Modelling reproductive allocation of dusky salamanders using optimal control theory: Pros,cons and caveats

Summary Optimal control theory has been used to examine the evolution of life history characters in a variety of plant and animal species. In this paper, I examine control theoretic models of reproductive allocation in female dusky salamanders and consider some practical aspects of modelling, including the appropriateness of nonlinear formulations, methods for describing semelparous reproduction, and data needed to parameterize models. The model analysed includes state variables for somatic and reproductive tissue, energy intake and requirements for physiological maintenance, and iteroparous reproduction. It predicts that female salamanders should spend the first part of their lives growing. After reaching sexual maturity, females should either spend the remainder of their lives reproducing at the expense of decreasing body size, possibly resulting in death by starvation, or maintain approximately constant body size at the expense of low reproductive output. This lack of correspondence to the observed biology of dusky salamanders suggests that not all the appropriate biology has been described. In particular, inclusion of a storage variable may be necessary in future modelling efforts.     

Evolution of body size: an optimization model

The growth of individuals is often described by bioenergetic equations which partition assimilated energy into maintenance, growth, reproduction, and so on. Such energy flows vary with body size. The bioenergetic equations in this paper, under the assumptions that organisms will adopt behavior that channels a maximum amount of energy into the production of surviving progeny, produce a model optimizing growth and reproduction. Using the Weierstrass theorem, we show that a solution of the optimization problem exists. The problem is further solved analytically using the Pontryagin maximum principle. The main conclusion of the paper is that in a given environment an optimal body size exists, one which maximizes the energy channeled to the production of progeny. This body size depends on the mortality rate, the maximum life span, and the derivative of the growth equation with respect to body size. The biological results predicted from the model are compared with ecological data for zooplankton and vertebrate species, which support the conclusions obtained.     

饥饿对中华倒刺鲃幼鱼代谢、个性和集群的影响

在自然界中,环境变化、季节更替和人为因素造成食物资源时空分布的不均一性,导致鱼类经常面临食物资源短缺的环境胁迫,对其能量代谢和行为造成一定影响。为考察食物资源短缺下暖水性鲤科鱼类能量代谢、个性与集群行为的应对策略及其可能的内在关联,选取中华倒刺鲃(Spinibarbus sinensis)幼鱼为实验对象,分别测定饥饿组(2周)和对照组(维持日粮)在处理前后实验鱼的标准代谢率(Standard metabolic rate,SMR)、个性行为(勇敢性、探索性和活跃性)以及实验处理后的集群行为(凝聚力和协调性)。研究发现:(1)饥饿组和对照组实验过程中实验鱼SMR均显著下降,但仅饥饿组实验鱼SMR具有重复性;(2)饥饿导致中华倒刺鲃幼鱼勇敢性、探索性、活跃性均显著增加;(3)饥饿导致群体成员间距离缩短,游泳速度及其同步性上升。研究表明:饥饿后的中华倒刺鲃不仅适应性降低SMR以减少能量消耗,而且呈现出更高的勇敢性、探索性和活跃性以利于获取食物资源;饥饿迫使中华倒刺鲃群体提高凝聚力和协调性,可能有助于提高群体的生存能力。     

Experimental testing of dynamic energy budget models

1. Dynamic energy budget (DEB) models describing the allocation of assimilate to the competing processes of growth, reproduction and maintenance in individual organisms have been applied to a variety of species with some success. There are two contrasting model formulations based on dynamic allocation rules that have been widely used (net production and net assimilation formulations). However, the predictions of these two classes of DEB models are not easily distinguished on the basis of simple growth and fecundity data.
2. It is shown that different assumptions incorporated in the rules determining allocation to growth and reproduction in two classes of commonly applied DEB models predict qualitatively distinct patterns for an easily measured variable, cumulative reproduction by the time an individual reaches an arbitrary size.
3. A comparison with experimental data from Daphnia pulex reveals that, in their simplest form, neither model predicts the observed qualitative pattern of reproduction, despite the fact that both formulations capture basic growth features.
4. An examination of more elaborate versions of the two models, in which the allocation rules are modified to account for brief periods of starvation experienced in the laboratory cultures, reveals that a version of the net production model can predict the qualitative pattern seen for cumulative eggs as a function of mass in D. pulex . The analysis leads to new predictions which can be easily tested with further laboratory experiments.     

