Temporal variability can promote migration between habitats.

Understanding the conditions that promote the evolution of migration is important in ecology and evolution. When environments are fixed and there is one most favorable site, migration to other sites lowers overall growth rate and is not favored. Here we ask, can environmental variability favor migration when there is one best site on average? Previous work suggests that the answer is yes, but a general and precise answer remained elusive. Here we establish new, rigorous inequalities to show (and use simulations to illustrate) how stochastic growth rate can increase with migration when fitness (dis)advantages fluctuate over time across sites. The effect of migration between sites on the overall stochastic growth rate depends on the difference in expected growth rates and the variance of the fluctuating difference in growth rates. When fluctuations (variance) are large, a population can benefit from bursts of higher growth in sites that are worse on average. Such bursts become more probable as the between-site variance increases. Our results apply to many (≥ 2) sites, and reveal an interplay between the length of paths between sites, the average differences in site-specific growth rates, and the size of fluctuations. Our findings have implications for evolutionary biology as they provide conditions for departure from the reduction principle, and for ecological dynamics: even when there are superior sites in a sea of poor habitats, variability and habitat quality across space determine the importance of migration.

Revisiting nocturnal heart rate and heart rate variability in insomnia: A polysomnography-based comparison of young self-reported good and poor sleepers.

Primary insomnia is often considered a disorder of 24-hr hyperarousal. Numerous attempts have been made to investigate nocturnal heart rate (HR) and its variability (HRV) as potential pathophysiological hallmarks of altered arousal levels in insomnia, with mixed results. We have aimed to overcome some of the pitfalls of previous studies by using a young, medication-free, age- and gender-matched population consisting of 43 students aged 18-30 years half with a subthreshold insomnia complaint. We employed at-home ambulatory polysomnography and compared this attenuated insomnia group to a good sleeping group. The poor sleepers had significantly higher wake after sleep onset, arousal count, mean HR in all sleep stages (with the exception of Stage 1) and lower sleep efficiency. Consistent with previous research, we also found a significant group-by-sleep stage interaction in the prediction of nocturnal HR, highlighting the insomnia group to have a lower wake-sleep HR reduction compared to good sleepers. When restricting our analyses to insomnia with objectively determined short sleep duration, we found significantly lower standard deviation of RR intervals (SDNN; a measure of HRV) compared to good sleepers. Taken together, this lends credence to the hyperarousal model of insomnia and may at least partially explain the increased prevalence of cardiovascular morbidity and mortality observed in patients with insomnia.

The human sex ratio from conception to birth.

We describe the trajectory of the human sex ratio from conception to birth by analyzing data from (i) 3- to 6-d-old embryos, (ii) induced abortions, (iii) chorionic villus sampling, (iv) amniocentesis, and (v) fetal deaths and live births. Our dataset is the most comprehensive and largest ever assembled to estimate the sex ratio at conception and the sex ratio trajectory and is the first, to our knowledge, to include all of these types of data. Our estimate of the sex ratio at conception is 0.5 (proportion male), which contradicts the common claim that the sex ratio at conception is male-biased. The sex ratio among abnormal embryos is male-biased, and the sex ratio among normal embryos is female-biased. These biases are associated with the abnormal/normal state of the sex chromosomes and of chromosomes 15 and 17. The sex ratio may decrease in the first week or so after conception (due to excess male mortality); it then increases for at least 10-15 wk (due to excess female mortality), levels off after ∼20 wk, and declines slowly from 28 to 35 wk (due to excess male mortality). Total female mortality during pregnancy exceeds total male mortality. The unbiased sex ratio at conception, the increase in the sex ratio during the first trimester, and total mortality during pregnancy being greater for females are fundamental insights into early human development.

Evolutionary shaping of demographic schedules.

