SELECTION ON VARIANCE IN FLOWERING TIME WITHIN AND AMONG INDIVIDUALS

We model the impact of pollinator visitation rate and behavior on the short‐term evolution of population flowering phenologies determined by the distributions of flowering times within and among individual plants. Evolution of population flowering phenologies depends on the phenotypic variances and heritabilities of the within‐individual mean and variance of flowering time. In the ecological scenarios we investigate selection does not produce a correlation of the mean and variance of individual flowering time. Self‐incompatibility causes weak stabilizing selection on flowering time that acts to reduce the within‐individual variance in flowering time. Disruptive selection due to pollinator limitation acts mostly to increase the among‐individual variance in flowering time. Stabilizing selection due to pollinator attraction, or short reproductive season, acts mostly to decrease the within‐individual variance in flowering time. Temporal autocorrelation of environmental stochasticity in pollinator visitation rate strongly selects to increase the within‐individual variance in flowering time. These predictions can be tested by measuring the causal factors described above, partitioning the variance in population phenology within and among individuals, and estimating the inheritance of, and selection on, within‐individual mean and variance of flowering time.     

Adaptation and functional integration in primate phylogenetics

In two areas of phylogenetics, contrary predictions have been developed and maintained for character analysis and weighting. With regard to adaptation, many have argued that adaptive characters are poorly suited to phylogenetic analysis because of a propensity for homoplasy, while others have argued that complex adaptive characters should be given high weight because homoplasy in complex characters is unlikely. Similarly, with regard to correlated sets of characters, one point of view is that such sets should be collapsed into a single character-a single piece of phylogenetic evidence. Another point of view is that a suite of correlated characters should be emphasized in phylogenetics, again because recurrence of detailed similarity in the same suite of features is unlikely. In this paper, I discuss the theoretical background of adaptation and functional integration with respect to phylogenetic systematics of primates. Several character examples are reviewed with regard to their functional morphology and phylogenetic signal: postorbital structures, tympanic morphology, fusion of the mandibular symphysis, the tooth comb, strepsirrhine talar morphology, and the prehensile tail. It is clear when considering characters such as these that some characters are synapomorphic of major clades and at the same time functionally important. This appears particularly to be the case when characters are integrated into a complex and maintained as stable configurations. Rather than being simply a problem in character analysis, processes of integration may help to explain the utility of phylogenetically informative characters. On the other hand, the character examples also highlight the difficulty in forming a priori predictions about a character's phylogenetic signal. Explanations of patterns of character evolution are often clade-specific, which does not allow for a simple framework of character selection and/or weighting.     

Statistical Genetics of an Annual Plant, Impatiens Capensis. I. Genetic Basis of Quantitative Variation

Analysis of quantitative genetics in natural populations has been hindered by computational and methodological problems in statistical analysis. We developed and validated a jackknife procedure to test for existence of broad sense heritabilities and dominance or maternal effects influencing quantitative characters in Impatiens capensis. Early life cycle characters showed evidence of dominance and/or maternal effects, while later characters exhibited predominantly environmental variation. Monte Carlo simulations demonstrate that these jackknife tests of variance components are extremely robust to heterogeneous error variances. Statistical methods from human genetics provide evidence for either a major locus influencing germination date, or genes that affect phenotypic variability per se. We urge explicit consideration of statistical behavior of estimation and testing procedures for proper biological interpretation of statistical results.     

用方差分析法对葡萄分类性状的评价

本文根据方差分析原理,提出了用F值作为葡萄植物分类性状的评价方法．该法客现可靠,能够区分性状在不同分类水平下的作用大小．文中对156个葡萄分类性状进行了评价,我们认为这种方法同样适合其他植物分类性状的评价．     

GENETICS OF BRASSICA CAMPESTRIS. 1. GENETIC CONSTRAINTS ON EVOLUTION OF LIFE-HISTORY CHARACTERS

Energy allocation arguments suggest a possible tradeoff between timing and magnitude of reproduction: plants that postpone reproduction may accumulate greater resources and consequently produce more offspring. However, early reproduction may be favored when adult mortality is high. Tradeoffs among life-history characters may be a consequence of constraints imposed by genetic and environmental covariation among traits. In this paper we examine the genetic basis of the relationship between timing and magnitude of reproduction in an annual plant, Brassica campestris, by selecting to change flowering date and plant size in each of four directions (early and large, late and large, early and small, or late and small). There is a strong positive relationship between flowering date and flowering height. The response to selection was greatest along the axis of positive genetic covariation. Populations may evolve to become early flowering and small or late flowering and tall, but there is little response for the alternative combinations of characters. In this instance, the constraints imposed by quantitative genetics are in striking accord with predictions that might be made on physiological, energetic, or ecological grounds.     