Energy allocation rules inDaphnia magna: clonal and age differences in the effects of food limitation

Summary The allocation of energy to carapace formation, respiration, growth, and reproduction were examined in two parthenogenetic clones ofDaphnia magna (Cladocera) cultured at two levels of food (Chlorella) concentration. Clonal differences in energy allocation were more apparent at high ration (1.5 g C mL^-1) than at low ration (0.3 g C mL^-1). These differences included respiratory and molting costs, and the timing of energy allocation to growth and reproduction. A comparison of active vs. anesthetized animals revealed that the interclonal difference in respiration rate was the result of a difference in activity level. In both clones mass-specific rates of respiration, growth, and brood production all decreased at low vs. high ration levels, whereas mass-specific molt-loss rate increased. Lowered food concentration decreased the relative allocation of energy to growth and reproduction, but increased allocation to maintenance (respiration and carapace formation). These allocation responses to food limitation indicated that for both clones the highest energy priority was carapace formation. However, the relative priority of respiration, growth and reproduction varied with age and clone. In juveniles (instars 1–4) the priority ranking of growth was essentially equal to that of respiration, whereas respiration always had higher priority in adults (instars 5–9). All three possibilities for the relative ranking of growth and reproduction (i.e., growth>reproduction, growth=reproduction, and reproduction>growth), as specified by different models in the literature, were observed depending on age and clone. The energy allocation rules were also shown to vary between other daphniid species. Furthermore, metabolic responses to chronic food limitation may be different from responses to acute food deprivation. In this study, one clone showed a greater decrease in respiration rate as a result of lifetime food limitation than did the other, but the opposite was true when these clones were exposed to 48 h of starvation. These differences in allocation rules and in acute vs. chronic responses may have to be considered when using physiological data to modelDaphnia populations.     

Effects of Growth Curve Plasticity on Size-Structured Population Dynamics

The physiological-structured population models assume that a fixed fraction of energy intake is utilized for individual growth and maintenance while the remaining for adult fertility. The assumption results in two concerns: energy loss for juveniles and a reproduction dilemma for adults. The dilemma results from the possibility that adults have to breed even if metabolic costs fail to be covered. We consider a size-structured population model, where standard metabolism is given top priority for utilizing energy intake and the surplus energy, if there is any, is distributed to individual growth and reproduction. Moreover, the portion of surplus energy for reproduction is size-dependent and increases monotonically with size. Using the newly developed parameter continuation, we demonstrate their disparate effects on population dynamics. Results show that the size-dependent mechanism of energy allocation primarily exerts destabilizing effects on the system but considerably promotes species coexistence, in comparison with the size-independent mechanism. We conclude that the size-dependent mechanism is, to a large extent, a dispensable component of model ingredients when ontogeny is explicitly taken into consideration.     

Lipid storage in Diaptomus kenai (Copepoda; Calanoida): effects of inter- and intraspecific variation in food quality

In nature, changes in nutrient levels and phytoplankton community structure can represent variation in food quality and quantity. Because zooplankton can be highly susceptible to starvation, individuals could enhance their survival, growth, and reproduction during periods of unfavorable food conditions by maintaining and utilizing energy stores. Patterns of lipid accumulation and depletion in Diaptomus kenai, a calanoid copepod from an oligotrophic montane lake, were monitored over a variety of food conditions. The results suggest that, while lipid storage in D. kenai is affected by phytoplankton community structure and abundance, total lipid stores respond more to gradual changes in food regime than to sudden changes in food supply.     

Mechanisms of energy allocation to reproduction in the cladoceran Daphnia magna Straus

Understanding rules of resource allocation within individuals is helpful in explaining population dynamics. This is particularly the case under the conditions of resource limitation that are commonly experienced by zooplankton. Here, we evaluate assumptions underlying models of resource allocation in Daphnia and test the predictions of two models of response to starvation.
We also test the predictions of two simple models concerning the mechanisms of egg provisioning in Daphnia magna. Our results: (1) demonstrate that provisioning is discontinuous, occurring over a discrete period of the instar; (2) support the hypothesis that egg production occurs in a serial fashion; (3) show that Daphnia magna responds to starvation by ceasing egg production but that there is an increase in mean size of eggs provisioned during the instar, prior to starvation; and (4) broadly support predictions that the response of Daphnia to starvation is an instantaneous cessation of reproduction but that there is a time lag before death.     

