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.     

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.     

Growth after maturity as a sub-optimal strategy

Patterns of optimal resource allocation to growth and reproduction were investigated using a numerical simulation. As in most previous analyses, cessation of growth when reproduction begins (the determinate strategy) appeared optimal. Here, it was additionally found that fitness was only slightly lower for individuals that continue to grow after maturation. Therefore, it is argued that selection for a determinate strategy may be too weak to overwhelm random processes like environmental stochasticity or genetic drift that shape patterns of growth, especially under low mortality. The consequences of an indeterminate strategy for optimal size at maturity and final size were investigated: prolonging the period in which growth and reproduction co-occurred decreased size at maturity only slightly but markedly increased the final size.     

Size and temperature in the evolution of fish life histories

Body size and temperature are the two most important variablesaffecting nearly all biological rates and times, especiallyindividual growth or production rates. By favoring an optimalmaturation age and reproductive allocation, natural selectionlinks individual growth to the mortality schedule. A recentmodel for evolution of life histories for species with indeterminategrowth, which includes most fish, successfully predicts thenumeric values of two key dimensionless numbers and the allometryof the average reproductive allocation versus maturation sizeacross species. Here we use this new model to predict the relationshipsof age-at-maturity, adult mortality and reproductive effortto environmental temperature and maturation size across species.Age-at-maturity, adult mortality and the proportion of the bodymass given to reproduction per year are predicted to show ±0.25power allometries with mass at maturity, and an exponential(Boltzmann) temperature dependence. Temperature is assumed toaffect only body size growth, so the temperature linkages ofmaturation, mortality and reproductive effort are indirect vialife history optimization; this is briefly contrasted with theidea that (for example) temperature directly affects mortality.     

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.     

Heuristic optimization of the general life history problem: A novel approach

Summary The general life history problem concerns the optimal allocation of resources to growth, survival and reproduction. We analysed this problem for a perennial model organism that decides once each year to switch from growth to reproduction. As a fitness measure we used the Malthusian parameterr, which we calculated from the Euler-Lotka equation. Trade-offs were incorporated by assuming that fecundity is size dependent, so that increased fecundity could only be gained by devoting more time to growth and less time to reproduction. To calculate numerically the optimalr for different growth dynamics and mortality regimes, we used a simplified version of the simulated annealing method. The major differences among optimal life histories resulted from different accumulation patterns of intrinsic mortalities resulting from reproductive costs. If these mortalities were accumulated throughout life, i.e. if they were senescent, a bangbang strategy was optimal, in which there was a single switch from growth to reproduction: after the age at maturity all resources were allocated to reproduction. If reproductive costs did not carry over from year to year, i.e. if they were not senescent, the optimal resource allocation resulted in a graded switch strategy and growth became indeterminate. Our numerical approach brings two major advantages for solving optimization problems in life history theory. First, its implementation is very simple, even for complex models that are analytically intractable. Such intractability emerged in our model when we introduced reproductive costs representing an intrinsic mortality. Second, it is not a backward algorithm. This means that lifespan does not have to be fixed at the begining of the computation. Instead, lifespan itself is a trait that can evolve. We suggest that heuristic algorithms are good tools for solving complex optimality problems in life history theory, in particular questions concerning the evolution of lifespan and senescence.     

Evolution of longevity through optimal resource allocation

Models of life history evolution predict optimal traits of a simplified organism under various environmental conditions, but they at most acknowledge the existence of ageing. On the other hand, genetic models of ageing do not consider the effects of ageing on life histroy traits other than fecundity and longevity. This paper reports the results of a dynamic programming model which optimizes resource allocation to growth, reproduction and somatic repair. A low extrinsic (environmentally caused) mortality rate and high repair efficiency promote allocation to repair, especially early in life, resulting in delayed ageing and low growth rates, delayed maturity, large body size and dramatic enhancement of survival and maximum lifespan. The results are generally consistent with field, comprative and experimental data. They also suggest that the relationships between maximum lifespan and age at maturity and body size observed in nature may be by-products of optimal allocation strategies.     

