A Note on Testing Equality of Means when Sample Sizes are Random with Application

The problem of testing the equality of means of two normal populations is considered when independent random samples of random sizes are given with the total number of observations from both populations being a fixed number. An application in forestry is discussed.     

Fecundity compromises attractiveness when pigments are scarce

Theory predicts that the trade-off between ornamentation andfecundity limits female attractiveness. However, there is littleevidence on this theoretical trade-off and its proximate background.Our aim was to study whether pigment availability modulatesthis potential relationship in blue-footed booby females. Wesupplemented females with dietary carotenoids after laying thefirst egg and assessed the change in foot color, a carotenoid-basedsexually selected trait in both sexes. We measured the changein body mass and in the levels of plasma antioxidants and carotenoids.Also, we registered the mass and volume of eggs. Surprisingly,experimental females reduced zeaxanthin concentration in plasma,but not other carotenoids or total antioxidant levels. Conversely,they increased foot color intensity and laid heavier secondeggs and larger second and third eggs than controls. Furthermore,under natural conditions (controls), ornamentation was negativelyassociated with the mass and volume of second eggs, but theassociation was reversed under conditions of high carotenoidavailability (experimental females). Results suggest that carotenoidavailability may mediate the theoretical trade-off between ornamentationand fecundity. We highlight that pigment limitation for femalescould represent an evolutionary pathway to male choosiness inthe blue-footed booby.     

Barn swallow chicks beg more loudly when broodmates are unrelated

Parents of a variety of animal species distribute critical resources among their offspring according to the intensity of begging displays. Kin selection theory predicts that offspring behave more selfishly in monopolizing parental care as relatedness with competitors declines. We cross-fostered two eggs between barn swallow (Hirundo rustica) clutches and compared the loudness of begging between mixed and control broods under normal feeding conditions and after a period of food deprivation. Begging loudness was higher in mixed broods under normal but not poor feeding conditions. Survival was reduced in mixed than control broods. Call features varied according to parentage, possibly serving as a cue for self-referent phenotype matching in mixed broods. This is the first evidence within a vertebrate species that competitive behaviour among broodmates depends on their relatedness. Thus, kin recognition and relatedness may be important determinants of communication among family members, care allocation and offspring viability in barn swallows.     

Optimal growth strategies when mortality and production rates are size-dependent

Summary Pontryagin's maximum principle from optimal control theory is used to find the optimal allocation of energy between growth and reproduction when lifespan may be finite and the trade-off between growth and reproduction is linear. Analyses of the optimal allocation problem to date have generally yielded bang-bang solutions, i.e. determinate growth: life-histories in which growth is followed by reproduction, with no intermediate phase of simultaneous reproduction and growth. Here we show that an intermediate strategy (indeterminate growth) can be selected for if the rates of production and mortality either both increase or both decrease with increasing body size, this arises as a singular solution to the problem. Our conclusion is that indeterminate growth is optimal in more cases than was previously realized. The relevance of our results to natural situations is discussed.     

Populational Heritability: Extending Punnett Square Concepts to Evolution at the Metapopulation Level

In a previous study, using experimental metapopulations of the flour beetle, Tribolium castaneum, we investigated phase III of Wright's shifting balance process (Wade and Griesemer 1998). We experimentally modeled migration of varying amounts from demes of high mean fitness into demes of lower mean fitness (as in Wright's characterization of phase III) as well as the reciprocal (the opposite of phase III). We estimated the meta-populational heritability for this level of selection by regression of offspring deme means on the weighted parental deme means.Here we develop a Punnett Square representation of the inheritance of the group mean to place our empirical findings in a conceptual context similar to Mendelian inheritance of individual traits. The comparison of Punnett Squares for individual and group inheritance shows how the latter concept can be rigorously defined and extended despite the lack of explicitly formulated, simple Mendelian laws of inheritance at the group level. Whereas Wright's phase III combines both interdemic selection and meta-populational inheritance, our formulation separates the issue of meta-populational heritability from that of interdemic selection. We use this conceptual context to discuss the controversies over the levels of selection and the units of inheritance.     

