EVOLUTION IN FLUCTUATING ENVIRONMENTS: DECOMPOSING SELECTION INTO ADDITIVE COMPONENTS OF THE ROBERTSON–PRICE EQUATION

We analyze the stochastic components of the Robertson–Price equation for the evolution of quantitative characters that enables decomposition of the selection differential into components due to demographic and environmental stochasticity. We show how these two types of stochasticity affect the evolution of multivariate quantitative characters by defining demographic and environmental variances as components of individual fitness. The exact covariance formula for selection is decomposed into three components, the deterministic mean value, as well as stochastic demographic and environmental components. We show that demographic and environmental stochasticity generate random genetic drift and fluctuating selection, respectively. This provides a common theoretical framework for linking ecological and evolutionary processes. Demographic stochasticity can cause random variation in selection differentials independent of fluctuating selection caused by environmental variation. We use this model of selection to illustrate that the effect on the expected selection differential of random variation in individual fitness is dependent on population size, and that the strength of fluctuating selection is affected by how environmental variation affects the covariance in Malthusian fitness between individuals with different phenotypes. Thus, our approach enables us to partition out the effects of fluctuating selection from the effects of selection due to random variation in individual fitness caused by demographic stochasticity.     

GENETIC CONSTRAINTS ON ADAPTATION TO A CHANGING ENVIRONMENT

Genetic correlations between traits can constrain responses to natural selection. To what extent such correlations limit adaptation depends on patterns of directional selection. I derive the expected rate of adaptation (or evolvability) under randomly changing selection gradients. When directional selection gradients have an arbitrary covariance matrix, the average rate of adaptation depends on genetic correlations between traits, contrary to the isotropic case investigated in previous studies. Adaptation may be faster on average with more genetic correlation between traits, if these traits are selected to change jointly more often than the average pair of traits. However, natural selection maximizes the long‐term fitness of a population, not necessarily its rate of adaptation. I therefore derive the average lag load caused by deviations of the mean phenotype from an optimum, under several forms of environmental changes typically experienced by natural populations, both stochastic and deterministic. Simple formulas are produced for how the G matrix affects long‐term fitness in these contexts, and I discuss how their parameters can be estimated empirically.     

EVOLUTION OF PHENOTYPE–ENVIRONMENT ASSOCIATIONS BY GENETIC RESPONSES TO SELECTION AND PHENOTYPIC PLASTICITY IN A TEMPORALLY AUTOCORRELATED ENVIRONMENT

Covariation between population‐mean phenotypes and environmental variables, sometimes termed a “phenotype–environment association” (PEA), can result from phenotypic plasticity, genetic responses to natural selection, or both. PEAs can potentially provide information on the evolutionary dynamics of a particular set of populations, but this requires a full theoretical characterization of PEAs and their evolution. Here, we derive formulas for the expected PEA in a temporally fluctuating environment for a quantitative trait with a linear reaction norm. We compare several biologically relevant scenarios, including constant versus evolving plasticity, and the situation in which an environment affects both development and selection but at different time periods. We find that PEAs are determined not only by biological factors (e.g., magnitude of plasticity, genetic variation), but also environmental factors, such as the association between the environments of development and of selection, and in some cases the level of temporal autocorrelation. We also describe how a PEA can be used to estimate the relationship between an optimum phenotype and an environmental variable (i.e., the environmental sensitivity of selection), an important parameter for determining the extinction risk of populations experiencing environmental change. We illustrate this ability using published data on the predator‐induced morphological responses of tadpoles to predation risk.     

ECOLOGICAL HISTORY AND EVOLUTION IN A NOVEL ENVIRONMENT: HABITAT HETEROGENEITY AND INSECT ADAPTATION TO A NEW HOST PLANT

Environmental heterogeneity has often been implicated in the maintenance of genetic variation. However, previous research has not considered how environmental heterogeneity might affect the rate of adaptation to a novel environment. In this study, I used an insect-plant system to test the hypothesis that heterogeneous environments maintain more genetic variation in fitness components in a novel environment than do uniform environments. To manipulate recent ecological history, replicate populations of the dipteran leafminer Liriomyza trifolii were maintained for 20 generations in one of three treatments: a heterogeneous environment that contained five species of host plant, and two uniform environments that contained either a susceptible chrysanthemum or tomato. The hypothesis that greater genetic variance for survivorship and developmental time on a new host plant (a leafminer-resistant chrysanthemum) would be maintained in the heterogeneous treatment relative to the uniform environments was then tested with a sib-analysis and a natural selection experiment. Populations from the heterogeneous host plant treatment had no greater genetic variance in either larval survivorship or developmental time on the new host than did populations from either of the other treatments. Moreover, the rate of adaptation to the new host did not differ between the ecological history treatments, although the populations from the uniform chrysanthemum treatment had higher mean survivorship throughout the selection experiment. The estimates of the heritability of larval survivorship from the sib-analysis and selection experiment were quite similar. These results imply that ecologically realistic levels of environmental heterogeneity will not necessarily maintain more genetic variance than uniform environments when traits expressed in a particular novel environment are considered.     

