Explaining the optimality of U-shaped age-specific mortality

Mortality is U-shaped with age for many species, declining from birth to sexual maturity, then rising in adulthood, sometimes with postreproductive survival. We show analytically why the optimal life history of a species with determinate growth is likely to have this shape. An organism allocates energy among somatic growth, fertility and maintenance/survival at each age. Adults may transfer energy to juveniles, who can then use more energy than they produce. Optimal juvenile mortality declines from birth to maturity, either to protect the increasingly valuable cumulative investments by adults in juveniles or to exploit the compounding effects of early investment in somatic growth, since early growth raises subsequent energy production, which in turn supports further growth. Optimal adult mortality rises after maturity as expected future reproduction declines as in Hamilton, but intergenerational transfers lead to postreproductive survival as in Lee. Here the Hamilton and transfer effects are divided by probabilities of survival in contrast to the fitness impact measures, which are relevant for mutation-selection balance. If energetic efficiency rises strongly with adult experience, then adult mortality could initially be flat or declining.     

Growth of juvenile steelhead Oncorhynchus mykiss under size‐selective pressure limited by seasonal bioenergetic and environmental constraints

Increased freshwater growth of juvenile steelhead Oncorhynchus mykiss improved survival to smolt and adult stages, thus prompting an examination of factors affecting growth during critical periods that influenced survival through subsequent life stages. For three tributaries with contrasting thermal regimes, a bioenergetics model was used to evaluate how feeding rate and energy density of prey influenced seasonal growth and stage‐specific survival of juvenile O. mykiss. Sensitivity analysis examined target levels for feeding rate and energy density of prey during the growing season that improved survival to the smolt and adult stages in each tributary. Simulated daily growth was greatest during warmer months (1 July to 30 September), whereas substantial body mass was lost during cooler months (1 December to 31 March). Incremental increases in annual feeding rate or energy density of prey during summer broadened the temperature range at which faster growth occurred and increased the growth of the average juvenile to match those that survived to smolt and adult stages. Survival to later life stages could be improved by increasing feeding rate or energy density of the diet during summer months, when warmer water temperatures accommodated increased growth potential. Higher growth during the summer period in each tributary could improve resiliency during subsequent colder periods that lead to metabolic stress and weight loss. As growth and corresponding survival rates in fresh water are altered by shifting abiotic regimes, it will be increasingly important for fisheries managers to better understand the mechanisms affecting growth limitations in rearing habitats and what measures might maintain or improve growth conditions and survival.     

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.     

Optimum body size: effects of food quality and temperature,when reproductive growth rate is restricted,with examples from aphids

Most models of optimum energy partitioning predict variability in adult size, although not always explicitly. Increase in size is usually attributed to an increase in the growth rate or decline in mortality. The model presented shows that this may not always be the case. Even when mortality is kept constant in organisms with overlapping generations, a constraint on the maximum reproductive growth rate may lead, when the rate of overall growth increases, to either an increase or a decline in the optimum adult body size. It is shown that adult size could be a consequence of the differential responses of life history traits to changes in temperature and food quality. This is clearly advantageous for short lived organisms, like aphids, each generation of which only experience a very small part of the great seasonal range in conditions. This hypothesis complements Iwasa's (1991) explanation of the phenotypic plasticity observed in long lived organisms. The predictions are illustrated with empirical data from aphids. The model presented, which has been verified against a very large data set, indicates that for aphids the adult weight observed at a particular combination of temperature and food quality is that at which the population growth rate, r_m, is maximized. We conclude that predictions about adult size from models based on the partitioning of energy are more likely to apply to organisms that scramble for resources, i.e., “r” selected species. The size of organisms that contest for resources is more likely to be determined by competitive status and avoidance of natural enemies.     

