Size-number Trade-off Research Articles

Sperm size and number variation in the red flour beetle

Disruptive selection between large, nutritive gametes and numerous, competing gametes may have driven the evolution and maintenance of anisogamy. Sperm competition can explain why there are so many tiny sperm because numerical competition between rival gametes drives males to maximize sperm number and this may be achieved by minimizing sperm size. Since males operate within a finite reproductive budget and ejaculate production is limited, we might predict that, when variation in sperm size exists, males must trade increases in sperm size against a decrease in sperm number. We use Tribolium castaneum as our model to investigate the existence of a sperm size–number trade-off. We sampled 14 different populations that have been isolated for different periods (up to 39 years) and find across this sample of 70 males that there is significant variation in both sperm length and ejaculate sperm number between males. Despite this significant variance, we find no evidence for any relationship between sperm size and number across males. There is some evidence for a trade-off when we analyse across 14 population means, but this relationship is not robust and disappears when a single outlier is omitted. We conclude that sperm size and ejaculate sperm number vary independently, but that differential allocation to gonadal tissue and/or ejaculation frequency would permit this independent variation.

Maternal investment and size-number trade-off in a bee, Megachile apicalis, in seasonal environments.

Maternal investment in offspring size and number differed between spring- and summer-emerging individual females of Megachile apicalis, a solitary multivoltine bee. Data from experimentally initiated female populations indicated that spring-emerging females produced a relatively large number of progeny but allocated a small amount of food to each, resulting in small progeny. Adult females of larger body sizes provisioned food at a greater rate than did smaller females, and this body-size effect was significant in spring-emerging females. The large body size of these females allowed them to increase the number of progeny produced under the abundant floral resources that occurred during the spring. Conversely, summer-emerging females produced fewer progeny under the diminishing resources for brood production, but allocated each with more food, producing larger progeny, most of which emerged in the spring of the following year. Field data using trap-nests also indicated the same pattern of seasonal offspring size allocation found in the experimental populations. This maternal investment strategy entails a trade-off between the size and number of progeny, so that the daughters upon emergence can best perform in their brood production under the seasonally variable environments where they reproduce.

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 allocation to flower production in animal-pollinated flowers

The evolutionarily stable size of attractive structures of a flower was analyzed theoretically to examine the factors that select for the differences in the size of attractive structures of a flower depending on the sexuality and self-fertilization rate. In the first analysis, it was assumed that the size–number trade-off for flowers is non-linear (the size of individual flowers increases less rapidly than in a linear trade-off with a decrease in the number of flowers, as would occur during a linear trade-off) and the frequency of pollinator visits per flower depends on the size of attractive structures of individual flowers, but is independent of the number of flowers on the plant. In this case the size of attractive structures is larger in male flowers than in female flowers in dioecious plants, and this size decreases with an increase in the self-fertilization rate for hermaphroditic plants (where both are consistent with the general trends observed). In the second analysis, it was assumed that the size–number trade-off for flowers is linear and the frequency of pollinator visits per flower depends not only on the size of attractive structures of individual flowers, but also on the number of flowers on the plant. However, the results were inconsistent with the general trends in this case; namely, that the size of the attractive structures is smaller in male flowers than in female flowers in dioecious plants, and this size increases with an increase in self-fertilization rate for hermaphroditic plants. I therefore conclude that the non-linearity in size–number trade-offs for flowers is a more useful factor to use to explain the general trends in the size of attractive structures of a flower. This also suggests that the attractive function hypothesis, that is, the differences in fitness gains through allocation to attractive structures between males and females and among plants with different self-fertilization rates, are important factors, but alone cannot explain the general trends.

Evolutionarily Stable Reproductive Strategies in Sexual Organisms: IV. Parent-Offspring Conflict and Selection of Seed Size in Perennial Plants

