A Model for Antagonistic Pleiotropic Gene Action for Mortality and Advanced Age

Association or linkage studies involving control and long-lived populations provide information on genes that influence longevity. However, the relationship between allele-specific differences in survival and the genetic structure of aging cohorts remains unclear. We model a heterogeneous cohort comprising several genotypes differing in age-specific mortality. In its most general form, without any specific assumption regarding the shape of mortality curves, the model permits derivation of a fundamental property underlying abrupt age-related changes in the composition of a cohort. The model is applied to sex-specific survival curves taken from period life tables, and Gompertz-Makeham mortality coefficients are calculated for the French population. Then, adjustments are performed under Gompertz-Makeham mortality functions for three genotypes composing a heterogeneous cohort, under the constraint of fitting the resultant mortality to the real French population mortality obtained from life tables. Multimodal curves and divergence after the 8th decade appear as recurrent features of the frequency trajectories. Finally, a fit to data previously obtained at the angiotensin-converting-enzyme locus is realized, explaining what had seemed to be paradoxical results-namely, that the frequency of a genotype known as a cardiovascular risk factor was increased in centenarians. Our results help explain the well-documented departure from Gompertz-Makeham mortality kinetics at older ages. The implications of our model are discussed in the context of known genetic effects on human longevity and age-related pathologies. Since antagonistic pleiotropy between early and late survival emerges as a general rule, extrapolating the effects measured for a gene in a particular age class to other ages could be misleading.     

Biodemographic analysis of male honey bee mortality

Biodemographic studies of insects have significantly enhanced our understanding of the biology of aging. Eusocial insects have evolved to form different groups of colony members that are specialized for particular tasks and highly dependent on each other. These different groups (castes and sexes) also differ strongly in their life expectancy but relatively little is known about their mortality dynamics. In this study we present data on the age-specific flight activity and mortality of male honey bees from two different genetic lines that are exclusively dedicated to reproduction. We show that males initiating flight at a young age experience more flight events during their lifetime. No (negative) relation between the age at flight initiation and lifespan exists, as might be predicted on the basis of the antagonistic pleiotropy theory of aging. Furthermore, we fit our data to different aging models and conclude that overall a slight deceleration of the age-dependent mortality increase at advanced ages occurs. However, mortality risk increases according to the Gompertz-Makeham model when only days with flight activity (active days) are taken into account. Our interpretation of the latter is that two mortality components act on honey bee males during flight: increasing, age-dependent deaths (possibly from wear-and-tear), and age-independent deaths (possibly due to predation). The overall mortality curve is caused by the interaction of the distribution of age at foraging initiation and the mortality function during the active (flight) lifespan.     

Construction of expanded infant life tables: A method based on a new mortality law

A mortality law for infants is developed for constructing augmented-period infant life tables. For advanced countries, the three-parameter model is found to fit the mortality data for subdivisions of the first year of life extremely well, with estimates of the life-table functions calculated from the proposed model closely matching those constructed by the traditional method. Thus, considerable benefit is derived by replacing a large accumulation of data, marred by inevitable irregularities and errors arising from incomplete reporting and other sources, with a simple formula that can produce life-table functions at any age point and for any age interval and can be handled with some facility. We have also demonstrated how the model is used to calculate a number of new life-table functions and parameters of the lifetime distribution with their attendant applications, which include determination of the maximum life expectancy and the force of mortality at birth as well as certain average lifetimes for the stationary population. It is found that over 97% of the information contained in an augmented infant life table can be summarized by three parameters, with the remaining portion captured by another three parameters.     

HUMAN ACTUARIAL AGING INCREASES FASTER WHEN BACKGROUND DEATH RATES ARE LOWER: A CONSEQUENCE OF DIFFERENTIAL HETEROGENEITY?