Diet and a developmental time constraint alter life‐history trade‐offs in a caddis fly (Trichoptera: Limnephilidae)

Environmental factors influence variation in life histories by affecting growth, development, and reproduction. We conducted an experiment in outdoor mesocosms to examine how diet and a time constraint on juvenile development (pond‐drying) influence life‐history trade‐offs (growth, development, adult body mass) in the caddis fly Limnephilus externus (Trichoptera: Limnephilidae). We predicted that: (1) diet supplementation would accelerate larval growth and development, and enhance survival to adulthood; (2) pond‐drying would accelerate development and increase larval mortality; and (3) the relationship between adult mass and age at maturity would be negative. Diet supplementation did lead to larger adult mass under nondrying conditions, but did not significantly alter growth or development rates. Contrary to predictions, pond‐drying reduced growth rates and delayed development. The slope (positive or negative) of the female mass–age at maturity relationship depended on interactions with diet or pond‐drying, but the male mass–age relationship was negative and independent of treatment. Our results suggest that pond‐drying can have negative effects on the future fitness of individuals by increasing the risk of desiccation‐induced, pre‐reproductive mortality and decreasing adult body size at maturity. These negative effects on life history cannot be overcome with additional nutritional resources in this species. © 2008 The Linnean Society of London, Biological Journal of the Linnean Society, 2008, 95 , 495–504.     

A mathematical model of glioma growth: the effect of extent of surgical resection

Abstract. We have developed a mathematical model based on proliferation and infiltration of neoplastic cells that allows predictions to be made concerning the life expectancies following various extents of surgical resection of gliomas of all grades of malignancy. The key model parameters are the growth rate and the diffusion rate. These rates were initially derived from analysis of a case of recurrent anaplastic astrocytoma treated by chemotherapies. Numerical simulations allow us to estimate what would have happened to that patient if various extents of surgical resection, rather than chemotherapies, had been used. In each case, the shell of the infiltrating tumour that remains after 'gross total removal' or even a maximal excision continues to grow and regenerates the tumour mass remarkably rapidly. By developing a model that allows the growth and diffusion rates to define the distribution of cells at the time of diagnosis, and then varying these rates by about 50%, we created a hypothetical tumour patient population whose survival times show good agreement with the results recently reported by Kreth for treatments of glioblastomas. Tenfold decreases in the rates of growth and diffusion mimic the results reported by many other investigators with more slowly growing gliomas. Thus, the model quantitatively supports the ideas that (i) gliomas infiltrate so diffusely that they cannot be cured by resection alone, surgical or radiological, no matter how extensive that may be; (ii) the more extensive the resection, regardless of the degree of malignancy of the glioma, the greater the life expectancy; and (iii) measurements of the two rates, growth and diffusion, may be able to predict survival rates better than the current histological estimates of the type and grade of gliomas.     

Winter compensatory growth under field conditions partly offsets low energy reserves before winter in a damselfly

Despite the survival value of high energy reserves during winter, animals often face energy deficits when entering winter. Compensatory growth in energy reserves during the winter period to buffer such deficits may increase winter survival and alleviate the need for costly compensatory mechanisms before or after winter when predation risk is much higher. However, such compensatory responses in energy reserves during winter have not been demonstrated under field conditions. We explored if Lestes eurinus damselfly larvae can compensate for suboptimal energy reserves during winter at 4°C when their ponds are covered with ice. In a field enclosure experiment, we demonstrated compensatory growth in terms of body mass and energy reserves in larvae whose energy status was previously manipulated in the laboratory. These results were supported by patterns in body mass and energy reserves over winter in two natural unmanipulated populations. Winter survival was high overall and not affected by compensatory growth. We hypothesize that the observed compensatory growth in energy reserves during winter may shape life history decisions in autumn and spring, and may make resource availability during winter as or more important than energy reserves before winter.     

