Optimal allocation of energy to growth and reproduction

The optimal allocation of energy to growth and reproduction is considered for three different cases, i.e., a single reproduction (semelparity), reproduction through repeated discrete clutches, and continuous reproduction. The problem reduces to optimizing age and size at maturity. The best strategy is to continue growth until the change of production rate with respect to increasing body size, multiplied by life expectancy for those attaining adulthood and reproducing successfully, is greater than one. The time at which semelparous species reproduce may also be optimized; for the other modes of reproduction only physiological factors or seasonality can limit the maximum age. A brief growing season or high mortality rate are factors leading to early maturity and small adult body size.     

A full lifecycle bioenergetic model for bluefin tuna

We formulated a full lifecycle bioenergetic model for bluefin tuna relying on the principles of Dynamic Energy Budget theory. Traditional bioenergetic models in fish research deduce energy input and utilization from observed growth and reproduction. In contrast, our model predicts growth and reproduction from food availability and temperature in the environment. We calibrated the model to emulate physiological characteristics of Pacific bluefin tuna (Thunnus orientalis, hereafter PBT), a species which has received considerable scientific attention due to its high economic value. Computer simulations suggest that (i) the main cause of different growth rates between cultivated and wild PBT is the difference in average body temperature of approximately 6.5°C, (ii) a well-fed PBT individual can spawn an average number of 9 batches per spawning season, (iii) food abundance experienced by wild PBT is rather constant and sufficiently high to provide energy for yearly reproductive cycle, (iv) energy in reserve is exceptionally small, causing the weight-length relationship of cultivated and wild PBT to be practically indistinguishable and suggesting that these fish are poorly equipped to deal with starvation, (v) accelerated growth rate of PBT larvae is connected to morphological changes prior to metamorphosis, while (vi) deceleration of growth rate in the early juvenile stage is related to efficiency of internal heat production. Based on these results, we discuss a number of physiological and ecological traits of PBT, including the reasons for high Feed Conversion Ratio recorded in bluefin tuna aquaculture.     

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.     

Optimal growth strategies when mortality and production rates are size-dependent

Summary Pontryagin's maximum principle from optimal control theory is used to find the optimal allocation of energy between growth and reproduction when lifespan may be finite and the trade-off between growth and reproduction is linear. Analyses of the optimal allocation problem to date have generally yielded bang-bang solutions, i.e. determinate growth: life-histories in which growth is followed by reproduction, with no intermediate phase of simultaneous reproduction and growth. Here we show that an intermediate strategy (indeterminate growth) can be selected for if the rates of production and mortality either both increase or both decrease with increasing body size, this arises as a singular solution to the problem. Our conclusion is that indeterminate growth is optimal in more cases than was previously realized. The relevance of our results to natural situations is discussed.     

Optimal patterns of growth and reproduction for perennial plants with persisting or not persisting vegetative parts

Summary Optimal allocation of energy to growth, reproduction and storage was considered for perennial plants differing in the proportion of vegetative structures persisting over winter and/or in the amount of resources which can be relocated to storage before abscission of some organs. It was found that for every mortality level there exists a critical proportion of persistent organs. Below this critical value it is optimal to grow without reproduction for the first years until a characteristic size is reached; afterwards, that size is maintained year after year and all extra resources are devoted to reproduction. Some storage is also necessary to maintain constant size. If the proportion of retained vegetative mass is above the critical value, the optimal strategy is gradual growth to an asymptotic size, with growth and reproduction occurring in several years following maturation. In this case real storage occurs only until maturation is reached, then storage is realized only by energy relocation from the vegetative body. Although the optimal solution changes abruptly qualitatively at a given proportion of resources saved from year to year, further growth of this proportion above the critical level brings about a greater difference between size reached at maturity and final size. The predictions of the model seem to follow the pattern of nature qualitatively.     

Metabolic capacity of Bacillus subtilis for the production of purine nucleosides, riboflavin, and folic acid

We developed a stoichiometric model of Bacillus subtilis metabolism for quantitative analysis of theoretical growth and biochemicals production capacity. This work concentrated on biochemicals that are derived from the purine biosynthesis pathway; inosine, guanosine, riboflavin, and folic acid. These are examples of commercially relevant biochemicals for which Bacillus species are commonly used production hosts. Two previously unrecognized, but highly desirable properties of good producers of purine pathway-related biochemicals have been identified for optimally engineered product biosynthesis; high capacity for reoxidation of NADPH and high bioenergetic efficiency. Reoxidation of NADPH, through the transhydrogenase or otherwise, appears to be particularly important for growth on glucose, as deduced from the corresponding optimal carbon flux distribution. The importance of cellular energetics on optimal performance was quantitatively assessed by including a bioenergetic efficiency parameter as an unrestricted, ATP dissipating flux in the simulations. An estimate for the bioenergetic efficiency was generated by fitting the model to experimentally determined growth yields. The results show that the maximum theoretical yields of all products studied are limited by pathway stoichiometry at high bioenergetic efficiencies. Simulations with the estimated bioenergetic efficiency of B. subtilis, growing under glucose-limiting conditions, indicate that the yield of these biochemicals is primarily limited by energy and thus is very sensitive to the process conditions. The maximum yields that can reasonably be expected with B. subtilis on glucose were estimated to be 0.343, 0.160, and 0.161 (mol product/mol glucose) for purine nucleosides, riboflavin, and folic acid, respectively. Potential strategies for improving these maximum yields are discussed.     

