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.     

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.     

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.     

Natural selection of life history attributes: An analytical approach

The life history attributes which maximize fitness can be established analytically through Fisher's equation for reproductive value. Maximizing the reproductive value at age zero is equivalent to maximizing the ultimate rate of increase. As an example of the usefulness of this equality it is shown that when survivorship is uniformly reduced, the corresponding optimal maternal frequency is unaltered, even though the ultimate rate of increase is lowered by a known amount. A general life history model is proposed which links these demographic determinants of rate of increase with the energy utilization alternatives (as among maintenance, growth, and reproduction) characterizing an individual organism's development. Since the energy partitioning alternatives at any age may depend on previous allocations, an organism state variable is introduced to describe the domain over which the maximization of reproductive value may take place. Further, if the reproductive value is to be a maximum at age zero, it must be maximized at every age. An optimal life history, then, is characterized by the energy allocations which maximize sequential reproductive values. Further examples of the utility of the model focus on growth vs reproduction decisions under biomass specific life history attributes. It is shown that if births per unit energy is a linear or convex function, then an organism will not simultaneously grow and reproduce. Determinant growth, biomass at first reproduction, and explicit calculation of the maximum ultimate rate of increase are also illustrated.     

Drought effect on plant biomass allocation: A meta‐analysis

Drought is one of the abiotic stresses controlling plant function and ecological stability. In the context of climate change, drought is predicted to occur more frequently in the future. Despite numerous attempts to clarify the overall effects of drought stress on the growth and physiological processes of plants, a comprehensive evaluation on the impacts of drought stress on biomass allocation, especially on reproductive tissues, remains elusive. We conducted a meta‐analysis by synthesizing 164 published studies to elucidate patterns of plant biomass allocation in relation to drought stress. Results showed that drought significantly increased the fraction of root mass but decreased that of stem, leaf, and reproductive mass. Roots of herbaceous plants were more sensitive to drought than woody plants that reduced reproductive allocation more sharply than the former. Relative to herbaceous plants, drought had a more negative impact on leaf mass fraction of woody plants. Among the herbaceous plants, roots of annuals responded to drought stress more strongly than perennial herbs, but their reproductive allocation was less sensitive to drought than the perennial herbs. In addition, cultivated and wild plants seemed to respond to drought stress in a similar way. Drought stress did not change the scaling exponents of the allometric relationship between different plant tissues. These findings suggest that the allometric partitioning theory, rather than the optimal partitioning theory, better explains the drought‐induced changes in biomass allocation strategies.     

Timing of seed germination and the reproductive effort in Xanthium canadense

The effect of different dates of germination on the timing of flowering and the final reproductive yield was examined in a short-day annual plant Xanthium canadense (cocklebur). Delays in germination of 30 and 60 days deferred flower initiation by 2 and 9 days, respectively. Although plants that germinated later were smaller because of the shorter growing period, the reproductive yields did not show as much reduction as the vegetative biomass. The reproductive effort (RE, defined as the ratio of final reproductive yield to the vegetative biomass at the end of the growing season) increased 1.5 and 2.5 times with delays in germination of 30 and 60 days, respectively. A simple model of plant growth was used to analyse the factors involved in the control of RE, which depends only on the dry mass productivity and its partitioning in the reproductive phase, and is independent of the productivity and partitioning in the vegetative phase. Since relative allocation of dry mass to the reproductive part in the reproductive phase was similar for plants with different germination dates, the different REs could be ascribed mainly to differences in productivity of the vegetative parts in the reproductive period. The dependence of RE on plant size is discussed.     

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.     

植物种群的繁殖对策

植物种群的繁殖对策钟章成（西南师范大学,重庆６３０７１５）ＲｅｐｒｏｄｕｃｔｉｖｅＳｔｒａｔｅｇｉｅｓｏｆＰｌａｎｔＰｏｐｕｌａｔｉｏｎｓ．￥ＺｈｏｎｇＺｈａｎｇｃｈｅｎｇ（ＳｏｕｔｈｗｅｓｔＣｈｉｎａＴｅａｃｈｅｒｓＵ－ｎｉｖｅｒｓｉｔｙ,Ｃｈｏｎ...     

