A Dynamic Energy Budget model based on partitioning of net production

We formulate a Dynamic Energy Budget (DEB) model for the growth and reproduction of individual organisms based on partitioning of net production (i.e. energy acquisition rate minus maintenance rate) between growth and energy reserves. Reproduction uses energy from reserves. The model describes both feeding and non-feeding stages, and hence is applicable to embryos (which neither feed nor reproduce), juveniles (which feed but do not reproduce), and adults (which commonly both feed and reproduce). Embryonic growth can have two forms depending on the assumptions for acquisition of energy from yolk. By default, when the energy acquisition rate exceeds the maintenance rate, a fixed proportion of the resulting net production is spent on growth (increase in structural biomass), and the remaining portion is channelled to the reserves. Feeding organisms, however, modulate their allocation of net production energy in response to their total energy content (energy in the reserves plus energy bounded to structural biomass). In variable food environment an organism alternates between periods of growth, no-growth, and balanced-growth. In the latter case the organism adopts an allocation strategy that keeps its total energy constant. Under constant environmental conditions, the growth of a juvenile is always of von Bertalanffy type. Depending on the values of model parameters there are two long-time possibilities for adults: (a) von Bertalanffy growth accompanied by reproduction at a rate that approaches zero as the organism approaches asymptotic size, or (b) abrupt cessation of growth at some finite time, following which, the rate of reproduction is constant. We illustrate the model's applicability in life history theory by studying the optimum values of the energy allocation parameters for constant environment and for each of the dynamic regimes described above. Received: 11 May 1998 / Revised version: 18 February 2000 / Published online: 4 October 2000     

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.     

Theoretical consideration of effect of fishing mortality on growth and reproduction of fish populations

An increase in fish mortality due to fishing can theoretically change the growth and reproduction of fish populations from the viewpoint of adaptation. We address the issue of how an iteroparous fish should convert surplus energy into somatic growth and reproduction at each age under given conditions of mortality. A model of life history, which maximizes the net reproductive rate using the discrete maximum principle, is improved employing a new relationship between body weight and surplus energy which we have recently proposed. The model is applied to the North Sea plaice Pleuronectes platessa, for which it has been reported that the average length of young fish had increased whereas that of old ones had decreased for some decades. Although the model cannot directly explain the former phenomenon, the two phenomena can be interpreted as a change in the optimal life history due mainly to an increase in mortality.     

Life‐history strategy and behavioral type: risk‐tolerance reflects growth rate and energy allocation in ant colonies

Despite the recent interest in animal personality and behavioral syndromes, there is a paucity of explanations for why distinct behavioral traits should evolve to correlate. We investigate whether such correlations across apparently distinct behavioral traits may be explained by variation in life history strategy among individual ant colonies. Life history theory predicts that the way in which individuals allocate energy towards somatic maintenance or reproduction drives several distinct traits in physiology, morphology, and energy use; it also predicts that an individual's willingness to engage in risky behaviors should depend on reproductive strategy. We use Temnothorax ants, which have been shown to exhibit ‘personalities’ and a syndrome that may reflect risk tolerance at the colony level. We measure colonies' relative investment in growth rate (new workers produced) compared to reproductive effort (males and queens produced). Comparing sterile worker production to reproductive alate production provides a direct measure of how colonies are investing their energy, analogous to investment in growth versus reproduction in a unitary organism. Consistently with this idea, we found that behavioral type of ant colonies was associated with their life history strategy: risk‐tolerant colonies grew faster and invested more in reproduction, whereas risk‐averse colonies had lower growth rate but invested relatively more in workers. This provides evidence that behavioral syndromes can be a consequence of life‐history strategy variation, linking the two fields and supporting the use of an integrative approach.     

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.     