The bioenergetics of the southern catfish (Silurus meridionalis Chen): growth rate as a function of ration level, body weight, and temperature

A feeding-growth experiment was conducted in the laboratory on 114 young southern catfish ( Silurus meridionalis Chen) with initial weights of 8.71–127.9g at 15, 20, 25 and 30°C. The experiment consisted of eight weight-temperature groups, with five ration levels ranging from starvation to satiation in each group. A multiple regression equation fitted to the experimental data was developed to describe the relation between specific growth rate (SGR) and the three factors, ration level (RL), body weight ( W ) and temperature ( T ): SGR = 0.471 + 0.172ln W −0.0443 T +0.0682 T ln(RL + l). This predicts that with increasing temperature the specific growth rate decreases at lower ration levels and increases at higher ration levels. The equation, SGR = a + b ln(RL + l), may be considered as the basic growth model where a is the maintenance metabolism exponent and b is the conversion exponent of the net energy; body weight and temperature influence the two parameters. With this relationship the two antagonistic effects of temperature on growth can be understood, increasing temperature imposes a negative effect on growth due to increment in energy cost for maintenance metabolism, and a positive effect due to higher efficiency of transforming food energy into net energy; the positive effect will increase at higher ration levels. This could also explain why at a restricted ration level relationships between growth and temperature are different in different species.     

Effects of various environmental conditions on growth and reproduction of the sea hareAplysia oculifera (Adams and Reeve, 1850)

We studied the influences of food type, food quantity, water currents, starvation and light on growth and reproduction of the sea hareaplysia oculifera (Adams and Reeve, 1850) under laboratory conditions. Out of five species of algae served as food,Enteromorpha intestinalis promoted the fastest growth ofA. oculifera, Ulva spp. slower growth,Cladophora sp. allowed maintenance spp. slower growth,Cladophora sp. allowed maintenance of steady body mass, and the brown algaeColpomenia sp. andPadina pavonia were rejected by the sea hares. When sea hares were exposed to four levels of water currents, growth rates decreased as water currents increased. Sea hares fed on 50% ration grew slower than those fed on 100% ration (ad libitum). During 10 days of starvation sea hares lost weight, but when subsequently fed 100% ration they recovered and grew at a rate similar to those fed continuously with 100% ration. Under shade and under natural sunlight sea hares grew at the same rates. Whenever growth rates decreased, sea hares began to spawn at a smaller body size.A. oculifera demonstrated physiological plasticity that adapted them to varied and unpredictable environmental conditions. At different conditions of food availability they applied different tactics of resource allocation between growth and reproduction.     

Temperature dependence of vegetative growth and dark respiration: a mathematical model

A mathematical model of the processes involved in carbon metabolism is described that predicts the influence of temperature on the growth of plants. The model assumes that the rate of production of dry matter depends both on the temperature and the level of nonstructural carbohydrate. The level of nonstructural carbohydrate is determined by the rates of photosynthesis, growth, and maintenance respiration. The model describes the rate of growth and dark respiration, and the levels of carbohydrate seen in vegetative growth of carnation and tomato. The model suggests that the growth of plants at low temperatures is limited by a shortage of respiratory energy, whereas at high temperatures growth is limited by the shortage of carbohydrate. Thermoperiodism, wherein a warm day and cool night results in faster growth than does constant temperature, is explained by the model as an increase in the level of nonstructural carbohydrate which promotes the rate of growth relative to the rate of maintenance respiration.     

NATURAL SELECTION REDUCES ENERGY METABOLISM IN THE GARDEN SNAIL, HELIX ASPERSA (CORNU ASPERSUM)

Phenotypic selection is widely recognized as the primary cause of adaptive evolution in natural populations, a fact that has been documented frequently over the last few decades, mainly in morphological and life-history traits. The energetic definition of fitness predicts that natural selection will maximize the residual energy available for growth and reproduction, suggesting that energy metabolism could be a target of selection. To address this problem, we chose the garden snail, Helix aspersa ( Cornu aspersum ). We performed a seminatural experiment for measuring phenotypic selection on standard metabolic rate (SMR), the minimum cost of maintenance in ectotherm organisms. To discount selection on correlated traits, we included two additional whole-organism performance traits (mean speed and maximum force of dislodgement). We found a combination of linear (negative directional selection, β=−0.106 ± 0.06; P = 0.001) and quadratic (stabilizing selection, γ=−0.012 ± 0.033; P = 0.061) selection on SMR. Correlational selection was not significant for any possible pair of traits. This suggests that individuals with average-to-reduced SMRs were promoted by selection. To the best of our knowledge, this is the first study showing significant directional selection on the obligatory cost of maintenance in an animal, providing support for the energetic definition of fitness.     

