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.     

Females better face senescence in the wandering albatross

Sex differences in lifespan and aging are widespread among animals. Since investment in current reproduction can have consequences on other life-history traits, the sex with the highest cost of breeding is expected to suffer from an earlier and/or stronger senescence. This has been demonstrated in polygynous species that are highly dimorphic. However in monogamous species where parental investment is similar between sexes, sex-specific differences in aging patterns of life-history traits are expected to be attenuated. Here, we examined sex and age influences on demographic traits in a very long-lived and sexually dimorphic monogamous species, the wandering albatross (Diomedea exulans). We modelled within the same model framework sex-dependent variations in aging for an array of five life-history traits: adult survival, probability of returning to the breeding colony, probability of breeding and two measures of breeding success (hatching and fledging). We show that life-history traits presented contrasted aging patterns according to sex whereas traits were all similar at young ages. Both sexes exhibited actuarial and reproductive senescence, but, as the decrease in breeding success remained similar for males and females, the survival and breeding probabilities of males were significantly more affected than females. We discuss our results in the light of the costs associated to reproduction, age-related pairing and a biased operational sex-ratio in the population leading to a pool of non-breeders of potentially lower quality and therefore more subject to death or breeding abstention. For a monogamous species with similar parental roles, the patterns observed were surprising and when placed in a gradient of observed age/sex-related variations in life-history traits, wandering albatrosses were intermediate between highly dimorphic polygynous and most monogamous species.     

Sociality as a life-history tactic of ground squirrels

Summary Multi-variate analysis of life-history traits of 18 species of burrowing sciurids indicates that reproductive effort is determined by body-size energetics. Other traits, such as age adult weight reached, age of dispersal, length of time of gestation, were significantly correlated with body size. A principal component analysis suggested that the complex of life-history traits could be reduced to four components: body size (=weight), seasonality, specific reproductive effort, and maturity. The variation in the sociality index was best explained by age of first reproduction and age adult weight reached. Generally, species are more social when large body size combined with a relatively short growing season is associated with delayed dispersal and occurs in those species typically breeding for the first time at age two or older. Sociality in these species may have evolved through retention of daughters within the maternal home range as a means of continuing reproductive investment beyond weaning.     

Biphasic growth in fish II: empirical assessment

In [Quince, et al., 2008. Biphasic growth in fish I: Theoretical foundations. J. Theor. Biol., doi:10.1016/j.jtbi.2008.05.029], we developed a set of biphasic somatic growth models, where maturation is accompanied by a deceleration of growth due to allocation of energy to reproduction. Here, we use growth data from both hatchery-raised and wild populations of a large freshwater fish (lake trout, Salvelinus namaycush) to test these models. We show that a generic biphasic model provides a better fit to these data than the von Bertalanffy model. We show that the observed deceleration of somatic growth in females varies directly with gonad weight at spawning, with observed egg volumes roughly 50% of the egg volumes predicted under the unrealistic assumption of perfectly efficient energy transfer from somatic lipids to egg lipids. We develop a Bayesian procedure to jointly fit a biphasic model to observed growth and maturity data. We show that two variants of the generic biphasic model, both of which assume that annual allocation to reproduction is adjusted to maximise lifetime reproductive output, provide complementary fits to wild population data: maturation time and early adult growth are best described by a model with no constraints on annual reproductive investment, while the growth of older fish is best described by a model that is constrained so that the ratio of gonad size to somatic weight (g) is fixed. This behaviour is consistent with the additional observation that g increases with size and age among younger, smaller breeding females but reaches a plateau among older, larger females. We then fit both of these optimal models to growth and maturation data from nineteen wild populations to generate population-specific estimates of ‘adapted mortality’ rate: the adult mortality consistent with observed growth and maturation schedules, given that both schedules are adapted to maximise lifetime reproductive output. We show that these estimates are strongly correlated with independent estimates of the adult mortality experienced by these populations.     