Evolutionary processes of natural selection may be expected to leave their mark on age patterns of survival and reproduction. Demographic theory includes three main strands--mutation accumulation, stochastic vitality, and optimal life histories. This paper reviews the three strands and, concentrating on mutation accumulation, extends a mathematical result with broad implications concerning the effect of interactions between small age-specific effects of deleterious mutant alleles. Empirical data from genomic sequencing along with prospects for combining strands of theory hold hope for future progress.

A Bayesian approach to sequential meta-analysis.

As evidence accumulates within a meta-analysis, it is desirable to determine when the results could be considered conclusive to guide systematic review updates and future trial designs. Adapting sequential testing methodology from clinical trials for application to pooled meta-analytic effect size estimates appears well suited for this objective. In this paper, we describe a Bayesian sequential meta-analysis method, in which an informative heterogeneity prior is employed and stopping rule criteria are applied directly to the posterior distribution for the treatment effect parameter. Using simulation studies, we examine how well this approach performs under different parameter combinations by monitoring the proportion of sequential meta-analyses that reach incorrect conclusions (to yield error rates), the number of studies required to reach conclusion, and the resulting parameter estimates. By adjusting the stopping rule thresholds, the overall error rates can be controlled within the target levels and are no higher than those of alternative frequentist and semi-Bayes methods for the majority of the simulation scenarios. To illustrate the potential application of this method, we consider two contrasting meta-analyses using data from the Cochrane Library and compare the results of employing different sequential methods while examining the effect of the heterogeneity prior in the proposed Bayesian approach. Copyright © 2016 John Wiley & Sons, Ltd.

A randomised double-blind placebo-controlled trial investigating the behavioural effects of vitamin, mineral and n-3 fatty acid supplementation in typically developing adolescent schoolchildren.

Nutrient deficiencies have been implicated in anti-social behaviour in schoolchildren; hence, correcting them may improve sociability. We therefore tested the effects of vitamin, mineral and n-3 supplementation on behaviour in a 12-week double-blind randomised placebo-controlled trial in typically developing UK adolescents aged 13-16 years (n 196). Changes in erythrocyte n-3 and 6 fatty acids and some mineral and vitamin levels were measured and compared with behavioural changes, using Conners' teacher ratings and school disciplinary records. At baseline, the children's PUFA (n-3 and n-6), vitamin and mineral levels were low, but they improved significantly in the group treated with n-3, vitamins and minerals (P=0·0005). On the Conners disruptive behaviour scale, the group given the active supplements improved, whereas the placebo group worsened (F=5·555, d=0·35; P=0·02). The general level of disciplinary infringements was low, thus making it difficult to obtain improvements. However, throughout the school term school disciplinary infringements increased significantly (by 25 %; Bayes factor=115) in both the treated and untreated groups. However, when the subjects were split into high and low baseline infringements, the low subset increased their offences, whereas the high-misbehaviour subset appeared to improve after treatment. But it was not possible to determine whether this was merely a statistical artifact. Thus, when assessed using the validated and standardised Conners teacher tests (but less clearly when using school discipline records in a school where misbehaviour was infrequent), supplementary nutrition might have a protective effect against worsening behaviour.

The age-specific force of natural selection and biodemographic walls of death.

W. D. Hamilton's celebrated formula for the age-specific force of natural selection furnishes predictions for senescent mortality due to mutation accumulation, at the price of reliance on a linear approximation. Applying to Hamilton's setting the full nonlinear demographic model for mutation accumulation recently developed by Evans, Steinsaltz, and Wachter, we find surprising differences. Nonlinear interactions cause the collapse of Hamilton-style predictions in the most commonly studied case, refine predictions in other cases, and allow walls of death at ages before the end of reproduction. Haldane's principle for genetic load has an exact but unfamiliar generalization.

Derivatives of the stochastic growth rate.