The provisioning of offspring in sexually reproducing organisms provides an arena in which genetic conflict of interests between parents and their offspring may be expressed. While most existing models of parent-offspring-conflict consider the case of a parent that rears one offspring a year, this paper is concerned with perennial plants that produce many seeds at one time. Parent-offspring conflict is examined in the context of an integrated analysis of reproductive allocation, sex allocation, and the amount of resources invested in each offspring. I derive the evolutionarily stable strategy (ESS) results for the allocation of resources when the mother plant is in control as well as when the offspring are in control taking into account both density-independent and density-dependent population growth. To the extent that the relationships between gamete output and resource investment are linear for both sex functions, the separate treatment of reproductive effort, sex allocation, and offspring size-number compromise in modern life-history theories is justified, regardless of which side, parents or offspring, wins the conflict. In such cases, the ESS sex allocation is exactly what is found in traditional sex allocation theory, and the ESS reproductive effort maximizes the rate of population growth in density-independent populations, or the amount of resources allocated to reproduction during an average lifespan in density-dependent populations. In contrast to the previous theoretical conclusions based on the analyses of single-offspring cases, the ESS reproductive effort under the offspring's control of allocation to individual offspring is found to be lower than that when mothers are in control. This paradoxical result occurs because a mother producing fewer ovules fares better if she knows that each of her seed offspring will get more resources than the amount she is selected to give. The evolutionarily stable offspring size in both density-independent and density-dependent populations does not depend on mother's reproductive effort and investment-independent mortality, just as traditional models of offspring size-number trade-offs would predict.

Vegetative propagation and sexual reproduction in the woodland understorey pseudo-annual Circaea lutetiana L.

On the forest floor of deciduous woodlands, relative light intensity gradually declines during the early growing season. The woodland understorey pseudo-annual Circaea lutetiana L. completes its life-cycle at the end of summer. These pseudo-annuals are clonal plants which survive the winter only as seeds and as hibernacles produced by the rhizome apices. In this paper, we asked several questions related to the life-history of C. lutetiana. It was found that shoot formation in early spring did not exhaust the old hibernacle. A trade-off between rhizome + hibernacle number and weight might be expected when plants grow under resource limitation. It was hypothesised that both number and weight of rhizomes and hibernacles will be affected by light availability. Since the effect of resource supply on the size number trade-off will depend on the developmental pattern of the rhizome system, rhizome development was studied as well. Soon after the shoots emerged, 1st order rhizomes were formed in May on the nodes of the old hibernacle. First-order rhizomes branched in June and 2nd order rhizomes (side-branches) were continuously produced throughout the growing season. The phenology and developmental rate of plants growing in different light treatments were plastic. On average 30% of rhizome biomass was formed during the vegetative phase, and rhizome and fruit production were only partly separated in time. The ratio of total rhizome biomass to total fruit biomass was not affected by light. Also flower bud removal did not lead to an increase in rhizome production, which suggests that division of biomass to both reproductive modes is rather rigid. The number of 1st order rhizomes was not affected by the light treatments. Under light limitation, both rhizome number and weight of single rhizomes were reduced. In contrast, fruit number, but not weight of single fruits, was limited.

Reproductive characteristics of the flower breedingDrosophila hibisciBock (Drosophilidae) along a latitudinal gradient in eastern Australia: relation to flower and habitat features

For many insect species, egg and larval substrate characteristics are significantly correlated with interspecific differences in female reproductive allocation and egg size-number tradeoffs. We tested the hypothesis that a similar pattern occurred within the Australian drosophilid,Drosophila hibisci, that is restricted throughout its life cycle to flowers of species in the genusHibiscus. These plants occur as small, isolated, normally monospecific stands that should facilitate differentiation of the fly populations in relation to specific oviposition and larval substrates. Data from 38 sites ranging from 20.8° to 34.4° S latitude in eastern Australia indicated no relationship between female body size, egg size, or ovariole numbers and floral size or mass among four species ofHibiscus. However, the flies did show a latitudinal cline in ovariole number that was independent of floral variation. Females averaged 15–20 ovarioles per female in the south (32–34° S latitude) and 10–12 ovarioles in the north (21–22° S latitude). The increase in ovariole number with latitude was due to divergence in the ovariole number of the largest females. In contrast, small females in the north and south had the same number of ovarioles. Reproductive allocation of female flies in the northern region was less than females in the southern region. The latitudinal divergence in ovariole number was not associated with habitat differences (density of trees, density of flies and beetles), nor with differences in floral characteristics (flower weight, petal length, yeast species present). Short term weather patterns in daily temperature and rainfall preceding collections partly explain the variation in ovariole number. These observations in conjunction with preliminary genetic results suggest the cline is associated with genetic differences that interact with environmental determinants such as the temperature during larval development.