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.     

Variation in biomass allocation of Nitraria tangutorum during different phenological phases

植物生物量的分配模式是植物对环境适应的结果, 并伴随着植物生活史的每一个阶段, 与植物的生长和发育息息相关。目前关于植物生物量分配的大小依赖性已有相关报道, 但关于其对物候期的响应尚鲜有报道。该研究以乌兰布和沙漠地区白刺(Nitraria tangutorum)为研究对象, 通过对其2016与2017年连续2个生长季里盛花期、盛果期与营养生长期3个物候期的根、压条、新枝、老枝、叶、繁殖器官等部分的生物量测定, 采用标准化主轴回归方程的斜率和截距的显著性比较, 分别探讨了白刺在不同物候期的异速生长的大小依赖程度和相对生物量分配比例, 特别是地上与地下部分之间、支持与同化器官之间, 在不同物候期的生物量分配规律。结果表明: 白刺的繁殖生长对生物量分配模式造成的影响主要体现在相对生物量分配比例(36.00%)而不是个体大小的依赖性程度上(16.67%), 且对新枝的影响较大, 使其不同物候期的大小依赖性程度发生了改变, 但是变化趋势不一致, 同时繁殖生长增加对叶片的相对生物量分配比例, 减少对老枝的相对生物量分配比例, 但并没有改变他们的大小依赖性程度。白刺生长过程中的地下部分生物量分配率随个体生物量的累积均增大, 而繁殖分配会在一定程度内减弱这种速率。白刺随着个体生物量的增大其生物量向支持器官分配率也越大, 但随着生长时间推移, 更倾向于将生物量分配给同化吸收器官。     

白刺不同物候期的生物量分配规律

植物生物量的分配模式是植物对环境适应的结果, 并伴随着植物生活史的每一个阶段, 与植物的生长和发育息息相关。目前关于植物生物量分配的大小依赖性已有相关报道, 但关于其对物候期的响应尚鲜有报道。该研究以乌兰布和沙漠地区白刺(Nitraria tangutorum)为研究对象, 通过对其2016与2017年连续2个生长季里盛花期、盛果期与营养生长期3个物候期的根、压条、新枝、老枝、叶、繁殖器官等部分的生物量测定, 采用标准化主轴回归方程的斜率和截距的显著性比较, 分别探讨了白刺在不同物候期的异速生长的大小依赖程度和相对生物量分配比例, 特别是地上与地下部分之间、支持与同化器官之间, 在不同物候期的生物量分配规律。结果表明: 白刺的繁殖生长对生物量分配模式造成的影响主要体现在相对生物量分配比例(36.00%)而不是个体大小的依赖性程度上(16.67%), 且对新枝的影响较大, 使其不同物候期的大小依赖性程度发生了改变, 但是变化趋势不一致, 同时繁殖生长增加对叶片的相对生物量分配比例, 减少对老枝的相对生物量分配比例, 但并没有改变他们的大小依赖性程度。白刺生长过程中的地下部分生物量分配率随个体生物量的累积均增大, 而繁殖分配会在一定程度内减弱这种速率。白刺随着个体生物量的增大其生物量向支持器官分配率也越大, 但随着生长时间推移, 更倾向于将生物量分配给同化吸收器官。     

Multiple switches between vegetative and reproductive growth in annual plants

A model of growth and reproduction in annual plants was developed by Cohen (1971, J. Theor. Biol.33, 299–307) to determine the allocation strategy which maximizes seed yield. The model divides the plant into vegetative and reproductive parts and predicts that yield is maximized by a strategy consisting of a switch from purely vegetative to strictly reproductive growth. We generalize Cohen's model to include vegetative and reproductive loss terms. Both growth and loss rates are allowed to vary with time. Using optimal control theory we find that seed yield is maximized by a strategy consisting of multiple switches between vegetative and reproductive growth, for certain ranges of the model parameters. In natural systems a predictable vegetative loss burst may be necessary to promote multiple switches.     

