogens towards low R0 in heterogeneous populations

Maximization of the basic reproduction ratio or R(0) is widely believed to drive the emergence of novel pathogens. The presence of exploitable heterogeneities in a population, such as high variance in the number of potentially infectious contacts, increases R(0) and thus pathogens that can exploit heterogeneities in the contact structure have an advantage over those that do not. However, exploitation of heterogeneities results in a more rapid depletion of the potentially susceptible neighbourhood for an infected host. Here a simple model of pathogen evolution in a heterogeneous environment is developed and placed in the context of HIV transmission. In this model, it is shown that pathogens may evolve towards lower R(0), even if this results in pathogen extinction. For sufficiently high transmissibility, two locally stable strategies exist for an evolving pathogen, one that exploits heterogeneities and results in higher R(0), and one that does not, and results in lower R(0). While the low R(0) strategy is never evolutionarily stable, invading strains with higher R(0) will also converge to the low R(0) strategy if not sufficiently different from the resident strain. Heterogenous transmission is increasingly recognized as fundamental to epidemiological dynamics and the evolution of pathogens; here, it is shown that the ability to exploit heterogeneity is a strategy that can itself evolve.     

On treatment of tuberculosis in heterogeneous populations

Global eradication of tuberculosis (TB) is an international agenda. Thus understanding effects of treatment of TB in different settings is crucial. In previous work, we introduced the framework for a mathematical model of epidemic TB in demographically distinct, heterogeneous populations. Simulations showed the importance of genetic susceptibility in determining endemic prevalence levels. In the work presented here, we include treatment and investigate different strategies for treatment of latent and active TB disease in heterogeneous populations. We illustrate how the presence of a genetically susceptible subpopulation dramatically alters effects of treatment in the same way a core population does in the setting of sexually transmitted diseases. In addition, we evaluate treatment strategies that focus specifically on this subpopulation, and our results indicate that genetically susceptible subpopulations should be accounted for when designing treatment strategies to achieve the greatest reduction in disease prevalence.     

On selection criteria and estimation of parameters when the variance is heterogeneous

Summary Procedures for ranking candidates for selection and for estimating genetic and environmental parameters when variances are heterogeneous are discussed. The best linear unbiased predictor (BLUP) accounts automatically for heterogeneous variance provided that the covariance structure is known and that the assumptions of the model hold. Under multivariate normality BLUP allowing for heterogeneous variance maximizes expected genetic progress. Examples of application of BLUP to selection when residual or genetic variances are heterogeneous are given. Restricted maximum likelihood estimation of heterogeneous variances and covariances via the expectation-maximization algorithm is presented.     

Testing the 'free radical theory of aging' hypothesis: physiological differences in long-lived and short-lived colubrid snakes

We test the 'free radical theory of aging' using six species of colubrid snakes (numerous, widely distributed, non-venomous snakes of the family Colubridae) that exhibit long (> 15 years) or short (< 10 years) lifespans. Because the 'rate of living theory' predicts metabolic rates to be correlated with rates of aging and oxidative damage results from normal metabolic processes we sought to answer whether physiological parameters and locomotor performance (which is a good predictor of survival in juvenile snakes) mirrored the evolution of lifespans in these colubrid snakes. We measured whole animal metabolic rate (oxygen consumption Vo2), locomotor performance, cellular metabolic rate (mitochondrial oxygen consumption), and oxidative stress potential (hydrogen peroxide production by mitochondria). Longer-lived colubrid snakes have greater locomotor performance and reduced hydrogen peroxide production than short-lived species, while whole animal metabolic rates and mitochondrial efficiency did not differ with lifespan. We present the first measures testing the 'free radical theory of aging' using reptilian species as model organisms. Using reptiles with different lifespans as model organisms should provide greater insight into mechanisms of aging.     

An exact procedure for the analysis of heterogeneous kinetics in polyclonal antibody populations

Antibody populations with heterogeneous binding properties exhibit complex first-order dissociation kinetics. An analytical method has been developed to determine the average dissociation rate constant and the heterogeneity index of a specific antibody population. This procedure was based on Laplace transformation of the gamma distribution function, which yielded an exact, macroscopic rate law for the entire antibody population. Linearization of the macroscopic rate law is achieved by plotting data points versus their numerical derivatives using log-log axes. Linear regression of such plots yields the average dissociation rate constant from the Y-intercept, and heterogeneity index from the slope. This analytic method is transparent to the antibody system and kinetic assay employed, requiring only a programmable calculator to perform the necessary calculations. The usefulness of this analytic method was demonstrated by the evaluation of dissociation kinetics in murine monoclonal and rabbit polyclonal anti-fluorescyl-IgG antibody populations.     

Thymic cell populations in amphibia: Quantitative study of the growth,stability, and regression of the cell populations in the thymus of the newtPleurodeles waltlii Michah

Summary Twenty days after fertilization (stage 40) the thymus ofPleurodeles waltlii consists of two main cell types: epithelial reticular cells (71%) and lymphoid stem-cells (24%).Between day 20 and day 72 (stage 53) the lymphoid stem-cells differentiate into lymphocytes, via the lymphoblast state. Commencing at day 20, epithelial reticular cells are transformed into epithelial reticular dense cells. Following day 65, other epithelial reticular cells begin to differentiate into epithelial hypertrophic cells, and these subsequently form thymic cysts. During this whole period intense proliferation takes place.The three types of polynuclear cells (neutrophil, eosinophil, and basophil), the macrophages, and the plasmocytes differentiate outside the thymus then migrate into it through the vascular system.Around day 72 (stage 53), the mature thymus consists of two parts: the first is visible as a background or cortex-like area, the second comprises medulla like spots, formed by small numbers of cysts.Around metamorphosis the cell populations reach a stable state.After metamorphosis the relative frequency of the lymphoid cell population progressively decreases, while the proportion of epithelial hypertrophic cells, together with cyst surface area, is increased. Consequently the ratio of cysts/background area increases with age.     

Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread

Summary In this paper we use Aronson's and Weinberger's [1–4] concept of asymptotic speed to estimate the asymptotic behaviour of the solution of a nonlinear integral equation (with the nonlinearity not being monotone), which describes the development of a spatially distributed population.     

Density-dependent mortality,growth and size inequality in roadside populations of the annual herbGalium aparine L.

Biomass, plant size, plant density and the inequality of sizes were assessed for autumn-emerging roadside populations dominated byGalium aparine during early stages of growth in two independent studies. A third data set dealt with the survival of labelled seedlings belonging to different cohorts of emergence. One data set showed that the slope of the log-log size/density relationship for all plant species present in the samples was closer to −1.5 and that forG. aparine was closer to −1.0 in five separate populations. Biomass increase and density decrease was not found to take place in any of these simultaneously. The size inequality ofG. aparine tended to increase or to remain constant during periods of high mortality, and in the early harvests it was negatively related to population density. The second data set revealed simultaneous decreases of both biomass and density ofG. aparine and of all plant species during a period of a month soon after emergence, and a higher size inequality ofG. aparine in those patches where plant density (and that ofG. aparine) was lower. The labelling of seedlings indicated density-dependent mortality and a higher probability of survival for seedlings emerging very early. The size/density relationship of roadside populations dominated byG. aparine may follow a trajectory over time similar to that predicted by the 3/2 power law of self-thinning, but this species seems to have a weak size hierarchy development and limited individual growth at high population densities. The importance of plant architecture in relation to this response is discussed.     

Survival in continuous structured populations models

The extended McKendrick-von Foerster structured population model is employed to derive a nonautonomous ordinary differential equation model of a population. The derivation assumes that the individual life history can be delineated into several physiological stages. We study the persistence of the population when the model is autonomous and base the nonautonomous survival analysis on the autonomous case and a comparison principle. A brief excursion into alternate life history strategies is presented.This work was supported in part by the U.S. Environmental Protection Agency under cooperative agreement CR 813353010     

Natural selection of cooperation and degree hierarchy in heterogeneous populations

One of the current theoretical challenges to the explanatory powers of Evolutionary Theory is the understanding of the observed evolutionary survival of cooperative behavior when selfish actions provide higher fitness (reproductive success). In unstructured populations natural selection drives cooperation to extinction. However, when individuals are allowed to interact only with their neighbors, specified by a graph of social contacts, cooperation-promoting mechanisms (known as lattice reciprocity) offer to cooperation the opportunity of evolutionary survival. Recent numerical works on the evolution of Prisoner's Dilemma in complex network settings have revealed that graph heterogeneity dramatically enhances the lattice reciprocity. Here we show that in highly heterogeneous populations, under the graph analog of replicator dynamics, the fixation of a strategy in the whole population is in general an impossible event, for there is an asymptotic partition of the population in three subsets, two in which fixation of cooperation or defection has been reached and a third one which experiences cycles of invasion by the competing strategies. We show how the dynamical partition correlates with connectivity classes and characterize the temporal fluctuations of the fluctuating set, unveiling the mechanisms stabilizing cooperation in macroscopic scale-free structures.     

Generational coexistence and ancestor's inhibition in bacterial populations

Generational coexistence in structured environments raises the possibility of a competition between ancestors and descendents. This type of kin competition, and in particular, the possibility that descendents might actively repress the ancestor's dominance, has been rarely considered in microbial evolutionary ecology. The recent discovery of the phenomenon of stationary-phase contact-dependent inhibition of bacterial ancestor cells by late descendents provides a new theoretical perspective to analyze intrapopulational evolutionary changes. The ancestor's inhibition effect might accelerate such changes, particularly when the descendents have acquired small adaptive advantages that are insufficient to rapidly displace the well-settled ancestors in a complex niche. Besides this effect of triggering selection of small genetic differences, the opportunities for intergenerational coexistence in bacteria, where ancestor's inhibition might occur, are reviewed in this work. A theoretical analysis is provided about the explanatory possibilities of the ancestor's inhibition effect in the controversies about intraspecific (in a large sense, including intrapopulational) genetic diversification, and the discontinuities observed in such processes, giving rise to the emergence of individualities and therefore differential units of selection.     

Migration-selection polymorphism in dioecious populations

Summary Conditions are derived for a protected polymorphism in a dioecious population subdivided into an arbitrary number of demes which exchange migrants. Generations are discrete and nonoverlapping; mutation and random drift are neglected. The analysis is restricted to a diallelic autosomal locus. In contrast to the monoecious case, the protection criteria depend on the order of migration and selection; they become identical for adult and juvenile migration if both the male and female backward migration matrices are symmetric, or the migration or selection patterns in the two sexes are the same. The protection conditions are presented explicitly for the Levene model. A recessive allele is protected in a panmictic dioecious population if the unweighted average of the recessive-to-dominant fitness ratios in the two sexes exceeds unity.Supported by the National Science Foundation (Grant No. DEB77-21494)