Sexual dimorphism and intercorhort variation in reindeer calf antler length is associated with density and weather

We analysed intercohort variability of live weight and antler length of 5,123 reindeer calves. We further assessed the influence of climate and density on the interannual variation in antler length, and discussed sex-specific resource allocation and response to climate variability. Antler length varied significantly among years and between sexes, with interaction between year and sex. Body weight and antler length were highly positively correlated, showed similar intercohort variability, and had a strong allometrical link, suggesting that antler length could be an equally reliable measure of calf condition as live weight. We found a relative measure of antler length (i.e. antler length corrected for the allometric effect of body mass) to be positively influenced by increasing density and May–June precipitation, and also decreasing May–June temperature. We attributed the effect of early summer weather to its influence on forage availability and quality as well as the level of parasitic insect harassment. Gender difference in both the allometric exponents and the interannual variability suggest that young males and females may have different tactics for relative resource allocation towards growth of antlers as compared to body mass. Because antlers are costly to produce, they may be an honest signal of individual quality for both sexes. However, we found gender-specific allometry, as female calves more than males appear to prioritize their antler growth over body mass, especially when resources are limited. Thus, our results suggest that environmental variation may influence the extent of sexual dimorphism in antler length. Electronic Supplementary Material Supplementary material is available for this article at     

How outcrossing hermaphrodites sense the presence of conspecifics and suppress female allocation

One of the greatest remaining problems in the field of sex allocationis the variation across species of the extent to which individualsadjust their offspring sex ratio or sex allocation accordingto environmental conditions. Particularly in the field of sexallocation, there is a lack of research on the mechanisms andcues involved. We address this problem in the outcrossing simultaneoushermaphroditic polychaete Ophryotrocha diadema, which shiftssex allocation by suppressing the female function in the presenceof reproductive competitors or multiple partners. We documentthat O. diadema hermaphrodites can evaluate group size by meansof a species-specific chemical released by mature individualsin water. The perception of such a water-borne signal is sufficientto trigger the observed shift in sex allocation, i.e., a suppressionof the female function, irrespective of the frequency of encounterswith conspecifics. Under natural conditions, such a pheromonewill favor partners' encounters and the adjustment of individualsex allocation according to the numbers of reproductive competitorsand/or potential partners.     

Against the odds? Nestling sex ratio variation in green-rumped parrotlets

We investigated nestling sex ratio variation in the green-rumpedparrotlet (Forpus passerinus), a small neotropical parrot breedingin central Venezuela. There are strong theoretical reasons topredict a female-biased sex ratio in this system according tothe local resource hypothesis; juvenile males are philopatricand there are high levels of competition between male siblingsfor access to breeding females. Data were collected from twobreeding sites over a 14-year period incorporating 564 broodswith a total of 2728 nestlings. The mean percentage of malenestlings across years was 51%. Despite extreme hatching asynchronyin this system and increased survival of earlier hatched offspring,there was no bias in sex allocation associated with egg sequence.Patterns in sex allocation were not associated with clutch size,age, or size of the breeding female or breeding site. The potentialfor selective resorption of eggs was considered; however, nosignificant relationship was found between extended laying intervalsand the sex of subsequent eggs. Together, these results suggestthat female parrotlets are unable to regulate the sex ratioof their clutch at laying or that facultative manipulation ofnestling sex ratio may not confer a fitness benefit to breedersin these populations.     

Production of male flowers does not decrease with plant size in insect‐pollinated Sagittaria trifolia,contrary to predictions of size‐dependent sex allocation

Abstract It has been proposed that relative allocation to female function increases with plant size in animal‐pollinated species. Previous investigations in several monoecious Sagittaria species seem to run contrary to the prediction of size‐dependent sex allocation (SDS), throwing doubt on the generalization of SDS. Plant size, phenotypic gender, and flower production were measured in experimental populations of an aquatic, insect‐pollinated herb Sagittaria trifolia (Alismataceae) under highly different densities. The comparison of ramets produced clonally can reduce confounding effects from genetic and environmental factors. In the high‐density population, 48% of ramets were male without female flowers, but in the low‐density population all ramets were monoecious. We observed allometric growth in reproductive allocation with ramet size, as evident in biomass of reproductive structures and number of flowers. However, within both populations female and male flower production were isometric with ramet size, in contrast to an allometric growth in femaleness as predicted by SDS. Phenotypic gender was not related to ramet size in either population. The results indicated that large plants may increase both female and male function even in animal‐pollinated plants, pointing towards further studies to test the hypothesis of size‐dependent sex allocation using different allocation currencies.     

