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.     

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.     

Evolutionary ecology of egg size and number in a seed beetle: genetic trade-off differs between environments

Abstract In many organisms, large offspring have improved fitness over small offspring, and thus their size is under strong selection. However, due to a trade-off between offspring size and number, females producing larger offspring necessarily must produce fewer unless the total amount of reproductive effort is unlimited. Because differential gene expression among environments may affect genetic covariances among traits, it is important to consider environmental effects on the genetic relationships among traits. We compared the genetic relationships among egg size, lifetime fecundity, and female adult body mass (a trait linked to reproductive effort) in the seed beetle, Stator limbatus , between two environments (host-plant species Acacia greggii and Cercidium floridum ). Genetic correlations among these traits were estimated through half-sib analysis, followed with artificial selection on egg size to observe the correlated responses of lifetime fecundity and female body mass. We found that the magnitude of the genetic trade-off between egg size and lifetime fecundity differed between environments–a strong trade-off was estimated when females laid eggs on C. floridum seeds, yet this trade-off was weak when females laid eggs on A. greggii seeds. Also differing between environments was the genetic correlation between egg size and female body mass–these traits were positively genetically correlated for egg size on A. greggii seeds, yet uncorrelated on C. floridum seeds. On A. greggii seeds, the evolution of egg size and traits linked to reproductive effort (such as female body mass) are not independent from each other as commonly assumed in life-history theory.     

Hormonal manipulation of offspring number: maternal effort and reproductive costs

We used exogenous gonadotropin hormones to physiologically enlarge litter size in the bank vole (Clethrionomys glareolus). This method allowed the study design to include possible production costs of reproduction and a trade-off between offspring number and body size at birth. Furthermore, progeny rearing and survival and postpartum survival of the females took place in outdoor enclosures to capture salient naturalistic effects that might be present during the fall and early winter. The aim of the study was to assess the effects of the manipulation on the growth and survival of the offspring and on the reproductive effort, survival, and future fecundity of the mothers. Mean offspring body size was smaller in enlarged litters compared to control litters at weaning, but the differences disappeared by the winter. Differences in litter sizes disappeared before weaning age due to higher mortality in enlarged litters. In addition to the effects of the litter size, offspring performance was probably also influenced by the ability of the mother to support the litter. Experimental females had higher reproductive effort at birth, and they also tended to have higher mortality during nursing. Combined effects of high reproductive effort at birth and high investment in nursing the litter entailed costs for the experimental females in terms of decreased probability of producing a second litter and a decreased body mass gain. Thus, enlarged litter size had both survival and fecundity costs for the mothers. Our results suggest that the evolution of litter size and reproductive effort is determined by reproductive costs for the mothers as well as by a trade-off between offspring number and quality.     

Production of offspring using current income and reserves: size-number trade-off and optimal offspring size

To analyse the effects of current income on the nature of size-number trade-off and optimal offspring size, we developed a model in which offspring grow by absorbing current income and reserves. The offspring continue to grow while the current income is available or the reserves exist, and they cease to grow when the reserves are depleted and the current income ceases. We showed that the size-number trade-off is nonlinear in the region where the number of offspring is smaller than the critical number and linear in the region where the number of offspring is greater than the critical number. In the former region, the reserves are not depleted by the time the current income ceases and the offspring cease to grow when the reserves are depleted, whereas in the latter region, the reserves are depleted before the current income ceases and the offspring production is completed when the current income ceases. The optimal offspring size is the same as that shown in Sakai and Harada (Evolution 55 (2001) 467) if this optimal size is realized in the region of nonlinear trade-off, whereas the optimal offspring size is the same as that shown in Smith and Fretwell (Am. Natur. 108 (1974) 499) if this optimal size is realized in the region of linear trade-off.     

Smaller amphipod mothers show stronger trade-offs between offspring size and number

Trade-offs between embryo mass and number were studied in 10 populations of the freshwater amphipod Gammarus minus . Trade-offs were stronger in populations with small brooding females than in those with larger brooding females. Relationships between embryo mass and maternal body mass were also stronger in populations dominated by small versus large brooding females. These patterns are likely the result of morphological constraints, at least in part. Embryo size is more affected by brood size and maternal size in small mothers, probably because of offspring-packaging constraints associated with small brood pouches. Energy constraints appear to be less important. These results suggest that body size may not only affect the magnitude of individual life-history traits, as is well known, but also the covariance between 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.     