MEASURING SELECTION AND CONSTRAINT IN THE EVOLUTION OF GROWTH

We present a quantitative genetic model for the evolution of growth trajectories that makes no assumptions about the shapes of growth trajectories that are possible. Evolution of a population's mean growth trajectory is governed by the selection gradient function and the additive genetic covariance function. The selection gradient function is determined by the impact of changes in size on the birth and death rates at different ages, and can be estimated for natural populations. The additive genetic covariance function can also be estimated empirically, as we demonstrate with four vertebrate populations. Using the genetic data from mice, a computer simulation shows that evolution of a growth trajectory can be constrained by the absence of genetic variation for certain changes in the trajectory's shape. These constraints can be visualized with an analysis of the covariance function. Results from four vertebrate populations show that while each has substantial genetic variation for some evolutionary changes in its growth trajectory, most types of changes have little or no variation available. This suggests that constraints may often play an important role in the evolution of growth.     

QUANTITATIVE GENETICS OF BRYOZOAN PHENOTYPIC EVOLUTION. II. ANALYSIS OF SELECTION AND RANDOM CHANGE IN FOSSIL SPECIES USING RECONSTRUCTED GENETIC PARAMETERS

The roles of natural selection and random genetic change in the punctuated phenotypic evolution of eight Miocene-Pliocene tropical American species of the cheilostome bryozoan Metrarabdotos are analyzed by quantitative genetic methods. Trait heritabilities and genetic covariances reconstructed by partitioning within- and among-colony phenotypic variance are similar to those previously obtained for living species of the cheilostome Stylopoma using breeding data. The hypothesis that differences in skeletal morphology between species of Metrarabdotos are entirely due to mutation and genetic drift cannot be rejected for reasonable rates of mutation maintained for periods brief enough to account for the geologically abrupt appearances of these species in the fossil record. Except for one pair of species, separated by the largest morphologic distance, directional selection acting alone would require unrealistically high rates of selective mortality to be maintained for these periods. Thus, directional selection is not strongly implicated in the divergence of Metrarabdotos species. Within species, rates of net phenotypic change are slow enough to require stabilizing selection, but mask large, relatively rapid fluctuations, all of which, however, can be attributed to chance departures from the mean phenotype by mutation and genetic drift, rather than to tracking environmental fluctuation by directional selection. The results are consistent with genetic models involving shifts between multiple adaptive peaks on which phenotypes remain more or less static through long-term stabilizing selection. Regardless of the degree to which directional selection may be involved in peak shifts, phenotypic differentiation is thus related to processes different than the pervasive stabilizing selection acting within species.     

EVOLUTION OF RESISTANCE IN CULEX PIPIENS: ALLELE REPLACEMENT AND CHANGING ENVIRONMENT

Fixation of adaptive mutations in populations is often constrained by pleiotropic fitness costs. The evolutionary pathways that compensate such fitness disadvantages are either the occurrence of modifier genes or replacement of the adaptive allele by less costly ones. In this context, 23 years of evolution of insecticide resistance genes in the mosquito Culex pipiens from southern France are analyzed. The aim of this study is to answer the following points. Is there a fitness cost associated with these resistance genes in natural populations? Does evolution proceed through allele replacement or through selection of modifiers? And finally, how do environmental changes affect the evolution of resistance genes? Samples from the same transect, crossing the boundary between an insecticide-treated and a nontreated area, are analyzed. Clinal analyses indicate a variable fitness cost among the resistance genes and show that allele replacement has been the primary mechanism of resistance evolution in this area. It is also shown that replacement was probably due to environmental changes corresponding to modification in pesticide-treatment intensity.     