Optimal age and size at maturity in annuals and perennials with determinate growth

Summary A model predicting optimal age and size at maturity is presented, exploring the conflict between growth and energy allocation to reproduction. According to the model, the factors promoting delayed maturity and large adult body size are as follows: (1) high rate of somatic growth, (2) high percentage increase in reproductive rate with body size increase, (3) long life expectancy at maturity for annuals or large number of expected productive days (when either growth or reproduction is possible) for perennials with growth ceasing at maturity, (4) life expectancy increasing with body size. All these factors are combined in the mathematical formula predicting optimal age and size at maturity, which allows for quantitative predictions. The optimal schedule of growth and reproduction may be achieved by natural selection, developmental plasticity, or when one species replaces another. Sexual size dimorphism is also discussed, resulting from different optimal age at maturity for either sex.     

Phenotypic plasticity of life history traits in relation to reproductive strategies in <Emphasis Type="Italic">Boa constrictor occidentalis</Emphasis>

The close connection between reproductive ecology and life history in snakes leads to trade-offs between reproductive and other life-history traits. Optimal energy allocation to growth and reproduction is a key factor to determine life history structure. Therefore, elucidating the relationship between body size variations and reproductive characters is essential for a better understanding of life-history plasticity. The aim of this work was to determine to what extent life-history differs among populations of Boa constrictor occidentalis and to identify possible life-history trade-offs between morphological and reproductive traits. We compared two populations from areas that are separated latitudinally, with different climatic conditions and vegetation landscape structure. Reproductive and morphological data of specimens were recorded. Although populations had a similar mean length of mature snakes, the frequency of some size classes tended to be different. Size at sexual maturity differed between populations for females, generating variations in the proportion of mature individuals. Reproductive threshold and follicular size also varied, but female reproductive frequency was similar between populations. Reproductive frequency of males varied between populations although their body condition was similar. We discussed two major issues: (1) implications of size at sexual maturity for body size and fecundity; (2) trade-offs in reproductive characters.     

Optimal resource allocation of the marine bivalve Yoldia notabilis: The effects of size-limited reproductive capacity and size-dependent mortality

The effects of the morphological constraint of maximum reproductive output (reproductive capacity) and the size at which individuals can avoid heavy mortality (refuge size) on the resource allocation pattern between growth and reproduction are investigated using a dynamic modelling approach for a population of Yoldia notabilis (Mollusca: Bivalvia) in Otsuchi Bay, northeastern Japan. A state variable model is developed using field data on shell length, somatic weight, production, survivorship and reproductive capacity of the bivalve. The optimal allocation pattern is characterized by sudden switching from growth to reproduction without the assumption of reproductive capacity, while simultaneous investment in growth and reproduction becomes optimal when maximum reproductive output is limited by reproductive capacity. Size-specific reproductive effort, size at maturity and the growth curve predicted by the latter model fit more closely to the field data, suggesting that size-limited reproductive capacity can play an important role in the evolution of the observed resource allocation pattern. The mortality pattern affects optimal size at maturity, but not size-specific reproductive effort after maturity. When refuge size is fixed, optimal size at maturity increases with survivorship above refuge size. Optimal size at maturity changes in a more complex way with changes in refuge size. Size at maturity remains constant when refuge size is small, increases when it is intermediate, and decreases when it is large. The results suggest that refuge size is an important factor in the evolution of size at maturity, although its contribution varies depending on the values of other factors, such as size-dependent production and survivorship above refuge size. This revised version was published online in July 2006 with corrections to the Cover Date.     

