We age because we grow

Why do we age? Since ageing is a near-universal feature of complex organisms, a convincing theory must provide a robust evolutionary explanation for its ubiquity. This theory should be compatible with the physiological evidence that ageing is largely due to deterioration, which is, in principle, reversible through repair. Moreover, this theory should also explain why natural selection has favoured organisms that first improve with age (mortality rates decrease) and then deteriorate with age (mortality rates rise). We present a candidate for such a theory of life history, applied initially to a species with determinate growth. The model features both the quantity and the quality of somatic capital, where it is optimal to initially build up quantity, but to allow quality to deteriorate. The main theoretical result of the paper is that a life history where mortality decreases early in life and then increases late in life is evolutionarily optimal. In order to apply the model to humans, in particular, we include a budget constraint to allow intergenerational transfers. The resultant theory then accounts for all our basic demographic characteristics, including menopause with extended survival after reproduction has ceased.     

Implicit frequency dependence and kin selection in fluctuating environments

Summary I consider a general model of a fluctuating environment in which the environmental state each year is drawn at random from some given distribution. Each year organisms must choose what action to perform before the environmental state for that year is known. There is no interaction with kin. In this scenario, natural selection will tend to produce organisms which maximize their geometric mean fitness. In this paper I introduce the idea of the profile of a strategy. This function quantifies how the strategy peforms for each environmental state. I show that there is a unique profile such that a strategy is optimal if and only if it has this profile. I then give a characterization of the optimal profile which generalizes previous work by others in this area. The characterization of the optimal profile has a game theoretical interpretation. Motivated by this I introduce a game in which individuals play the field in a constant environment. This game may be interpreted as a cooperative game between kin. The key result of this paper shows that a strategy maximizes geometric mean fitness in the original fluctuating environment problem if and only if it is an evolutionarily stable strategy of the deterministic environment game. It is well known that an optimal strategy in a fluctuating environment may be mixed, involving adaptive coin-flipping. Others have previously noted that this may result in some individuals sacrificing individual reproductive success for the good of the genotype. My analysis shows that one may regain the concept of individual optimization if the quantity maximized is suitably defined. Under an optimal strategy every action taken maximizes the expected number of offspring produced, where this expectation is not calculated using the true distribution of environmental states, but a distribution modified to take account of the actions of kin.     

Sexually extravagant males age more rapidly

Evolutionary theories of ageing posit that increased reproductive investment occurs at the expense of physiological declines in later life. Males typically invest heavily in costly sexual ornaments and behaviour, but evidence that the expression of these traits can cause senescence is lacking. Long-lived houbara bustards (Chlamydotis undulata) engage in extravagant sexual displays to attract mates and here we show that males investing most in these displays experience a rapid senescent deterioration of spermatogenic function at a younger age. This effect is sufficiently large that the expected links between male 'showiness' and fertility reverse in later life, despite 'showy' males continuing to display at near maximal levels. We show that our results cannot be explained by the selective disappearance of competitive phenotypes and that they are instead consistent with an early vs. late life trade-off in male reproductive competence, highlighting the potential significance of sexual selection in explaining rates of ageing.     

The evolution of plant life span: facts and hypotheses

There are two different views on the evolution of life forms in Cormophyta: from woody plants to herbaceous ones or in opposite direction - from herbs to trees. In accordance with these views it is supposed that life span in plants changed in the course of evolution from many years (perennials) to few years (annuals, biennials), or went in reverse - from few years to many years. The author discusses the problems of senescence and longevity in Cormophyta in the context of various hypotheses of ageing (programmed death theory, mutation accumulation, antagonistic pleiotropy, disposable soma, genes of ageing, genes of longevity). Special attention is given to bio-morphological aspects of longevity and cases of non-ageing plants ("negative senescence", "potential immortality"). It is proposed to distinguish seven models of simple ontogenesis in Cormophyta that can exemplify the diversity of mechanisms of ageing and longevity. The evolution of life span in plants is considered as an indirect result of natural selection of other characteristics of organisms or as a consequence of fixation of modifications (episelectional evolution). It seems that short life span could emerge several times during evolution of one group of plants, thus favoring its adaptive radiation.     

The evolution of ageing and longevity.

