Sink-limitation and the size-number trade-off of organs: production of organs using a fixed amount of reserves

To analyze the nature of size-number trade-off of organs, we develop models in which the effects of sink-limitation in the growth of organs and the loss of resources by maintenance respiration are taken into consideration. In these models, the resource absorption rate of an organ is proportional to either its absolute size or its surface area and either the initial size of an organ or the total initial size of the organs produced is fixed. In all models, organs are produced using a fixed amount of reserved resources and no additional resources become newly available for their growth. We theoretically show that size-number trade-offs are nonlinear if the resource absorption rate of an organ is proportional to the absolute size of the organ and the initial size of the individual organs is fixed or if the resource absorption rate of an organ is proportional to the surface area of the organ. In these nonlinear size-number trade-offs, the size of individual organs increases less rapidly than in linear trade-offs with a decrease in the number of organs and the total size of organs is an increasing function of the number of organs produced. This implies that increasing the number of organs produced is advantageous in terms of resource-use efficiency. In contrast, size-number trade-off is linear if the resource absorption rate of an organ is proportional to the absolute size of the organ and there is a linear trade-off between the initial size of organs and their number. To exemplify the effects of those size-number trade-offs on the life-history evolution, we calculate the optimal offspring sizes that maximize the number of offspring successfully being established. In the case of nonlinear size-number trade-offs, the optimal offspring sizes are smaller than the optimal offspring size in the case of linear size-number trade-offs, namely, that in the model of Smith and Fretwell (1974). Our optimal offspring size depends on the metabolism of organ development; the optimal offspring size decreases with an increase in maintenance respiration rate relative to the growth coefficient of organs.     

Size-number trade-off and optimal offspring size for offspring produced sequentially using a fixed amount of reserves

We analysed the nature of size-number trade-off of offspring when multiple cohorts of such offspring are produced sequentially using a fixed amount of reserves. In the model, we incorporated sink-limitation in the resource absorption rate of offspring from the mother tissue and the loss of resources by maintenance respiration. We found that the later the initiation of a cohort, the greater the cost of producing a cohort with the same size and number of offspring. This is due to the loss of resources by maintenance respiration during the period from the beginning of reproduction to the initiation of the cohort. Also, the extra cost increases with an increase in the specific maintenance respiration rate. Thus, resources lost to respiration over time reduces the fitness value of producing late cohorts. Hence, it is advantageous to produce all offspring simultaneously unless there are fitness advantages of producing offspring sequential which overcome this cost or constraints preventing simultaneous production. Sequentially offspring production evolves if there is a constraint on the number of offspring of each cohort. With this constraint, the optimal offspring size decreases with the production sequence of cohorts.     

Clutch frequency affects the offspring size-number trade-off in lizards

Background

Studies of lizards have shown that offspring size cannot be altered by manipulating clutch size in species with a high clutch frequency. This raises a question of whether clutch frequency has a key role in influencing the offspring size-number trade-off in lizards.

Methodology/Principal Findings

To test the hypothesis that females reproducing more frequently are less likely to tradeoff offspring size against offspring number, we applied the follicle ablation technique to female Eremias argus (Lacertidae) from Handan (HD) and Gonghe (GH), the two populations that differ in clutch frequency. Follicle ablation resulted in enlargement of egg size in GH females, but not in HD females. GH females switched from producing a larger number of smaller eggs in the first clutch to a smaller number of larger eggs in the second clutch; HD females showed a similar pattern of seasonal shifts in egg size, but kept clutch size constant between the first two clutches. Thus, the egg size-number trade-off was evident in GH females, but not in HD females.

Conclusions/Significance

As HD females (mean  = 3.1 clutches per year) reproduce more frequently than do GH females (mean  = 1.6 clutches per year), our data therefore validate the hypothesis tested. Our data also provide an inference that maximization of maternal fitness could be achieved in females by diverting a large enough, rather than a higher-than-usual, fraction of the available energy to individual offspring in a given reproductive episode.     

Optimal offspring sizes in small litters

Summary Numerous evolutionary models explore the trade-off between offspring size and offspring number. However, such models often fail when the number of offspring is small because optimal litter size (or litter size at optimal offspring size) may fall between the necessarily integer values for real litters. This paper extends a classic model for optimal investment per offspring to the case of small litters and predicts that range in offspring size and the largest (smallest) offspring size should decline (increase) with increased litter size. Application of the model to egg size data from a poeciliid fish,Gambusia hubbsi, reveals a surprisingly close approximation to the largest offspring size and variation in offspring size at small litter sizes.     