Many analyses of human populations have found that age-specific mortality rates increase faster across most of adulthood when overall mortality levels decline. This contradicts the relationship often expected from Williams' classic hypothesis about the effects of natural selection on the evolution of senescence. More likely, much of the within-species difference in actuarial aging is not due to variation in senescence, but to the strength of filters on the heterogeneity of frailty in older survivors. A challenge to this differential frailty hypothesis was recently posed by an analysis of life tables from historical European populations and traditional societies that reported variation in actuarial aging consistent with Williams' hypothesis after all. To investigate the challenge, we reconsidered those cases and aging measures. Here we show that the discrepancy depends on Ricklefs' aging rate measure, ω, which decreases as mortality levels drop because it is an index of mortality level itself, not the rate of increase in mortality with age. We also show unappreciated correspondence among the parameters of Gompertz-Makeham and Weibull survival models. Finally, we compare the relationships among mortality parameters of the traditional societies and the historical series, providing further suggestive evidence that differential heterogeneity has strong effects on actuarial aging.     

Age‐specific mortality analysis of the dry forest kissing bug,Rhodnius neglectus

Age‐specific mortality patterns can be very different across insects with different life histories. Some holometabolous insects (like mosquitoes, fruit flies) show a pattern where mortality rate decelerates at older ages, whereas other holometabolous insects (bruchid beetles) and hemimetabolous insects (cotton stainers, milkweed bugs, and kissing bugs) show an age‐specific mortality pattern that increases through all ages. Kissing bugs are strictly hematophagous and are vectors of Trypanosoma cruzi Chagas, the etiologic agent of Chagas disease. Here, we tested whether cohort data from the dry forest kissing bug, Rhodnius neglectus Lent (Hemiptera: Reduviidae), supports an increase of mortality rate that decelerates with age. We analyzed the age‐specific mortality pattern of a cohort of 250 individuals of R. neglectus. We used a suite of seven models with different degrees of complexity, to model age‐dependent forms of change in mortality rate increase in R. neglectus in the laboratory. We used the Akaike model selection criterion to choose between models that consider absence or presence of mortality deceleration. Five of the seven models (logistic, Gavrilovs, Gompertz, DeMoivre, and exponential) showed a statistically significant fit to the mortality rate. Weak late‐age mortality deceleration in R. neglectus was supported by the best fit (logistic model), and this result is consistent with predictions of the disposable soma theory of senescence.     

The age-related dynamics of mortality and the Gompertz-Makeham law

Using the statistics of mortality of Caucasian population of 48 states of the USA (1969-1971) it was demonstrated that the real age dynamics of human mortality may differ significantly both from the Gompertz law and from the Gompertz-Makeham law. Using of the Gompertz-Makeham formula leads to appearance of negative A value in 77 cases out of 96. This makes it difficult to interpret this parameter as a "background" component of mortality. Using of the Gompertz formula in different age groups leads uncoordinated changes in alpha and R0 values in every state. Hence, it is impossible to plot geographically stable characters for Gompertz parameters alpha for subsequent epidemiological analysis. The "aging rate", estimated by parameter is not stable throughout the life span of 30-92 years, but changes with certain pattern.     

Factors affecting infant and child mortality

This paper examines the determinants of infant and child mortality variations in Jordan, Yemen, Egypt, and Tunisia using data from WFS surveys. The analysis considers biological correlates of mortality--mother's age, birth order, birth interval, and previous infant loss--and several social factors--mother's and father's education, mother's residence, father's occupation, and mother's work experience since marriage. The estimates for the 4 countries show large variations in the mortality rates and an expected pattern of declining infant and child mortality during the period of 20 years prior to the survey. Further, the proportionate decline in child mortality in each country was generally greater than the proportionate decline in infant mortality. A persistent pattern of higher child mortality for females than for males is found, suggesting preferential care and treatment of male offspring. The higher mortality risk is found for infants born to very young and very old mothers, with short previous birth intervals, of higher birth orders, and where the previous infant had died. Among the socioeconomic characteristics, the education of the mother and rural-urban residence are found to affect infant survival. In childhood, among the demographic factors, only birth interval shows a significant effect on mortality. The risk of child mortality decreases considerably with the increase in the birth interval. The analysis of the effect of breastfeeding on mortality, although based on limited information, clearly shows the beneficial effect of breastfeeding on the infant's survival, especially during the early months of life. For all countries, the mortality rate for the non-breastfeeders is substantially higher than for the breastfeeders even when the effect of the other covariates is controlled.     