Ageing is not adaptive since it reduces reproductive potential, and the argument that it evolved to provide offspring with living space is hard to sustain for most species. An alternative theory is based on the recognition that the force of natural selection declines with age, since in most environments individuals die from predation, disease or starvation. Ageing could therefore be the combined result of late-expressed deleterious genes which are beyond the reach of effective negative selection. However, this argument is circular, since the concept of 'late expression' itself implies the prior existence of adult age-related physiological processes. Organisms that do not age are essentially in a steady state in which chronologically young and old individuals are physiologically the same. In this situation the synthesis of macromolecules must be sufficiently accurate to prevent error feedback and the development of lethal 'error catastrophes'. This involves the expenditure of energy, which is required for both kinetic proof-reading and other accuracy promoting devices. It may be selectively advantageous for higher organisms to adopt an energy saving strategy of reduced accuracy in somatic cells to accelerate development and reproduction, but the consequence will be eventual deterioration and death. This 'disposable soma' theory of the evolution of ageing also proposes that a high level of accuracy is maintained in immortal germ line cells, or alternatively, that any defective germ cells are eliminated. The evolution of an increase in longevity in mammals may be due to a concomitant reduction in the rates of growth and reproduction and an increase in the accuracy of synthesis of macromolecules. The theory can be tested by measuring accuracy in germ line and somatic cells and also by comparing somatic cells from mammals with different longevities.     

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.     

Computing the partition function for kinetically trapped RNA secondary structures

An RNA secondary structure is locally optimal if there is no lower energy structure that can be obtained by the addition or removal of a single base pair, where energy is defined according to the widely accepted Turner nearest neighbor model. Locally optimal structures form kinetic traps, since any evolution away from a locally optimal structure must involve energetically unfavorable folding steps. Here, we present a novel, efficient algorithm to compute the partition function over all locally optimal secondary structures of a given RNA sequence. Our software, RNAlocopt runs in O(n3) time and O(n2) space. Additionally, RNAlocopt samples a user-specified number of structures from the Boltzmann subensemble of all locally optimal structures. We apply RNAlocopt to show that (1) the number of locally optimal structures is far fewer than the total number of structures--indeed, the number of locally optimal structures approximately equal to the square root of the number of all structures, (2) the structural diversity of this subensemble may be either similar to or quite different from the structural diversity of the entire Boltzmann ensemble, a situation that depends on the type of input RNA, (3) the (modified) maximum expected accuracy structure, computed by taking into account base pairing frequencies of locally optimal structures, is a more accurate prediction of the native structure than other current thermodynamics-based methods. The software RNAlocopt constitutes a technical breakthrough in our study of the folding landscape for RNA secondary structures. For the first time, locally optimal structures (kinetic traps in the Turner energy model) can be rapidly generated for long RNA sequences, previously impossible with methods that involved exhaustive enumeration. Use of locally optimal structure leads to state-of-the-art secondary structure prediction, as benchmarked against methods involving the computation of minimum free energy and of maximum expected accuracy. Web server and source code available at http://bioinformatics.bc.edu/clotelab/RNAlocopt/.     

Evolutionarily optimal age schedule of repair: Computer modelling of energy partition between current and future survival and reproduction

The aim of this study was to clarify the relationships between environmental conditions and physiological constraints that persist during the evolution of a species on the one hand, and the strategies of energy investment used by an individual to repair on the other. We take as a basis for our study the evolutionary optimization approach and use as a criterion of optimality the individual's lifetime reproductive success. Using methods of mathematical theory of optimal control, we calculated some optimal strategies of energy partition between repair, current survival and reproduction for various levels of uncontrollable (external) mortality. The results are presented in the form of dependencies of mortality on age and dependencies of optimal energy partitioning on age and accumulated mortality risk. Three cases of energy partitioning were considered: that between reproduction and current survival, that between reproduction and repair, and that between current survival and repair. In the case of the trade-off between reproduction and current survival, we noted opposite influences of the levels of increase of uncontrollable and controllable sources of mortality on the strategy of energy partitioning, and the crucial role of the finiteness of maximum lifespan when age-independent sources of mortality only were present. In the case of the trade-off between reproduction and repair, we noted that controllable repair leads to the emergence of accelerated growth of mortality with age, which may be considered one possible cause of the accelerated ageing often observed in nature and expressed sometimes in the form of a Gompertz-Makeham equation. In the case of the trade-off between current survival and repair, we found that, in the case of increasing mortality, repair is sacrificed not only in favour of reproduction, but also in favour of current survival, so that accelerated ageing should be expected even when investment in reproduction does not increase with age. In general, we conclude that when mortality increases, the priority when expending energy is shifted primarily in favour of reproduction, then in favour of current survival, with repair having the lowest priority. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effects of d‐galactose‐induced ageing on the heart and its potential interventions

