EFFECTIVE POPULATION SIZE IN A CONTINUOUSLY DISTRIBUTED POPULATION

An individual-based simulation model was created to examine genetic variability, time until fixation and spatial genetic structure in a continuously distributed population. Previous mathematical models for continuously distributed populations have the difficulty that the assumption of independent reproduction and independent dispersal of offspring cause clumped spatial distribution and thus violate an assumption of random spatial distribution. In this study, this problem is avoided by considering the dispersal behavior of offspring. The simulation results showed that the inbreeding effective population size estimated by the rate of decrease of heterozygosity during the first 15 generations corresponds to the neighborhood size calculated by the standard deviation of the dispersal distance (σ_T). This inbreeding effective population size does not greatly change with the area of simulation when the densities and σ_T are the same. However, the inbreeding effective population size estimated by heterozygosity using the first 500 generations is larger than the neighborhood size calculated by the dispersal distance and increases with the area of simulation with the same densities. The variance effective population size, estimated by time until fixation of alleles, increases with dispersal distance (σ_T) and with the area of simulation given the same densities. The inbreeding effective population size and variance effective population size were smaller than the actual population size unless σ_T is sufficiently large (2 σ_T > approximate L/2, where L is a side of the simulation square).     

THE EFFECTS OF POPULATION BOTTLENECKS ON CLONAL INTERFERENCE, AND THE ADAPTATION EFFECTIVE POPULATION SIZE

Clonal interference refers to the competition that arises in asexual populations when multiple beneficial mutations segregate simultaneously. A large body of theoretical and experimental work now addresses this issue. Although much of the experimental work is performed in populations that grow exponentially between periodic population bottlenecks, the theoretical work to date has addressed only populations of a constant size. We derive an analytical approximation for the rate of adaptation in the presence of both clonal interference and bottlenecks, and compare this prediction to the results of an individual-based simulation, showing excellent agreement in the parameter regime in which clonal interference prevails. We also derive an appropriate definition for the effective population size for adaptive evolution experiments in the presence of population bottlenecks. This "adaptation effective population size" allows for a good approximation of the expected rate of adaptation, either in the strong-selection weak-mutation regime, or when clonal interference comes into play. In the multiple mutation regime, when the product of the population size and mutation rate is extremely large, these results no longer hold.     

GENOME SIZE IS NOT CORRELATED WITH EFFECTIVE POPULATION SIZE IN THE ORYZA SPECIES

Genome sizes vary widely across the tree of life and the evolutionary mechanism underlined remains largely unknown. Lynch and Conery (2003) proposed that evolution of genome complexity was driven mainly by nonadaptive stochastic forces and presented the observation that genome size was negatively correlated with effective population size (N_e) as a strong support for their hypothesis. Here, we analyzed the relation between N_e and genome size for 10 diploid Oryza species that showed about fourfold genome size variation. Using sequences of more than 20 nuclear genes, we estimated N_e for each species after correction for the effects of demography and heterogeneity of mutation rates among loci and species. Pairwise comparisons and correlation analyses did not detect a negative relationship between N_e and genome size despite about 6.5‐fold interspecies N_e variation. By calculating phylogenetically independent contrasts (PICs) for N_e, we repeated correlation analysis and did not find any correlation between N_e and genome size. These observations suggest that the genome size variation in the Oryza species cannot be explained simply by the effect of effective population size.     

THE EFFECTIVE SIZE OF A HIERARCHICALLY STRUCTURED POPULATION

A knowledge of the effective size of a population (N_e) is important in understanding its current and future evolutionary potential. Unfortunately, the effective size of a hierarchically structured population is not, in general, equal to the sum of its parts. In particular, the inbreeding structure has a major influence on N_e. Here I link N_e to Wright's hierarchical measures of inbreeding, F_IS and F_ST, for an island-structured population (or metapopulation) of size N_T. The influence of F_ST depends strongly on the degree to which island productivity is regulated. In the absence of local regulation (the interdemic model), interdemic genetic drift reduces N_e. When such drift is combined with local inbreeding under otherwise ideal conditions, the effects of F_IS and F_ST are identical: increasing inbreeding either within or between islands reduces N_e, with N_e = N_T/[(1 + F_IS)(1 + F_ST) ? 2F_ISF_ST]. However, if islands are all equally productive because of local density regulation (the traditional island model), then N_e = N_T/[(1 + F_IS)(1 –F_ST)] and the effect of F_ST is reversed. Under the interdemic model, random variation in the habitat quality (and hence productivity) of islands act to markedly decrease N_e. This variation has no effect under the island model because, by definition, all islands are equally productive. Even when no permanent island structure exists, spatial differences in habitat quality can significantly increase the overall variance in reproductive success of both males and females and hence lower N_e. Each of these basic results holds when other nonideal factors are added to the model. These factors, deviations from a 1:1 sex ratio, greater than Poisson variance in female reproductive success, and variation in male mating success due to polygynous mating systems, all act to lower N_e. The effects of male and female variance on N_e have important differences because only females affect island productivity. Finally, it is noted that to use these relationships, F_IS and F_ST must be estimated according to Wright's definition (and corrected to have a zero expectation under the null model). A commonly used partitioning (θ, θ_g) can be biased if either island size or the number of islands is small.     