A model for optimal offspring size in fish, including live-bearing and parental effects

Since Smith and Fretwell's seminal article in 1974 on the optimal offspring size, most theory has assumed a trade-off between offspring number and offspring fitness, where larger offspring have better survival or fitness, but with diminishing returns. In this article, we use two ubiquitous biological mechanisms to derive the shape of this trade-off: the offspring's growth rate combined with its size-dependent mortality (predation). For a large parameter region, we obtain the same sigmoid relationship between offspring size and offspring survival as Smith and Fretwell, but we also identify parameter regions where the optimal offspring size is as small or as large as possible. With increasing growth rate, the optimal offspring size is smaller. We then integrate our model with strategies of parental care. Egg guarding that reduces egg mortality favors smaller or larger offspring, depending on how mortality scales with size. For live-bearers, the survival of offspring to birth is a function of maternal survival; if the mother's survival increases with her size, then the model predicts that larger mothers should produce larger offspring. When using parameters for Trinidadian guppies Poecilia reticulata, differences in both growth and size-dependent predation are required to predict observed differences in offspring size between wild populations from high- and low-predation environments.     

Offspring size-number strategy in the bethylid parasitoid Laelius pedatus

I observed clutch size and body size of resulting offspringfor the parasitoid Laelies pedatus (Say) (Hymenoptera: Bethylidae)on hosts of different sizes. Results were compared with thepredictions of offspring size-number models and clutch-sizemodels. Larger clutches were laid on larger hosts. However,even after females had adjusted dutch size to the size of thehost, offspring size was larger in larger broods. The variancein offspring size between broods decreased with increasing dutchsize as expected, but the decrease was smaller than predictedby Charaov and Downhower's trade-off invariant rule. Theorypredicts such trends when the shape of the trade-off betweenper capita investment and per capita offspring fitness dependson dutch size or host size. By observing how this assumptionmight apply to bethylid wasps, I generate a number of testablehypotheses to explain the observed trends.     

How effective are maternal effects at having effects?

The well studied trade-off between offspring size and offspring number assumes that offspring fitness increases with increasing per-offspring investment. Where mothers differ genetically or exhibit plastic variation in reproductive effort, there can be variation in per capita investment in offspring, and via this trade-off, variation in fecundity. Variation in per capita investment will affect juvenile performance directly--a classical maternal effect--while variation in fecundity will also affect offspring performance by altering the offsprings' competitive environment. The importance of this trade-off, while a focus of evolutionary research, is not often considered in discussions about population dynamics. Here, we use a factorial experiment to determine what proportion of variation in offspring performance can be ascribed to maternal effects and what proportion to the competitive environment linked to the size-number trade-off. Our results suggest that classical maternal effects are significant, but that in our system, the competitive environment, which is linked to maternal environments by fecundity, can be a far more substantial influence.     

Evidence for the morphological constraint hypothesis and optimal offspring size theory in the Mexican mud turtle (Kinosternon integrum)

Optimal offspring size theory states that natural selection should balance reproductive output by optimizing between offspring size and offspring number. If a species has evolved an optimal offspring size, the fitness of larger females should be increased by simply producing more offspring of an optimum size. In contrast, when offspring size is not optimized, the morphological constraint hypothesis may apply, and in this case, maternal fitness is increased by producing the greatest number of the largest offspring that mothers are physically capable of producing. We used a log-log allometric regression approach on clutch size, egg size, and body size data to test the application of optimal offspring size theory and the morphological constraint hypothesis in the Mexican mud turtle (Kinosternon integrum) in southern Mexico. Our results indicate that this turtle seems to follow the morphological constraint hypothesis when all data are analyzed together, but when data are divided between small (< 140 mm plastron length) and large females (> 140 mm plastron length), optimal offspring (egg) size theory was supported only in large females, while the morphological constraint hypothesis was supported in small females. Our results thus indicate that K. integrum females may increase their fitness in two different, size-dependent ways as they grow from size at sexual maturity to maximum body size.     