水蓼花大小在花序和个体上的变化及其与数量权衡关系研究

探讨一年生植物水蓼花大小在花序上和个体上的变化及花大小与花数量的权衡关系。在54株植物个体上随机选取一花序,在花序的基部、中部和顶部各选取1～2朵花,花大小(生物量)以基部最大(0.851mg),顶部最小(0.715mg),可能是由结构效应引起的。在每个体上随机采集4～20朵花,以其均值表示植物个体的花大小,花大小不随植物个体大小变化而变化。花朵展示和总花数均随个体增大而增加。在控制植物个体大小(地上部分营养器官生物量)后,没有发现花朵展示或花数量与花大小之间的权衡关系,表明个体资源水平的差异可能掩盖了花数量与大小间的权衡关系。     

The genetic basis of adaptive population differentiation: a quantitative trait locus analysis of fitness traits in two wild barley populations from contrasting habitats

We used a quantitative trait locus (QTL) approach to study the genetic basis of population differentiation in wild barley, Hordeum spontaneum. Several ecotypes are recognized in this model species, and population genetic studies and reciprocal transplant experiments have indicated the role of local adaptation in shaping population differences. We derived a mapping population from a cross between a coastal Mediterranean population and a steppe inland population from Israel and assessed F3 progeny fitness in the natural growing environments of the two parental populations. Dilution of the local gene pool, estimated as the proportion of native alleles at 96 marker loci in the recombinant lines, negatively affected fitness traits at both sites. QTLs for fitness traits tended to differ in the magnitude but not in the direction of their effects across sites, with beneficial alleles generally conferring a greater fitness advantage at their native site. Several QTLs showed fitness effects at one site only, but no opposite selection on individual QTLs was observed across the sites. In a common-garden experiment, we explored the hypothesis that the two populations have adapted to divergent nutrient availabilities. In the different nutrient environments of this experiment, but not under field conditions, fitness of the F3 progeny lines increased with the number of heterozygous marker loci. Comparison of QTL-effects that underlie genotype x nutrient interaction in the common-garden experiment and genotype x site interaction in the field suggested that population differentiation at the field sites may have been driven by divergent nutrient availabilities to a limited extent. Also in this experiment no QTLs were observed with opposite fitness effects in contrasting environments. Our data are consistent with the view that adaptive differentiation can be based on selection on multiple traits changing gradually along ecological gradients. This can occur without QTLs showing opposite fitness effects in the different environments, that is, in the absence of genetic trade-offs in performance between environments.     

Geographic variation in reproductive traits and trade-offs between size and number of eggs of the Chinese cobra (Naja atra)

We collected gravid Chinese cobras (Naja atra) from one island (Dinghai) and three mainland (Yiwu, Lishui and Quanzhou) populations in south‐eastern China to study geographical variation in female reproductive traits and the trade‐off between the size and number of eggs. We then conducted an common experiment on cobras from two of the four populations to further identify factors contributing to the observed trade‐offs. The mean size (snout–vent length) of the smallest five reproductive females increased with increasing latitude. Oviposition occurred between late June and early August, with females from the warmer localities laying eggs earlier than those from the colder localities. Maternal size was a major determinant of the reproductive investment in all populations, with larger females producing not only more but also larger eggs. Clutch size was more variable than egg size within and among populations. The observed geographical variation in clutch size, egg size, clutch mass and post‐oviposition body condition was not a simple consequence of variation in maternal size among populations, because interpopulation differences in these traits were still evident when the influence of maternal size was removed. The upper limit to reproductive investment was more likely to be set by the space availability in the island population, but by the resource availability in the three mainland populations. Trade‐offs between size and number of eggs were detected in all populations, with females that had larger clutches for their size having smaller eggs. Egg size at any given level of relative fecundity differed among populations, primarily because of interpopulation differences in the resource availability rather than the space availability. Except for the timing date of oviposition and the mean size of the smallest five reproductive females, all other examined traits did not vary in a geographically continuous trend. The common garden experiment, which standardized environmental factors, synchronized the timing date of oviposition, but it did not modify the conclusion drawn from the gravid females collected from the field. The observed geographical variation in the female reproductive traits could be attributed to the consequence of the effects of either proximate or ultimate factors. © 2005 The Linnean Society of London, Biological Journal of the Linnean Society, 2005, 85 , 27–40.     