Reconstruction of the probe angular distribution from a series of electron spin resonance spectra of tilted oriented samples.

Model-independent methods for the reconstruction of the nitroxide spin probe angular distribution of labeled oriented biological assemblies from electron spin resonance (ESR) spectra were investigated. We found that accurate probe angular distribution information could be obtained from the simultaneous consideration of a series of ESR spectra originating from a sample at differing tilt angles relative to the Zeeman magnetic field. Using simulated tilt series data sets, we developed a consistent criteria for judging the reliability of the simulated fit to the data as a function of the free spectral parameters and thereby have increased the significance of the model-independent reconstruction of the probe angular distribution derived from the fit. We have also enhanced the angular resolution measurable with the model-independent methodology by increasing the rank of the order parameters that we can reliably deduce from a spectrum. This enhancement allows us to accurately deduce higher resolution features of the spin probe distribution. Finally we investigated the usefulness of fitting the tilt series data in multiple data sets such that tilt series data from many identical sample preparations are fitted simultaneously. This method proved to be useful in rapidly reducing a large amount of data by eliminating any redundant computations in the application of the enhanced model-independent analysis to identical sets of tilt series data. We applied the methodology developed here to ESR spectra from probe labeled muscle fibers to study the orientation of myosin cross-bridges in fibers. This application is described in the accompanying paper.     

Reparameterizing the pattern mixture model for sensitivity analyses under informative dropout

Pattern mixture models are frequently used to analyze longitudinal data where missingness is induced by dropout. For measured responses, it is typical to model the complete data as a mixture of multivariate normal distributions, where mixing is done over the dropout distribution. Fully parameterized pattern mixture models are not identified by incomplete data; Little (1993, Journal of the American Statistical Association 88, 125-134) has characterized several identifying restrictions that can be used for model fitting. We propose a reparameterization of the pattern mixture model that allows investigation of sensitivity to assumptions about nonidentified parameters in both the mean and variance, allows consideration of a wide range of nonignorable missing-data mechanisms, and has intuitive appeal for eliciting plausible missing-data mechanisms. The parameterization makes clear an advantage of pattern mixture models over parametric selection models, namely that the missing-data mechanism can be varied without affecting the marginal distribution of the observed data. To illustrate the utility of the new parameterization, we analyze data from a recent clinical trial of growth hormone for maintaining muscle strength in the elderly. Dropout occurs at a high rate and is potentially informative. We undertake a detailed sensitivity analysis to understand the impact of missing-data assumptions on the inference about the effects of growth hormone on muscle strength.     

Ecology and multilevel selection explain aggression in spider colonies

Progress in sociobiology continues to be hindered by abstract debates over methodology and the relative importance of within‐group vs. between‐group selection. We need concrete biological examples to ground discussions in empirical data. Recent work argued that the levels of aggression in social spider colonies are explained by group‐level adaptation. Here, we examine this conclusion using models that incorporate ecological detail while remaining consistent with kin‐ and multilevel selection frameworks. We show that although levels of aggression are driven, in part, by between‐group selection, incorporating universal within‐group competition provides a striking fit to the data that is inconsistent with pure group‐level adaptation. Instead, our analyses suggest that aggression is favoured primarily as a selfish strategy to compete for resources, despite causing lower group foraging efficiency or higher risk of group extinction. We argue that sociobiology will benefit from a pluralistic approach and stronger links between ecologically informed models and data.     