Reproductive investment and somatic growth rates in longear sunfish

Synopsis Allocation of energy to current reproduction at the expense of other functions, such as growth, can limit future reproductive potential. This cost of reproduction is a central concept of life history theory but has been difficult to verify in comparative field studies. Three levels of comparison of growth rates and reproductive investments were evaluated within and among populations of longear sunfish,Lepomis megalotis. All three demonstrated high levels of reproductive investment associated with reduced somatic growth. Within populations of central longear sunfish there are precociously mature sneaker makes and later maturing parental makes; sneakers have greater gonadosomatic index (GSI) values and slower somatic growth rates than parental makes. Between subspecies of longear sunfish grown under common conditions, there are differences in age at maturity and in the level of physiological reproductive investment that are associated with distinct differences in growth rates. Between populations of central longear sunfish inhabiting different sites, there are differences in the level of reproductive investment that are also associated with differences in somatic growth. Each comparison produced evidence that trade-offs occur between these life history traits, supporting the hypothesis that there is a cost of reproduction among male sunfish and suggesting that differences in strategies of reproductive investment contribute to variation in somatic growth.     

Estimating age at maturation and energy-based life-history traits from individual growth trajectories with nonlinear mixed-effects models

A new method is presented to estimate individuals’ (1) age at maturation, (2) energy acquisition rate, (3) energy expenditure for body maintenance, and (4) reproductive investment, and the multivariate distribution of these traits in a population. The method relies on adjusting a conceptual energy allocation model to individual growth curves using nonlinear mixed-effects modelling. The method’s performance was tested using simulated growth curves for a range of life-history types. Individual age at maturation, energy acquisition rate and the sum of maintenance and reproductive investment rates, and their multivariate distribution, were accurately estimated. For the estimation of maintenance and reproductive investment rates separately, biases were observed for life-histories with a large imbalance between these traits. For low reproductive investment rates and high maintenance rates, reproductive investment rate estimates were strongly biased whereas maintenance rate estimates were not, the reverse holding in the opposite situation. The method was applied to individual growth curves back-calculated from otoliths of North Sea plaice (Pleuronectes platessa) and from scales of Norwegian spring spawning herring (Clupea harengus). For plaice, maturity ogives derived from our individual estimates of age at maturation were almost identical to the maturity ogives based on gonad observation in catch samples. For herring, we observed 51.5 % of agreement between our individual estimates and those directly obtained from scale reading, with a difference lower than 1 year in 97 % of cases. We conclude that the method is a powerful tool to estimate the distribution of correlated life-history traits for any species for which individual growth curves are available.     

Variation in life-history traits of male Japanese fluvial sculpin Cottus pollux in relation to nest abundance along a stream course

Life-history theory predicts the occurrence of variation in the life-history traits of fish populations under different environmental conditions; however, most studies have focused on such variation between geographically separated populations. We compared breeding characteristics and life-history traits of the Japanese fluvial sculpin (Cottus pollux), a bottom-dwelling nest-holding fish, between two adjacent sites sub-divided by a weir along a stream course in central Japan. Males in the area with a lower abundance of nest sites reached sexual maturity at an earlier age and had a shorter life span than males in the area with sufficient nest abundance. Size-dependent male reproduction was found only in areas with a shortage of nest sites, supporting the assumption of competitive exclusion among males for nests. Females matured at the same age in both sites with no differences in age-specific growth rates and mortality. Our results provide evidence for life-history variation in age and size at maturity and age-specific mortality schedule of males in nest-holding fishes in a single stream population via different sexual selection regimes related to differences in nest abundance between sites.     

Consistency in the life history traits of four invasive pseudorasbora parva populations in Southern England

Life history plasticity can be a strong predictor of the establishment and invasion success of introduced fishes. Here, the life-history traits of four P. parva populations in adjacent ponds in Southern England were measured throughout 2013 to determine the timing and length of their reproductive season and the extent of trait plasticity. The relative abundance of the populations (as catch per unit effort) was similar, with low variability in their traits relating to reproductive effort and somatic growth. All the populations were male dominated. Both sexes matured at small body sizes, with fish as small as 30 mm being mature in both sexes, with the age at maturity for both sexes being age 1+ years. The peak spawning period, characterised by female fish investing heavily in reproduction when their gonado-somatic index (GSI) values were highest and declined thereafter, occurred in May and June, and after a mean of 212 ± 24 degree-days >12°C, and with water temperatures being 13.2–14.6°C. There were no further peaks in GSI, despite the species being considered to have prolonged spawning periods across spring and summer. These results also suggest that whilst the expression of life-history traits of invasive fishes often vary with density, they can be highly consistent between populations at similar abundances and locations.     