Optimal resource allocation in perennial plants: A continuous-time model

A continuous-time model, similar to W. M. Schaffer's (1983, Amer. Nat. 121, 418–431), of growth and reproduction for a perennial herb with discrete growing seasons is considered. Assuming that metabolic rates of reproductive and storage structures are equal, it was possible, through the reduction of the continuous model to a discrete one, to find the optimal allocations to the vegetative, reproductive, and reserve structures. The main feature of the optimal strategy is the existence of an optimal reserve size. The allocation to vegetative structures is, every growing season, the allocation which maximizes the total of reproductive and reserve structures at the end of the season. The relative allocation between reserve and reproductive structures is given, when reproductive success is a linear function of investment, by the fastest growth to the optimal size: no reproduction until the optimal size is reached, and, afterwards, allocation to reproduction of everything beyond what is needed to maintain size R*. Asymptotic growth to the equilibrium and cycles are possible, when reproductive success is a nonlinear function of investment (A. Pugliese, 1988, in “Biomathematics and Related Computational Problems” (L. M. Ricciardi, Ed.), Reidel, Dordrecht, to appear). It has therefore been possible to solve the “general life history problem” ( Schaffer, 1983) when growth is in general a concave function of body size. In the Discussion discrete and continuous-time models are compared; if the real dynamics is described by a continuous model of the type analyzed here, life history predictions made by analyzing the system with a discrete model are upheld.     

植物同化物分配及其模型研究综述

目前生态系统模型模拟中所用的大多数同化物分配模型是经验性的。同化物分配对植物的生长、竞争及结构的形成有重要的影响,是植物生长的关键,也是植物生长模型中的薄弱环节。总结了影响同化物分配的因素：生理过程和环境因子。指出植物作为一个有机的整体,所有的生理过程都对其有影响,维管束作为各器官间的连接系统,以及同化物的运输管道,其性质对同化物分配有重要的影响。综述了环境因子特别是环境水分条件对同化物分配的影响。总结了以往研究中发现的、主要的同化物分配规律,指出同化物分配的模式极其复杂,分配过程完全是根据环境以及生长阶段变化而变化的、随机应变的过程。 对于同化物分配模型按照经验模型,目的性模型,源汇关系模型进行了总结归纳,分析指出：经验性模型应用最多但机理性差;功能平衡模型在模拟营养生长阶段同化物在条与根之间的分配很成功,但应用于其它器官之间很困难;最优化模型适于模拟平衡态下同化物的分配;源汇关系模型机理性最强,可模拟任何器官间的同化物分配,应用范围最广泛。 同化物研究取得了很大的进展,但研究中仍存在很多不足：对于各相关过程的研究存在不平衡性;整体水平上同化物分配的机理仍缺乏深入研究;同化物分配对于环境的响应方面的研究相对较弱;缺乏多环境因素的研究;缺乏长期的实验观测研究。作者认为环境与同化物分配相互关系的研究将成为日后研究中的热点问题。     

羌塘雪兔子繁殖特征及资源分配的海拔差异

植物种群的生殖特性和资源配置策略是植物生活史研究的重要内容之一,对于理解和预测植被结构和全球变化过程中的适应策略至关重要。该文以青藏高原特有风毛菊属植物羌塘雪兔子(Saussurea wellbyi)为试验材料,分析6个海拔梯度18个居群的花期繁殖特征的变化,并用异速生长模型分析资源投入及资源分配的个体大小依赖关系。结果显示:(1)个体大小、繁殖器官生物量、营养器官生物量、管状小花数目、雄蕊重量、花药长度及花粉数与海拔高度呈负相关(P<0.05),管状小花重量、雌蕊重量、花丝长度及花柱长度与海拔高度呈正相关(P<0.01);(2)营养分配与海拔高度呈负相关(P<0.01),繁殖分配与海拔高度呈正相关(P<0.01);(3)管状小花的数量与重量(P<0.05)、雌蕊重量与雄蕊重量(P<0.01)、花丝长度与花药长度(P<0.01)、花丝长度与花粉数(P<0.01)之间均存在权衡关系;(4)资源投入及资源分配在不同海拔间与个体大小都呈显著正相关(P<0.05),且截距在海拔间差异极显著(P<0.01)。综合分析认为:羌塘雪兔子在不同海拔下的繁殖特征以及大小依赖的资源投入和资源分配模式是羌塘雪兔子与其所处的高山环境长期适应和进化的结果。     