Daisyworld is Darwinian: constraints on adaptation are important for planetary self-regulation

The Daisyworld model demonstrates that self-regulation of the global environment can emerge from competition amongst types of life altering their local environment in different ways. Robertson & Robinson (1998. J. theor. Biol.195, 129-134) presented what they describe as a "Darwinian Daisyworld" in which the ability of organisms to adapt their internal physiology in response to environmental change undermines their ability to regulate their environment. They assume that there are no bounds on the environmental conditions that organisms can adapt to and that equal growth rates can potentially be achieved under any conditions. If adaptation could respond sufficiently rapidly to changes in the environment, this would eliminate any need for the environment to be regulated in the first place, because all possible states of the environment would be equally tolerable to life. However, the thermodynamics, chemistry and structure of living organisms set bounds on the range of environmental conditions that can be adapted to. As these bounds are approached, environmental conditions limit growth rate, and adaptations necessary for survival can also cost energy. Here we take account of such constraints and find that environmental regulation is recovered in the Daisyworld model. Hence, we suggest that constraints are an important part of a self-regulating planetary system.     

Evolution vs the number of gene copies per primitive cell

Summary Computer simulations are presented of the rate at which an advantageous mutant would displace the prototype in a replicating system without an accurate segregation mechanism. If the number of gene copies in the system is indefinitely large, Darwinian evolution is essentially stopped because there is no coupling of phenotype with genotype, i.e., there is no growth advantage to the advantageous gene relative to the prototype and therefore no survival of the fittest. The inhibition of evolution due to a number of gene copies<100 would have been not insurmountable. Although the presence of multiple copies would have allowed replacement by an advantageous mutant, it provided a way for the primitive cell to conserve less immediately useful genes that could evolve into different or more effective genes. This possibility was lost as accurate segregation mechanisms evolved and cells with few copies of each gene, such as modern procaryotes, arose.     

What is life? Prerequisites for a definition

Biologists view life as transient while theologians see it as eternal. An unbiased definition for life would respect both views until one or both were eliminated by evidence. This paper identifies pre-requisites for such a definition. First among these is that all assumptions be made explicit. Currently "life" is surrounded by implicit assumptions, e.g., that it is what organisms lose at death or that it is eternal, that its quality is inversely related to personal distress, that it originated some four billion years ago, and that animate matter can be distinguished from inanimate matter. None of these assumptions are supported by data. It is possible therefore that "life" is as meaningless as phlogiston. If life has meaning, i.e., if it is true, it must be as permanent as buoyancy, gravity, electricity, and the other truths of nature. Any definition for life that would permit such truth to be seen must be free of unwarranted assumptions. For the moment, at least, such a definition would need to be loosely structured and broadly focused. It would need to describe the long and convoluted process by which matter and energy form organisms which then evolve to form conscious organisms which then explore nature and eventually discover truth. Such a definition would include all the reactions and interactions of matter and energy and all the aspects of conscious discovery. It would suffer from superficiality, but, by being free from bias, provide a foundation for dialogue between biologists and theologians.     

Alpine ibex males grow large horns at no survival cost for most of their lifetime

Large horns or antlers require a high energy allocation to produce and carry both physiological and social reproductive costs. Following the principle of energy allocation that implies trade-offs among fitness components, growing large weapons early in life should thus reduce future growth and survival. Evidence for such costs is ambiguous, however, partly because individual heterogeneity can counterbalance trade-offs. Individuals with larger horns or antlers may be of better quality and thus have a greater capacity to survive. We investigated trade-offs between male early horn growth and future horn growth, baseline mortality, onset of actuarial senescence, and rate of ageing in an Alpine ibex (Capra ibex ibex) population. Horn growth of males in early life was positively correlated to their horn length throughout their entire life. Cohort variation and individual heterogeneity both accounted for among-individual variation in horn length, suggesting both long-lasting effects of early life conditions and individual-specific horn growth trajectories. Early horn growth did not influence annual survival until 12 years of age, indicating that males do not invest in horn growth at survival costs over most of their lifetime. However, males with fast-growing horns early in life tended to have lower survival at very old ages. Individual heterogeneity, along with the particular life-history tactic of male ibex (weak participation to the rut until an old age after which they burn out in high mating investment), are likely to explain why the expected trade-off between horn growth and survival does not show up, at least until very old ages.     