Modeling the evolution of genetic architecture: A continuum of alleles model with pairwise AxA epistasis

A continuum of alleles model with pair-wise AxA epistasis is proposed and its transmission genetic, and variational properties are analysed. The basic idea is that genes control the values of underlying variables, which affect the genotypic value of phenotypic characters proportional to a "scaling factor". Epistasis is the influence of one gene on the average effect of another gene. In this model, epistasis is introduced as a mutational effect of one gene on the scaling factors of another gene. In accordance with empirical results, the model assumes that the average direct effect of mutations is zero, as is the average epistatic effect. The model predicts that, on average, a mutation at one locus increases the expected mutational variance of mutations at another interacting locus. The increase in mutational variance is predicted to be equal to the variance of the pair-wise epistatic effects. This result is consistent with the observation that mutant phenotypes tend to be more variable than the wildtype phenotype. Another generic result of this model is that the frequency of canalizing mutations can at most be equal to the frequency of de-canalizing mutations. Furthermore, it is predicted that the mutational variance of a character increases at least linearly with the size of the character; hence this model is scale variant. In the case of two characters it is shown that the dimensionality of the locus-specific mutational effect distribution is invariant, i.e. the rank of the mutational covariance matrix M is invariant. While in additive models the mutational covariance matrix is always and entirely invariant, the invariance in the case of epistatic models is unexpected. Epistatic interactions can change the magnitude of the mutational (co)variances at a locus and can thus influence the structure of the mutational covariance matrix. However, in the present model the dimensionality of the mutational effect distribution remains the same. A consequence of this result is that, in this model, the genetic architecture of a set of characters is always evolvable i.e. no hard constraints can evolve.     

The ecology and genetics of fitness in forest plants. IV. Quantitative genetics of fitness components in Impatiens pallida (Balsaminaceae)

Genetic and environmental variances were estimated for a number of characters in the annual plant Impatiens pallida by planting seed obtained through controlled crosses into their native field site or pots maintained in the greenhouse. Significant additive genetic variance was detected for three of 11 characters studied—germination date, cotyledon area, and date of first flower production. Significant dominance and/or maternal variance was found for seed weight, proportion of seeds germinating, cotyledon area, plant height, and number of leaves produced. Environmental variance was greater in the field compared with the greenhouse. Characters found to be under strong directional selection in a previous study showed no detectable additive genetic variance. While these populations exhibit conditions that in theory could contribute to the maintenance of genetic variation (limited pollen and seed dispersal distances and small-scale variation for edaphic characteristics influencing plant growth), levels of additive genetic variance for most characters were not significantly different from zero.     

A navigational guide to variable fitness: common methods of analysis,where they break down,and what you can do instead

Our methods for analyzing stochastic fitness are mostly approximations, and the assumptions behind these approximations are not always well understood. Furthermore, many of these approximations break down when fitness variance is high. This review covers geometric mean growth, diffusion approximations, and Markov processes. It discusses where each is appropriate, the conditions under which they break down, and their advantages and disadvantages, with special attention to the case of high fitness variance. A model of sessile and site-attached coastal species is used as a running example, and fully worked calculations and code are provided. Summary: The logarithm of geometric mean growth is usually only appropriate when (a) an invader growth rate is needed and (b) fitness variability is driven by environmental fluctuations. The usual approximation breaks down when fitness variance is high. Diffusion approximations can provide a reasonable guide to the expected change in frequency over a time step if expected fitnesses and fitness variances are appropriately scaled by the average expected fitness. Diffusion approximations can perform less well for fixation probabilities, especially since further approximations may be required. Fixation probabilities can be calculated exactly using a Markov process, regardless of how large fitness variance is, although an analytic expression is frequently not possible. If an analytic expression is desired, it may be worth using a diffusion approximation and checking it with a Markov process calculation.     

青藏高原东缘高寒草甸常见植物种子形状对萌发的影响

以青藏高原东缘高寒草甸383种常见植物种子为材料,分析种子萌发特性与种子形状(长、宽、高的三维方差)、体积及相对表面积之间的相关性,研究高寒草甸地区植物种子性状对其萌发特性的影响。结果显示:(1)种子萌发率和萌发速率与种子三维方差、相对表面积呈极显著正相关,与体积呈显著负相关;(2)种子平均萌发时间与种子体积呈显著正相关、与种子相对表面积呈显著负相关、与种子三维方差无显著相关性。表明体积较小而形状细长的种子具有较高的萌发率及萌发速率,体积大而圆的种子需要更长的萌发时间;小种子具有较大的相对表面积可能是其具有较高萌发率和萌发速率的原因之一。研究结果为土壤种子库形成机制的研究提供了一定的理论依据。     

Effects of parental survival on clutch size decisions in fluctuating environments

Whereas in constant environments parental survival has no effect on optimal clutch size in the absence of trade-offs between juvenile and parental survival, the situation is drastically different in fluctuating environments. We consider a model in which, with respect to reproduction, parents and offspring are equivalent at the start of the next breeding season. When generations are non-overlapping, the clutch size maximizing geometric mean surviving number of offspring is optimal among all pure clutch size strategies. We prove that, as parental survival increases relative to that of the offspring, the optimal clutch size converges to the arithmetic mean maximizing clutch size (the so-called ‘Lack clutch size’). We also give a numerical procedure for calculating optimal mixed strategies and we show that, as environmental variance increases and/or parental survival decreases, mixed rather than pure strategies become optimal. Furthermore, we explain how to estimate fitness from empirical data under the assumptions of our model. This revised version was published online in July 2006 with corrections to the Cover Date.     