Maternal effects on offspring size and number in mosquitofish,Gambusia holbrooki

Given a trade-off between offspring size and number, all mothers are predicted to produce the same optimal-sized offspring in a given environment. In many species, however, larger and/or older mothers produce bigger offspring. There are several hypotheses to explain this but they lack strong empirical support. In organisms with indeterminate growth, there is the additional problem that maternal size and age are positively correlated, so what are their relative roles in determining offspring size? To investigate this, we measured the natural relationship between maternal and offspring size in a wild population of Gambusia holbrooki (eastern mosquitofish), and experimentally disentangled the effects of maternal age and size on offspring size in the laboratory. In combination, our data indicate that the relationship between maternal and offspring size is nonlinear. Small mothers seem to produce larger than average offspring due to integer effects associated with very small broods. For extremely large mothers, which were only sampled in our wild data, these larger than average offspring may result from greater maternal resources or age effects. However, maternal age had no effect on offspring size or number in the laboratory experiment. Our results highlight the importance of sampling the full size–range of mothers when investigating maternal effects on offspring size. They also point to the difficulty of experimentally manipulating maternal size, because any change in size is invariably associated with a change in at least one factor affecting growth (be it temperature, food availability, or density) that might also have an indirect effect on offspring size.     

The trade-off between number and size of offspring in humans and other primates

Life-history theory posits a fundamental trade-off between number and size of offspring that structures the variability in parental investment across and within species. We investigate this 'quantity-quality' trade-off across primates and present evidence that a similar trade-off is also found across natural-fertility human societies. Restating the classic Smith-Fretwell model in terms of allometric scaling of resource supply and offspring investment predicts an inverse scaling relation between birth rate and offspring size and a (-1/4) power scaling between birth rate and body size. We show that these theoretically predicted relationships, in particular the inverse scaling between number and size of offspring, tend to hold across increasingly finer scales of analyses (i.e. from mammals to primates to apes to humans). The advantage of this approach is that the quantity-quality trade-off in humans is placed into a general framework of parental investment that follows directly from first principles of energetic allocation.     

Effects of adult-derived carbohydrates, amino acids and micronutrients on female reproduction in a fruit-feeding butterfly

It is generally believed that butterflies (and other holometabolous insects) rely primarily on reserves accumulated during the larval stage for reproduction, whereas the carbohydrate-rich adult diet is thought to mainly cover energy requirements. In at least some species though, realization of the full reproductive potential is extensively affected by post-eclosion nutrition. While the importance of carbohydrates is fairly well understood, the role of adult-derived amino acids and micronutrients is controversial and largely unknown, respectively. We here focus on the effects of different adult diets on female reproduction in the tropical, fruit-feeding butterfly Bicyclus anynana (Nymphalidae). Carbohydrates were the most important adult-derived nutrients affecting reproduction. Adding amino acids, vitamins or minerals to sucrose-based solutions did not yield a reproductive output equivalent to that of fruit-fed females, which showed the highest performance throughout. This suggests that either not yet identified compounds of fruit substantially contribute to reproduction, or that resource congruence (the use of nutrient types in a specified ratio) rather than any specific nutrient component is of key importance. Apart from adult income, realized fecundity depended on egg size and longevity, with the former dominating when dietary quality was low, but the latter when quality was high. Thus, the egg size-number trade-off seems to be affected by female nutrition.     

Selection for increased allocation to offspring number under environmental unpredictability

According to life-history theory, the evolution of offspring size is constrained by the trade-off between allocation of resources to individual offspring and the number of offspring produced. Existing models explore the ecological consequences of offspring size, whereas number is invariably treated simply as an outcome of the trade-off with size. Here I ask whether there is a direct evolutionary advantage of increased allocation to offspring number under environmental unpredictability. Variable environments are expected to select for diversification in the timing of egg hatch and seed germination, yet the dependence of the expression of diversification strategies, and thus parental fitness, on offspring number has not previously been recognized. I begin by showing that well-established sampling theory predicts that a target bethedging diversification strategy is more reliably achieved as offspring number increases. I then use a simulation model to demonstrate that higher offspring number leads to greater geometric mean fitness under environmental uncertainty. Natural selection is thus expected to act directly to increase offspring number under assumptions of environmental unpredictability in season quality.     