Phenotypic plasticity and interpopulation differences in life history traits of<Emphasis Type="Italic"> Armadillidium vulgare</Emphasis> (Isopoda:Oniscidae)

The hypothesis that the balance of trade-offs between survivorship, growth and reproductive allocation in the terrestrial isopod Armadillidium vulgare will change when resource input is increased has been investigated experimentally. When the quality of food available was increased, by adding a mixture of litter from herbaceous dicotyledonous plants to a background low-quality food of dead grasses, survivorship was found to be the most phenotypically plastic trait, increasing by 168%. Growth rates increased by 99% but reproductive allocation by only 21%. In the field, members of a population from a site with more high-quality food grew more than twice as fast as those from a site where less high-quality food was available. The population from the site with higher food availability, contrary to predictions from the laboratory study, did not survive as well as that from the site with less available high-quality food. This may be because the site that is more favourable for growth has a more stressful physical environment due to much bigger temperature fluctuations, which are known to be an important cause of mortality in this species. When individuals from both populations were reared under controlled laboratory conditions, both the parental and F1 generations from the poor growth environment survived better than those from the good growth habitat. However, even when given an excess of high-quality food those from the poor growth environment continued to grow more slowly and had a lower reproductive allocation than those from the site with higher food availability. We conclude that microevolutionary changes may have occurred in the balance of resource allocation between survivorship, growth and reproductive allocation, to favour higher survivorship during the longer prereproductive period at the site where growth to the threshold size for reproduction takes longer.     

Conserved ontogeny and allometric scaling of resource acquisition and allocation in the Daphniidae

Life histories vary widely among taxa, but within phylogenetic groups there may be a fundamental framework around which trait variation is organized, perhaps as a consequence of lineage-specific developmental constraints. In organisms with indeterminate growth, there is an ongoing problem of optimally allocating resources between growth and reproduction, and that allocation decision may manifest itself through allometric scaling. Previous work on freshwater zooplankton has shown that the ontogenetic pattern of resource allocation can be described by simple mathematical functions. An important component of understanding how such functions can explain life-history variation is to discover which parameters in these functions are robust, with respect to both resource availability and evolutionary diversification, and which parameters exhibit interspecific allometry. To shed light on these issues, detailed life table experiments were conducted on eight species in the family Daphniidae (Crustacea) at high and low levels of resources. Using data on growth, reproduction, and instar duration, the ontogeny of resource allocation to growth and reproduction could be described as functions that plateau at or shortly after the onset of maturity. To be sure that the results were not an artifact of phylogenetic structure, the parameters were tested in a phylogenetically controlled fashion. The results suggest a simple set of resource allocation rules for daphniids, whereby all species exhibit a similar form of ontogenetic change in allocation, and reach a plateau where approximately 94% of available resources are allocated to reproduction. The asymptotically maximal rate of net resources incorporated in growth and reproduction was positively related to size at maturity, whereas the rates of approach to plateaus (for both net resource assimilation and proportional allocation to reproduction) were negatively related to body size. Per-offspring investment was positively related to the square root of size at maturity. Using this approach, a wide range of interspecific variation in life-history features can be related to a single underlying trait, the size at first reproductive investment.     

Habitat quality and among-population differentiation in reproductive effort and flowering phenology in the perennial herb <Emphasis Type="Italic">Primula farinosa</Emphasis>