Resource allocation to reproduction in animals

The standard Dynamic Energy Budget (DEB) model assumes that a fraction κ of mobilised reserve is allocated to somatic maintenance plus growth, while the rest is allocated to maturity maintenance plus maturation (in embryos and juveniles) or reproduction (in adults). All DEB parameters have been estimated for 276 animal species from most large phyla and all chordate classes. The goodness of fit is generally excellent. We compared the estimated values of κ with those that would maximise reproduction in fully grown adults with abundant food. Only 13% of these species show a reproduction rate close to the maximum possible (assuming that κ can be controlled), another 4% have κ lower than the optimal value, and 83% have κ higher than the optimal value. Strong empirical support hence exists for the conclusion that reproduction is generally not maximised. We also compared the parameters of the wild chicken with those of races selected for meat and egg production and found that the latter indeed maximise reproduction in terms of κ, while surface‐specific assimilation was not affected by selection. We suggest that small values of κ relate to the down‐regulation of maximum body size, and large values to the down‐regulation of reproduction. We briefly discuss the ecological context for these findings.     

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.     

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.     

Facultative Vivipary is a Life-History Trait in Caenorhabditis elegans

Organisms partition their resources among growth, maintenance, and reproduction and, when resources become limiting, the allocation to one process necessitates reduced allocation to others. When starved, Caenorhabditis elegans adults retain progeny internally which then consume the parent body contents, and some of those larvae use the resources to reach the resistant, long-lived dauer stage. If starved under similarly extreme conditions, larvae from eggs laid outside of the body are unable to develop into dauers. We interpret this switch from ovipary, or laying eggs, to bearing live young as facultative vivipary. This switch is induced by starvation of late fourth-stage larvae, young adults, or gravid adults. In C. elegans, vivipary is the altruistic allocation of all available parental energy and nutrients to progeny, with the associated costs to adult hermaphrodites of truncated life span and fecundity. As a life-history trait, facultative vivipary is a survival-enhancing response to stress that may provide insights into the evolution of reproduction and longevity.     

Body size and the timing of egg production in parasitoid wasps

In insects several key fitness-related variables are positively correlated with intraspecific variation in body size, but little is known about size-related variation in the timing of egg production within species. Female insects are known to vary in the degree to which they concentrate egg production into the early part of life. This variation has been quantified as the ovigeny index, defined as the proportion of the maximum potential lifetime complement of eggs that is mature following emergence from the pupa. We tested the hypothesis that the timing of egg production depends both on body size and on host availability, by means of a dynamic programming model that predicted optimal resource allocation to reproduction and survival together with the resulting ovigeny index, in non-feeding synovigenic parasitoids of different sizes. As body size increases, the proportionate increase in resource allocation to initial egg load is less than the proportionate increase in allocation to lifetime fecundity and potential life span, leading to a deferred investment in reproduction as shown by a decrease in ovigeny index. High habitat quality and high habitat stochasticity in reproductive opportunities have a significant effect on the optimal allocation of resources to reproduction and survival, and thus select for early reproduction, i.e. an increased ovigeny index. The ovigeny concept – ovigeny index together with its life-history correlates – enables understanding of the general occurrence of size-related deferment of reproductive investment in parasitoid wasps and also helps explain a significant part of the considerable life-history variation found among such insects.     

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.     

Variation in age at first reproduction of male Japanese fluvial sculpin induced by the timing of parental reproduction

The relationships between age and size at reproduction and lifetime reproductive output of male Japanese fluvial sculpin Cottus pollux were estimated by a mark-recapture study. Although all males were physiologically capable of breeding at age 2 years, age at first successful reproduction varied amongst individuals. Males with delayed reproduction had lower net reproductive rate than males that bred at age 2 years on average suggesting that age at first reproduction was a conditional strategy. Males that delayed reproduction were significantly smaller at age 1 and 2 years than males that bred at age 2 years. Despite no significant difference in body size of hatched yolk-sac larvae between the early and late phase of the breeding season, by May of the first year of life, progeny from nests in the early phase had hatched earlier and were larger than those from the nests in the late phase. The results suggested an important effect of timing of reproduction of parents on the growth and subsequent age at first reproduction of their progeny.     