Costs of reproduction in life history of a perennial plant <Emphasis Type="Italic">Carex secalina</Emphasis>

We tested a hypothesis based on life history theory that examines reproductive costs incurred by individuals in consecutive years of their life. A multi-year dataset of resource allocation to vegetative and reproductive structures was analysed in Carex secalina — a perennial, monoecious sedge, reproducing only sexually. In a four-year garden experiment, we assessed above-ground biomass at the end of each season and reproductive allocation expressed as the total length of male and female spikes. The study was aimed at determining how size and age of a plant relates to its reproduction, and how the rate of reproduction affects the year-toyear biomass change in Carex secalina. We observed that after each reproductive episode, individuals had significantly smaller sizes and produced a lower number of generative tillers. The total production of reproductive structures decreased significantly with age in all populations. Moreover, the decrease in plant biomass was greater when more reproductive structures were produced in a previous year, which indicates that the plants incur costs of reproduction in terms of above-ground biomass production.     

生长环境与株龄对凤丹当年生果枝的生物量分配的影响

生物量分配研究是了解作物产量形成机制的基础。凤丹是以杨山牡丹（Paeonia ostii）为原种形成的栽培类群,也是新型木本油料作物油用牡丹的主栽品种。该文通过比较凤丹主要产区6龄种群、以及安徽铜陵和上海地区的4、6、8龄种群的当年生果枝大小与生物量分配,探讨环境和株龄对小枝生长与繁殖的影响。结果表明,凤丹植株的果枝数量随株龄增大而上升,不同株龄植株的单个果枝大小和果枝内生物量分配没有明显差异,果枝水平上没有株龄效应,但整株水平上株龄效应明显;果枝大小及生物量各指标之间存在明显相关性,但相关性在种群间变化较大;不同种群的果枝大小及生物量分配差异明显,果枝生物量分配明显随纬度、降水和光辐射强度变化而变化;异速生长方程模拟显示,大部分种群的果枝繁殖与营养生物量或总生物量之间为等速生长关系（斜率=1）,但种群间截距变化较大。这些结果表明栽培环境对凤丹果枝的生长与繁殖有显著效应。     

Age and season impact resource allocation to eggs and nesting behavior in the painted turtle

Theory predicts that in long-lived organisms females should invest less energy in reproduction and more in growth and self-maintenance early in life, with this balance shifting as females age and the relative value of each reproductive event increases. We investigated this potential trade-off by characterizing within-population variation in resource allocation to eggs by female painted turtles (Chrysemys picta) and relating this variation to their nesting ecology and life history. We examined lipid and protein allocation to yolks, accounting for both relative female age and seasonal effects (first vs. second clutches within a female). Older females appear to increase their investment in reproduction by producing larger eggs, but these eggs are not disproportionately more lipid or protein rich than the smaller eggs from younger females. Within the nesting season, first clutches have more lipid and protein than second clutches. We also found that younger females nest closer to the water than older females. Our results indicate that trade-offs involving resource allocation and nesting behavior do occur both seasonally and with age, suggesting ontogenetic variation in life-history strategies in this long-lived organism.     

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.     

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.     

Female red squirrels fit Williams' hypothesis of increasing reproductive effort with increasing age

Williams predicted that reproductive effort should increase as individuals age and their reproductive value declines. This simple prediction has proven difficult to test because conventional measures of energy expenditure on reproduction may not be a true reflection of reproductive effort. We investigated age-specific variation in female reproductive effort in a stable population of North American red squirrels where energy expenditure on reproduction is likely to reflect actual reproductive effort. We used seven measures of reproductive effort spanning conception to offspring weaning. We found that females completed growth by age 3 and that reproductive value decreased after this age likely because of reproductive and survival senescence. We therefore, predicted that reproductive effort would increase from age 3 onwards. The probability of breeding, litter mass at weaning, and likelihood of territory bequeathal were all lower for 1- and 2-year-old females than for females older than 3 years, the age at which growth is completed. That growing females are faced with additional energetic requirements might account for their lower allocation to reproduction as compared with older females. The probability of attempting a second reproduction within the same breeding season and the propensity to bequeath the territory to juveniles increased from 3 years of age onwards, indicating an increase in reproductive effort with age. We think this increase in reproductive effort is an adaptive response of females to declining reproductive values when ageing, thereby supporting Williams' prediction.     