Genetic and phenotypic correlations among size-related traits, and heritability variation between body parts in Drosophila buzzatii

Recent studies have shown that body size is a heritable trait phenotypically correlated with several fitness components in wild populations of the cactophilic fly Drosophila buzzatii. To obtain further information on size-related variation, heritabilities as well as genetic and phenotypic correlations among size-related traits of several body parts (head, thorax and wings) were estimated. The study was carried out on an Argentinean natural population in which size-related selection was previously detected. The genetic parameters were estimated using offspring-parent regressions (105 families) in the laboratory G₂ generation of a sample of wild flies. The traits were also scored in Wild-Caught Flies (WCF). Laboratory-Reared Flies (LRF) were larger and less variable than WCF. Although heritability estimates were significant for all traits, heritabilities were higher for thorax-wing traits than for head traits. Phenotypic and genetic correlations were all positive. The highest genetic correlations were found between traits which are both functionally and developmentally related. Genetic and phenotypic correlations estimated in the lab show similar correlation patterns (r = 0.49; TP = 0.02, Mantel's test). However, phenotypic correlations were found to be typically larger in WCF than in LRF. The genetic correlation matrix estimated in the relatively homogeneous lab environment is not simply a constant multiplicative factor of the phenotypic correlation matrix estimated in WCF. This revised version was published online in July 2006 with corrections to the Cover Date.     

Selection and constraints on offspring size‐number trade‐offs in sand lizards (Lacerta agilis)

The trade‐off between offspring size and number is a central component of life‐history theory, postulating that larger investment into offspring size inevitably decreases offspring number. This trade‐off is generally discussed in terms of genetic, physiological or morphological constraints; however, as among‐individual differences can mask individual trade‐offs, the underlying mechanisms may be difficult to reveal. In this study, we use multivariate analyses to investigate whether there is a trade‐off between offspring size and number in a population of sand lizards by separating among‐ and within‐individual patterns using a 15‐year data set collected in the wild. We also explore the ecological and evolutionary causes and consequences of this trade‐off by investigating how a female's resource (condition)‐ vs. age‐related size (snout‐vent length) influences her investment into offspring size vs. number (OSN), whether these traits are heritable and under selection and whether the OSN trade‐off has a genetic component. We found a negative correlation between offspring size and number within individual females and physical constraints (size of body cavity) appear to limit the number of eggs that a female can produce. This suggests that the OSN trade‐off occurs due to resource constraints as a female continues to grow throughout life and, thus, produces larger clutches. In contrast to the assumptions of classic OSN theory, we did not detect selection on offspring size; however, there was directional selection for larger clutch sizes. The repeatabilities of both offspring size and number were low and we did not detect any additive genetic variance in either trait. This could be due to strong selection (past or current) on these life‐history traits, or to insufficient statistical power to detect significant additive genetic effects. Overall, the findings of this study are an important illustration of how analyses of within‐individual patterns can reveal trade‐offs and their underlying causes, with potential evolutionary and ecological consequences that are otherwise hidden by among‐individual variation.     

Female fertility per flower and trade-offs between size and number in Claytonia virginica (Portulacaceae)

A consistent and paradoxical feature in flowering plants is the production of many more flowers than appear required for female fertility through fruit and seed production. Many mechanistic hypotheses for this observation share key assumptions about (1) limited resources available for reproduction and (b) greater female fertility benefits from larger flowering-time investment. Here I investigate these assumptions in two populations of Claytonia virginica. I also test predictions from theoretical analyses, comparing patterns of flowering allocation and fertility per flower in 18 populations of C. virginica. Results support the assumption that larger benefits accrue from greater flowering-time investment. The between-population pattern of flowering allocation and fertility per flower is also consistent with theoretical expectation, although not statistically significant. Not supported is the assumption that reproduction occurs under strong resource constraint. Possible reasons for this discrepancy are discussed.     