The importance of growth and mortality costs in the evolution of the optimal life history

A central assumption of life history theory is that the evolution of the component traits is determined in part by trade-offs between these traits. Whereas the existence of such trade-offs has been well demonstrated, the relative importance of these remains unclear. In this paper we use optimality theory to test the hypothesis that the trade-off between present and future fecundity induced by the costs of continued growth is a sufficient explanation for the optimal age at first reproduction, alpha, and the optimal allocation to reproduction, G, in 38 populations of perch and Arctic char. This hypothesis is rejected for both traits and we conclude that this trade-off, by itself, is an insufficient explanation for the observed values of alpha and G. Similarly, a fitness function that assumes a mortality cost to reproduction but no growth cost cannot account for the observed values of alpha. In contrast, under the assumption that fitness is maximized, the observed life histories can be accounted for by the joint action of trade-offs between growth and reproductive allocation and between mortality and reproductive allocation (Individual Juvenile Mortality model). Although the ability of the growth/mortality model to fit the data does not prove that this is the mechanism driving the evolution of the optimal age at first reproduction and allocation to reproduction, the fit does demonstrate that the hypothesis is consistent with the data and hence cannot at this time be rejected. We also examine two simpler versions of this model, one in which adult mortality is a constant proportion of juvenile mortality [Proportional Juvenile Mortality (PJM) model] and one in which the proportionality is constant within but not necessarily between species [Specific Juvenile Mortality (SSJM) model]. We find that the PJM model is unacceptable but that the SSJM model produces fits suggesting that, within the two species studied, juvenile mortality is proportional to adult mortality but the value differs between the two species.     

Sex‐specific reproductive investment of summer spawners of Illex argentinus in the southwest Atlantic

Energy investment in reproduction and somatic growth was investigated for summer spawners of the Argentinean shortfin squid Illex argentinus in the southwest Atlantic Ocean. Sampled squids were examined for morphometry and intensity of feeding behavior associated with reproductive maturation. Residuals generated from length‐weight relationships were analyzed to determine patterns of energy allocation between somatic and reproductive growth. Both females and males showed similar rates of increase for eviscerated body mass and digestive gland mass relative to mantle length, but the rate of increase for total reproductive organ weight relative to mantle length in females was three times that of males. For females, condition of somatic tissues deteriorated until the mature stage, but somatic condition improved after the onset of maturity. In males, there was no correlation between somatic condition and phases of reproductive maturity. Reproductive investment decreased as sexual maturation progressed for both females and males, with the lowest investment occurring at the functionally mature stage. Residual analysis indicated that female reproductive development was at the expense of body muscle growth during the immature and maturing stages, but energy invested in reproduction after onset of maturity was probably met by food intake. However, in males both reproductive maturation and somatic growth proceeded concurrently so that energy allocated to reproduction was related to food intake throughout the process of maturation. For both males and females, there was little evidence of trade‐offs between the digestive gland and reproductive growth, as no significant correlation was found between dorsal mantle length‐digestive gland weight residuals. The role of the digestive gland as an energy reserve for gonadal growth should be reconsidered. Additionally, feeding intensity by both males and females decreased after the onset of sexual maturity, but feeding never stopped completely, even during spawning.     

Diversity of age‐specific reproductive rates may result from ageing and optimal resource allocation

This paper reports the results of a dynamic programming model which optimizes resource allocation to growth, reproduction and repair of somatic damage, based on the disposable soma theory of ageing. Here it is shown that different age‐dependent patterns of reproductive rates are products of optimal lifetime strategies of resource partitioning. The array of different reproductive patterns generated by the model includes those in which reproduction begins at the maximum rate at maturity and then declines to the end of life, or increases up to a certain age and then drops. The observed patterns reflect optimal resource allocation shaped by the level of extrinsic mortality. A continuous decline in the reproductive rate from the start of reproduction is associated with high extrinsic mortality, and an early increase in the reproductive rate occurs under low extrinsic mortality. A long‐lived organism shows a low reproductive rate early in life, and short‐lived organisms start reproduction at the maximum rate.     

