Expanding evolutionary theories of ageing to better account for symbioses and interactions throughout the Web of Life.

How, when, and why organisms age are fascinating issues that can only be fully addressed by adopting an evolutionary perspective. Consistently, the main evolutionary theories of ageing, namely the Mutation Accumulation theory, the Antagonistic Pleiotropy theory, and the Disposable Soma theory, have formulated stimulating hypotheses that structure current debates on both the proximal and ultimate causes of organismal ageing. However, all these theories leave a common area of biology relatively under-explored. The Mutation Accumulation theory and the Antagonistic Pleiotropy theory were developed under the traditional framework of population genetics, and therefore are logically centred on the ageing of individuals within a population. The Disposable Soma theory, based on principles of optimising physiology, mainly explains ageing within a species. Consequently, current leading evolutionary theories of ageing do not explicitly model the countless interspecific and ecological interactions, such as symbioses and host-microbiomes associations, increasingly recognized to shape organismal evolution across the Web of Life. Moreover, the development of network modelling supporting a deeper understanding on the molecular interactions associated with ageing within and between organisms is also bringing forward new questions regarding how and why molecular pathways associated with ageing evolved. Here, we take an evolutionary perspective to examine the effects of organismal interactions on ageing across different levels of biological organisation, and consider the impact of surrounding and nested systems on organismal ageing. We also apply this perspective to suggest open issues with potential to expand the standard evolutionary theories of ageing.

Drewnowski's index to measure lifespan variation: Revisiting the Gini coefficient of the life table.

The Gini coefficient of the life table is a concentration index that provides information on lifespan variation. Originally proposed by economists to measure income and wealth inequalities, it has been widely used in population studies to investigate variation in ages at death. We focus on the complement of the Gini coefficient, Drewnowski's index, which is a measure of equality. We study its mathematical properties and analyze how changes over time relate to changes in life expectancy. Further, we identify the threshold age below which mortality improvements are translated into decreasing lifespan variation and above which these improvements translate into increasing lifespan inequality. We illustrate our theoretical findings simulating scenarios of mortality improvement in the Gompertz model, and showing an example of application to Swedish life table data. Our experiments demonstrate how Drewnowski's index can serve as an indicator of the shape of mortality patterns. These properties, along with our analytical findings, support studying lifespan variation alongside life expectancy trends in multiple species.

Slow and negligible senescence among testudines challenges evolutionary theories of senescence.

Is senescence inevitable and universal for all living organisms, as evolutionary theories predict? Although evidence generally supports this hypothesis, it has been proposed that certain species, such as turtles and tortoises, may exhibit slow or even negligible senescence-i.e., avoiding the increasing risk of death from gradual deterioration with age. In an extensive comparative study of turtles and tortoises living in zoos and aquariums, we show that ~75% of 52 species exhibit slow or negligible senescence. For ~80% of species, aging rates are lower than those in modern humans. We find that body weight positively relates to adult life expectancy in both sexes, and sexual size dimorphism explains sex differences in longevity. Unlike humans and other species, we show that turtles and tortoises may reduce senescence in response to improvements in environmental conditions.

Coevolution of relative brain size and life expectancy in parrots.

Previous studies have demonstrated a correlation between longevity and brain size in a variety of taxa. Little research has been devoted to understanding this link in parrots; yet parrots are well-known for both their exceptionally long lives and cognitive complexity. We employed a large-scale comparative analysis that investigated the influence of brain size and life-history variables on longevity in parrots. Specifically, we addressed two hypotheses for evolutionary drivers of longevity: the cognitivebuffer hypothesis, which proposes that increased cognitive abilities enable longer lifespans, and the expensive brain hypothesis, which holds that increases in lifespan are caused by prolonged developmental time of, and increased parental investment in, large-brained offspring. We estimated life expectancy from detailed zoo records for 133 818 individuals across 244 parrot species. Using a principled Bayesian approach that addresses data uncertainty and imputation of missing values, we found a consistent correlation between relative brain size and life expectancy in parrots. This correlation was best explained by a direct effect of relative brain size. Notably, we found no effects of developmental time, clutch size or age at first reproduction. Our results suggest that selection for enhanced cognitive abilities in parrots has in turn promoted longer lifespans.