Seed Germination in Desert Annuals: An Empirical Test of Adaptive Bet Hedging

Temporal variability in survivorship and reproduction is predicted to affect the evolution of life-history characters. Desert annual plants experience temporal variation in reproductive success that is largely caused by precipitation variability. We studied several populations of the desert annual Plantago insularis along a precipitation gradient. Whereas models of bet hedging in unpredictable environments generally predict one optimal germination fraction for a population, empirical studies have shown that environmental conditions during germination can cause a range of germination fractions to be expressed. In a 4-yr field study, we found that populations in historically more xeric environments had lower mean germination fractions, as is predicted by bet-hedging models. However, populations exhibited significant variation in germination among years. Two experimental studies measuring germination under several environment conditions were conducted to elucidate the source of this in situ variation. Germination fractions exhibited phenotypic plasticity in response to water availability and date within the season. Populations differed in their norms of reaction such that seeds from more xeric populations germinated under less restrictive conditions. A pattern of delayed germination consistent with among-year bet-hedging predictions arose in the field through the interaction of seed germinability and the distribution of environmental conditions during germination.     

Seed dormancy and delayed flowering in monocarpic plants: selective interactions in a stochastic environment

We explore the effects of temporal variation in multiple demographic rates on the joint evolution of delayed reproduction and seed dormancy using integral projection models (IPMs). To do this, we extend the standard IPM to include a discrete state variable representing the number of seeds in the seed bank, density-dependent recruitment, and temporal variation in demography. Parameter estimates for Carlina vulgaris and Carduus nutans are obtained from long-term studies. Carlina is relatively long lived and has a short-lived seed bank, whereas most Carduus plants flower in their first year and the seed bank is long lived. Using the evolutionarily stable strategy (ESS) approach, we predict the observed flowering and germination strategies. There is excellent agreement between the predictions and the field observations. The effects of temporal variation on the joint ESS are partitioned into components arising from nonlinear averaging (systematic changes in the mean resulting from the interaction between variability and nonlinearity) and nonequilibrium dynamics (fluctuations in fitness caused by temporal variation). This shows that temporal variation can have substantial effects on the observed flowering and germination strategies and that covariance between demographic processes is important. We extend the models to include spatial population structure and assess the robustness of the results from the nonspatial models.     

Effects of Pleiotropy on Predictions concerning Mutation-Selection Balance for Polygenic Traits

Previous mathematical analyses of mutation-selection balance for metric traits assume that selection acts on the relevant loci only through the character(s) under study. Thus, they implicitly assume that all of the relevant mutation and selection parameters are estimable. A more realistic analysis must recognize that many of the pleiotropic effects of loci contributing variation to a given character are not known. To explore the consequences of these hidden effects, I analyze models of two pleiotropically connected polygenic traits, denoted P1 and P2. The actual equilibrium genetic variance for P1, based on complete knowledge of all mutation and selection parameters for both P1 and P2, can be compared to a prediction based solely on observations of P1. This extrapolation mimics empirically obtainable predictions because of the inevitability of unknown pleiotropic effects. The mutation parameters relevant to P1 are assumed to be known, but selection intensity is estimated from the within-generation reduction of phenotypic variance for P1. The extrapolated prediction is obtained by substituting these parameters into formulas based on single-character analyses. Approximate analytical and numerical results show that the level of agreement between these univariate extrapolations and the actual equilibrium variance depends critically on both the genetic model assumed and the relative magnitudes of the mutation and selection parameters. Unless per locus mutation rates are extremely high, i.e., generally greater than 10(-4), the widely used gaussian approximation for genetic effects at individual loci is not applicable. Nevertheless, the gaussian approximations predict that the true and extrapolated equilibria are in reasonable agreement, i.e., within a factor of two, over a wide range of parameter values. In contrast, an alternative approximation that applies for moderate and low per locus mutation rates predicts that the extrapolation will generally overestimate the true equilibrium variance unless there is little selection associated with hidden effects. The tendency to overestimate is understandable because selection acts on all of the pleiotropic manifestations of a new mutation, but equilibrium covariances among the characters affected may not reveal all of this selection. This casts doubt on the proposal that much of the additive polygenic variance observed in natural populations can be explained by mutation-selection balance. It also indicates the difficulty of critically evaluating this hypothesis.     