The evolution of self-incompatibility when mates are limiting

Self-incompatibility (SI) is a genetic barrier to inbreeding that is broadly distributed in angiosperms. In finite populations of SI plants, the loss of S-allele diversity can limit plant reproduction by reducing the availability of compatible mates. Many studies have shown that small or fragmented plant populations suffer from mate limitation. The advent of molecular typing of S-alleles in many species has paved the way to address quantitatively the importance of mate limitation, and to provide greater insight into why and how SI systems breakdown frequently in nature. In this review, we highlight the ecological factors that contribute to mate limitation in SI taxa, discuss their consequences for the evolution and functioning of SI, and propose new empirical research directions.     

Heritability and genetic covariation of sensitivity to PROP, SOA, quinine HCl, and caffeine

The perceived bitterness intensity for bitter solutions of propylthiouracil (PROP), sucrose octa-acetate (SOA), quinine HCl and caffeine were examined in a genetically informative sample of 392 females and 313 males (mean age of 17.8 +/- 3.1 years), including 62 monozygotic and 131 dizygotic twin pairs and 237 sib pairs. Broad-sense heritabilities were estimated at 0.72, 0.28, 0.34, and 0.30 for PROP, SOA, quinine, and caffeine, respectively, for perceived intensity measures. Modeling showed 1) a group factor which explained a large amount of the genetic variation in SOA, quinine, and caffeine (22-28% phenotypic variation), 2) a factor responsible for all the genetic variation in PROP (72% phenotypic variation), which only accounted for 1% and 2% of the phenotypic variation in SOA and caffeine, respectively, and 3) a modest specific genetic factor for quinine (12% phenotypic variation). Unique environmental influences for all four compounds were due to a single factor responsible for 7-22% of phenotypic variation. The results suggest that the perception of PROP and the perception of SOA, quinine, and caffeine are influenced by two distinct sets of genes.     

Sexual selection favours male parental care, when females can choose

Explaining the evolution of male care has proved difficult. Recent theory predicts that female promiscuity and sexual selection on males inherently disfavour male care. In sharp contrast to these expectations, male-only care is often found in species with high extra-pair paternity and striking variation in mating success, where current theory predicts female-only care. Using a model that examines the coevolution of male care, female care and female choice; I show that inter-sexual selection can drive the evolution of male care when females are able to bias mating or paternity towards parental males. Surprisingly, female choice for parental males allows male care to evolve despite low relatedness between the male and the offspring in his care. These results imply that predicting how sexual selection affects parental care evolution will require further understanding of why females, in many species, either do not prefer or cannot favour males that provide care.     

Removing Cancer when it is Correlated with other Causes of Death

This paper presents an identifiability theorem in the theory of dependent competing risks and it applies the result by examining the effect of removing cancer from the United States population when cancer is correlated with the other causes of death. The paper shows how dependence can be modeled with copula functions and it shows that calculating the survival probabilities after cancer is removed is equivalent to solving a system of nonlinear differential equations.     

性状遗传力与QTL方差对标记辅助选择效果的影响

在采用动物模型标记辅助最佳线性无偏预测方法对个体育种值进行估计的基础上,模拟了在一个闭锁群体内连续对单个性状选择10个世代的情形,并系统地比较了性状遗传力和QTL方差对标记辅助选择所获得的遗传进展、QTL增效基因频率和群体近交系数变化的影响。结果表明：在对高遗传力和QTL方差较小的性状实施标记辅助选择时,可望获得更大的遗传进展;遗传力越高,QTL方差越大,则QTL增效基因频率的上升速度越快;遗传力较高时,群体近交系数上升的速度较为缓慢,而QTL方差对群体近交系数上升速度的影响则不甚明显。结合前人关于标记辅助选择相对效率的研究结果,可以认为：当选择性状的遗传力和QTL方差为中等水平时,标记辅助选择可望获得理想的效果。     