Data gaps and opportunities for comparative and conservation biology.

Biodiversity loss is a major challenge. Over the past century, the average rate of vertebrate extinction has been about 100-fold higher than the estimated background rate and population declines continue to increase globally. Birth and death rates determine the pace of population increase or decline, thus driving the expansion or extinction of a species. Design of species conservation policies hence depends on demographic data (e.g., for extinction risk assessments or estimation of harvesting quotas). However, an overview of the accessible data, even for better known taxa, is lacking. Here, we present the Demographic Species Knowledge Index, which classifies the available information for 32,144 (97%) of extant described mammals, birds, reptiles, and amphibians. We show that only 1.3% of the tetrapod species have comprehensive information on birth and death rates. We found no demographic measures, not even crude ones such as maximum life span or typical litter/clutch size, for 65% of threatened tetrapods. More field studies are needed; however, some progress can be made by digitalizing existing knowledge, by imputing data from related species with similar life histories, and by using information from captive populations. We show that data from zoos and aquariums in the Species360 network can significantly improve knowledge for an almost eightfold gain. Assessing the landscape of limited demographic knowledge is essential to prioritize ways to fill data gaps. Such information is urgently needed to implement management strategies to conserve at-risk taxa and to discover new unifying concepts and evolutionary relationships across thousands of tetrapod species.

The diversity of population responses to environmental change.

The current extinction and climate change crises pressure us to predict population dynamics with ever-greater accuracy. Although predictions rest on the well-advanced theory of age-structured populations, two key issues remain poorly explored. Specifically, how the age-dependency in demographic rates and the year-to-year interactions between survival and fecundity affect stochastic population growth rates. We use inference, simulations and mathematical derivations to explore how environmental perturbations determine population growth rates for populations with different age-specific demographic rates and when ages are reduced to stages. We find that stage- vs. age-based models can produce markedly divergent stochastic population growth rates. The differences are most pronounced when there are survival-fecundity-trade-offs, which reduce the variance in the population growth rate. Finally, the expected value and variance of the stochastic growth rates of populations with different age-specific demographic rates can diverge to the extent that, while some populations may thrive, others will inevitably go extinct.

Complexity of the relationship between life expectancy and overlap of lifespans.

Longevity has long been recognised as a key facilitator of reciprocal altruism because repeated cooperation of partners hinges on mutual survival. Although demographic tools can be used to quantify mutual survival and expected overlapping lifespans, studies on the evolutionary theory of cooperation take only limited advantage of demography. Overlap of lifespans depends on variation in survival across ages and can be high or low independently of high or low life expectancies. Here we develop formal demographic measures to study the complex relationships between shared life expectancy of two birth cohort peers, the proportion of their lives that they can expect to overlap, and longevity. We simulate age-specific mortality schedules using a Siler model to reveal how infant and senescent mortality, along with age-independent mortality, affect the relationship between the proportion of life shared and life expectancy. We find that while the proportion of life shared can vary vastly for similar life expectancies, almost all changes to mortality schedules that result in higher life expectancies also result in higher proportions of life shared. A distinct exception occurs if life expectancy increases due to lowering the rate of senescence. In this case the proportion of life shared decreases. Our work shows that almost all selective pressures that result in higher life expectancies also result in a larger proportion of life shared. Therefore, selective forces that extend life also improve the chances that a cooperative system would be stable in terms of reciprocal interactions. Since reciprocal interactions may also reduce mortality and result in a feedback loop with the evolution of longevity, our measures and findings can be used for future cross-species comparisons that aim to disentangle predecessor and successor in the evolution of longevity and cooperation.

Rectangularization of the survival curve reconsidered: The maximum inner rectangle approach.

Rectangularization of the survival curve-a key analytical framework in mortality research-relies on assumptions that have become partially obsolete in high-income countries due to mortality reductions among the oldest old. We propose refining the concept to adjust for recent and potential future mortality changes. Our framework, the 'maximum inner rectangle approach' (MIRA) considers two types of rectangularization. Outer rectangularization captures progress in mean lifespan relative to progress in maximum lifespan. Inner rectangularization captures progress in lifespan equality relative to progress in mean lifespan. Empirical applications show that both processes have generally increased since 1850. However, inner rectangularization has displayed country-specific patterns since the onset of sustained old-age mortality declines. Results from separating premature and old-age mortality, using the MIRA, suggest there has been a switch from reducing premature deaths to extending the premature age range; a shift potentially signalling a looming limit to the share of premature deaths.