Size‐dependent sex allocation in a simultaneous hermaphrodite parasite

Most models of sex allocation distinguish between sequential and simultaneous hermaphrodites, although an intermediate sexual pattern, size‐dependent sex allocation, is widespread in plants. Here we investigated sex allocation in a simultaneous hermaphrodite animal, the tapeworm Schistocephalus solidus, in which adult size is highly variable. Sex allocation was determined using stereological techniques, which allow measuring somatic and reproductive tissues in a common currency, namely volume. We investigated the relationships between individual volume and allocation to different reproductive tissues using an allometric model. One measure of female allocation, yolk gland volume, increased more than proportionally with individual volume. This is in contrast to the measure of male allocation, testis volume, which showed a strong tendency to increase less than proportionally with individual volume. Together these patterns led to sex allocation being strongly related to individual volume, with large individuals being more biased towards female allocation. We discuss these findings in the light of current ideas about size‐dependent sex allocation in, primarily, plants and try to extend them to simultaneous hermaphrodite animals.     

Influence of inflorescence size on sexual expression and female reproductive success in a monoecious species

Sex allocation theory forecasts that larger plant size may modify the balance in fitness gain in both genders, leading to uneven optimal male and female allocation. This reasoning can be applied to flowers and inflorescences, because the increase in flower or inflorescence size can differentially benefit different gender functions, and thus favour preferential allocation to specific floral structures. We investigated how inflorescence size influenced sexual expression and female reproductive success in the monoecious Tussilago farfara, by measuring patterns of biomass, and N and P allocation. Inflorescences of T.?farfara showed broad variation in sex expression and, according to expectations, allocation to different sexual structures showed an allometric pattern. Unexpectedly, two studied populations had a contrasting pattern of sex allocation with an increase in inflorescence size. In a shaded site, larger inflorescences were female-biased and had disproportionately more allocation to attraction structures; while in an open site, larger inflorescences were male-biased. Female reproductive success was higher in larger, showier inflorescences. Surprisingly, male flowers positively influenced female reproductive success. These allometric patterns were not easily interpretable as a result of pollen limitation when na?vely assuming an unequivocal relationship between structure and function for the inflorescence structures. In this and other Asteraceae, where inflorescences are the pollination unit, both male and female flowers can play a role in pollinator attraction.     

Constraint on Reproductive Output in Brachyuran Crabs: Pinnotherids Test the Rule

Brood weight and number of eggs per brood are primarily determinedby female body size in brachyuran crabs. Brood weight exhibitsan isometric relationship spanning more than four orders ofmagnitude in body weight among 33 non-pinnotherid species, withbrood size being constrained to about 10% of female body weightby the space available for yolk accumulation within the cephalothorax.In contrast, two pinnotherids (Pinnotheres ostreum, Fabiasubquadrata)have relative brood sizes which are 66% and 97%, respectively,of body weight. The allometric constraint is circumvented inthese extraordinarily large brood sizes by two pinnotherid featureswhich allow more space for yolk accumulation. Unlike other brachyurans,their ovaries extend out of the cephalothorax into the abdomen,and calcification of their exoskeleton is greatly reduced, potentiallyallowing distension of the body. As in crabs, pinnotherid eggsize is highly variable among species, which tends to increasethe variance among species in fecundity per brood, making pinnotheridfecundities not extraordinary. Thenumber of broods producedper year in these two species is limited by short reproductiveseasons, which tends to bring their annual reproductive outputin line with other brachyurans. The trade-offs among reproductivevariables in pinnotherids is adaptive for the small body sizeand parasitic niche of these species.     