NEUTRAL THEORY OF QUANTITATIVE GENETIC VARIANCE IN AN ISLAND MODEL WITH LOCAL EXTINCTION AND COLONIZATION

Additive genetic variance maintained by mutation in a selectively neutral quantitative character is analyzed for an ideal population distributed on n islands, each with local effective size N, that exchange migrants at a small rate, m. In a stable population structure, the expected genetic variance maintained within islands is identical to that in a panmictic population of the same total size, regardless of the migration rate (m > 0). This result contrasts with Wright's classical conclusion, based on inbreeding coefficients, that at least one immigrant per island every other generation (Nm > ½) is necessary for the genetic variance within local populations to approach that under panmixia. The expected genetic variance maintained among islands is inversely proportional to m and increases with the number of islands, but is independent of N. Local extinction and colonization diminish the genetic variance maintained within islands by reducing the effective size of island populations through the founder effect, although the expected genetic variance within islands is nearly as large as that in a panmictic population of the same total effective size. If the founders of new colonies originate from more than one island, rates of local extinction and colonization larger than about twice the migration rate will substantially reduce the genetic variance maintained among islands. These results indicate the importance of mutation and migration in maintaining quantitative genetic variance within small local populations.     

二叠纪-三叠纪礁相房室海绵演化与灭绝

就礁相房室海绵而言,早二叠世的物种数最少,中二叠世的分异度最高,晚二叠世的其次,中三叠世的较少,卡尼斯的增多,诺利期的更多。礁相房室海绵的演化反映出二叠纪－三叠纪有3次灭绝事件,分别发生在中二叠世末期、长兴期末期、卡尼期末期。这3次灭绝事件的规模各不相同：中二叠世末期的灭绝事件规模较小,它使83．8％的中二叠世礁相房室海绵种灭绝;长兴期末期的灭绝规模最大,它使100％的长兴期种灭绝;卡尼期末的灭绝事件规模也较大,它使97．7％的卡尼期种灭绝。     

MATERNAL INHERITANCE AND ITS EFFECT ON ADAPTIVE EVOLUTION: A QUANTITATIVE GENETIC ANALYSIS OF MATERNAL EFFECTS IN A NATURAL PLANT POPULATION

A mother can influence a trait in her offspring both by the genes she transmits (Mendelian inheritance) and by maternal attributes that directly affect that trait in her offspring (maternal inheritance). Maternal inheritance can alter the direction, rate, and duration of adaptive evolution from standard Mendelian models and its impact on adaptive evolution is virtually unexplored in natural populations. In a hierarchical quantitative genetic analysis to determine the magnitude and structure of maternal inheritance in the winter annual plant, Collinsia verna, I consider three potential models of inheritance. These range from a standard Mendelian model estimating only direct (i.e., Mendelian) additive and environmental variance components to a maternal inheritance model estimating six additive and environmental variance components: direct additive and environmental variances; maternal additive and environmental variances; and the direct-maternal additive () and environmental covariances. The structure of maternal inheritance differs among the 10 traits considered at four stages in the life cycle. Early in the life cycle, seed weight and embryo weight display substantial , a negative , and a positive . Subsequently, cotyledon diameter displays and of roughly the same magnitude and negative . For fall rosettes, leaf number and length are best described by a Mendelian model. In the spring, leaf length displays maternal inheritance with significant and and a negative . All maternally inherited traits show significant negative . Predicted response to selection under maternal inheritance depends on and as well as . Negative results in predicted responses in the opposite direction to selection for seed weight and embryo weight and predicted responses near zero for all subsequent maternally inherited traits. Maternal inheritance persists through the life cycle of this annual plant for a number of size-related traits and will alter the direction and rate of evolutionary response in this population.     

THE EVOLUTION OF ASYMMETRY IN SEXUAL ISOLATION: A MODEL AND A TEST CASE

We constructed a model for the evolution of sexual isolation by extending Lande's (1981) model of sexual selection. The model predicts that asymmetric sexual isolation is a transient phenomenon, characteristic of intermediate stages of divergence in sexually selected traits. Unlike the Kaneshiro (1976, 1980) proposal, our model does not depend upon drift and the loss of courtship elements to produce asymmetries in sexual isolation. According to our model, the direction of evolution cannot be predicted from asymmetry in sexual isolation. We tested some features of the model using data from an experimental study of sexual isolation in the salamander Desmognathus ochrophaeus. We tested for sexual isolation between 12 allopatric populations and found significant asymmetry in sexual isolation in about a quarter of the test cases. The highest degrees of asymmetry were associated with intermediate levels of divergence. A curvilinear relationship between isolation asymmetry and divergence was predicted by our model and was supported by statistical analysis of the salamander data.     