We consider stochastic matrix models for population driven by random environments which form a Markov chain. The top Lyapunov exponent a, which describes the long-term growth rate, depends smoothly on the demographic parameters (represented as matrix entries) and on the parameters that define the stochastic matrix of the driving Markov chain. The derivatives of a-the "stochastic elasticities"-with respect to changes in the demographic parameters were derived by Tuljapurkar (1990). These results are here extended to a formula for the derivatives with respect to changes in the Markov chain driving the environments. We supplement these formulas with rigorous bounds on computational estimation errors, and with rigorous derivations of both the new and old formulas.

A kernel- and optimal transport- based test of independence between covariates and right-censored lifetimes.

We propose a nonparametric test of independence, termed optHSIC, between a covariate and a right-censored lifetime. Because the presence of censoring creates a challenge in applying the standard permutation-based testing approaches, we use optimal transport to transform the censored dataset into an uncensored one, while preserving the relevant dependencies. We then apply a permutation test using the kernel-based dependence measure as a statistic to the transformed dataset. The type 1 error is proven to be correct in the case where censoring is independent of the covariate. Experiments indicate that optHSIC has power against a much wider class of alternatives than Cox proportional hazards regression and that it has the correct type 1 control even in the challenging cases where censoring strongly depends on the covariate.

On Negative Heritability and Negative Estimates of Heritability.

We consider the problem of interpreting negative maximum likelihood estimates of heritability that sometimes arise from popular statistical models of additive genetic variation. These may result from random noise acting on estimates of genuinely positive heritability, but we argue that they may also arise from misspecification of the standard additive mechanism that is supposed to justify the statistical procedure. Researchers should be open to the possibility that negative heritability estimates could reflect a real physical feature of the biological process from which the data were sampled.

Statistical properties of simple random-effects models for genetic heritability.

Random-effects models are a popular tool for analysing total narrow-sense heritability for quantitative phenotypes, on the basis of large-scale SNP data. Recently, there have been disputes over the validity of conclusions that may be drawn from such analysis. We derive some of the fundamental statistical properties of heritability estimates arising from these models, showing that the bias will generally be small. We show that that the score function may be manipulated into a form that facilitates intelligible interpretations of the results. We go on to use this score function to explore the behavior of the model when certain key assumptions of the model are not satisfied - shared environment, measurement error, and genetic effects that are confined to a small subset of sites. The variance and bias depend crucially on the variance of certain functionals of the singular values of the genotype matrix. A useful baseline is the singular value distribution associated with genotypes that are completely independent - that is, with no linkage and no relatedness - for a given number of individuals and sites. We calculate the corresponding variance and bias for this setting.

Re-evaluating a test of the heterogeneity explanation for mortality plateaus.

[Drapeau, M.D., Gass, E.K., Simison, M.D., Mueller, L.D., Rose, M.R., 2000. Testing the heterogeneity theory of late-life mortality plateaus by using cohorts of Drosophila melanogaster, Experimental Gerontology, 35 71-84.] tested, in populations of Drosophila melanogaster, a prediction of the heterogeneity explanation for mortality plateaus. They concluded that heterogeneity could not explain their results. We contend here that the statistical analysis was flawed. It was declared that there was no difference between the mortality plateaus of three different strains, on the basis of averaged outcomes. In fact, the results for the different strains were quite different. Most trials showed the expected lowering of the mortality plateaus for the flies selected for robustness, but these effects were washed out by a small number of very large opposing deviations. There is ample reason to believe that the opposing deviations are artifacts of fitting an overly restrictive hazard-rate model. When we fit more appropriate models, the evidence points toward a rejection of the null hypothesis (of identical plateaus), hence toward modest support for the heterogeneity explanation.

Markov models of aging: theory and practice.