Birth-sex ratios and local resource competition in roe deer, Capreolus capreolus

We investigated variation in the primary sex ratio within andbetween 14 populations of roe deer (Capreolus capreolus) inrelation to maternal body condition. The sex ratio was increasinglymale biased as average maternal body weight decreased. Thisrelationship did not vary according to the population consideredand was not affected by the litter size produced. This relationshipwas also apparent within populations. These results indicatethat, where environmental conditions are limiting, roe doestend to produce male-biased litters. Dispersal is more commonand occurs at an earlier age among male juveniles in this species,particularly as density increases and resources become increasinglyscarce. Thus, we suggest that where females experience environmentalstress, they tend to produce male kids to avoid potential futurelocal resource competition posed by female offspring. [BehavEcol 7: 461–464 (1996)]     

Lethal combat and sex ratio evolution in a parasitoid wasp

Sex allocation theory provides excellent opportunities for testinghow behavior and life histories are adjusted in response toenvironmental variation. One of the most successful areas fromthis respect is Hamilton's local mate competition theory. Aspredicted by theory, a large number of animal species have beenshown to adjust their offspring sex ratios (proportion male)conditionally, laying less female-biased sex ratios as the numberof females that lay eggs on a patch increases. However, recentstudies have shown that this predicted pattern is not followedby 2 parasitoid species in the genus Melittobia, which alwaysproduce extremely female-biased sex ratios. A possible explanationfor this is that males fight fatally and that males producedby the first female to lay eggs on a patch have a competitiveadvantage over later emerging males. This scenario would negatethe advantage of later females producing a less female-biasedsex ratio. Here we examine fatal fighting and sex ratio evolutionin another species, Melittobia acasta. We show that femalesof this species also fail to adjust their offspring sex ratioin response to the number of females laying eggs on a patch.We then show that although earlier emerging males do have anadvantage in winning fights, this advantage 1) can be reducedby an interaction with body size, with larger males more likelyto win fights and 2) only holds for a brief period around thetime at which the younger males emerge from their pupae. Thissuggests that lethal male combat cannot fully explain the lackof sex ratio shift observed in Melittobia species. We discussalternative explanations.     

Multiple mating, paternity, and body size in a simultaneous hermaphrodite, Aplysia californica

Sperm displacement and sperm competition prove difficult tomeasure, but are crucial elements in predicting sex allocationstrategies of sperm-storing hermaphrodites. Body size is predictedto affect sex allocation so that within a population, largeanimals invest a greater proportion of resources in female functionthan do small animals. These mating strategies depend on spermdisplacement abilities and lead to similar levels of paternityacross body sizes despite differences in resource level. Thepresent study investigated mating patterns, multiple paternity,and sperm competition in a field population of a simultaneouslyhermaphroditic sea slug, Aplysia californica (California seahare). Animals mating in the female role were larger than themean for the population, indirectly supporting theoretical predictionsfor increased investment in female function with body size.However, contrary to predictions, animals mating in the malerole were not different in size from the population mean orthe animals they inseminated. Individual tagging revealed thatsea slugs are capable of moving across distances that allowfor the sampling of many potential mates, and that they materepeatedly in both sexual roles. Microsatellite paternity analysisdemonstrated that multiple mating in the field leads to multiplepaternity, and last-sperm donors achieve high levels of paternity.There was no effect of body size on paternity. Further paternitystudies are needed to reveal the mechanisms of sperm precedencepatterns in A. californica.     

Behavior of current-year shoots as a mechanism to determine the floral sex allocation at the level of individual tree and population in Siberian alder (Alnus hirsuta var. sibirica)

Floral sex allocation (weight of male flower buds over weight of female flower buds) was examined at the levels of current-year shoot, individual tree and population, and the tree individual level and population level floral sex ratio was explained as a consequence of the behavior of current-year shoots in the shoot-level monoecious (flowering current-year shoots have both male and female flowers) species, Siberian alder (Alnus hirsuta var. sibirica). The current-year shoot level floral sex allocation was not size-dependent and not different over years. However, in the year when the reproductive intensity was high, individual tree level floral sex allocation was size-dependent and the population level floral sex allocation was relatively female-biased. The female-biased floral sex allocation at the population level resulted from many gynoecious shoots (current-year shoots which have only female flowers). These results suggest that the floral sex allocation of Siberian alder was controlled not by changing the floral sex allocation of each current-year shoot, but by shifting the sex expression of current-year shoots from shoot-level monoecy to shoot-level gynomonoecy.     