Approximation of a physiologically structured population model with seasonal reproduction by a stage-structured biomass model

Seasonal reproduction causes, due to the periodic inflow of young small individuals in the population, seasonal fluctuations in population size distributions. Seasonal reproduction furthermore implies that the energetic body condition of reproducing individuals varies over time. Through these mechanisms, seasonal reproduction likely affects population and community dynamics. While seasonal reproduction is often incorporated in population models using discrete time equations, these are not suitable for size-structured populations in which individuals grow continuously between reproductive events. Size-structured population models that consider seasonal reproduction, an explicit growing season and individual-level energetic processes exist in the form of physiologically structured population models. However, modeling large species ensembles with these models is virtually impossible. In this study, we therefore develop a simpler model framework by approximating a cohort-based size-structured population model with seasonal reproduction to a stage-structured biomass model of four ODEs. The model translates individual-level assumptions about food ingestion, bioenergetics, growth, investment in reproduction, storage of reproductive energy, and seasonal reproduction in stage-based processes at the population level. Numerical analysis of the two models shows similar values for the average biomass of juveniles, adults, and resource unless large-amplitude cycles with a single cohort dominating the population occur. The model framework can be extended by adding species or multiple juvenile and/or adult stages. This opens up possibilities to investigate population dynamics of interacting species while incorporating ontogenetic development and complex life histories in combination with seasonal reproduction.     

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

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

Effects of varying temperature and food availability on growth and reproduction in first‐time spawning female Atlantic cod

The somatic growth, sexual maturation and fecundity of individually marked first‐time spawning female Atlantic cod Gadus morhua were examined under different varying temperature and feeding regimes over the months preceding spawning. A negative correlation between somatic and oocyte growth was found, reflecting the changing energy allocation pattern. Nevertheless, the somatic growth of mature individuals was at least as high as those of immature fish over the period of vitellogenesis. Potential fecundity was positively correlated with body size, but neither temperature or feeding regime significantly affected this relationship. Consequently, fish with unlimited feeding opportunity invested more energy into somatic growth during vitellogenesis compared to those held under a restricted ration. This indicated that once Atlantic cod had made the decision to invest in first reproduction, they allocated a certain amount of energy relative to their size into egg production and any surplus was invested into somatic growth. Low temperature led to an arrest in the onset of vitellogenesis and significantly affected the number of females that matured.     

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.     

Capital energy drives production of multiple clutches whereas income energy fuels growth in female collared lizards Crotaphytus collaris

Animals invest energy in reproduction that is obtained at two distinct times relative to the reproductive cycle. Energy obtained during egg production is referred to as income energy whereas stored energy acquired prior to reproduction is capital energy. Similar to most ectotherms, squamate reptiles are generally hypothesized to be capital breeders. Nearly all squamates in which income/capital energy investment has been examined thus far produce only one clutch per reproductive season. Although it is likely that squamates producing multiple seasonal clutches fuel first clutches with capital energy, either capital or income energy may be used to produce later clutches. We first monitored female eastern collared lizards over 14 reproductive seasons to confirm that the number of clutches females produce seasonally is a plastic response to variable environmental parameters, and to examine the effects of female body condition at the beginning of the reproductive season on clutch production. Clutch production varied annually and both the size and number of clutches were positively correlated with body condition. We then tested the competing predictions of the income and capital hypotheses experimentally by supplementing the diets of female collared lizards in situ for one season. Diet‐supplementation had no effect on the number of clutches produced but increased growth rates of gravid females. We further tested the competing predictions of these two hypotheses by examining variation in maternal energy investment per clutch using preserved specimens collected near our primary field site. Clutch size was highly correlated with female body size. Together, our results suggest that variation in reproductive output by female collared lizards is linked to stored capital energy rather than income energy, similar to most ectotherms.     

高浓度三聚氰胺对萼花臂尾轮虫 生殖策略的影响

以萼花臂尾轮虫(Brachionus calyciflorus)为受试动物,研究了不同浓度(400、800和1 200 mg/L)的三聚氰胺对萼花臂尾轮虫种群增长、有性生殖、个体大小和卵大小的影响.结果显示,三聚氰胺对萼花臂尾轮虫的24 h LC50值为2 627.00 mg/L.与空白对照组相比,800和1 200 ...     

Reproductive potential of the earthworm Eisenia foetida

Summary Regression equations are provided for the earthworm Eisenia foetida with respect to age at which 50% of the population became clitellate at 25° C in relation to population density in activated sludge and in horse manure. Regression equations are provided for progeny per cocoon versus weight of cocoon, and weight of cocoon in relation to weight of parent; from these an equation is derived for progeny per cocoon relative to worm weight. Regression equations are given on (a) number of cocoons produced per adult in relation to age and population density from onset of adulthood to median peak production of cocoons, age 10 weeks, and from age 10 weeks to age 27 weeks, and (b) weight of worm in relation to population density and age between ages 5 and 27 weeks. From (a) and (b) a family of equations (c) are derived giving progeny per cocoon in relation to age of adult and population density. From equations (a) and (c) two families of equations are generated giving progeny per adult in relation to ascent to, and descent from, the median week of peak cocoon production in relation to population density. Data also are provided on age at which reproduction terminates in relation to population density, optimum population density for reproduction, and hatchability.