Life history implications of allocation to growth versus reproduction in dynamic energy budgets

We compare the implications of determinate vs. indeterminate growth of a parthenogenetic iteroparous ectotherm at constant food density in the context of the dynamic energy budget theory, which specifies the tight links between life history traits, such as feeding, aging, growth and reproduction. We do a comparative analysis using, as measure of fitness, the life span reproduction, the population growth rate, and the conversion efficiency of food to biomass. When extrinsic mortality is constant, indeterminate growth cannot maximize fitness if measured by the population growth rate or the conversion efficiency, except when mortality is low, in which case both types of animals are similar. If the fitness measure is life span reproduction, indeterminate growth maximizes fitness even with constant mortality, provided it is not very high. When mortality decreases with size, indeterminate growth maximizes fitness for almost all measures of fitness. Finally, we suggest an evolutionary link between allocation strategies and expected life span. In populations of long living species, each type of animal can establish in the population of the other. In populations of short living species, determinate growers can invade, and displace, a population of indeterminate ones. However, when the mortality risk of organisms with small size is much higher than those of large size, indeterminate growers can be superior.     

Optimal Reproductive Strategy of Plants, with Special Reference to the Modes of Reproductive Resource Allocation

Abstract A growth model for reproductive energy allocation pattern and schedule is proposed. Assumptions are as follows: (1) the assimilation rate for an individual is given by a logistic curve of vegetative dry weight; (2) size variability is expressed by the parameter W of the logistic curve (asymptotic value of vegetative dry weight); (3) a plant controls allocation of the assimilate to vegetative and reproductive structures so as to maximize the reproductive energy investment at the end of the growth period. The models were analyzed in comparison with field and experimental observations and gave reasonable explanations for the reproductive allocation pattern of individuals which reflects ecological preferences and life history characteristics, such as environmental conditions of habitats (stable or changing), length of life span (annual, biennial or perennial) and growth form (erectophile or planophile). Decreasing RA (reproductive allocation) with individual size and delayed switchover time from vegetative to reproductive growth were found in plants which occur in stable environments and have a more or less fixed growth period; in those which occur in changing environments where growth period depends on individual size, RAs that remain constant or increase with variations in individual size and early switchover time were detected. Most perennials conform to the former case, but annuals and biennials conform to the latter case. Under extremely overcrowded conditions, planophiles, which are much more subject to crowding effect than erectophiles, tend to have increasing RA with increasing size, while erectophiles tend to have almost constant RA irrespective of size. These trends are discussed in the light of the life history characteristics and ecological distribution of plant species studied.     

青藏高原特有植物露蕊乌头（毛茛科）从冰期避难所扩张后繁殖资源分配的变化

物种分布范围的形成是进化生态学研究的基本问题之一。但植物的资源分配策略是否与物种边界形成有关一直没有相关研究。青藏高原特有植物露蕊乌头在末次最大冰期时有4个避难所,但冰期后只有一个避难所的种群发生了扩张并最终形成了现代分布格局。以露蕊乌头的避难所种群（同仁种群）和扩张后邻近分布区边缘的两个种群（兴海种群和海北种群）为研究对象,通过比较避难所种群和边缘种群的资源分配方式,探讨露蕊乌头的资源分配与该植物分布区及边界形成的关系。结果发现：1）兴海和海北种群的营养结构（包括根、植株高度和茎叶生物量）均显著低于同仁种群．海北种群的繁殖结构（花数量和花生物量）显著低于同仁和兴海种群,但海北和兴海的繁殖分配均显著高于同仁种群;2）3个种群的繁殖资源与个体大小呈现显著的正相关关系,投入到繁殖资源的比例（繁殖分配）与个体大小呈显著的负相关关系。对露蕊乌头的研究结果一方面进一步证明了个体大小依赖的繁殖分配,但不符合“植物开始繁殖必须达到一定的大小（阈值）”这一结论,这可能与露蕊乌头的生活史特征有关：而另一方面,露蕊乌头在扩张过程中逐渐增加了对繁殖资源投资的比例,说明胁迫生境中有性繁殖对该植物具有更为重要的意义,且露蕊乌头在扩张过程中可能逐渐实现繁殖产出最大化,并可能在边缘种群实现最优繁殖分配进而最终形成该物种分布区的边界,但这一结论仍需在更多的植物类群中验证。     

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.     