Ageing is a strong independent risk factor for disability, morbidity and mortality. Post‐mitotic cells including those in the heart are a particular risk to age‐related deterioration. As the occurrence of heart disease is increasing rapidly with an ageing population, knowledge regarding the mechanisms of age‐related cardiac susceptibility and possible therapeutic interventions needs to be acquired to prevent advancing levels of heart disease. To understand more about the ageing heart, numerous aged animal models are being used to explore the underlying mechanisms. Due to time‐consuming for investigations involving naturally aged animals, mimetic ageing models are being utilized to assess the related effects of ageing on disease occurrence. d ‐galactose is one of the substances used to instigate ageing in various models, and techniques involving this have been widely used since 1991. However, the mechanism through which d ‐galactose induces ageing in the heart remains unclear. The aim of this review was to comprehensively summarize the current findings from in vitro and in vivo studies on the effects of d ‐galactose‐induced ageing on the heart, and possible therapeutic interventions against ageing heart models. From this review, we hope to provide invaluable information for future studies and based on the findings from experiments involving animals, we can inform possible therapeutic strategies for the prevention of age‐related heart diseases in clinical settings.     

ADAPTIVE DYNAMICS IN ALLELE SPACE: EVOLUTION OF GENETIC POLYMORPHISM BY SMALL MUTATIONS IN A HETEROGENEOUS ENVIRONMENT

We demonstrate how a genetic polymorphism of distinctly different alleles can develop during long-term frequency-dependent evolution in an initially monomorphic diploid population, if mutations have only small phenotypic effect. As a specific example, we use a version of Levene's (1953) soft selection model, where stabilizing selection acts on a continuous trait within each of two habitats. If the optimal phenotypes within the habitats are sufficiently different, then two distinctly different alleles evolve gradually from a single ancestral allele. In a wide range of parameter values, the two locally optimal phenotypes will be realized by one of the homozygotes and the heterozygote, rather than by the two homozygotes. Unlike in the haploid analogue of the model, there can be multiple polymorphic evolutionary attractors with different probabilities of convergence. Our results differ from the population genetic models of short-term evolution in two aspects: (1) a polymorphism that is population genetically stable may be invaded by a new mutant allele and, as a consequence, the population may fall back to monomorphism, (2) long-term evolution by allele substitutions may lead from a population where polymorphism is not possible into one where polymorphism is possible.     

Is the Rate of Metabolic Ageing and Survival Determined by Basal Metabolic Rate in the Zebra Finch?

The relationship between energy metabolism and ageing is of great interest because aerobic metabolism is the primary source of reactive oxygen species which is believed to be of major importance in the ageing process. We conducted a longitudinal study on captive zebra finches where we tested the effect of age on basal metabolic rate (BMR), as well as the effect of BMR on the rate of metabolic ageing (decline in BMR with age) and survival. Basal metabolic rate declined with age in both sexes after controlling for the effect of body mass, indicating a loss of functionality with age. This loss of functionality could be due to accumulated oxidative damage, believed to increase with increasing metabolic rate, c.f. the free radical theory of ageing. If so, we would expect the rate of metabolic ageing to increase and survival to decrease with increasing BMR. However, we found no effect of BMR on the rate of metabolic ageing. Furthermore, survival was not affected by BMR in the males. In female zebra finches there was a tendency for survival to decrease with increasing BMR, but the effect did not reach significance (P<0.1). Thus, the effect of BMR on the rate of functional deterioration with age, if any, was not strong enough to influence neither the rate of metabolic ageing nor survival in the zebra finches.     