The evolution of life-history traits in parasitic and free-living platyhelminthes: a new perspective

Parasite life histories have been assumed to be shaped by their particular mode of existence. To test this hypothesis, we investigate the relationships between life-history traits of free-living and parasitic platyhelminthes. Using phylogenetically independent contrasts we examine patterns of interspecific covariation in adult size, progeny volume, daily fecundity, total reproductive capacity, age at first reproduction and longevity. The correlations obtained indicate a similar causal chain of life history variations for free-living and parasitic platyhelminthes. These results suggest that increased longevity favours delayed reproduction. Furthermore, growth pattern determines adult body size and age at maturity. For platyhelminthes, whether free-living or parasitic, the total reproductive capacity is found to be directly determined by the size of the worm. Within this group the parasitic way of life does not seem to influence the basic patterns of life history evolution. Received: 20 September 1997 / Accepted: 1 March 1998     

Herbivores and the evolution of the semelparous perennial life-history of plants

The relationship between a plant and its potential enemies changes drastically after reproduction has started. Using a dynamic modelling approach we study the effects of herbivores and pathogens, that are attracted by reproducing plants, on optimal allocation of resources, and life-history strategies. We assume that the level of attack increases with the investment in reproduction, which may lead to a reduction of current years reproductive success, a reduction of storage efficiency or an increase of plant mortality. If herbivores or pathogens attracted by flowering plants mainly reduce current years reproductive success, the optimal life-history is annual or iteroparous perennial if the attack is an all or nothing event. If the level of consumption increases with the number of herbivores attracted, the optimal life-history is most likely iteroparity with or without mast years. Only under very restricted conditions this may lead to semelparity. If herbivores mainly reduce the efficiency of the resources stored for next year, the optimal life-history is iteroparity. If herbivores mainly reduce survival, the optimal solution is likely to be mast years or semelparity. For parameter values that are realistic for Cynoglossum officinale, a semelparous perennial from calcereous soils, the model predicts that reproduction should start in the third year and that 99% of the available resources at the end of season should be invested in reproduction and only 1% saved for growth next year. With such an investment only c. 1% of the plants would survive after reproduction, so the optimal life-history is close to semelparity. For the small fraction of plants that reproduce more than once, years of vegetative growth only and years with reproduction should alternate. Multiple reproduction is rare in C. officinale. However, such a life history is very common for plants known as semelparous perennial. Although the available empirical evidence is, as yet, circumstantial rather than conclus ive we propose that reproduction related mortality mediated through herbivores or pathogens may play a role in the evolution of the semelparous perennial life-history.     

Reproductive traits of the dwarf gobies Pandaka trimaculata and Pandaka lidwilli in the western Pacific Ocean: histological evidence from one of the smallest fishes in the world

Gobies are generally small fishes which play important roles in estuarine ecosystems, yet little attention has been paid to their life-history traits in the western Pacific region. In the present study, the reproductive traits of the dwarf gobies Pandaka trimaculata and Pandaka lidwilli were explored by examining their populations in a subtropical estuary on Okinawa-jima Island, Japan, over 15 months. The Okinawan populations of both species shared similar reproductive traits. Pandaka trimaculata and P. lidwilli exhibited early female maturation at minimum sizes of 8.8 and 9.4 mm standard length (SL), respectively, which indicate that populations of the Pandaka species in the subtropical region represent some of the smallest fishes in the world. Nonetheless, they also had high relative body sizes at maturity relative to the attained asymptotic SLs, ranging from 75.8% to 80.4%, which suggests that their populations are vulnerable to negative impacts. Both the species also had prolonged spawning periods, extending from February to November (P. trimaculata) and from January to October (P. lidwilli), indicating that these local populations have a high potential for maintenance and resilience. Their spawning periods, sizes at maturity and fecundities varied among seasons and latitudes, possibly because of low water temperatures affecting the relative allocation of energy to growth and reproduction. Such plasticity of life-history traits in these small fishes indicates that they would be suitable models for understanding the evolution of life-history strategies and monitoring the responses of organisms to climate change.     