Experimental manipulation of maternal effort produces differential effects in sons and daughters: implications for adaptive sex ratios in the blue-footed booby

Sex allocation theory predicts that mothers in good conditionshould bias their brood sex ratio in response to the differentialbenefits obtained from increased maternal expenditure in sonsand daughters. Although there is well-documented variationof offspring sex ratios in several bird species according tomaternal condition, the assumption that maternal condition has different fitness consequences for male and for female offspringremains unclear. The blue-footed booby (Sula nebouxii) is asexually size-dimorphic seabird, with females approximately31% heavier than males. It has been reported that the sex ratiois male biased in years with poor feeding conditions, whichsuggests that either females adjust their sex ratio in accordancewith their condition or that they suffer differential brood mortality before their sex can be determined. In this studyI tested whether the condition of mothers affected their daughters'fitness more than their sons' fitness. I manipulated maternalinvestment by trimming the flight feathers and thereby handicappingfemales during the chick-rearing period. Adult females in thehandicapped group had a poorer physical condition at end ofchick growth, as measured by mass and by the residuals of masson wing length compared to control birds. Female chicks wereaffected by the handicapping experiment, showing a lower massand shorter wing length (reduced approximately 8% in both measures)than controls. However, this effect was not found in male chicks.Hatching sex ratios were also related to female body conditionat hatching. The brood sex ratio of females in poor conditionwas male biased but was female biased for females in good condition.Overall, these results suggest that the variation in the sexratio in blue-footed boobies is an adaptive response to thedisadvantage daughters face from being reared under poor conditions.     

Reproductive constraints,not environmental conditions,shape the ontogeny of sex‐specific mass–size allometry in roe deer

In polygynous mammals, sex‐specific patterns of body growth are linked to divergent selection pressures on male and female body size, resulting in sexual dimorphism (SD). For males, reproductive success is generally linked to body size, hence, males should prioritise early growth. For females, reproductive success is linked to resource availability, so they may adopt a more conservative growth tactic. Using longitudinal monitoring of known‐age animals in two contrasting populations and an allometric approach to disentangle the relative contribution of structural size and physiological condition to SD, we addressed these issues in the weakly polygynous roe deer. Despite very different environmental conditions, we found remarkably similar patterns in the two populations in the mass–size allometric relationship at each life history stage, suggesting that relative allocation to structural size and physiological condition is highly constrained. SD in structural size (indexed by hind foot length) involved sex‐specific growth trajectories governed by a single mass–size allometric relationship during the juvenile stage, such that males were both bigger and heavier than females. In contrast, SD in physiological condition (indexed by the allometric relationship between body mass and hind foot length, expressed as body mass for a given body size) developed markedly during the sub‐adult stage in relation to sex differences in the timing of first reproduction. Among adults, males were heavier for a given size than females, suggesting that, relative to females, males express a capital breeder tactic, accumulating fat reserves to offset reproductive costs. By the senescent stage, SD in physiological condition had disappeared, with both sexes governed by a single allometric relationship, suggesting more rapid senescence in males than females. Individuals born into poor cohorts were generally lighter for a given size, indicating growth priority for skeletal size over physiological condition in both sexes. However, sex differences in cohort effects among sub‐adults resulted in lower size‐specific SD in poor cohorts, indicating that body condition of sub‐adult females is buffered against environmental harshness. We conclude that sex‐differences in reproductive tactics impose constraints on the ontogeny of SD in roe deer, leading to sex‐specific trajectories in structural size and physiological condition.     

Sex Ratios and Resource Allocation among Sexually Reproducing Plants of Rubus chamaemorus

Sex ratios and patterns of size variation and resource allocationwere investigated in the dioecious species Rubus chamaemorus.Sex ratios among flowering ramets varied from 6% to 40% of females.Female ramets were slightly, although not significantly, tallerthan males. It appeared that population effects (including bothgenetic population and environmental site effects) on plantsize and allocation patterns at flowering are considerably greaterthan sex effects. If both flowering and fruit production areconsidered, then female allocation to reproduction clearly exceedsmale allocation. In females, no significant relationship wasdetected between the mass of reproductive and vegetative tissues,while males did exhibit such a relationship. Reproductive effortwas less for tall males than for small males. Despite the occurrence of sexual reproduction, the main modeof reproduction in R. chamaemorus is vegetative propagation,which is the best strategy for reproduction in the unpredictableclimate of high latitudes but which leads to skewed sex ratios.As a consequence of vigorous vegetative reproduction, individualclones can grow to be large. The results of electrophoreticstudies show that the numbers of clones per population are low.Copyright1994, 1999 Academic Press Rubus chamaemorus, cloudberry, sex ratios, resource allocation, clonal structure, electrophoresis     