Game-Theoretical Evolution of Seed Mass in Multi-Species Ecological Models

Within plant communities seed mass often varies over 3 to 5 orders of magnitude, yet simple evolutionary models predict a single optimum seed mass. Here we explore a class of models where seed mass determines 1) the number of seeds produced via a size-number trade-off and 2) competitive ability - plants arising from large seeds are assumed to have a competitive advantage over those derived from small seeds. In this setting the existence of a single-species global ESS seed mass requires the competitive advantage of large seeds over small ones to be unbounded. If there is a limit on the competitive advantage that large seeds obtain then it is always possible to find a smaller seed mass that will successfully invade. In such circumstances there might be a multi-species coevolutionarily stable coalition of several species each with a different seed mass. In this way a wide range of seed masses could be promoted by evolution. In general the adaptive landscape generated by these models is extremely flat leading to slow evolutionary dynamics. The implications of these results for the interpretation of observational, comparative and experimental studies are discussed.

Flower Size-Dependent Variation in Seed Size: Theory and a Test

We developed an optimal-allocation model for the variation in seed size among and within plants of the same species and tested the predictions using naturally growing plants of Lilium auratum. In the model, we considered size-number trade-offs among seeds and assumed that pollen capture is an increasing but diminishing function of allocation to pollen capture mechanisms. We predicted that seed size is positively correlated with allocation to pollen capture. This is because the increased cost of pollen capture makes it more advantageous to increase seed size to enhance the establishment probability of individual seeds than to increase seed number. Field tests were consistent with the predictions. First, hand pollination increased seed number per fruit, which indicated that pollen capture limited seed production, as is assumed in the model analyses. Both ovule size and mean seed weight per fruit were positively correlated with corolla dry weight. In addition, mean seed weight per fruit was negatively correl...

Size-Number Trade-Offs and Pollen Production by Papilionaceous Legumes

Size-Number Trade-Offs and Pollen Production by Papilionaceous Legumes

Clutch Size in Spiders: Is More Better?

1. After controlling for phylogenetic correlation, clutch size in spiders (suborder Araneomorphae) increases with body mass. 2. Clutch mass scales isometrically with adult female body mass while individual egg mass scales with negative allometry. Clutch size therefore is a result of scaling constraints on egg size and total clutch mass. 3. There is no empirical evidence for a size-number trade-off in allocation of resources within clutches. Theory predicts that spiders are selected to maximize clutch size, with no cost of decreased egg size. Spiders are constrained from achieving an optimal clutch size

Sperm competition games: sperm size and number under gametic control

This paper examines sperm competition games in which both size and number of gametes in an ejaculate can be varied strategically, but under the control of the haploid sperm. It is a companion to the previous paper (Parker (Proc. R. Soc. Lond. B 253, 245 (1993))) for the case where the strategic control is by the diploid parent. Under haploid control, the optimal balance between size and number of sperm in an ejaculate becomes quite different from that predicted for diploid control; there is a conflict between parental and gametic interests over sperm size and number. This occurs because both intra-ejaculate and inter-ejaculate sperm competition are present with haploid control, whereas intra-ejaculate competition is absent under diploid control. The magnitude of this conflict is affected by the risk of inter-ejaculate sperm competition, and by the fact that gametic interests depend on the nature of available mutations. If ejaculate expenditure trades off against numbers of matings achieved, with haploid control there is escalation towards maximal expenditure on the ejaculate. If the ejaculate expenditure is fixed by the diploid parent, but there is a size-number trade-off under haploid control, solutions depend on the mode of action of the mutation affecting sperm size or number. If mutant-bearing sperm deviate entirely at the expense of non-mutant sperm, any increase in size or number will spread. If mutant sperm deviate entirely at their own expense, the evolutionarily stable strategy (ESS) is the same as for diploid control; there is no conflict.(ABSTRACT TRUNCATED AT 250 WORDS)

Size-Number Trade-Offs and the Variation of Seed Size with Plant Resource Status

I develop a general treatment of the effects of parental resource status on optimal offspring size. The model shows that even when there is a resource trade-off between size and number of offspring within individuals, positive correlations between size and number may occur among individuals due to individual variation in resources. Such positive correlations imply that parental resource status affects the fitness-maximizing offspring size, in contrast to the predictions of the standard Smith-Fretwell model. I show that parental resource status affects the fitness-maximizing offspring size whenever the size-number fitness function is nonhomogeneous in offspring number. This condition implies some sort of density-dependent interactions among offspring, although it is possible to have either positive or negative sib interactions in fitness functions that are homogeneous in offspring number. In the latter case offspring size should be insensitive to parental resource status. I explore several cases including ...