In heterogeneous environments, selection on life-history traits and flowering time may vary considerably among populations because of differences in the extent to which mortality is related to age or size, and because of differences in the seasonal patterns of resource availability and intensity of biotic interactions. Spatial variation in optimal reproductive effort and flowering time may result in the evolution of genetic differences in life-history traits, but also in the evolution of adaptive phenotypic plasticity. The perennial herb Primula farinosa occurs at sites that differ widely in soil depth and therefore in water-holding capacity, vegetation cover, and frost-induced soil movement in winter. We used data from eight natural populations and a common-garden experiment to test the predictions that reproductive allocation is negatively correlated with soil depth while age at first reproduction and first flowering date among reproductive individuals are positively correlated with soil depth. In the common-garden experiment, maternal families collected in the field were grown from seed and monitored for 5 years. In the field, reproductive effort (number of flowers in relation to rosette area) varied among populations and was negatively related to soil depth. In the common-garden experiment, among-population differences in age at first reproduction, and reproductive effort were statistically significant, but relatively small and not correlated with soil depth at the site of origin. Flowering time varied considerably among populations, but was not related to soil depth at the site of origin. Taken together, the results suggest that among-population variation in reproductive effort observed in the field largely reflects phenotypic plasticity. They further suggest that among-population differentiation in flowering time cannot be attributed to variation in environmental factors correlated with soil depth.     

Physiological dynamics,reproduction‐maintenance allocations,and life history evolution

Allocation of resources to competing processes of growth, maintenance, or reproduction is arguably a key process driving the physiology of life history trade‐offs and has been shown to affect immune defenses, the evolution of aging, and the evolutionary ecology of offspring quality. Here, we develop a framework to investigate the evolutionary consequences of physiological dynamics by developing theory linking reproductive cell dynamics and components of fitness associated with costly resource allocation decisions to broader life history consequences. We scale these reproductive cell allocation decisions to population‐level survival and fecundity using a life history approach and explore the effects of investment in reproduction or tissue‐specific repair (somatic or reproductive) on the force of selection, reproductive effort, and resource allocation decisions. At the cellular level, we show that investment in protecting reproductive cells increases fitness when reproductive cell maturation rate is high or reproductive cell death is high. At the population level, life history fitness measures show that cellular protection increases reproductive value by differential investment in somatic or reproductive cells and the optimal allocation of resources to reproduction is moulded by this level of investment. Our model provides a framework to understand the evolutionary consequences of physiological processes underlying trade‐offs and highlights the insights to be gained from considering fitness at multiple levels, from cell dynamics through to population growth.     

Twelve fundamental life histories evolving through allocation‐dependent fecundity and survival

An organism's life history is closely interlinked with its allocation of energy between growth and reproduction at different life stages. Theoretical models have established that diminishing returns from reproductive investment promote strategies with simultaneous investment into growth and reproduction (indeterminate growth) over strategies with distinct phases of growth and reproduction (determinate growth). We extend this traditional, binary classification by showing that allocation‐dependent fecundity and mortality rates allow for a large diversity of optimal allocation schedules. By analyzing a model of organisms that allocate energy between growth and reproduction, we find twelve types of optimal allocation schedules, differing qualitatively in how reproductive allocation increases with body mass. These twelve optimal allocation schedules include types with different combinations of continuous and discontinuous increase in reproduction allocation, in which phases of continuous increase can be decelerating or accelerating. We furthermore investigate how this variation influences growth curves and the expected maximum life span and body size. Our study thus reveals new links between eco‐physiological constraints and life‐history evolution and underscores how allocation‐dependent fitness components may underlie biological diversity.     

Life-history plasticity under resource stress in a clonal fish (Poeciliidae: Poeciliopsis)

Within-individual plasticity for reproductive investment was examined in a clonal fish (Poeciliidae: Poeciliopsis) grown under six levels of resource stress. Growth, age at first reproduction, egg production, egg size, egg energetic content, and survivorship were measured from fish grown in three dietary and two density treatments. Growth and fecundity decreased with both increased density and food stress. Age at first reproduction increased with increased density, but was unaffected by the diet treatments. Reproductive effort (clutch size per female weight), offspring investment (egg size and egg energetic content), and survivorship were invariant across all treatment combinations. We compare these results with predictions based on theoretical treatments of optimal reproductive investment.     