We review and structure some of the mathematical and statistical models that have been developed over the past half century to grapple with theoretical and experimental questions about the stochastic development of aging over the life course. We suggest that the mathematical models are in large part addressing the problem of partitioning the randomness in aging: How does aging vary between individuals, and within an individual over the lifecourse? How much of the variation is inherently related to some qualities of the individual, and how much is entirely random? How much of the randomness is cumulative, and how much is merely short-term flutter? We propose that recent lines of statistical inquiry in survival analysis could usefully grapple with these questions, all the more so if they were more explicitly linked to the relevant mathematical and biological models of aging. To this end, we describe points of contact among the various lines of mathematical and statistical research. We suggest some directions for future work, including the exploration of information-theoretic measures for evaluating components of stochastic models as the basis for analyzing experiments and anchoring theoretical discussions of aging.

Vital Rates from the Action of Mutation Accumulation.

New models for evolutionary processes of mutation accumulation allow hypotheses about the age-specificity of mutational effects to be translated into predictions of heterogeneous population hazard functions. We apply these models to questions in the biodemography of longevity, including proposed explanations of Gompertz hazards and mortality plateaus.

Validated analysis of mortality rates demonstrates distinct genetic mechanisms that influence lifespan.

A key goal of gerontology is to discover the factors that influence the rate of senescence, which in this context refers to the age-dependent acceleration of mortality, inversely related to the morality rate doubling time. In contrast factors that influence only initial mortality rate are thought to be less relevant to the fundamental processes of aging. To resolve these two determinants of mortality rate and lifespan, initial morality rate and rate of senescence are calculated using the Gompertz equation. Despite theoretical and empirical evidence that the Gompertz parameters are most consistently and reliably estimated by maximum-likelihood techniques, and somewhat less so by non-linear regression, many researchers continue to use linear regression on the log-transformed hazard rate. The present study compares these three methods in the analysis of several published studies. Estimates of the mortality rate parameters were then used to compare the theoretical values to the actual values of the following parameters: maximal lifespan, 50% survival times, variance in control groups and agreement with the distribution of deaths. These comparisons indicate that maximum-likelihood and non-linear regression estimates provide better estimates of mortality rate parameters than log-linear regression. Of particular interest, the improved estimates indicate that most genetic manipulations in mice that increase lifespan do so by decreasing initial mortality rate, not rate of senescence, whereas most genetic manipulations that decrease lifespan surprisingly do so by increasing the rate of senescence, not initial mortality rate.

Damage segregation at fissioning may increase growth rates: a superprocess model.

A fissioning organism may purge unrepairable damage by bequeathing it preferentially to one of its daughters. Using the mathematical formalism of superprocesses, we propose a flexible class of analytically tractable models that allow quite general effects of damage on death rates and splitting rates and similarly general damage segregation mechanisms. We show that, in a suitable regime, the effects of randomness in damage segregation at fissioning are indistinguishable from those of randomness in the mechanism of damage accumulation during the organism's lifetime. Moreover, the optimal population growth is achieved for a particular finite, non-zero level of combined randomness from these two sources. In particular, when damage accumulates deterministically, optimal population growth is achieved by a moderately unequal division of damage between the daughters, while too little or too much division is sub-optimal. Connections are drawn both to recent experimental results on inheritance of damage in protozoans, and to theories of aging and resource division between siblings.

Markov mortality models: implications of quasistationarity and varying initial distributions.

This paper explains some implications of Markov-process theory for models of mortality. We show that an important qualitative feature common to empirical mortality data, and which has been found in certain models-the convergence to a "mortality plateau"-is, in fact, a generic consequence of the models' convergence to a "quasistationary distribution". This phenomenon has been explored extensively in the mathematical literature. Not only does this generalization free important results from specifics of the models, it also suggests a new explanation for the convergence to constant mortality. At the same time that we show that the late behavior of these models-convergence to a finite asymptote-is almost logically immutable, we also point out that the early behavior of the mortality rates can be more flexible than has been generally acknowledged. We show, in particular, that an appropriate choice of initial conditions enables one popular model to approximate any reasonable hazard-rate data. This illustrates how precarious it can be to read a model's vindication from its consilience with a favored hazard-rate function, such as the Gompertz exponential.