Influences of sex, size, and symmetry on ejaculate expenditure in a moth

Although sperm fundamentally function to fertilize eggs, forcesarising from both sexes select for optimal ejaculate composition.Sperm competition is one recognized agent in the evolution ofsperm and ejaculate structure. Few studies, however, have examinedhow female factors influence ejaculate structure, despite somebehavioral evidence for male mate choice. Male Plodia interpunctella(Lepidoptera, Pyralidae) accrue all resources for reproductionas larvae. Adults emerge with a limited sperm complement andare therefore under intense selection to optimize gamete allocation.I detected no effect of male body weight on ejaculate size.However, female reproductive potential (ovary masses) was dictatedby body weight In addition, heavier females had greater spermathecalvolumes, but there was no such relationship with bursal size.Finally, heavier females showed a higher mating frequency. Ifound that mating males were sensitive to female size and producedlarger ejaculates when mating with heavier females. Males mayejaculate more sperm into larger females either because it paysthem to "spend" more reproductive resources on matings thatprovide greater reproductive potential, or because heavier (longerlived and more attractive) females mate more frequently andhave larger spermathecal volumes. Alternatively, females maycontrol spermatophore formation and "accept" an appropriateejaculate to maximize fertility. Males may therefore be alsoselected to ejaculate more sperm into larger females to counteractgreater risks of sperm competition associated with heavier females.There was no association between male or female femur asymmetryand ejaculate size. P.interpunctella may be selected to exercisemodulation of ejaculate size because males invest paternally,sperm for the single reproductive episode are limited, and femalefecundity and mating pattern vary between individuals and areassociated with body weight. More obvious variability in malereproductive behavior and choice may therefore be paralleledat the cryptic gametic level by plasticity in ejaculate allocation.     

Local resource competition and sex ratio in the ant Cataglyphis cursor

The local resource competition (LRC) hypothesis predicts thatwherever philopatric offspring compete for resources with theirmothers, offspring sex ratios should be biased in favor of thedispersing sex. In ants, LRC is typically found in polygynous(multiple queen) species where foundation of new nests occursby budding, which results in a strong population structure anda male-biased population-wide sex ratio. However, under polygyny,the effect of LRC on sex allocation is often blurred by theeffect of lowered relatedness asymmetries among colony members.Moreover, environmental factors, such as the availability ofresources, have also been shown to deeply influence sex ratioin ants. We investigated sex allocation in the monogynous (singlequeen) ant Cataglyphis cursor, a species where colonies reproduceby budding and both male and female sexuals are produced throughparthenogenesis, so that between-colony variations in relatednessasymmetries should be reduced. Our results show that sex allocationin C. cursor is highly male biased both at the colony and populationlevels. Genetic analyses indicate a significant isolation-by-distancein the study population, consistent with limited dispersal offemales. As expected from asexual reproduction, only weak variationsin relatedness asymmetry of workers toward sexual offspringoccur across colonies, and they are not associated with colonysex ratio. Inconsistent with the predictions of the resourceavailability hypothesis, the male bias significantly increaseswith colony size, and investment in males, but not in females,is positively correlated with total investment in sexuals. Overall,our results are consistent with the predictions of the LRC hypothesisto account for sex ratio variation in this species.     

阿根廷滑柔鱼年间生长及体征变化

阿根廷滑柔鱼(Illex argentinus)的生长发育及体征变化,可表征其能量积累和生殖投入方面的生活史策略,并随之影响繁殖成效和资源补充量。为此,研究根据2012—2014年在西南大西洋索饵育肥场采集的阿根廷滑柔鱼样本,采用残差指标分析方法和广义线性混合效应模型,分析了阿根廷滑柔鱼个体的体质量-胴长关系和体征变化的差异性。结果显示,阿根廷滑柔鱼样本的总体雌雄比例为1.25﹕1;雌性和雄性个体体型均以2014年的为最大,分别为(271.7±28.3)和(244.7±17.3) mm; 2012年和2013年样本的胴长差异性不显著,前者雌性和雄性胴长分别为(207.9±31.0)和(201.1±28.9) mm,后者雌性和雄性胴长分别为(213.6±18.0)和(203.5±19.0) mm。每个年份雌性和雄性个体的体质量与胴长呈显著的幂函数关系,且每个年份幂函数关系式的b值与匀速生长b=3存在差异。雌性和雄性个体体征的年间差异明显,同年度不同月份之间的体征亦存在显著差异(2012年雌性除外)。雌性和雄性个体的体征与胴长密切相关,胴长×月份作用对不同月份个体体征的影响效应具有一致性,...     