腾格里沙漠人工固沙植被中油蒿的生长及生物量分配动态

植物的资源分配模式反映了对环境的生态适应对策。2007年整个生长季, 采用生物量法对腾格里沙漠东南缘固沙植被区半灌木油蒿(Artemisia ordosica)地上部分各器官的生长及资源分配格局动态进行了研究。结果表明: 不同时期各器官的生长速率不同, 光合产物在各器官中的分配也不是等量的, 而是按一定的顺序在不同时期有不同的分配中心; 2007年油蒿的营养生长、繁殖输出、生殖枝大小都显著大于年降水量不足其一半的年份, 而繁殖分配和头状花序大小没有差异; 营养器官生物量大的油蒿总的繁殖输出也大, 但生殖期内营养生长和生殖生长既不同时也不等速, 表明资源分配的权衡(Trade-off)是存在的; 固沙植被建立以后, 随着时间延长, 油蒿的当年总生物量、繁殖输出、繁殖器官生物量分配有减小的趋势, 但不显著。     

Life history strategy of Leptinaria unilamellata (d'Orbigny, 1835) (Mollusca,Pulmonata, Subulinidae)

Abstract

Life history theory predicts that the patterns of resource allocation in animals are associated with different strategies, selected in the course of evolution. In the present study, the life history of Leptinaria unilamellata was characterized under laboratory conditions. We determined the growth, reproduction, and longevity patterns of this species and elucidated the strategy related to the development of embryos, through direct observations and examination of the morphology of the gravid uterus. Furthermore, we attempted to analyze the glycogen and galactogen contents of the albumen gland, digestive gland and cephalopedal mass in order to understand energy allocation to life history traits, for three life stages. Leptinaria unilamellata's life history is characterized by great longevity, a short juvenile phase, early sexual maturity, and repeated reproductive events, with little reproductive effort at each event and some mortality shortly after the first reproduction. In the terraria, we found juveniles but no eggs. However, the results of the anatomical study showed no morphological connection between the embryos and the parental organism. Thus, this species should be described as ovoviviparous rather than viviparous. Egg retention in the parent organism is the primary cause of the release of juveniles, instead of eggs, enabling the offspring to withstand environmental stress. The higher quantity of galactogen found in the adults' albumen gland, as compared to juveniles and senescent individuals, as well as the ratio of glycogen to galactogen, reveal the allocation of energy to reproduction rather than to growth. The remaining energy is directed to the maintenance of omeostasis. Such pattern was confirmed by the low levels of glycogen and galactogen observed in the senescent stage, compared to the juvenile and adult stages. In the life strategy of L. unilamellata, the distribution of the reproductive effort among many events associated with ovoviviparity indicates a long-term investment in reproductive success.     

THE EVOLUTION OF REPRODUCTIVE EFFORT IN LIZARDS AND SNAKES

Life history theory suggests that the optimal evolved level of reproductive effort (RE) for an organism depends upon the degree to which additional current reproductive investment reduces future reproductive output. Future reproduction can be decreased in two ways, through (i) decreases in the organism's survival rate, and/or (ii) decreases in the organism's growth (and hence subsequent fecundity). The latter tradeoff–that is, the “potential fecundity cost”—should affect the evolution of RE only in species with relatively high survival rate, a relatively high rate of fecundity increase with body size, or a relatively high reproductive frequency per annum. Unless these conditions are met, the probable benefit in future fecundity obtained from decreasing present reproductive output is too low for natural selection to favor any reduction in RE below the maximum physiologically possible. Published data on survival rate, reproductive frequency and relative clutch mass (RCM) suggest that many lizard species fall well below the level at which natural selection can be expected to influence RE through such “potential fecundity” tradeoffs. Hence, the relative allocation of resources between growth and reproduction is unlikely to be directly optimized by natural selection in these animals. Instead, energy allocation should influence the evolution of RE only indirectly, via effects on an organism's probability of survival during reproduction. Survival costs of reproduction may be the most important evolutionary determinants of RE in many reptiles, and information on the nature and extent of such costs is needed before valid measures of reptilian RE can be constructed.     