An ESS for the Height of a Plant Population, or an Optimal Height for an Individual?—Rethinking Game-Theoretic Models for Plant Height

Plants only interact with neighbors over restricted distances, so local conditions are of great significance for plants. It is therefore important to consider spatial structure and neighborhood effects if we are to understand plants' strategies. We constructed a spatially-explicit, game theory model to explore optimal height growth at the individual-level. In the model, there is no ESS for height growth at the population level, because there is an “instantaneous” optimal height growth strategy for the individual plant that changes depending on the local light environment. The optimal strategy is plasticity in response to local conditions. Game-theoretic models for plant phenotypic traits should move from “mean-field approximations” towards explicit modeling of local interactions.     

Maximum sustainable yield of populations with continuous age-structure.

We address the problem of finding the harvesting policy that will maximize the yield and maintain a population in a steady state. The population is characterized by continuous age classes and therefore follows differential equations. Here, we assume that the equations are linear (no density dependence). Two possible constraints are considered: either recruitment or total population are fixed to a constant. Under these conditions, the optimal policy is to harvest the fraction theta of a younger age class ? and to harvest totally an older age class b. The optimal solution (theta, ?, b) can be calculated explicitly if the fecundity and mortality schedules are given. The solution is compared to the simpler strategy of harvesting all individuals beyond a single age class a. It is shown that the latter strategy can be much less profitable than harvesting two age classes because it cannot take account of the different values of individuals according to their age.     

Epigenetic age prediction

Advanced age is the main common risk factor for cancer, cardiovascular disease and neurodegeneration. Yet, more is known about the molecular basis of any of these groups of diseases than the changes that accompany ageing itself. Progress in molecular ageing research was slow because the tools predicting whether someone aged slowly or fast (biological age) were unreliable. To understand ageing as a risk factor for disease and to develop interventions, the molecular ageing field needed a quantitative measure; a clock for biological age. Over the past decade, a number of age predictors utilising DNA methylation have been developed, referred to as epigenetic clocks. While they appear to estimate biological age, it remains unclear whether the methylation changes used to train the clocks are a reflection of other underlying cellular or molecular processes, or whether methylation itself is involved in the ageing process. The precise aspects of ageing that the epigenetic clocks capture remain hidden and seem to vary between predictors. Nonetheless, the use of epigenetic clocks has opened the door towards studying biological ageing quantitatively, and new clocks and applications, such as forensics, appear frequently. In this review, we will discuss the range of epigenetic clocks available, their strengths and weaknesses, and their applicability to various scientific queries.     

Neighbor intervention: a game-theoretic model

It has long been argued that a resident may benefit from helping its neighbor defend a territory against a challenger to avoid renegotiating its boundaries with a new and potentially stronger individual. We quantify this theory by exploring games involving challengers, residents and potential allies. In a simplified discrete game with zero variation of fighting strength, helping neighbors is part of an evolutionarily stable strategy (ESS) only if fighting costs are low relative to those of renegotiation. However, if relative fighting costs are high then an interventional ESS remains possible with finite variation of strength. Under these conditions, neighbors may help residents fight off intruders, but only when the resident does not stand a reliable chance of winning alone. We show that neighbor intervention is more likely with low home advantage to occupying a territory, strengths combining synergistically or low probability that an ally will be usurped, amongst other factors. Our parameterized model readily explains occasional intervention in the Australian fiddler crab, including why the ally tended to be larger than both the assisted neighbor and the intruder. Reciprocity is not necessary for this type of cooperation to persist, but also it is by no means inevitable in territorial species.     

Is ageing the result of dominant and co-dominant mutations?

A number of unexplained features of ageing can be accounted for if cellular ageing is due to dominant or co-dominant mutations. The experimental evidence both for and against this hypothesis is weak, but experiments involving direct testing are possible.     

Optimal antiviral treatment strategies and the effects of resistance

Recent pandemic planning has highlighted the importance of understanding the effect that widespread antiviral use will have on the emergence and spread of resistance. A number of recent studies have determined that if resistance to antiviral medication can evolve, then deploying treatment at a less than maximum rate often minimizes the outbreak size. This finding, however, involves the assumption that treatment levels remain constant during the entire outbreak. Using optimal control theory, we address the question of optimal antiviral use by considering a large class of time-varying treatment strategies. We prove that, contrary to previous results, it is always optimal to treat at the maximum rate provided that this treatment occurs at the right time. In general the optimal strategy is to wait some fixed amount of time and then to deploy treatment at the maximum rate for the remainder of the outbreak. We derive analytical conditions that characterize this optimal amount of delay. Our results show that it is optimal to start treatment immediately when one of the following conditions holds: (i) immediate treatment can prevent an outbreak, (ii) the initial pool of susceptibles is small, or (iii) when the maximum possible rate of treatment is low, such that there is little de novo emergence of resistant strains. Finally, we use numerical simulations to verify that the results also hold under more general conditions.     