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.     

The cost of enzyme synthesis in the genetics of energy balance and physiological performance

The study of metabolism has traditionally focused upon factors that influence metabolic rate, at levels of both the metabolic pathway and the whole organism. This paper focuses on the cost, and thereby the efficiency, of metabolic processes. The genotype-dependent cost of enzyme turnover is proposed as a biochemical genetic mechanism for relating genetic variation at single genes to phenotypic variation in quantitative traits of energy metabolism. Decreased costs of maintenance metabolism can accompany artificial selection for increased production (e.g. growth, reproduction, etc.) and lower maintenance is correlated with multiple locus heterozygosity in outbred populations. In both cases, high production has been associated with lower rates of protein turnover. Several factors influence the ATP-equivalent cost of enzyme turnover. These factors are used to calculate the cost of turnover for a single enzyme. This cost can conservatively constitute up to several percent of the total daily mass-specific energy demands of maintenance metabolism. Genetic variants of an enzyme can differ in the cost of turnover. These differences can constitute the basis for metabolic changes associated with artificial selection for production and the metabolic differences that are associated with individual levels of heterozygosity. The metabolic and evolutionary significance of genotype-dependent turnover costs is a function of individual energy balance. The strength of selection against increases in cost will be an inverse function of individual energy balance and is therefore influenced by both environmental and genetic factors.     

Strategies in energy consumption and partitioning in Collembola

Abstract. 1. Consumption (in Joules), partitioning of assimilated energy between maintenance (standard metabolism and locomotory activity) and prcduction (growth and reproduction) and assimilation efficiency were studied in the laboratory using adults of the coexisting species Orchesella cincta (L.) and Tomocents minor Lubbock (Collembola, Entomobryidae).
2. A higher energy demand for maintenance was established in O.cincta , compared with T.minor , caused by a higher mobility and a higher live weight-specific oxygen consumption (metabolic rate).
3. The energy required for higher maintenance in O.cincta , compared with T.minor , was derived from production, both from growth and reproduction.
4. The increase in live weight (in mg) during a moulting interval (feeding instar plus reproductive instar) was less in O.cincta than in T.minor , and was less in males than in females.
5. Reproduction (in Joules) was less in O.cincta than in T.ninor . The numbers of eggs produced were equal, but their energetic content was less in O.cincta . Survival of the eggs was similar.
6. Consumption (in Joules) and assimilation efficiency (on an energetic basis) during a moulting interval (feeding instar plus reproductive instar) were similar in both species.     

Balance of production and consumption of ATP in ammonium-starved Saccharomyces cerevisiae

To establish a balance between the ATP produced in catabolism and the ATP consumed in net biosynthesis of cellular components the energy metabolism of Saccharomyces cerevisiae utilizing glucose in the absence of a nitrogen source (resting cells) was studied. The following results were obtained. (i) Cell number and biomass increased 2- and 2.5-fold, respectively, during the first 8 h of ammonium starvation. After this period, both values remained constant. (ii) The rate of sugar consumption and ATP production decreased with the duration of starvation to about 20% of the original in 24 h. (iii) About 60% of the sugar consumed was fermented to ethanol and about 10% assimilated as cellular material. Of the assimilated sugar, as much as 80% was accumulated as carbohydrate. (iv) Only 15% of the total ATP produced in catabolism seems to be consumed in net biosynthesis and maintenance of intracellular pH. The fate of the remaining 85% is unknown.     