Genetic basis of the trade-off between offspring number and quality in the bank vole

One of the main tenets of modern life-history theory is the negative relationship (trade-off) between the number and quality of offspring produced. Theory predicts a negative genetic correlation between these traits since both are closely related to fitness of individuals. However, the genetic basis of the trade-off has only been tested to a limited extent in natural populations. We examined whether size and quality of offspring are negatively related to litter size in the bank vole Clethrionomys glareolus. First, we found a significant negative phenotypic correlation between the number and size of offspring at birth in both laboratory and field populations of the bank vole. Second, a larger size at birth decreased the maturation age of female offspring in the laboratory, and increased the probability of breeding and the size of the first litter in the field. Furthermore, manipulation of offspring size at weaning indicated that structural effects of birth size in mammals have a more profound effect on the expression of life-history traits than weaning size. Finally, in addition to the phenotypic negative correlation between the number and size of offspring, we found evidence for a negative genetic correlation between these two traits, which confirms the genetic basis of the trade-off. This negative genetic covariation may have considerable effects on the rate and direction of evolution of the two related life-historical traits.     

The influence of a positive correlation between clutch size and offspring fitness on the optimal offspring size

Summary The effect is modeled of a positive relationship between clutch size and offspring fitness on the optimal investment in offspring. In species which meet the assumptions of the model, the model predicts a positive correlation between maternal resource level and offspring size. If larger mothers are able to allocate more resources to offspring, then the model would also predict a positive correlation between maternal size and offspring size when the assumptions of the model are met. Thus, this model may help explain both among and within individual variation in offspring size. When offspring are produced in groups and the number of offspring killed per clutch is limited by predator satiation, offspring in larger clutches may experience a higher probability of survival. Such a life style may be found in animals such as sea turtles. Offspring size is positively correlated with maternal size in some members of this group.     

Short-term versus long-term effects of food intake on reproductive output in a viviparous snake, Vipera aspis

Feeding rates influence reproductive output in many kinds of animals, but we need to understand the timescale of this influence before we can compare reproductive energy allocation to energy intake. A central issue is the extent to which reproduction is fuelled by long-term energy stores ("capital" breeding) versus recently-acquired resources ("income" breeding). Our data on free-living aspic vipers show that there is no simple answer to this question: reproductive frequency is determined by long-term energy stores, offspring size is influenced by maternal food intake immediately before ovulation, and litter size is influenced by both long-term stores and short-term energy acquisition. Thus, offspring size in free-living vipers reflects the mother's energy balance over the preceding year (via a trade-off between litter size and offspring size) as well as her energy balance in the current breeding season. Hence, different components of a given reproductive output (litter) are not only functionally linked, but also respond to different temporal scales of prey availability. A female's body size has little effect on her reproductive output. Attempts to quantify reproductive energy allocation must take into account the fact that different reproductive traits (such as offspring size versus number) may respond to energy availability over different timespans. Thus, although the aspic viper is a typical "capital breeder" in terms of its reliance on stored reserves for maternal "decisions" concerning reproductive frequency, it is to some degree a facultative "income breeder" with respect to the determination of offspring size and litter size.     

Maternal condition influences phenotypic selection on offspring

1. Environmentally induced maternal effects are known to affect offspring phenotype, and as a result, the dynamics and evolution of populations across a wide range of taxa. 2. In a field experiment, we manipulated maternal condition by altering food availability, a key factor influencing maternal energy allocation to offspring. We then examined how maternal condition at the time of gametogenesis affects the relationships among early life-history traits and survivorship during early development of the coral reef fish Pomacentrus amboinensis. 3. Maternal condition did not affect the number of embryos that hatched or the number of hatchlings surviving to a set time. 4. We found no significant difference in egg size in relation to the maternal physiological state. However, eggs spawned by supplemented mothers were provisioned with greater energy reserves (yolk-sac and oil globule size) than nonsupplemented counterparts, suggesting that provision of energy reserves rather than egg size more closely reflected the maternal environment. 5. Among offspring originating from supplemented mothers, those with larger yolk-sacs were more likely to successfully hatch and survive for longer periods after hatching. However, among offspring from nonsupplemented mothers, yolk-sac size was either inconsequential to survival or offspring with smaller yolk-sac sizes were favoured. Mothers appear to influence the physiological capacity of their progeny and in turn the efficiency of individual offspring to utilize endogenous reserves. 6. In summary, our results show that the maternal environment influences the relationship between offspring characteristics and survival and suggest that energy-driven selective mechanisms may operate to determine progeny viability.     