Heritability of male secondary sexual traits in feral guppies in Japan

Secondary sexual traits of male guppies show remarkable geographic variation, and male guppies can flexibly change the conspicuousness of their sexual traits within a few generations when they are introduced into new habitats. We examined the degree of conspicuousness and heritabilities of male secondary sexual traits in a feral guppy population in Okinawa, a subtropical island of Japan. Male guppies in this population showed high variation of their sexual traits such as dorsal and caudal fin lengths and red-orange color spot patterns on their bodies. Offspring–parent regressions revealed significant heritabilities of male body size, dorsal and caudal fin lengths, and the number and relative area of orange spots. Especially, the high heritability of the relative orange spot area of sons compared to that of fathers suggests some Y chromosome-linked contribution of the trait. On the other hand, coloration (hue and saturation) of orange spots did not show significant inheritance, probably because most components of orange spot coloration may be condition-dependent traits. These results compared with previous work in native guppy populations suggest female mate preferences based upon these male secondary sexual traits and low predation pressure in this population. Received: June 19, 2000 / Accepted: September 18, 2000     

Variation in the intensity of pollination inDrosera tracyi: Selection is strongest when resources are intermediate

Summary I propose that the strength of selection is greatest when resource levels are intermediate. This idea was partially tested using artificial character variation for petal size inDrosera tracyi. This plant opens one flower each morning, with stigmas becoming available and pollen being presented simultaneously throughout the population. Bees remove all the pollen that can be removed and deposit all the pollen that can be deposited in one or two visits. Visitation rates track blooming density, as do pollen removal and deposition. I measured selection as the difference in pollen removal and deposition between flowers with trimmed petals versus flowers with normal petals. In one meadow, I found a wide range of levels of pollination and corresponding levels of selection, and selection was strongest at intermediate levels of pollination. This might mean that organisms are adapted to conditions when resources are at intermediate levels even though they may experience those conditions relatively rarely.     

Heritability, plasticity and canalization of Ural owl egg size in a cyclic environment

Avian egg size is highly variable on the population level, but is considered inflexible on the individual level. On the basis of 2969 measurements of individual eggs collected during 1981-2005, we analysed heritability, plasticity and selection on egg size in the Ural owl, a long-lived bird that preys on voles. Vole abundance varied in a 3-year cycle, creating varying food supply across the cycle's phases. Ural owl egg size is heritable (h(2) = 60%). Ural owls lay larger eggs in improved food conditions. On the basis of repeated breeding records of 59 females that bred in all vole cycle phases, we show that intra-individual adjustment (plasticity) explained 22.4% of the variation in egg size across phases. Egg size was under stabilizing selection. Extremely small and extremely large eggs had reduced hatchability, and individuals who laid either large or small eggs had lower lifetime fledgling production than the ones laying intermediately sized eggs. Our findings illustrate how maternal investment in egg size can both be heritable and highly responsive to variable environmental conditions, and suggest that variation in the investment in egg size across individuals is canalized.     

The balance between pleiotropic mutation and selection,when alleles have discrete effects

The theory of pleiotropic mutation and selection is investigated and developed for a large population of asexual organisms. Members of the population are subject to stabilising selection on Omega phenotypic characters, which each independently affect fitness. Pleiotropy is incorporated into the model by allowing each mutation to simultaneously affect all characters. To expose differences with continuous-allele models, the characters are taken to originate from discrete-effect alleles and thus have discrete genotypic effects. Each character can take the values nxDelta where n=0,+/-1,+/-2, em leader, and the splitting in character effects, Delta, is a parameter of the model. When the distribution of mutant effects is normally distributed around the parental value, and Delta is large, a "stepwise" model of mutation arises, where only adjacent trait effects are accessible from a single mutation. The present work is primarily concerned with the opposite limit, where Delta is small and many different trait effects are accessible from a single mutation.In contrast to what has been established for continuous-effect models, discrete-effect models do not yield a singular equilibrium distribution of genotypic effects for any value of Omega. Instead, for different values of Omega, the equilibrium frequencies of trait values have very different dependencies on Delta. For Omega=1 and 2, decreasing Delta broadens the width of the frequency distribution and hence increases the equilibrium level of polymorphism. For all sufficiently large values of Omega, however, decreasing Delta decreases the width of the frequency distribution and the equilibrium level of polymorphism. The connection with continuous trait models follows when the limit Delta-->0 is considered, and a singular probability density of trait values is obtained for all sufficiently large Omega.     