Phenotypic evolution in stochastic environments: The contribution of frequency- and density-dependent selection

Understanding how environmental variation affects phenotypic evolution requires models based on ecologically realistic assumptions that include variation in population size and specific mechanisms by which environmental fluctuations affect selection. Here we generalize quantitative genetic theory for environmentally induced stochastic selection to include general forms of frequency- and density-dependent selection. We show how the relevant fitness measure under stochastic selection relates to Fisher's fundamental theorem of natural selection, and present a general class of models in which density regulation acts through total use of resources rather than just population size. In this model, there is a constant adaptive topography for expected evolution, and the function maximized in the long run is the expected factor restricting population growth. This allows us to generalize several previous results and to explain why apparently “-selected” species with slow life histories often have low carrying capacities. Our joint analysis of density- and frequency-dependent selection reveals more clearly the relationship between population dynamics and phenotypic evolution, enabling a broader range of eco-evolutionary analyses of some of the most interesting problems in evolution in the face of environmental variation.     

ADAPTIVE DYNAMICS IN ALLELE SPACE: EVOLUTION OF GENETIC POLYMORPHISM BY SMALL MUTATIONS IN A HETEROGENEOUS ENVIRONMENT

We demonstrate how a genetic polymorphism of distinctly different alleles can develop during long-term frequency-dependent evolution in an initially monomorphic diploid population, if mutations have only small phenotypic effect. As a specific example, we use a version of Levene's (1953) soft selection model, where stabilizing selection acts on a continuous trait within each of two habitats. If the optimal phenotypes within the habitats are sufficiently different, then two distinctly different alleles evolve gradually from a single ancestral allele. In a wide range of parameter values, the two locally optimal phenotypes will be realized by one of the homozygotes and the heterozygote, rather than by the two homozygotes. Unlike in the haploid analogue of the model, there can be multiple polymorphic evolutionary attractors with different probabilities of convergence. Our results differ from the population genetic models of short-term evolution in two aspects: (1) a polymorphism that is population genetically stable may be invaded by a new mutant allele and, as a consequence, the population may fall back to monomorphism, (2) long-term evolution by allele substitutions may lead from a population where polymorphism is not possible into one where polymorphism is possible.     

MUTATION AND EXTINCTION: THE ROLE OF VARIABLE MUTATIONAL EFFECTS,SYNERGISTIC EPISTASIS,BENEFICIAL MUTATIONS,AND DEGREE OF OUTCROSSING

Recent theoretical studies have illustrated the potential role of spontaneous deleterious mutation as a cause of extinction in small populations. However, these studies have not addressed several genetic issues, which can in principle have a substantial influence on the risk of extinction. These include the presence of synergistic epistasis, which can reduce the rate of mutation accumulation by progressively magnifying the selective effects of mutations, and the occurrence of beneficial mutations, which can offset the effects of previous deleterious mutations. In stochastic simulations of small populations (effective sizes on the order of 100 or less), we show that both synergistic epistasis and the rate of beneficial mutation must be unrealistically high to substantially reduce the risk of extinction due to random fixation of deleterious mutations. However, in analytical calculations based on diffusion theory, we show that in large, outcrossing populations (effective sizes greater than a few hundred), very low levels of beneficial mutation are sufficient to prevent mutational decay. Further simulation results indicate that in populations small enough to be highly vulnerable to mutational decay, variance in deleterious mutational effects reduces the risk of extinction, assuming that the mean deleterious mutational effect is on the order of a few percent or less. We also examine the magnitude of outcrossing that is necessary to liberate a predominantly selfing population from the threat of long-term mutational deterioration. The critical amount of outcrossing appears to be greater than is common in near-obligately selfing plant species, supporting the contention that such species are generally doomed to extinction via random drift of new mutations. Our results support the hypothesis that a long-term effective population size in the neighborhood of a few hundred individuals defines an approximate threshold, below which outcrossing populations are vulnerable to extinction via fixation of deleterious mutations, and above which immunity is acquired.     