No direct selection to increase offspring number of bet-hedging strategies in large populations: Simons' model revisited

In mixed or 'bet-hedging' strategies, offspring phenotypes are taken randomly from a distribution determined by the genotype and shaped by evolution. Offspring of a single parent represent a finite sample from this distribution, and therefore are subject to variability because of sampling. Contrary to a recent article by A.M. Simons (2007; J. Evol. Biol.20: 813-817), I show that selection does not favour the production of many offspring just to reduce sampling variability when such mixed strategies are used in large populations.     

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.     

A genotypic trade‐off between the number and size of clonal offspring in the stoloniferous herb Potentilla reptans

A negative, genetic correlation between the total number and average size of progeny is a classical life‐history trade‐off that can greatly affect the fitness of organisms in their natural environments. This trade‐off has been investigated for animals and for sexually reproducing plants. However, evidence for a genetical size‐number trade‐off for clonal progeny in plants is still scarce. This study provides experimental evidence for such a trade‐off in the stoloniferous herb Potentilla reptans, and it studies phenotypic plasticity to light availability for the involved traits. Genotypes of P. reptans were collected from distinctively different environments, clonally replicated and exposed to high light and to shaded conditions. We found a significant negative correlation between the average size and the total number of offspring across genotypes for both light environments. Shading reduced ramet numbers, but hardly affected average ramet size.     

Absence of the trade-off between the size and number of offspring in the natterjack toad (Bufo calamita)

Summary A trade-off between size and number of offspring was not found for females of similar sizes of the natterjack toad (Bufo calamita). Moreover, for large females, clutches with higher number of eggs had larger eggs as well. This suggests that larger females produce more numerous and larger eggs because they potentially have more energy available for reproduction. Egg size diminished allometrically with clutch size. Egg size, however, did not increase offspring fitness. Therefore, this allometric decrease may be considered a consequence of phylogenetic constraints rather than a result of optimizing selection.     

Genetic and phenotypic correlations in a natural population of song sparrows

We estimated heritabilities, and genetic and phenotypic correlations between beak and body traits in the song sparrow ( Melospiza melodia ). We compared these estimates to values for the same traits in the Galápagos finches, Geospiza (Boag, 1983; Grant, 1983). Morphological variance is low in the song sparrow, and our results show that genetic and phenotypic correlations are considerably lower than correlations in the morphologically more variable Geospiza. Comparison using a larger sample of Galapagos populations confirms the existence of an association between variance and correlation for phenotypic values. We suggest two possible explanations for this association. First, most traits studied are functionally related, and the joint evolution of variance and correlation may have resulted from stabilizing selection about a line of optimal allometry between traits. Alternatively, introgression between populations and species could have caused correlation and variance to evolve jointly. Both selection and introgression were probably influential in producing the observed pattern, but it is not possible to estimate their relative importance with current data. Genetic and phenotypic correlations were correlated in the song sparrow, but heritabilities of traits varied greatly. As a result, the genetic variance-covariance matrix for traits is not simply a constant multiple of the phenotypic matrix. Evolutionary response to natural selection cannot, therefore, be predicted from the measurement of phenotypic characteristics alone.     

The causes and consequences of variation in offspring size: a case study using Daphnia

Offspring size can have large and direct fitness implications, but we still do not have a complete understanding of what causes offspring size to vary. Daphnia (water fleas) generally produce fewer and larger offspring when food is limited. Here, we use a mathematical model to show that this could be explained by either: (1) an advantage of producing larger eggs when food is limited; or (2) a lower boundary on egg volume (below which eggs do not have sufficient resources to be viable), that is similar in volume to the evolutionarily stable egg volume predicted by standard clutch size models. We tested the first possibilities experimentally by placing offspring from mothers kept at two food treatments (high and low - leading to relatively small and large eggs respectively) into two food treatments (same as maternal treatments, in a fully factorial design) and measuring their fitness (reproduction, age at maturity, and size at maturity). We also tested survival under starvation conditions of offspring produced from mothers at low and high food treatments. We found that (larger) offspring produced by low-food mothers actually had lower fitness as they took longer to reproduce, regardless of their current food treatment. Additionally, we found no survival advantage to being born of a food-stressed mother. Consequently, our results do not support the hypothesis that there is an advantage to producing larger eggs when food is limited. In contrast, data from the literature support the importance of a lower boundary on egg size.