Phylogeny determines flower size‐dependent sex allocation at flowering in a hermaphroditic family

• In animal‐pollinated hermaphroditic plants, optimal floral allocation determines relative investment into sexes, which is ultimately dependent on flower size. Larger flowers disproportionally increase maleness whereas smaller and less rewarding flowers favour female function. Although floral traits are considered strongly conserved, phylogenetic relationships in the interspecific patterns of resource allocation to floral sex remain overlooked. We investigated these patterns in Cistaceae, a hermaphroditic family.
• We reconstructed phylogenetic relationships among Cistaceae species and quantified phylogenetic signal for flower size, dry mass and nutrient allocation to floral structures in 23 Mediterranean species using Blomberg's K‐statistic. Lastly, phylogenetically‐controlled correlational and regression analyses were applied to examine flower size‐based allometry in resource allocation to floral structures.
• Sepals received the highest dry mass allocation, followed by petals, whereas sexual structures increased nutrient allocation. Flower size and resource allocation to floral structures, except for carpels, showed a strong phylogenetic signal. Larger‐flowered species allometrically allocated more resources to maleness, by increasing allocation to corollas and stamens.
• Our results suggest a major role of phylogeny in determining interspecific changes in flower size and subsequent floral sex allocation. This implies that flower size balances the male–female function over the evolutionary history of Cistaceae. While allometric resource investment in maleness is inherited across species diversification, allocation to the female function seems a labile trait that varies among closely related species that have diversified into different ecological niches.

     

Production of male flowers does not decrease with plant size in insect-pollinated Sagittaria trifolia, contrary to predictions of size-dependent sex allocation

It has been proposed that relative allocation to female function increases with plant size in animalpollinated species.Previous investigations in several monoecious Sagittaria species seem to run contrary to the prediction of size-dependent sex allocation (SDS),throwing doubt on the generalization of SDS.Plant size,phenotypic gender,and flower production were measured in experimental populations of an aquatic,insect-pollinated herb Sagittaria trifolia (Alismataceae) under highly different densities.The comparison of ramets produced clonally can reduce confounding effects from genetic and environmental factors.In the high-density population,48％ of ramets were male without female flowers,but in the low-density population all ramets were monoecious.We observed allometric growth in reproductive allocation with ramet size,as evident in biomass of reproductive structures and number of flowers.However,within both populations female and male flower production were isometric with ramet size,in contrast to an allometric growth in femaleness as predicted by SDS.Phenotypic gender was not related to ramet size in either population.The results indicated that large plants may increase both female and male function even in animal-pollinated plants,pointing towards further studies to test the hypothesis of size-dependent sex allocation using different allocation currencies.     

A Canopy Photosynthesis Model for the Dynamics of Size Structure and Self-thinning in Plant Populations

A dynamic model for growth and mortality of individual plantsin a stand was developed, based on the process of canopy photosynthesis,and assuming an allometric relationship between plant heightand weight, i.e. allocation growth pattern of plant height andstem diameter. Functions G(t, x), for the mean growth rate ofindividuals of size x at time t, and M(t,x), for the mortalityrate of individuals of size x at time t, were developed fromthis model and used in simulations. The dynamics of size structurewere simulated, combining the continuity equation model, a simpleversion of the diffusion model, with these functions. Simulationsreproduced several well-documented phenomena: (1) size variabilityin terms of coefficient of variation and skewness of plant weightincreases at first with stand development and then stabilisesor decreases with an onset of intensive self-thinning; (2) duringthe course of self-thinning, there is a power relationship betweendensity and biomass per unit ground area, irrespective of theinitial density and of the allocation-growth pattern in termsof the allometric parameter relating plant height and weight.The following were further shown by simulation: (a) competitionbetween individuals in a crowded stand is never completely one-sidedbut always asymmetrically two-sided, even though competitionis only for light; (b) plants of ‘height-growth’type exhibit a greater asymmetry in competition than plantsof ‘diameter-growth’ type, (c) the effect of competitionon the growth of individuals in a crowded stand converges toa stationary state, even when the stand structure still changesgreatly. All of these theoretical results can explain recentempirical results obtained from several natural plant communities.Finally, a new, general functional form for G(t, x) in a crowdedstand is proposed based on these theoretical results, insteadof a priori or empirical growth and competition functions. Canopy photosynthesis, competition mode, continuity equation, self-thinning, simulation, size distribution