Age-specific resource investment strategies: evidence from female Richardson's ground squirrels (Spermophilus richardsonii)

To avoid a possible cost to their future survival and/or reproduction, individuals must balance their somatic and reproductive investments. The van Noordwijk and De Jong model of resource investment predicts that investments into reproduction and soma can vary among individuals of a population based on the variation in the total amount of energy that individuals acquire. With principal components analysis (PCA), we created two axes of life history for female Richardson's ground squirrels Spermophilus richardsonii : an index of total energy investment (PC1) and an index of investment tactic (PC2). Using these indices, we examined patterns of resource allocation to reproductive and somatic investments. Because yearling female Richardson's ground squirrels complete growth to adult size during pregnancy and early lactation, their somatic needs exceed those of older, fully grown females. Therefore, we predicted that yearlings would show more evidence of a tradeoff between reproductive and somatic investments compared with older females. Both yearling and older females invested four to five times more mass into their litters than into their own body mass. With increasing total investment, yearling females increased investment in both reproduction and themselves, whereas older females invested relatively more in reproduction than themselves. Regardless of age, females that emerged heavier from hibernation invested fewer resources into themselves and more into their litters. Variation in total energy investment and investment tactic indices was similar for yearling and older females. Contrary to our prediction, however, yearling females showed positive associations between reproductive and somatic investments, whereas older females exhibited showed no significant association between reproductive and somatic investments.     

Unexpected discontinuities in life-history evolution under size-dependent mortality

In many organisms survival depends on body size. We investigate the implications of size-selective mortality on life-history evolution by introducing and analysing a new and particularly flexible life-history model with the following key features: the lengths of growth and reproductive periods in successive reproductive cycles can vary evolutionarily, the model does not constrain evolution to patterns of either determinate or indeterminate growth, and lifetime number and sizes of broods are the outcomes of evolutionarily optimal life-history decisions. We find that small changes in environmental conditions can lead to abrupt transitions in optimal life histories when size-dependent mortality is sufficiently strong. Such discontinuous switching results from antagonistic selection pressures and occurs between strategies of early maturation with short reproductive periods and late maturation with long reproductive cycles. When mortality is size-selective and the size-independent component is not too high, selection favours prolonged juvenile growth, thereby allowing individuals to reach a mortality refuge at large body size before the onset of reproduction. When either component of mortality is then increased, the mortality refuge first becomes unattractive and eventually closes up altogether, resulting in short juvenile growth and frequent reproduction. Our results suggest a new mechanism for the evolution of life-history dimorphisms.     

How optimal life history changes with the community size-spectrum

This paper derives optimal life histories for fishes or other animals in relation to the size spectrum of the ecological community in which they are both predators and prey. Assuming log-linear size-spectra and well known scaling laws for feeding and mortality, we first construct the energetics of the individual. From these we find, using dynamic programming, the optimal allocation of energy between growth and reproduction as well as the trade-off between offspring size and numbers. Optimal strategies were found to be strongly dependent on size spectrum slope. For steep size spectra (numbers declining rapidly with size), determinate growth was optimal and allocation to somatic growth increased rapidly with increasing slope. However, restricting reproduction to a fixed mating season changed optimal allocations to give indeterminate growth approximating a von Bertalanffy trajectory. The optimal offspring size was as small as possible given other restrictions such as newborn starvation mortality. For shallow size spectra, finite optimal maturity size required a decline in fitness for large size or age. All the results are compared with observed size spectra of fish communities to show their consistency and relevance.