Life history trade-offs in Amphibromus scabrivalvis (Poaceae): allocation to clonal growth,storage, and cleistogamous reproduction

Life history trade-offs among clonal growth, storage, and sexual reproduction were investigated in the perennial grass Amphibromus scabrivalvis in relation to soil nutrients. This species exhibits clonal growth by producing rhizomes and stores reserves in the form of basal corms; seeds are matured in cleistogamous spikelets on panicles enclosed within the leaf sheaths along each culm. Ten seed-derived genotypes (clones) were separated into 72 ramets and planted in the greenhouse. Control ramets received only water while the remainder received fertilizer applied every 2 wk. Twenty-four ramets were harvested per clone at 11, 20, and 26 wk. The dry mass of corms, rhizomes, roots, shoots, and seeds were recorded. Biomass partitioning to rhizomes provided a measure of carbon allocation to clonal growth, partitioning to corms provided a measure of allocation to storage, and partitioning to seeds provided a measure of allocation to sexual reproduction. Allocation to most organs was significantly influenced by clone identity; fertilizer significantly increased allocation to corms and seeds at 20 wk, but never affected rhizome allocation at any age. Corm allocation increased from 2% at 11 wk to 27% at 26 wk; rhizome allocation decreased from 10% at 11 wk to 3% at 26 wk. Significant negative relationships were detected for rhizome vs. seed and corm vs. rhizome allocation in fertilized clones at 20 wk. This suggests an age-dependent physiological life history trade-off between clonality and sexual reproduction and between clonality and storage. In contrast, a significant positive relationship was consistently noted for corm vs. seed allocation in fertilized and unfertilized clones at 20 and 26 wk. The absence of a trade-off between storage and sexual reproduction may indicate that these two processes are not necessarily mutually exclusive components of life history.     

Control theory predictions of reproductive allocation in female dusky salamanders

A model of the reproductive ecology of female dusky salamanders was used to investigate the allocation scheme that a female might use to maximize her reproductive success. Analysis of the model with techniques of optimal control theory suggests that fecundity is maximized either by allocating food resources to reproduction for the entire time period prior to egg laying, or by growing first, then switching to reproduction later in the year. The analysis also indicates that egg mortality will be minimized if the female provides maternal care at the maximum level throughout egg brooding. These results are not specific to dusky salamanders, but can be extended to other organisms with similar reproductive characteristics.     

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.     

生长期-定时一年生植物群体光合产物的最优分配策略的理论分析

本工作建立了一个一年生植物群体的生长模型,利用以梯度法为基础的离散系统最优控制的计算方法,计算并分析了一年生植物群体光合产物的营养器官间分配的最优策略,以及这一策略对植物群体最大生长速率和消光系数的依赖关系。用Pontryagin最小值原理和奇异最优控制的条件证明了光合产物的最优分配方法是:在营养和生殖生长并行阶段,群体叶片的死亡量恰好等于新形成量,植物干重随时间线性增加。     

Long-term responses of Melilotus segetalis to salinity. I. Growth and partitioning

Annual sweetclover plants [Melilotus segetalis (Brot) Ser.] were grown for a complete life cycle with and without saline (NaCl treatment of CE=15 dS m⁻¹). Growth and partitioning analyses were performed. Sequential harvests (every 15 d) during the life cycle, and separation of plant material into roots, stems, petioles, leaves and reproductive structures were carried out Salt treatment reduced growth during the early and middle stages of the life of the plant, but did not significantly affect RGR in the reproductive phase. The root–shoot allometric coefficient of salinized plants in the generative phase decreased more than in control plants. We suggest that salinity-induced growth reduction in M. segetalis was primarily a result of a lower unit leaf rate (ULR) despite an increased leaf area ratio (LAR). Earlier flowering, higher biomass allocation to shoot and greater reproductive investment, but similar relative growth rate (RGR), were some of the main characteristics of salt-stressed plants compared to controls during the reproductive phase, these apparently being associated with increased sink strength caused by developing flowers and fruits.