Signalling and the evolution of cooperative foraging in dynamic environments

Understanding cooperation in animal social groups remains a significant challenge for evolutionary theory. Observed behaviours that benefit others but incur some cost appear incompatible with classical notions of natural selection; however, these behaviours may be explained by concepts such as inclusive fitness, reciprocity, intra-specific mutualism or manipulation. In this work, we examine a seemingly altruistic behaviour, the active recruitment of conspecifics to a food resource through signalling. Here collective, cooperative behaviour may provide highly nonlinear benefits to individuals, since group functionality has the potential to be far greater than the sum of the component parts, for example by enabling the effective tracking of a dynamic resource. We show that due to this effect, signalling to others is an evolutionarily stable strategy under certain environmental conditions, even when there is a cost associated to this behaviour. While exploitation is possible, in the limiting case of a sparse, ephemeral but locally abundant nutrient source, a given environmental profile will support a fixed number of signalling individuals. Through a quantitative analysis, this effective carrying capacity for cooperation is related to the characteristic length and time scales of the resource field.     

Optimal risk management of human alveolar echinococcosis with vermifuge

In this study, we develop a bioeconomic model of human alveolar echinococcosis (HAE) and formulate the optimal strategies for managing the infection risks in humans by applying optimal control theory. The model has the following novel features: (i) the complex transmission cycle of HAE has been tractably incorporated into the framework of optimal control problems and (ii) the volume of vermifuge spreading to manage the risk is considered a control variable. With this model, we first obtain the stability conditions for the transmission dynamics under the condition of constant control. Second, we explicitly introduce a control variable of vermifuge spreading into the analysis by considering the associated control costs. In this optimal control problem, we have successfully derived a set of conditions for a bang-bang control and singular control, which are mainly characterized by the prevalence of infection in voles and foxes and the remaining time of control. The analytical results are demonstrated by numerical analysis and we discuss the effects of the parameter values on the optimal strategy and the transmission cycle. We find that when the prevalence of infection in foxes is low and the prevalence of infection in voles is sufficiently high, the optimal strategy is to expend no effort in vermifuge spreading.     

Induction of replicative senescence by 5-azacytidine: fundamental cell kinetic differences between human diploid fibroblasts and NIH-3T3 cells

Abstract. To analyse the putative role of methylation of cytosine residues in the nuclear DNA as a regulatory step during cellular ageing, we incubated ageing human amniotic fluid derived fibroblast-like cells and non-ageing NIH-3T3 cells with 5-azacytidine. BrdUrd/Hoechst and acridine orange (AO) flow cytometry was used to compare the effects of the base analogue on cell proliferation and cell differentiation. In NIH-3T3 cultures, 96 h exposures to 4 μM 5-azacytidine caused diminished cell proliferation due to cell arrest in the G₁ compartments of the second and third cell cycles of serum stimulated cells. The exit from the G₀/G₁ compartment was not affected. The 5-azacytidine induced cell kinetic disturbances were unstable in NIH-3T3 cultures, such that pre-treated cells reverted to normal cell cycle transit within 2–3 days after termination of treatment. In contrast, 5-azacytidine pre-treated amniotic fluid derived fibroblast-like cell cultures showed persistently elevated G₂ phase arrests and delayed G₀/G₁ phase exit kinetics, which explain the premature cessation of proliferation observed in these primary cultures. In both cell systems, 5-azacytidine exposed cultures showed elevated numbers of G₁ phase cells with increased RNA content as revealed by AO flow cytometry. Again, this effect was reversible in NIH-3T3 cells but not in amniotic fluid derived fibroblast-like cells. These contrasting responses to 5-azacytidine are likely to reflect intrinsic differences in methylation patterns or de novo methylase activity between ageing cell strains and non-ageing cell lines.