Heritability estimates of phenthoate resistance in the diamond-back moth

Realized heritabilities were estimated for the character of phenthoate resistance in two local strains of the diamond-back moth, Plutella xylostella L. (Lepidoptera: Yponomeutidae), by performing artificial laboratory selection for resistance and susceptibility to phenthoate. Heritability estimates indicated that such traits are moderately heritable ( ²=0.42 and 0.41 in the resistant selection and ²=0.31 and 0.21 in the susceptible selection), and give an experimental basis accounting for rapid evolutionary changes of phenthoate resistance observed in field populations of this insect.The observed changes in variances of phenthoate susceptibility are discussed in relation to the additive genetic variance eliminated by directional selection. The explanation stresses the importance on the underlying genetic system.

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Résumé L'héritabilité de la résistance au phenthoate obtenue chez deux souches locales de P. xylostella L. (Lep.; Yponomeutidae) a été calculée en procédant au laboratoire à des sélections artificielles pour la résistance et pour la sensibilité à cet insecticide. Les calculs de l'héritabilité ont montré que de tels caractères sont moyennement héritables ( ²=0,42 et 0,41 lors de la sélection pour la résistance, et ²=0,31 et 0,21 lors de la sélection pour la sensibilité), et ont fourni la base expérimentale rendant compte des changements évolutifs rapides observés pour la résistance au phenthoate chez des populations naturelles de cet insecte.Les changements observés de la variance de la sensibilité au phenthoate sont discutés en fonction de la variance génétique additive éliminée par la sélection orientée. L'explication insiste sur l'importance du système génétique souligné.

     

Heritability of female extra-pair paternity rate in song sparrows (Melospiza melodia)

The forces driving the evolution of extra-pair reproduction in socially monogamous animals remain widely debated and unresolved. One key hypothesis is that female extra-pair reproduction evolves through indirect genetic benefits, reflecting increased additive genetic value of extra-pair offspring. Such evolution requires that a female's propensity to produce offspring that are sired by an extra-pair male is heritable. However, additive genetic variance and heritability in female extra-pair paternity (EPP) rate have not been quantified, precluding accurate estimation of the force of indirect selection. Sixteen years of comprehensive paternity and pedigree data from socially monogamous but genetically polygynandrous song sparrows (Melospiza melodia) showed significant additive genetic variance and heritability in the proportion of a female's offspring that was sired by an extra-pair male, constituting major components of the genetic architecture required for extra-pair reproduction to evolve through indirect additive genetic benefits. However, estimated heritabilities were moderately small (0.12 and 0.18 on the observed and underlying latent scales, respectively). The force of selection on extra-pair reproduction through indirect additive genetic benefits may consequently be relatively weak. However, the additive genetic variance and non-zero heritability observed in female EPP rate allow for multiple further genetic mechanisms to drive and constrain mating system evolution.     

Heritability of three condition surrogates in the yellow dung fly

Condition capture has been proposed as a general mechanism maintainingadditive genetic variation, V_a, in sexually selected traitsunder directional selection. It relies on two main assumptions:condition-dependent trait expression and V_a in condition. Althoughthere is evidence for the former, direct evidence that conditionis heritable is scarce, although this is a requirement of mostmodels of handicap sexual selection. We used a parent–offspring,full-sib, two-container laboratory breeding design in the yellowdung fly Scathophaga stercoraria to demonstrate the broad- andnarrow-sense heritability of three surrogates of condition commonlyused in sexual selection studies: lipid and glycogen reserves(i.e., physiological condition), body size, and fluctuatingasymmetry. All three measures are nutrition dependent and havebeen linked to sexual selection in free-living yellow dung flies.While lipid reserves and body size were heritable, asymmetryand glycogen reserves were not. Moreover, the evolvability ofphysiological condition was higher than that of the other twotraits. Of the three surrogates, physiological condition ismost akin to the original definition, but all have their limitations.We conclude that condition is a useful heuristic concept inevolutionary ecology, but its practical value may be limitedby the fact that it cannot be measured directly.