Terrestrial reproduction and parental care drive rapid evolution in the trade-off between offspring size and number across amphibians

The trade-off between offspring size and number is central to life history strategies. Both the evolutionary gain of parental care or more favorable habitats for offspring development are predicted to result in fewer, larger offspring. However, despite much research, it remains unclear whether and how different forms of care and habitats drive the evolution of the trade-off. Using data for over 800 amphibian species, we demonstrate that, after controlling for allometry, amphibians with direct development and those that lay eggs in terrestrial environments have larger eggs and smaller clutches, while different care behaviors and adaptations vary in their effects on the trade-off. Specifically, among the 11 care forms we considered at the egg, tadpole and juvenile stage, egg brooding, male egg attendance, and female egg attendance increase egg size; female tadpole attendance and tadpole feeding decrease egg size, while egg brooding, tadpole feeding, male tadpole attendance, and male tadpole transport decrease clutch size. Unlike egg size that shows exceptionally high rates of phenotypic change in just 19 branches of the amphibian phylogeny, clutch size has evolved at exceptionally high rates in 135 branches, indicating episodes of strong selection; egg and tadpole environment, direct development, egg brooding, tadpole feeding, male tadpole attendance, and tadpole transport explain 80% of these events. By explicitly considering diversity in parental care and offspring habitat by stage of offspring development, this study demonstrates that more favorable conditions for offspring development promote the evolution of larger offspring in smaller broods and reveals that the diversity of parental care forms influences the trade-off in more nuanced ways than previously appreciated.

What selective pressures alter the tradeoff between offspring size and number? A phylogenetic comparative approach shows that amphibians with direct development and those that lay eggs in terrestrial environments have larger eggs and smaller clutches, while different care behaviours and adaptations vary in their effects on the tradeoff.     

The offspring-size/clutch-size trade-off in mammals

The Smith-Fretwell model for optimal offspring size assumes the existence of an inverse proportional relationship (i.e., trade-off) between the number of offspring and the amount of resources invested in an individual offspring; virtually all of the many models derived from theirs make the same trade-off assumption. Over the last 30 years it has become apparent that the predicted proportionality is often not observed when evaluated across species. We develop a general allometric approach to correct for size-related differences in the resources available for reproduction. Using data on mammals, we demonstrate that the predicted inverse proportional relationship between number of offspring and offspring size is closely approached after correcting for allocation, though there is a slight curvature in the relationship. We discuss applications for this approach to other organisms, possible causes for the curvature, and the usefulness of allometries for estimating life-history variables that are difficult to measure.     

Optimal allocation of reproductive effort: manipulation of offspring number and size in the bank vole

The number of offspring attaining reproductive age is an important measure of an individual's fitness. However, reproductive success is generally constrained by a trade-off between offspring number and quality. We conducted a factorial experiment in order to study the effects of an artificial enlargement of offspring number and size on the reproductive success of female bank voles (Clethrionomys glareolus). We also studied the effects of the manipulations on growth, survival and reproductive success of the offspring. Potentially confounding effects of varying maternal quality were avoided by cross-fostering. Our results showed that the number of offspring alive in the next breeding season was higher in offspring number manipulation groups, despite their smaller body size at weaning. Offspring size manipulation had no effect on offspring growth or survival. Further, the first litter size of female offspring did not differ between treatments. In conclusion, females may be able to increase the number of offspring reaching reproductive age by producing larger litters, whereas increasing offspring size benefits neither the mother nor the offspring.     

One big, and many small reasons that direct selection on offspring number is still open for discussion

In a recent paper, I proposed that natural selection should act to increase offspring number when diversification bet hedging is favoured. The simple underlying reasoning is that a target diversification strategy is more reliably generated with increasing sample size. The intention of opening a discussion has been realized; recent criticisms of the idea argue that selection does not act to increase offspring number when population size is large or infinite. Here I agree that criticisms have merit; indeed they are largely confined to the caveats discussed in my original paper. The critique, however, implies a verdict of outright rejection of the idea of selection on offspring number, which would be erroneous. Contrary to the assertions of the criticism, then, the importance of selection acting directly on offspring number remains an open question.