Diet has independent effects on the pace and shape of aging in Drosophila melanogaster.

Studies examining how diet affects mortality risk over age typically characterise mortality using parameters such as aging rates, which condense how much and how quickly the risk of dying changes over time into a single measure. Demographers have suggested that decoupling the tempo and the magnitude of changing mortality risk may facilitate comparative analyses of mortality trajectories, but it is unclear what biologically meaningful information this approach offers. Here, we determine how the amount and ratio of protein and carbohydrate ingested by female Drosophila melanogaster affects how much mortality risk increases over a time-standardised life-course (the shape of aging) and the tempo at which animals live and die (the pace of aging). We find that pace values increased as flies consumed more carbohydrate but declined with increasing protein consumption. Shape values were independent of protein intake but were lowest in flies consuming ~90 µg of carbohydrate daily. As protein intake only affected the pace of aging, varying protein intake rescaled mortality trajectories (i.e. stretched or compressed survival curves), while varying carbohydrate consumption caused deviation from temporal rescaling (i.e. changed the topography of time-standardised survival curves), by affecting pace and shape. Clearly, the pace and shape of aging may vary independently in response to dietary manipulation. This suggests that there is the potential for pace and shape to evolve independently of one another and respond to different physiological processes. Understanding the mechanisms responsible for independent variation in pace and shape, may offer insight into the factors underlying diverse mortality trajectories.

The Rarity of Survival to Old Age Does Not Drive the Evolution of Senescence.

The evolution of senescence is often explained by arguing that, in nature, few individuals survive to be old and hence it is evolutionarily unimportant what happens to organisms when they are old. A corollary to this idea is that extrinsically imposed mortality, because it reduces the chance of surviving to be old, favors the evolution of senescence. We show that these ideas, although widespread, are incorrect. Selection leading to senescence does not depend directly on survival to old age, but on the shape of the stable age distribution, and we discuss the implications of this important distinction. We show that the selection gradient on mortality declines with age even in the hypothetical case of zero mortality, when survivorship does not decline. Changing the survivorship function by imposing age independent mortality has no affect on the selection gradients. A similar result exists for optimization models: age independent mortality does not change the optimal result. We propose an alternative, brief explanation for the decline of selection gradients, and hence the evolution of senescence.

The emergence of longevous populations.

The human lifespan has traversed a long evolutionary and historical path, from short-lived primate ancestors to contemporary Japan, Sweden, and other longevity frontrunners. Analyzing this trajectory is crucial for understanding biological and sociocultural processes that determine the span of life. Here we reveal a fundamental regularity. Two straight lines describe the joint rise of life expectancy and lifespan equality: one for primates and the second one over the full range of human experience from average lifespans as low as 2 y during mortality crises to more than 87 y for Japanese women today. Across the primate order and across human populations, the lives of females tend to be longer and less variable than the lives of males, suggesting deep evolutionary roots to the male disadvantage. Our findings cast fresh light on primate evolution and human history, opening directions for research on inequality, sociality, and aging.

The Effect of Post-Reproductive Lifespan on the Fixation Probability of Beneficial Mutations.

Post-reproductive lifespan is a common trait among mammals and is usually considered to be neutral; i.e. with no influence on population dynamics. Here, we explore the role of post-reproductive lifespan in the fixation probability of beneficial genetic variation. We compare two separate, stationary populations living in a constant environment that are equivalent except for the average time their respective members spend in the post-reproductive stage of life. Using a recently derived approximation, we show that fixation of a beneficial mutation is more likely in the population with greater post-reproductive longevity. This finding is surprising, as the population with more prolonged post-reproductive lifespan has smaller effective size and the classic population-genetic model would suggest that decreasing effective size reduces fixation chances of beneficial mutations. Yet, as we explain, in the age-structured case, when effective size gets smaller because of longer post-reproductive lifespan but census size is kept equal, a beneficial mutation has a higher likelihood to get fixed because it finds itself at higher initial frequency.