SEX-SPECIFIC GENETIC VARIANCE AND THE EVOLUTION OF SEXUAL DIMORPHISM: A SYSTEMATIC REVIEW OF CROSS-SEX GENETIC CORRELATIONS

The independent evolution of the sexes may often be constrained if male and female homologous traits share a similar genetic architecture. Thus, cross-sex genetic covariance is assumed to play a key role in the evolution of sexual dimorphism (SD) with consequent impacts on sexual selection, population dynamics, and speciation processes. We compiled cross-sex genetic correlations ( r _MF) estimates from 114 sources to assess the extent to which the evolution of SD is typically constrained and test several specific hypotheses. First, we tested if r _MF differed among trait types and especially between fitness components and other traits. We also tested the theoretical prediction of a negative relationship between r _MF and SD based on the expectation that increases in SD should be facilitated by sex-specific genetic variance. We show that r _MF is usually large and positive but that it is typically smaller for fitness components. This demonstrates that the evolution of SD is typically genetically constrained and that sex-specific selection coefficients may often be opposite in sign due to sub-optimal levels of SD. Most importantly, we confirm that sex-specific genetic variance is an important contributor to the evolution of SD by validating the prediction of a negative correlation between r _MF and SD.     

犀牛在中国灭绝与人口压力关系的初步分析

三千多年以前,犀牛沿黄河两岸自西向东约有１８００多公里的广阔的分布北界。近三千年来,犀牛在中国的分布北界不断南移,它是我国犀牛地减性灭绝的重要特征。北界南移速度相当惊人,平均每年以０．５ｋｍ的速度禹南消退。犀牛在中国灭绝的根本原因是人口压力、中国古代人口对犀牛的压力包括直接与间接两个方面,通过简单计算可知,犀牛种群承受人口压力阈值小于４人／ｋｍ＾２。     

PATTERNS OF EVOLUTION AND EXTINCTION IN THE LAST HARPETID TRILOBITES DURING THE LATE DEVONIAN (FRASNIAN)

Abstract: Late Devonian (Frasnian) harpetid trilobites have hitherto only been described from the western side of the Protethys Ocean, in what is now Europe and North Africa, as well as from Gondwana‐derived northwestern Kazakhstan (Mugodjar). However, late Frasnian strata in the Canning Basin, Western Australia, that were deposited on the eastern side of this ocean, contain a rich harpetid fauna. Described herein are two new harpetids: Eskoharpes gen. nov. and Globoharpes gen. nov., within which are placed six species: E. palanasus sp. nov., E. wandjina sp. nov., E. boltoni sp. nov., E. guthae sp. nov., G. teicherti sp. nov. and G. friendi sp. nov. The ontogenetic development of E. palanasus, E. wandjina and G. teicherti are described, including the first unequivocal harpetid protaspis. Globoharpes exhibits evidence of sexual dimorphism in the development of a pronounced preglabellar boss in some specimens. This structure is thought to have functioned as a brood pouch. Such structures have previously only been described in Cambrian and Ordovician trilobites, and never before in harpetids. It is suggested that the characteristic harpetid fringe functioned as a secondary respiratory structure. The Eskoharpes lineage shows evolutionary trends that mirror changes seen in ontogenetic development of the youngest species, suggesting the operation of peramorphic processes. This is the first record of heterochrony in harpetids and the first documented example of peramorphosis in Devonian trilobites. These harpetids demonstrate a stepped pattern of extinction during the late Frasnian, probably related to the effects of the two Kellwasser biocrises that have been well documented in European Frasnian sections. Highly vaulted species of Eskoharpes and the strongly vaulted Globoharpes became extinct at the Lower Kellwasser Event. The flatter species of Eskoharpes became extinct at the base of the Upper Kellwasser Event shortly prior to the Frasnian/Famennian boundary. The extinction of these harpetids, along with contemporaneous forms from Europe, which are also discussed herein, marks the end of the trilobite order Harpetida worldwide.     

SOCIAL SELECTION AND THE EVOLUTION OF ANIMAL SIGNALS

Social selection is presented here as a parallel theory to sexual selection and is defined as a selective force that occurs when individuals change their own social behaviors, responding to signals sent by conspecifics in a way to influence the other individuals' fitness. I analyze the joint evolution of a social signal and behavioral responsiveness to the signal by a quantitative-genetic model. The equilibria of average phenotypes maintained by a balance of social selection and natural selection and their stability are examined for two alternative assumptions on behavioral responsiveness, neutral and adaptive. When behavioral responsiveness is neutral on fitness, a rapid evolution by runaway selection occurs only with enough genetic covariance between the signal and responsiveness. The condition for rapid evolution also depends on natural selection and the number of interacting individuals. When signals convey some information on signalers (e.g., fighting ability), behavioral responsiveness is adaptive such that a receiver's fitness is also influenced by the signal. Here there is a single point of equilibrium. The equilibrium point and its stability do not depend on the genetic correlation. The condition needed for evolution is that the signal is beneficial for receivers, which results from reliability of the signal. Frequency-dependent selection on responsiveness has almost no influence on the equilibrium and the rate of evolution.