Gluttony in migratory waders – unprecedented energy assimilation rates in vertebrates

Maximum energy assimilation rate has been implicated as a constraint on maximal sustained energy expenditure, on biomass production, and in various behavioural and life history models. Data on the upper limit to energy assimilation rate are scarce, and the factors that set the limit remain poorly known. We studied migratory waders in captivity, given unlimited food supply around the clock. Many of these waders assimilated energy at rates of seven to ten times basal metabolism, exceeding maximum rates reported for vertebrates during periods of high energy demand, for example during reproduction and in extreme cold. One factor allowing the high energy assimilation rates may be that much of the assimilated energy is stored and not concomitantly expended by muscles or other organs. The remarkable digestive capacity in waders is probably an adaptation to long and rapid migrations, putting a premium on high energy deposition rates. The upper limit to daily energy assimilation in vertebrates is clearly higher than hitherto believed, and food availability, total daily feeding time and, possibly, the fate of assimilated energy may be important factors to take into account when estimating limits to energy budgets in animals.     

Temperature-dependent energy budget of an Arctic Cladoceran, Daphnia middendorffiana

1. Global change models predict the greatest impact in climate to occur in the northern polar region. Change in temperature will alter individual metabolism and has the potential to change community structure to an unknown degree.
2. The temperature-dependent energy budget of Arctic Daphnia middendorffiana was investigated by measuring respiration rates, ingestion rates and assimilation rates. The scope for growth and reproduction was determined and compared with data from the literature for a clone of Daphnia pulicaria collected in the temperate zone.
3. A difference was observed between the Arctic species and the temperate zone clone in both temperature tolerance, and the energy available for growth and reproduction at various temperatures. A low availability of energy for growth and reproduction indicated that life history patterns as well as physiological mechanisms are important in allowing D. middendorffiana to exist successfully in Arctic environments.
4. The lower available energy for growth compared to Daphnia clones from temperate zones may be detrimental to D. middendorffiana , which might have to compete with species expanding their range under the predicted temperature increase for Arctic regions.     

Autophagy in tumorigenesis and energy metabolism: friend by day, foe by night

Autophagy is the mechanism by which cells consume parts of themselves to survive starvation and stress. This self-cannibalization limits cell death and tissue inflammation, recycles energy and biosynthetic substrates and removes damaged proteins and organelles, accumulation of which is toxic. In normal tissues, autophagy-mediated damage mitigation may suppress tumorigenesis, while in advanced tumors macromolecular recycling may support survival by buffering metabolic demand under stress. As a result, autophagy-activation in normal cells may suppress tumorigenesis, while autophagy inhibition may be beneficial for the therapy of established tumors. The mechanisms by which autophagy supports cancer cell metabolism are slowly emerging. As cancer is being increasingly recognized as a metabolic disease, how autophagy-mediated catabolism impacts cellular and mammalian metabolism and tumor growth is of great interest. Most cancer therapeutics induce autophagy, either directly by modulating signaling pathways that control autophagy in the case of many targeted therapies, or indirectly in the case of cytotoxic therapy. However, the functional consequence of autophagy induction in the context of cancer therapy is not yet clear. A better understanding of how autophagy modulates cell metabolism under various cellular stresses and the consequences of this on tumorigenesis will help develop better therapeutic strategies against cancer prevention and treatment.     

Starvation tolerance associated with prolonged sleep bouts upon starvation in a single natural population of Drosophila melanogaster

Large genetic variations in starvation tolerance in animals indicate that there are multiple strategies to cope with low‐nutrient conditions. Fruit flies (Drosophila melanogaster) typically respond to starvation by suppressing sleep and enhancing locomotor activity presumably to search for food. However, we hypothesized that in a natural population, there are costs and benefits to sleep suppression under low‐nutrient conditions and that conserving energy through sleep could be a better strategy depending on food availability. In this study, we quantified the variation in sleep‐related traits in 21 wild‐derived inbred lines from Katsunuma, Japan, under fed and starved conditions and analysed the relationship between those traits and starvation tolerance. Although most of the lines responded to starvation by suppressing the total time in sleep, there were indeed two lines that responded by significantly increasing the sleep‐bout durations and thus not reducing the total time in sleep. These genotypes survived longer in acute starvation conditions compared to genotypes that responded by the immediate suppression of sleep, which could be due to the reduced metabolic rate during the long uninterrupted sleep bouts. The coexistence of the enhanced foraging and resting strategies upon starvation within a single population is consistent with the presence of a behavioural trade‐off between food search and energy conservation due to unpredictable food availability in nature. These results provide insights into the evolutionary mechanisms that contribute to the maintenance of genetic variations underlying environmental stress resistance.