Measuring size distribution in highly heterogeneous systems with fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) is a sensitive and widely used technique for measuring diffusion. FCS data are conventionally modeled with a finite number of diffusing components and fit with a least-square fitting algorithm. This approach is inadequate for analyzing data obtained from highly heterogeneous systems. We introduce a Maximum Entropy Method based fitting routine (MEMFCS) that analyzes FCS data in terms of a quasicontinuous distribution of diffusing components, and also guarantees a maximally wide distribution that is consistent with the data. We verify that for a homogeneous specimen (green fluorescent protein in dilute aqueous solution), both MEMFCS and conventional fitting yield similar results. Further, we incorporate an appropriate goodness of fit criterion in MEMFCS. We show that for errors estimated from a large number of repeated measurements, the reduced chi(2) value in MEMFCS analysis does approach unity. We find that the theoretical prediction for errors in FCS experiments overestimates the actual error, but can be empirically modified to serve as a guide for estimating the goodness of the fit where reliable error estimates are unavailable. Finally, we compare the performance of MEMFCS with that of a conventional fitting routine for analyzing simulated data describing a highly heterogeneous distribution containing 41 diffusing species. Both methods fit the data well. However, the conventional fit fails to reproduce the essential features of the input distribution, whereas MEMFCS yields a distribution close to the actual input.     

Distribution of postpartum amenorrhea in rural Bangladeshi women

Previous studies of postpartum amenorrhea (PPA) demonstrated distinct subgroups of women with short and long durations of amenorrhea. This phenomenon was attributed to cases where breastfeeding is absent because of pregnancy loss or infant death, or confusion of postpartum bleeding with resumption of menses. We explored these ideas using data from an 11-month prospective study in Bangladesh in which 858 women provided twice-weekly interviews and urine specimens for up to 9 months; 300 women were observed while experiencing PPA. The resulting exact, interval-censored, or right-censored durations were used to estimate parameters of two-component mixture models. A mixture of two Weibull distributions provided the best fit to the observations. The long-duration subgroup made up 84% (+/- 4% SE) of the population, with a mean duration of 457 (+/- 31) days. The short-duration subgroup had a mean duration of 94 (+/- 17) days. Three covariates were associated with the duration of PPA: women whose husbands had high-wage employment had a greater probability of falling in the short-duration subgroup; women in the long-duration subgroup whose husbands seasonally migrated had shorter periods of PPA within the subgroup; and mothers in the short-duration subgroup who gave birth during the monsoon season experienced a shortened duration of PPA within the subgroup. We conclude that the bimodal distribution of PPA reflects biological or behavioral heterogeneity rather than shortcomings of data collection.     

Culled males,infant mortality and reproductive success in a pre-industrial Finnish population

Theoretical and empirical literature asserts that the sex ratio (i.e. M/F) at birth gauges the strength of selection in utero and cohort quality of males that survive to birth. We report the first individual-level test in humans, using detailed life-history data, of the ‘culled cohort’ hypothesis that males born to low annual sex ratio cohorts show lower than expected infant mortality and greater than expected lifetime reproductive success. We applied time-series and structural equation methods to a unique multigenerational dataset of a natural fertility population in nineteenth century Finland. We find that, consistent with culled cohorts, a 1 s.d. decline in the annual cohort sex ratio precedes an 8% decrease in the risk of male infant mortality. Males born to lower cohort sex ratios also successfully raised 4% more offspring to reproductive age than did males born to higher cohort sex ratios. The offspring result, however, falls just outside conventional levels of statistical significance. In historical Finland, the cohort sex ratio gauges selection against males in utero and predicts male infant mortality. The reproductive success findings, however, provide weak support for an evolutionarily adaptive explanation of male culling in utero.     

The Distribution of Ocular Chlamydia Prevalence across Tanzanian Communities Where Trachoma Is Declining