Modeling evolutionary games in populations with demographic structure.

Classic life history models are often based on optimization algorithms, focusing on the adaptation of survival and reproduction to the environment, while neglecting frequency dependent interactions in the population. Evolutionary game theory, on the other hand, studies frequency dependent strategy interactions, but usually omits life history and the demographic structure of the population. Here we show how an integration of both aspects can substantially alter the underlying evolutionary dynamics. We study the replicator dynamics of strategy interactions in life stage structured populations. Individuals have two basic strategic behaviours, interacting in pairwise games. A player may condition behaviour on the life stage of its own, or that of the opponent, or the matching of life stages between both players. A strategy is thus defined as the set of rules that determines a player׳s life stage dependent behaviours. We show that the diversity of life stage structures and life stage dependent strategies can promote each other, and the stable frequency of basic strategic behaviours can deviate from game equilibrium in populations with life stage structures.

Quantifying the shape of aging.

In Biodemography, aging is typically measured and compared based on aging rates. We argue that this approach may be misleading, because it confounds the time aspect with the mere change aspect of aging. To disentangle these aspects, here we utilize a time-standardized framework and, instead of aging rates, suggest the shape of aging as a novel and valuable alternative concept for comparative aging research. The concept of shape captures the direction and degree of change in the force of mortality over age, which­on a demographic level­reflects aging. We 1) provide a list of shape properties that are desirable from a theoretical perspective, 2) suggest several demographically meaningful and non-parametric candidate measures to quantify shape, and 3) evaluate performance of these measures based on the list of properties as well as based on an illustrative analysis of a simple dataset. The shape measures suggested here aim to provide a general means to classify aging patterns independent of any particular mortality model and independent of any species-specific time-scale. Thereby they support systematic comparative aging research across different species or between populations of the same species under different conditions and constitute an extension of the toolbox available to comparative research in Biodemography.

Interaction mortality: senescence may have evolved because it increases lifespan.

Given an extrinsic challenge, an organism may die or not depending on how the threat interacts with the organism's physiological state. To date, such interaction mortality has been only a minor factor in theoretical modeling of senescence. We describe a model of interaction mortality that does not involve specific functions, making only modest assumptions. Our model distinguishes explicitly between the physiological state of an organism and potential extrinsic, age-independent threats. The resulting mortality may change with age, depending on whether the organism's state changes with age. We find that depending on the physiological constraints, any outcome, be it 'no senescence' or 'high rate of senescence', can be found in any environment; that the highest optimal rate of senescence emerges for an intermediate physiological constraint, i.e. intermediate strength of trade-off; and that the optimal rate of senescence as a function of the environment is driven by the way the environment changes the effect of the organism's state on mortality. We conclude that knowledge about the environment, physiology and their interaction is necessary before reasonable predictions about the evolution of senescence can be made.

Resource allocation as a driver of senescence: life history tradeoffs produce age patterns of mortality.

We investigate the effects of optimal time and resource allocation on age patterns of fertility and mortality for a model organism with (1) fixed maximum lifespan, (2) distinct juvenile and adult diets, and (3) reliance on nonrenewable resources for reproduction. We ask when it is optimal to tolerate starvation vs. conserve resources and then examine the effects of these decisions on adult mortality rates. We find that (1) age-related changes in tradeoffs partition the life cycle into as many as four discrete phases with different optimal behavior and mortality patterns, and (2) given a cost of reproduction, terminal investment can produce a signal of actuarial senescence. Also, given limitations imposed by non-replenishable resources, individuals beginning adult life with more replenishable resources do not necessarily live longer, since they can engage in capital breeding and need not defer reproduction to forage; low reproductive overheads and low costs of starvation also encourage capital breeding and may lead to earlier terminal investment and earlier senescence. We conclude that, even for species with qualitatively similar life histories, differences in physiological, behavioral and environmental tradeoffs or constraints may strongly influence optimal allocation schedules and produce variation in mortality patterns and life expectancy.

The causal pie model: an epidemiological method applied to evolutionary biology and ecology.