Phenotypic plasticity and priority rules for energy allocation in a freshwater clam: a field experiment

We studied resource allocation among maintenance, reproduction and growth in the freshwater clam Anodonta piscinalis. Recent theoretical and empirical studies imply that organisms with indeterminate growth may have priority rules for energy allocation. That being so, the traits involved should potentially be capable of considerable phenotypic modulation, as a mechanism to adjust allocation. We tested this hypothesis using a 1-year reciprocal transplant experiment at six sites. Experimental clams were caged at higher than natural densities in order to detect any phenotypic modulation of the traits and discover the putative priority rules in energy allocation. We recorded the survival and shell growth of clams during the experiment, and the reproductive output, somatic mass and fat content of clams at the end of the experiment. Shell growth, somatic mass, and the reproductive output of females varied more among transplant sites than among the populations of origin, suggesting a high capacity for phenotypic modulation. However, the reproductive investment, somatic mass and shell growth were also affected by origin; clams from productive habitats invested more in reproduction and were heavier. In comparison to undisturbed clams, the reproductive output of the experimental clams was similar and their fat content was higher, whereas their shell growth was considerably slower and their somatic mass lower. These results suggests that when resources are limiting (due to high density) reproductive allocation overrides allocation to somatic growth. The highest mortality during the experiment coincided with the period of reproductive stress in the spring. Additionally, the proportion of reproducing females was lower in those transplant groups where the survival rate was lowest, suggesting that maintenance allocation overrides allocation to reproduction when available resources are scarce. The results of this field experiment support theoretical predictions and results of previous laboratory experiments that suggest that there are priority rules for energy allocation in organisms with indeterminate growth.     

A dynamic model of size-dependent reproductive effort in a sequential hermaphrodite: a counterexample to Williams's conjecture

In 1966, G. C. Williams showed that for iteroparous organisms, the level of reproductive effort that maximizes fitness is that which balances the marginal gains through current reproduction against the marginal losses to expected future reproduction. When, over an organism's lifetime, the value of future reproduction declines relative to the value of current reproduction, the level of effort allocated to current reproduction should always increase with increasing age. Conversely, when the value of future reproduction increases relative to the value of current reproduction, the level of effort allocated to current reproduction should decrease or remain at zero. While this latter pattern occurs commonly in species that exhibit a delayed age at first reproduction, it may also occur following an initial period of reproduction in some sex-changing organisms that experience a dramatic increase in reproductive potential as they grow larger. Indeed, this schedule of reproductive effort is predicted by models of "early" sex change; however, these models may arrive at this result incidentally because they consider only two reproductive states: on and off. In order to examine the schedule of reproductive effort in greater detail in a system where the potential reproductive rate increases sharply, we adapt the logic and methods of time-dependent dynamic-programming models to develop a size-dependent model of reproductive effort for an example species that experiences a dramatic increase in reproductive potential at large sizes: the bluehead wrasse, Thalassoma bifasciatum. Our model shows that the optimal level of reproductive effort will decline with increasing size or age when increases to the residual reproductive value outpace the increases to current reproductive potential. This result confirms the logic of Williams's analysis of optimal life histories, while offering a realistic counterexample to his conjecture of ever-increasing allocation to current reproduction.     

Maturity, mating and age-specific reproductive effort of the snake Natrix maura

The ecology of reproduction was studied in the snake Natrix maura. The presence of sperm in cloacal fluid was used to show the size at maturity, the season of mating and, together with information on the persistence of sperm in cloacal fluid of females after mating, the frequency of mating. These results suggest that each female mated several times per year. Female N. maura grew substantially after maturity, and clutch size increased with body size. Current and expected future reproduction increased in parallel during the period of growth after maturity; subsequently they were constant. This pattern would be expected to lead to a constant proportional allocation of energy to current reproduction. Reproductive effort (eggs/body energy) was independent of age as measured by growth rings. There was some evidence that not all stored energy was used in reproduction in the current season even when some follicles regressed.