BackgroundMathematical models predict an exponential distribution of infection prevalence across communities where a disease is disappearing. Trachoma control programs offer an opportunity to test this hypothesis, as the World Health Organization has targeted trachoma for elimination as a public health concern by the year 2020. Local programs may benefit if a single survey could reveal whether infection was headed towards elimination. Using data from a previously-published 2009 survey, we test the hypothesis that Chlamydia trachomatis prevalence across 75 Tanzanian communities where trachoma had been documented to be disappearing is exponentially distributed.Methods/FindingsWe fit multiple continuous distributions to the Tanzanian data and found the exponential gave the best approximation. Model selection by Akaike Information Criteria (AIC_c) suggested the exponential distribution had the most parsimonious fit to the data. Those distributions which do not include the exponential as a special or limiting case had much lower likelihoods of fitting the observed data. 95% confidence intervals for shape parameter estimates of those distributions which do include the exponential as a special or limiting case were consistent with the exponential. Lastly, goodness-of-fit testing was unable to reject the hypothesis that the prevalence data came from an exponential distribution.ConclusionsModels correctly predict that infection prevalence across communities where a disease is disappearing is best described by an exponential distribution. In Tanzanian communities where local control efforts had reduced the clinical signs of trachoma by 80% over 10 years, an exponential distribution gave the best fit to prevalence data. An exponential distribution has a relatively heavy tail, thus occasional high-prevalence communities are to be expected even when infection is disappearing. A single cross-sectional survey may be able to reveal whether elimination efforts are on-track.     

The Body Mass Index-Mortality Link across the Life Course: Two Selection Biases and Their Effects

In this study, we investigated two selection biases that may affect the obesity-mortality link over the life course: mortality selection and healthy participant effects. If these selection mechanisms are stronger among obese adults than among non-obese adults, they may contribute to the weakening obesity-mortality link over the life course. We used data from the National Health and Nutrition Examination Survey 1988–2010 with linked mortality files from 1988–2011. We employed weighted Cox models to test and adjust for these two selection biases. We also used complementary log-log models, adjusted for a normal distribution of frailty, to test for mortality selection effects; accelerated failure-time models to mitigate the mortality selection effect; and ordinary least squares regression to test for healthy participant effects. The link between class II/III obesity and mortality weakens at older ages. We did not find evidence for significant mortality selection or healthy participant effects. Also, even if the healthy participant effects were stronger among obese adults, they are not strong enough to produce a weakening association between obesity and morbidity at higher ages at the time of the survey. Therefore, neither of these selection biases explains the diminishing effect of class II/III obesity on mortality over the life course.     

Biphasic growth in fish II: empirical assessment

In [Quince, et al., 2008. Biphasic growth in fish I: Theoretical foundations. J. Theor. Biol., doi:10.1016/j.jtbi.2008.05.029], we developed a set of biphasic somatic growth models, where maturation is accompanied by a deceleration of growth due to allocation of energy to reproduction. Here, we use growth data from both hatchery-raised and wild populations of a large freshwater fish (lake trout, Salvelinus namaycush) to test these models. We show that a generic biphasic model provides a better fit to these data than the von Bertalanffy model. We show that the observed deceleration of somatic growth in females varies directly with gonad weight at spawning, with observed egg volumes roughly 50% of the egg volumes predicted under the unrealistic assumption of perfectly efficient energy transfer from somatic lipids to egg lipids. We develop a Bayesian procedure to jointly fit a biphasic model to observed growth and maturity data. We show that two variants of the generic biphasic model, both of which assume that annual allocation to reproduction is adjusted to maximise lifetime reproductive output, provide complementary fits to wild population data: maturation time and early adult growth are best described by a model with no constraints on annual reproductive investment, while the growth of older fish is best described by a model that is constrained so that the ratio of gonad size to somatic weight (g) is fixed. This behaviour is consistent with the additional observation that g increases with size and age among younger, smaller breeding females but reaches a plateau among older, larger females. We then fit both of these optimal models to growth and maturation data from nineteen wild populations to generate population-specific estimates of ‘adapted mortality’ rate: the adult mortality consistent with observed growth and maturation schedules, given that both schedules are adapted to maximise lifetime reproductive output. We show that these estimates are strongly correlated with independent estimates of the adult mortality experienced by these populations.     