Changes in Reproductive Allocation after Expansion from the Glacial Refugium and Implications for the Distribution Range in the Qinghai Tibet Plateau Native Herb,Gymnaconitum gymnandrum (Ranunculaceae)

A fundamental goal of ecology and evolution is to explain patterns of species distribution and abundance. However, the way in which stable distribution ranges are shaped by natural selection is still poorly understood, especially whether patterns of resource allocation have contributed to the range size and the formation of range boundary received little attention. For annual herb, the maximum reproductive allocation is predicted to be 50%, and thus we predicted that reproductive allocation might contribute to the formation of range boundary since plant will enhance allocations to reproduction in stressful environments. In this study, we presented our data on resource allocation between population from the glacial refegium and those from the marginal populations in Gymnaconitum gymnandrum, an alpine biennial native to the Qinghai Tibet Plateau, aiming to find the contribution of resource allocation to the formation of range boundary. Our results showed that resource allocations to vegetative organs, including roots, plant height and stem leaf biomass, were significantly higher in the refugium population that in the two marginal populations, and allocations to reproductive organs, including flower number and flower biomass, were significantly lower in one marginal population (Haibei population) than in the other marginal population (Xinghai population) and the refugium population (Tongren population). However, reproductive allocation was significantly higher in the marginal populations than in the refugium population. In addition, in each of the three populations, we found a positive relationship between the plant size and flower biomass but a negative relationship between the plant size and reproductive allocation. Our results indicated a size dependent reproductive allocation in Ggymnandrum, but we did not find a size threshold for reproduction in each of the three populations of this plant, which might be attributed to the life history of this biennial herb. We also suggested that reproductive allocation was increased during the process of range expansion and may rise to the optimal reproductive allocation in the marginal populations, which suggested the important role of sexual reproduction for plants in more stressful environments and the formation of range boundary. However, these conclusions need to be further proved in other plant species.     

展毛翠雀花期繁殖特征和生物量分配对放牧的响应

生物量分配影响植物生长和繁殖,是植物生活史研究的重要内容。为了了解植物生活史性状对放牧的响应,该研究以青藏高原高寒草甸毒杂草展毛翠雀为对象,分析了放牧干扰对展毛翠雀的花期繁殖分配和性分配的影响。结果表明:放牧显著降低了展毛翠雀的总生物量、个体大小和繁殖投入; 放牧未改变展毛翠雀的营养部分与繁殖部分的等速生长关系,但显著增加了繁殖部分的生物量分配和总花数; 展毛翠雀的个体大小与总花数呈显著的正相关关系,但与性分配呈显著的负相关关系; 展毛翠雀的总花数与单花大小、单花的花瓣比例均表现出负相关关系,表明总花数与单花大小之间、总花数与单花的花瓣比例之间均存在权衡。因此,在放牧条件下,展毛翠雀的繁殖分配和性分配均表现出显著的可塑性。     

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.     

Comparing life histories of shrews and rodents

Small insectivores and rodents, despite similarities in body size and attributes scaling to body size, exhibit significant differences in other properties, including many life history traits. In this article major differences between life history traits of the two taxa are reviewed, with an indication of contrasting selection pressures related to somewhat different body size, as well as to differences in metabolic rates, diet and exposure to predation. Additionally, since the life history differences between small mammals are particularly well pronounced in highly seasonal habitats, the winter ecology of shrews and rodents is compared. Finally, the two different reproductive strategies typical for soricine shrews and small nonhibernating rodents, are presented. In conclusion, it is proposed that the reproduction delayed to the second calendar year of life in shrews is the result of selection for traits ensuring successful survival in winter, a period that is more perilous for shrews than for rodents. In rodents, in contrast, opportunistic reproduction is the most prominent characteristic which also helps to maximize their reproductive output. This ability for high reproduction seems to be the main antipredatory measure selected for in rodent evolution.