Indeterminate growth is selected by a trade-off between high fecundity and risk avoidance in stochastic environments

 We developed a stage-structured model to describe optimal energy allocation among growth, reproduction, and survival. Our model includes stochastic fluctuations in survival rate at age 0 but constant survival rate at older ages. Many mammals and birds cease to grow after maturity (i.e., determinate growth), whereas organisms in a number of other taxa grow beyond maturation (i.e., indeterminate growth). We discuss the conditions under which each of the following strategies is optimal: (I) semelparity, (II) iteroparity with determinate growth, and (III) iteroparity with indeterminate growth. Our model demonstrates that iteroparity with indeterminate growth is selected for when a nonlinear relationship exists between weight and energy production; this strategy is also often selected for in stochastic environments, even with a linear relationship between weight and energy production. The optimal strategy in stochastic environments is to maximize the long-term population growth rate, which does not correspond with maximization of total fecundity. The optimal life history is determined by a balance between spreading a risk and increasing the number of offspring. Our model suggests that optimal life history strategy depends on the magnitude of environmental fluctuations, the advantage of investing in growth, the cost of survival, and the nonlinearity between weight and energy production. Received: February 20, 2002 / Accepted: September 20, 2002 Acknowledgments We thank Drs. Y. Matsumiya, K. Morita, K. Shirakihara, and Y. Watanabe for encouragement and helpful advice. We also thank the responsible editor and anonymous reviewers for helpful comments. This work was supported by a Japan Society for the Promotion of Science grant to H.M. Correspondence to:Y. Katsukawa     

Pooled energy budgets: Resituating human energy ‐allocation trade‐offs

Across taxa, many life‐history traits vary as a function of differences in body size. 1 - 5 Among primates, including humans, allometric relationships explain many trends in metabolic, growth, reproductive, and mortality rates. 6 - 8 But humans also deviate from nonhuman primates with respect to other developmental, reproductive, and parenting characteristics. 9 - 13 Broad relationships between life‐history traits and body size assume that energy expended in activity (foraging effort) is proportional to body size, and that energy available for growth and reproduction are equivalent. Because human subsistence and parenting are based on food sharing, and cooperation in labor and childrearing, the ways by which energy is acquired and allocated to alternate expenditures are expanded. We present a modification of the general allocation model to include a mechanism for these energy transfers. Our goal is to develop a framework that incorporates this mechanism and can explain the human life‐history paradox; that is, slow juvenile growth and rapid reproduction. We suggest that the central characteristics of human subsistence and energy transfer need to be accounted for in order to more fully appreciate human life‐history variability.     

A Model for Studying the Hemostatic Consumption or Destruction of Platelets

A fundamental issue in understanding homeostasis of the hematopoietic system is to what extent intrinsic and extrinsic factors regulate cell fate. We recently revisited this issue for the case of blood platelets and concluded that platelet life span is largely regulated by internal factors, in contrast to the long-held view that accumulated damage from the environment triggers clearance. However, it is known that in humans there is an ongoing fixed requirement for platelets to maintain hemostasis and prevent bleeding; hence a proportion of platelets may be consumed in such processes before the end of their natural life span. Whether it is possible to detect this random loss of platelets in normal individuals at steady-state is unknown. To address this question, we have developed a mathematical model that independently incorporates age-independent random loss and age-dependent natural senescent clearance. By fitting to population survival curves, we illustrate the application of the model in quantifying the fixed requirement for platelets to maintain hemostasis in mice, and discuss the relationship with previous work in humans. Our results suggest a higher requirement for platelets in mice than in humans, however experimental uncertainty in the data limits our ability to constrain this quantity. We then explored the relationship between experimental uncertainty and parameter constraint using simulated data. We conclude that in order to provide useful constraint on the random loss fraction the standard error in the mean of the data must be reduced substantially, either through improving experimental uncertainty or increasing the number of experimental replicates to impractical levels. Finally we find that parameter constraint is improved at higher values of the random loss fraction; thus the model find utility in situations where the random loss fraction is expected to be high, for example during active bleeding or some types of thrombocytopenia.     