Properties of adaptive walks on uncorrelated landscapes under strong selection and weak mutation

We examine properties of adaptive walks on uncorrelated (i.e. random) fitness landscapes starting from moderately fit genotypes under strong selection weak mutation. As an extension of Orr's model for a single step in an adaptive walk under these conditions, we show that the fitness rank of the dominant genotype in a population after the fixation of a beneficial mutation is, on average, (i+6)/4, where i is the fitness rank of the starting genotype. This accounts for the change in rank due to acquiring a new set of single-mutation neighbors after fixing a new allele through natural selection. Under this scenario, adaptive walks can be modeled as a simple Markov chain on the space of possible fitness ranks with an absorbing state at i = 1, from which no beneficial mutations are accessible. We find that these walks are typically short and are often completed in a single step when starting from a moderately fit genotype. As in Orr's original model, these results are insensitive to both the distribution of fitness effects and most biological details of the system under consideration.     

Beyond the proportional frailty model: Bayesian estimation of individual heterogeneity on mortality parameters

Today, we know that demographic rates can be greatly influenced by differences among individuals in their capacity to survive and reproduce. These intrinsic differences, commonly known as individual heterogeneity, can rarely be measured and are thus treated as latent variables when modeling mortality. Finite mixture models and mixed effects models have been proposed as alternative approaches for inference on individual heterogeneity in mortality. However, in general models assume that individual heterogeneity influences mortality proportionally, which limits the possibility to test hypotheses on the effect of individual heterogeneity on other aspects of mortality such as ageing rates. Here, we propose a Bayesian model that builds upon the mixture models previously developed, but that facilitates making inferences on the effect of individual heterogeneity on mortality parameters other than the baseline mortality. As an illustration, we apply this framework to the Gompertz–Makeham mortality model, commonly used in human and wildlife studies, by assuming that the Gompertz rate parameter is affected by individual heterogeneity. We provide results of a simulation study where we show that the model appropriately retrieves the parameters used for simulation, even for low variances in the heterogeneous parameter. We then apply the model to a dataset on captive chimpanzees and on a cohort life table of 1751 Swedish men, and show how model selection against a null model (i.e., without heterogeneity) can be carried out.     

Optimal seasonal schedules and the relative dominance of heteromorphic and isomorphic life cycles in macroalgae

Marine macroalgae (seaweed) show diverse life cycles. Species with a heteromorphic life cycle have a large multicellular algal body in one generation but have a very small body in the second generation of the same year. In contrast, the diploid and haploid life forms of isomorphic species have similar morphology, and these species often have more than two generations in a year. Here, we first study the optimal life cycle schedule of marine macroalgae when daily mortality changes seasonally, and then we discuss the conditions for coexistence and relative dominance of different life cycles. According to the optimal life cycle schedule, heteromorphic species tend to have a generation with a large algal body when mortality is low, and a microscopic-sized generation when mortality is high. In contrast, isomorphic species tend to mature when body size reaches a threshold value that is the same for different generations. We then examine the coexistence of the two life cycles when growth rate decreases with biomass. The model predicts that (1) at high latitudes (i.e., in strongly seasonal environments), heteromorphic species are likely to dominate over isomorphic species, and (2) species with a heteromorphic life cycle should dominate in the supratidal and upper intertidal zones where macroalgae tend to suffer high mortality, and also in the subtidal zone, where mortality is low, whereas isomorphic species are likely to be more successful when mortality is intermediate. These predictions are consistent with the observed distribution patterns of the two life cycles in macroalgae.     

A Laplace mixture model for identification of differential expression in microarray experiments

Microarrays have become an important tool for studying the molecular basis of complex disease traits and fundamental biological processes. A common purpose of microarray experiments is the detection of genes that are differentially expressed under two conditions, such as treatment versus control or wild type versus knockout. We introduce a Laplace mixture model as a long-tailed alternative to the normal distribution when identifying differentially expressed genes in microarray experiments, and provide an extension to asymmetric over- or underexpression. This model permits greater flexibility than models in current use as it has the potential, at least with sufficient data, to accommodate both whole genome and restricted coverage arrays. We also propose likelihood approaches to hyperparameter estimation which are equally applicable in the Normal mixture case. The Laplace model appears to give some improvement in fit to data, though simulation studies show that our method performs similarly to several other statistical approaches to the problem of identification of differential expression.