七叶树花粉活力和柱头可授性变化的研究

采用花粉离体萌发法研究不同蔗糖浓度、硼酸浓度和不同温度对七叶树花粉萌发的影响及花粉活力测定,用联苯胺-过氧化氢法测定柱头可授性.结果表明:七叶树花粉萌发的最佳培养基是12％蔗糖+30 mg/L硼酸,花粉萌发的最适温度为25℃.雄花在开花当天花粉活力最高达75.69％,并在开花当天的上午10:00时,花粉活力最强,10:00～16:00花粉活力保持较高活力,是最佳授粉时段.两性花的柱头可授期持续时间较长,为8～9 d,开花3d达到最强,开花1～4 d柱头可授性保持较高水平,为授粉的最佳时间段.因此,从七叶树的花部特征、花粉活力与柱头可授性及花粉萌发的条件看,在长期的自然选择下七叶树在花部结构和开花生理上都是相配合的,以保障生殖成功.     

Genes and environment

Many quantitative characters depend on the action of a large number of genes and environmental factors. The mode of inheritance of these characters is polygenic. The phenotypic variance of the character is the sum of the components, thus the genetic and the environmental variances (VP = VG + VE). The degree of genetic determination VG/VP and VE/VP are difficult to estimate in man. The heritability a related coefficient to VG/VP can be estimated from the degree of ressemblance between relatives. The heritability is the additive genetique variance as a proportion of the phenotypic variance. Polygenic threshold inheritance can account for the familial non mendelian distribution of multifactorial diseases.     

Frequency- and density-dependent selection on a quantitative character

The equilibrium distribution of a quantitative character subject to frequency- and density-dependent selection is found under different assumptions about the genetical basis of the character that lead to a normal distribution in a population. Three types of models are considered: (1) one-locus models, in which a single locus has an additive effect on the character, (2) continuous genotype models, in which one locus or several loci contribute additively to a character, and there is an effectively infinite range of values of the genotypic contributions from each locus, and (3) correlation models, in which the mean and variance of the character can change only through selection at modifier loci. It is shown that the second and third models lead to the same equilibrium values of the total population size and the mean and variance of the character. One-locus models lead to different equilibrium values because of constraints on the relationship between the mean and variance imposed by the assumptions of those models.——The main conclusion is that, at the equilibrium reached under frequency- and density-dependent selection, the distribution of a normally distributed quantitative character does not depend on the underlying genetic model as long as the model imposes no constraints on the mean and variance.     

Ecological factors of flowering and pollen quality in three willow species

During 1977 to 1980 the course of flowering and pollen quality were investigated inSalix cinerea, S. fragilis, andS. pentandra, the dominant woody species in a wetland area called “Mokré louky” near T?eboň, South Bohemia, Czechoslovakia. Results were compared with basíc climatological data, and decisive factors of flowering were estimated. BothS. cinerea andS. pentandra produced morphologically well developed pollen with a high degree of viability. Comparison in twelve habitats showed that the pollen ofS. fragilis was very sensitive to climatic factors, and that the marsh habitat “Mokré Louky” was hostile to the generative reproduction of this species. Optimal conditions for pollen germination in vitro were defined for all the three willows.     

Spatial patterns in the distributions of polygenic characters

The spatial patterns in the mean and variance of a quantitative character that result from the interaction of spatially varying, optimizing selection and gene flow are considered. The model analyzed is an extension of those of Kimura (1965) and Lande (1976) for the distribution of a quantitative character maintained in a population by independent mutations. For weak selection, it is shown that there is only a small effect of gene flow on the variance of the character and that the mean value changes on a length scale that is large compared to the average dispersal distance. As in models of clines in allele frequencies, it is possible to define a “characteristic length” in terms of the average dispersal distance and strength of selection. The characteristic length is the smallest length scale environmental change to which the mean value of the character can significantly respond. It is also shown that, for weak selection, an asymmetry in dispersal can result in a significant shift in location of a cline. By considering an infinite linear cline in optimal values, it is shown that gene flow can increase the variance only when there is sufficient mixing in each generation of individuals from locations with different means. A model of selection in different niches is also considered. There is an increase in variance due to the effective weakening of the intensity of selection because of the differences in optimal values in different niches.The implications of the different models for maintenance of genetic polymorphism are discussed. Under some conditions gene flow can produce a significant increase in heterozygosity. It is also argued that spatial variation in selection on a polygenic character can be much more effective in increasing heterozygosity than temporal variation because of the potentially greater increase in phenotypic variance. The difference between some of the results for polygenic characters from those of similar models of one and two locus systems is accounted for by the fact that for normally distributed polygenic characters, changes in the variance are effectively decoupled from changes in the mean.