The evolution of intermittent breeding

A central issue in life history theory is how organisms trade off current and future reproduction. A variety of organisms exhibit intermittent breeding, meaning sexually mature adults will skip breeding opportunities between reproduction attempts. It’s thought that intermittent breeding occurs when reproduction incurs an extra cost in terms of survival, energy, or recovery time. We have developed a matrix population model for intermittent breeding, and use adaptive dynamics to determine under what conditions individuals should breed at every opportunity, and under what conditions they should skip some breeding opportunities (and if so, how many). We also examine the effect of environmental stochasticity on breeding behavior. We find that the evolutionarily stable strategy (ESS) for breeding behavior depends on an individual’s expected growth and mortality, and that the conditions for skipped breeding depend on the type of reproductive cost incurred (survival, energy, recovery time). In constant environments there is always a pure ESS, however environmental stochasticity and deterministic population fluctuations can both select for a mixed ESS. Finally, we compare our model results to patterns of intermittent breeding in species from a range of taxonomic groups.     

Reproductive allometry does not explain the temperature-size rule in water striders (Aquarius remigis)

Most ectotherms follow the temperature-size rule meaning that individuals growing up under cool conditions are larger as adults than those growing up in warm conditions. This pattern is difficult to explain because growth is usually slower in the cold meaning it takes longer to reach a larger adult size. One potential explanation for this pattern is that the typical increase in fecundity with body size is steeper in cool environments than it is in warm environments. As such, the relative gain in fecundity for being larger in the cold would compensate for the extra time it takes to grow to that size. We present the first empirical test of this model using the water strider Aquarius remigis. Individuals were reared at either 20° or 25°C with subsampling at each instar to estimate growth trajectories. At adult eclosion, half were switched to the alternate temperature and all females isolated, mated, and reproductive output measured for 3 weeks. We found that A. remigis does follow the temperature-size rule but that fecundity was highly plastic with respect to laying temperature such that the slightly greater fecundity of those reared at 20°C was due to their larger size. Overall, those laying at 25°C were more fecund and showed a positive relationship between body size and fecundity. Those laying at 20°C did not show a significant relationship between size and fecundity. As such, the reproductive allometry shows a pattern reverse to what would be needed for a larger size in the cold to be adaptive in this species. Although A. remigis follows the temperature-size rule over this temperature range, this is likely due to a constraint on growth and development rather than being adaptive plasticity.     

The stimulation of immune defence accelerates development in the red flour beetle (Tribolium castaneum)

The timing of the transition between life stages is of key importance for an organism. Depending on the environmental conditions, maturing earlier at a smaller size or maturing later at a larger size can be advantageous for fitness. Exposure to parasites and subsequent immune activation may lead to alterations in development. Immune defence often comes at a cost, such as energy drain towards immune function, which is likely to delay development. On the other hand, animals may react to an anticipated risk of infection with a phenotypically plastic shift in life history, which may more likely lead to accelerated development and earlier maturation. We tested these alternatives in the red flour beetle, Tribolium castaneum. Young larvae were exposed to a non-infectious immune challenge with heat-killed bacteria (either Escherichia coli or Bacillus thuringiensis) and they were followed up for their development, survival, adult size and reproduction. We found that animals that had experienced a bacterial challenge developed into adults earlier than sham-treated beetles, while they did not differ significantly in survival or adult size. Beetles exposed to E. coli produced fewer offspring, while exposure to B. thuringiensis did not affect offspring number. Taken together, our results indicate that T. castaneum is able to speed up its development when facing a risk of infection.     

