Generation time measures the trade-off between survival and reproduction in a life cycle

AbstractSurvival and fertility are the two most basic components of fitness, and they drive the evolution of a life cycle. A trade-off between them is usually present: when survival increases, fertility decreases?and vice versa. Here we show that at an evolutionary optimum, the generation time is a measure of the strength of the trade-off between overall survival and overall fertility in a life cycle. Our result both helps to explain the known fact that the generation time describes the speed of living in the slow-fast continuum of life cycles and may have implications for the extrapolation from model organisms of longevity to humans

Medawar and Hamilton on the selective forces in the evolution of ageing

Both Medawar and Hamilton contributed key ideas to the modern evolutionary theory of ageing. In particular, they both suggested that, in populations with overlapping generations, the force with which selection acts on traits declines with the age at which traits are expressed. This decline would eventually cause ageing to evolve. However, the biological literature diverges on the relationship between Medawar’s analysis of the force of selection and Hamilton’s. Some authors appear to believe that Hamilton perfected Medawar’s insightful, yet ultimately erroneous analysis of this force, while others see Hamilton’s analysis as a coherent development of, or the obvious complement to Medawar’s. Here, the relationship between the two analyses is revisited. Two things are argued for. First, most of Medawar’s alleged errors that Hamilton would had rectified seem not to be there. The origin of these perceived errors appears to be in a misinterpretation of Medawar’s writings. Second, the mathematics of Medawar and that of Hamilton show a significant overlap. However, different meanings are attached to the same mathematical expression. Medawar put forth an expression for the selective force on age-specific fitness. Hamilton proposed a full spectrum of selective forces each operating on age-specific fitness components, i.e. mortality and fertility. One of Hamilton’s expressions, possibly his most important, is of the same form as Medawar’s expression. But Hamilton’s selective forces on age-specific fitness components do not add up to yield Medawar’s selective force on age-specific fitness. It is concluded that Hamilton’s analysis should be considered neither as a correction to Medawar’s analysis nor as its obvious complement

On two conjectures about perturbations of the stochastic growth rate

The stochastic growth rate describes long-run growth of a population that lives in a fluctuating environment. Perturbation analysis of the stochastic growth rate provides crucial information for population managers, ecologists and evolutionary biologists. This analysis quantifies the response of the stochastic growth rate to changes in demographic parameters. A form of this analysis deals with changes that only occur in some environmental states. Caswell put forth two conjectures about environment-specific perturbations of the stochastic growth rate. The conjectures link the stationary distribution of the stochastic environmental process with the magnitude of some environment-specific perturbations. This note disproves one conjecture and proves the other

Selection on age-specific survival: constant versus fluctuating environment

According to a classic result in evolutionary biodemography, selection on age-specific survival invariably declines with reproductive age. The result assumes proportional changes in survival and a constant environment. Here, we look at selection on age-specific survival when changes are still proportional but the environment fluctuates. We find that selection may or may not decline with reproductive age depending on how exactly survival is proportionally altered by mutations. However, interpreted in neutral terms, the mathematics behind the classic result capture a general property that the genetics of populations with age structure possess both in a constant and in a fluctuating environment

Grace period of human mortality has declined for over a century

ObjectivesHuman mortality is U-shaped and, therefore, defines an age separating lives with an overall negative net change in mortality from lives with an overall positive net change in mortality. How has age changed, also relatively to life expectancy, over recent human history? And how does compare between humans and other primates, the mortality of which is also U-shaped?MethodsModeling data from the Human Mortality Database, the historical change of in advanced economies is reported and compared with that of primates in wild and captive conditions the demography of which was already modeled in the literature.ResultsIn humans, a marked decline in for both sexes, also relatively to their life expectancy, is associated with medical and economic progress. Comparing wild with captive conditions in nonhuman primates, magnitude, and direction of the change in , both relatively to life expectancy and absolutely, can depend on genus and sex.ConclusionsWith medical and economic progress, human lives have transitioned from a negative to a positive net change in mortality independently of sex. There is no evidence of an analogous transition occurring in other primates when their environment is made more benign

Age‐specific sensitivity analysis of stable, stochastic and transient growth for stage‐classified populations

Sensitivity analysis in ecology and evolution is a valuable guide to rank demographic parameters depending on their relevance to population growth. Here, we propose a method to make the sensitivity analysis of population growth for matrix models solely classified by stage more fine-grained by considering the effect of age-specific parameters. The method applies to stable population growth, the stochastic growth rate, and transient growth. The method yields expressions for the sensitivity of stable population growth to age-specific survival and fecundity from which general properties are derived about the pattern of age-specific selective forces molding senescence in stage-classified populations

The selection force weakens with age because ageing evolves and not vice versa

According to the classic theory of life history evolution, ageing evolves because selection on traits necessarily weakens throughout reproductive life. But this inexorable decline of the selection force with adult age was shown to crucially depend on specific assumptions that are not necessarily fulfilled. Whether ageing still evolves upon their relaxation remains an open problem. Here, we propose a fully dynamical model of life history evolution that does not presuppose any specific pattern the force of selection should follow. The model shows: (i) ageing can stably evolve, but negative ageing cannot; (ii) when ageing is a stable equilibrium, the associated selection force decreases with reproductive age; (iii) non-decreasing selection is either a transient or an unstable phenomenon. Thus, we generalize the classic theory of the evolution of ageing while overturning its logic: the decline of selection with age evolves dynamically, and is not an implicit consequence of certain assumptions

Applying symmetries of elasticities in matrix population models

Elasticity analysis is a key tool in the analysis of matrix population models, which describe the dynamics of stage-structured populations in ecology and evolution. Elasticities of the dominant eigenvalue of a matrix model to matrix entries obey certain symmetries. Yet not all consequences of these symmetries are fully appreciated, as they are sometimes hidden in mathematical detail. Here, we propose a method to reason about these symmetries directly by visual inspection of the life cycle graph that corresponds to the matrix model. We present two applications of this method, one in ecology and one in evolution. First, we prove several conjectures about elasticities that were obtained from purely numerical results and that can support population managers in decision-making under scarce demographic information. Second, we show how to identify candidates for invariant trade-offs in evolutionary optimal life cycles. The method extends to the elasticity analysis of non-dominant eigenvalues, of the stochastic growth rate and, in next-generation matrices, of the basic reproduction number

Juvenile mortality and sibling replacement: a kin selection approach

Mortality generally is higher around birth and then progressively declines through the juvenile stage. In species where offspring depend upon their parents during maturation, a factor behind this mortality decline could be sibling replacement: offspring sacrifice their survival to benefit future or present siblings as early as possible in order to minimize losses in parental investment. Here, we propose a kin-selection model of sibling replacement. Theoretical analysis of the model and its application to demographic data of mammals suggest that sibling replacement consistently generates a selective incentive for increasing juvenile mortality at early ages when this mortality increment is the result of positive selection for juvenile altruism within the nuclear family. The model highlights how sibling replacement goes beyond optimal allocation of parental resources into dependents and can provoke greater mortality closer to birth also in response to a more favorable ratio of actors to recipients of altruism among siblings