A general concept for thinking about causality facilitates swift comprehension of results, and the vocabulary that belongs to the concept is instrumental in cross-disciplinary communication. The causal pie model has fulfilled this role in epidemiology and could be of similar value in evolutionary biology and ecology. In the causal pie model, outcomes result from sufficient causes. Each sufficient cause is made up of a "causal pie" of "component causes". Several different causal pies may exist for the same outcome. If and only if all component causes of a sufficient cause are present, that is, a causal pie is complete, does the outcome occur. The effect of a component cause hence depends on the presence of the other component causes that constitute some causal pie. Because all component causes are equally and fully causative for the outcome, the sum of causes for some outcome exceeds 100%. The causal pie model provides a way of thinking that maps into a number of recurrent themes in evolutionary biology and ecology: It charts when component causes have an effect and are subject to natural selection, and how component causes affect selection on other component causes; which partitions of outcomes with respect to causes are feasible and useful; and how to view the composition of a(n apparently homogeneous) population. The diversity of specific results that is directly understood from the causal pie model is a test for both the validity and the applicability of the model. The causal pie model provides a common language in which results across disciplines can be communicated and serves as a template along which future causal analyses can be made.

No senescence despite declining selection pressure: Hamilton's result in broader perspective.

Theory predicts that senescence should inevitably evolve because selection pressure declines with age. Yet, data show that senescence is not a universal phenomenon. How can these observations peacefully coexist? Evolution of any trait hinges on its impact on fitness. A complete mathematical description of change in fitness, the total fitness differential, involves selection pressure along with a perturbation function that describes how the vital rates, mortality and fecundity, are affected across ages. We propose that the perturbation function can be used to model trade-offs when vital rates are perturbed in different directions and magnitude at different ages. We find that for every trade-off we can identify parameter values for which senescence does evolve and others for which it does not. We argue that this reconciles the apparent contradiction between data and theory. The total fitness differential is also instrumental in deriving mathematical relationships between alternative indicators of selection pressure. We show examples and highlight that any indicator combined with the right perturbation function can be used to parameterize a specific biological change. Biological considerations should motivate what perturbation functions are used. We interpret the relevance of Hamilton's finding that selection pressure declines for the evolution of senescence: declining selection pressure is a necessary but not a sufficient condition.

Diversity of ageing across the tree of life.

Evolution drives, and is driven by, demography. A genotype moulds its phenotype's age patterns of mortality and fertility in an environment; these two patterns in turn determine the genotype's fitness in that environment. Hence, to understand the evolution of ageing, age patterns of mortality and reproduction need to be compared for species across the tree of life. However, few studies have done so and only for a limited range of taxa. Here we contrast standardized patterns over age for 11 mammals, 12 other vertebrates, 10 invertebrates, 12 vascular plants and a green alga. Although it has been predicted that evolution should inevitably lead to increasing mortality and declining fertility with age after maturity, there is great variation among these species, including increasing, constant, decreasing, humped and bowed trajectories for both long- and short-lived species. This diversity challenges theoreticians to develop broader perspectives on the evolution of ageing and empiricists to study the demography of more species.

How evolving heterogeneity distributions of resource allocation strategies shape mortality patterns.

It is well established that individuals age differently. Yet the nature of these inter-individual differences is still largely unknown. For humans, two main hypotheses have been recently formulated: individuals may experience differences in aging rate or aging timing. This issue is central because it directly influences predictions for human lifespan and provides strong insights into the biological determinants of aging. In this article, we propose a model which lets population heterogeneity emerge from an evolutionary algorithm. We find that whether individuals differ in (i) aging rate or (ii) timing leads to different emerging population heterogeneity. Yet, in both cases, the same mortality patterns are observed at the population level. These patterns qualitatively reproduce those of yeasts, flies, worms and humans. Such findings, supported by an extensive parameter exploration, suggest that mortality patterns across species and their potential shapes belong to a limited and robust set of possible curves. In addition, we use our model to shed light on the notion of subpopulations, link population heterogeneity with the experimental results of stress induction experiments and provide predictions about the expected mortality patterns. As biology is moving towards the study of the distribution of individual-based measures, the model and framework we propose here paves the way for evolutionary interpretations of empirical and experimental data linking the individual level to the population level.