Warm temperatures during cold season can negatively affect adult survival in an alpine bird

Climate seasonality is a predominant constraint on the lifecycles of species in alpine and polar biomes. Assessing the response of these species to climate change thus requires taking into account seasonal constraints on populations. However, interactions between seasonality, weather fluctuations, and population parameters remain poorly explored as they require long‐term studies with high sampling frequency. This study investigated the influence of environmental covariates on the demography of a corvid species, the alpine chough Pyrrhocorax graculus, in the highly seasonal environment of the Mont Blanc region. In two steps, we estimated: (1) the seasonal survival of categories of individuals based on their age, sex, etc., (2) the effect of environmental covariates on seasonal survival. We hypothesized that the cold season—and more specifically, the end of the cold season (spring)—would be a critical period for individuals, and we expected that weather and individual covariates would influence survival variation during critical periods. We found that while spring was a critical season for adult female survival, it was not for males. This is likely because females are dominated by males at feeding sites during snowy seasons (winter and spring), and additionally must invest energy in egg production. When conditions were not favorable, which seemed to happen when the cold season was warmer than usual, females probably reached their physiological limits. Surprisingly, adult survival was higher at the beginning of the cold season than in summer, which may result from adaptation to harsh weather in alpine and polar vertebrates. This hypothesis could be confirmed by testing it with larger sets of populations. This first seasonal analysis of individual survival over the full life cycle in a sedentary alpine bird shows that including seasonality in demographic investigations is crucial to better understand the potential impacts of climate change on cold ecosystems.     

Protistan predation interferes with bacterial long‐term adaptation to substrate restriction by selecting for defence morphotypes

Bacteria that are introduced into aquatic habitats face a low substrate environment interspersed with rare productive ‘hotspots’, as well as high protistan grazing. Whereas the former condition should select for growth performance, the latter should favour traits that reduce predation mortality, such as the formation of large cell aggregates. However, protected morphotypes often convey a growth disadvantage, and bacteria thus face a trade‐off between investing in growth or defence traits. We set up an evolutionary experiment with the freshwater isolate Sphingobium sp. strain Z007 that conditionally increases aggregate formation in supernatants from a predator–prey coculture. We hypothesized that low substrate levels would favour growth performance and reduce the aggregated subpopulation, but that the concomitant presence of a flagellate predator might conserve the defence trait. After 26 (1‐week) growth cycles either with (P+) or without (P?) predators, bacteria had evolved into strikingly different phenotypes. Strains from P? had low numbers of aggregates and increased growth yield, both at the original rich growth conditions and on various single carbon sources. By contrast, isolates from the P+ treatment formed elevated proportions of defence morphotypes, but exhibited lower growth yield and metabolic versatility. Moreover, the evolved strains from both treatments had lost phenotypic plasticity of aggregate formation. In summary, the (transient) residence of bacteria at oligotrophic conditions may promote a facultative oligotrophic life style, which is advantageous for survival in aquatic habitats. However, the investment in defence against predation mortality may constrain microbial adaptation to the abiotic environment.     

Food Transfer and Development of Feeding Behavior and Food-Associated Vocalizations in Cotton-Top Tamarins

Food transfer between adults and infants is common in many marmoset and tamarin monkeys, and is often accompanied by vocalizations. We hypothesized that vocalizations by adults in a food transfer context creates an opportunity for infants to learn not only what foods are appropriate but what vocalizations are appropriate in feeding contexts. We studied the development of feeding behavior and food-associated vocalizations in 10 infant cotton-top tamarins through the first 20 wks of life. Infants obtained solid food through transfers from older group members, primarily the adult male, beginning at weeks 5–6. Both adults and infants vocalized during food transfers with adults, producing rapid sequences of the call types adults normally give when feeding. Infants were usually successful in obtaining food primarily when the adult was vocalizing. The sooner infants were active participants in food transfers, the sooner they began to feed independently. In the early weeks, infants produced a large number of vocal types during food transfers, but with increasing age there was a steady increase in the number of adult-form food calls and a reduction in other, non-food-associated calls. Infants that fed independently at an early age produced fewer non-food-associated calls by the last month of observation. Infants called at higher rates to their most preferred food. Food transfers accompanied by vocalizations may provide an opportunity for infants to learn about appropriate foods as well as the vocalizations that accompany feeding in adults, and may represent a form of 'coaching' or information donation by adults.