垂穗披硷草个体大小与种群密度的关系

本文以垂穗披硷草为材料研究了多年生植物群个体大小与密度的关系。研究结果表明,垂穗披硷草个体生物量与密度间的直线回归斜率β的绝对值于生长初期较小,随着生长时间的延长有所增加,但最大的β绝对值仅为１．０２从未达到－３／２。单株分孽数与密度间的回归斜率始终保持在较小的绝对值上。生活第三年种群密度对自生幼苗具有一定的影响。     

ESTIMATED POPULATION SIZE OF THE CALIFORNIA GRAY WHALE

Abstract: The 1987-1988 counts of gray whales passing Monterey are reanalyzed to provide a revised population size estimate. The double count data are modeled using iterative logistic regression to allow for the effects of various covariates on probability of detection, and a correction factor is introduced for night rate of travel. The revised absolute population size estimate is 20,869 animals, with CV = 4.37% and 95% confidence interval (19,200, 22,700). In addition the series of relative population size estimates from 1967-1968 to 1987-1988 is scaled to pass through this estimate and modeled to provide variance estimates from interannual variation in population size estimates. This method yields an alternative population size estimate for 1987-1988 of 21,296 animals, with CV = 6.05% and 95% confidence interval (18,900, 24,000). The average annual rate of increase between 1967-1968 and 1987-1988 was estimated to be 3.29% with standard error 0.44%.     

EFFECTIVE POPULATION SIZE AND THE FASTER-X EFFECT: AN EXTENDED MODEL

Current models of X-linked and autosomal evolutionary rates often assume that the effective population size of the X chromosome ( N_eX ) is equal to three-quarters of the autosomal population size ( N_eA ). However, polymorphism studies of Drosophila melanogaster and D. simulans suggest that there are often significant deviations from this value. We have computed fixation rates of beneficial and deleterious mutations at X - linked and autosomal sites when this occurs. We find that N_eX/N_eA is a crucial parameter for the rates of evolution of X-linked sites compared to autosomal sites. Faster-X evolution due to the fixation of beneficial mutations can occur under a much wider range of levels of dominance when N_eX/N_eA > ³/₄. We also examined various parameters that are known to influence the rates of evolution at X-linked and autosomal sites, such as different mutation rates in males and females and mutations that are sexually antagonistic, to determine which cases can lead to faster-X evolution. We show that, when the rate of nonsynonymous evolution is normalized by the rate of neutral evolution, a sex difference in mutation rate has no influence on the conditions for faster-X evolution.     

THE WELL-POSEDNESS OF SIZE STRUCTURED POPULATION MODELS WITH DENSITY DEPENDENT PARAMETERS

Thewell-posednessofnonlinearsizestructuredpopulationmodelsisstudied.Thenonlinearitiesareintroducedbyassumingthevitalparameters(thebirthrate,thedeathrate,andthegrowthrate)tobedensitydependent.TheidealadoptedhereisbasedonthemethodofGurtinandMacCamy[4]usedfornonlinearage-dependentpopulationmodels.Thenetreproductivenumberisintroducedandusedtodeterminethelocalandglobalstabilityoftrivialequilibrium.Thestabilityconditionsoftrivialequilibriumareobtained.     

LARGE POPULATION SIZE PREDICTS THE DISTRIBUTION OF ASEXUALITY IN SCALE INSECTS

Understanding why some organisms reproduce by sexual reproduction while others can reproduce asexually remains an important unsolved problem in evolutionary biology. Simple demography suggests that asexuals should outcompete sexually reproducing organisms, because of their higher intrinsic rate of increase. However, the majority of multicellular organisms have sexual reproduction. The widely accepted explanation for this apparent contradiction is that asexual lineages have a higher extinction rate. A number of models have indicated that population size might play a crucial role in the evolution of asexuality. The strength of processes that lead to extinction of asexual species is reduced when population sizes get very large, so that the long‐term advantage of sexual over asexual reproduction may become negligible. Here, we use a comparative approach using scale insects (Coccoidea, Hemiptera) to show that asexuality is indeed more common in species with larger population density and geographic distribution and we also show that asexual species tend to be more polyphagous. We discuss the implication of our findings for previously observed patterns of asexuality in agricultural pests.     

THE INFLUENCE OF MATING SYSTEM AND OVERLAPPING GENERATIONS ON EFFECTIVE POPULATION SIZE

The effective population size (N_e) depends strongly on mating system and generation time. These two factors interact such that, under many circumstances, N_e is close to N/2, where N is the number of adults. This is shown to be the case for both simple and highly polygynous mating systems. The random union of gametes (RUG) and monogamy are two simple systems previously used in estimating N_e, and here a third, lottery polygyny, is added. Lottery polygyny, in which all males compete equally for females, results in a lower N_e than either RUG or monogamy! Given nonoverlapping generations the reduction is 33% for autosomal loci and 25% for sex-linked loci. The highly polygynous mating systems, harem polygyny and dominance polygyny, can give very low values of N_e/N when the generation time (T) is short. However, as T is lengthened, N_e approaches N/2. The influence of a biased sex ratio depends on the mating system and, in general, is not symmetrical. Biases can occur because of sex differences in either survival or recruitment of adults, and the potential for a sex-ratio bias to change N_e is much reduced given a survival bias. The number of juveniles present also has some influence: as the maturation time is lengthened, N_e increases.     

截线法对西藏盘羊种群数量的估计

１９８７～１９９０年间,采用截线抽样法对西藏盘羊的种群数量及分布进行了全面调查。结果在１５５０ｋｍ样线上遇见９９头盘羊。由此资料,以傅立叶级数表达其探测函数,估计出了盘羊在西藏分布区内的平均分布密度为０．０８２０±０．００９７头／ｋｍ２,即每１２ｋｍ２约有１头,而波动在０．０１２１～０．３６７１头／ｋｍ２之间。并依此确定的１０．５万ｋｍ２的栖息面积计算、西藏盘羊的种群数量为８６３０±１０２１头。目前,盘羊群平均数下降为５～６头／群,亟待保护。     

INCREASED PROBABILITY OF EXTINCTION DUE TO DECREASED GENETIC EFFECTIVE POPULATION SIZE: EXPERIMENTAL POPULATIONS OF CLARKIA PULCHELLA

We established replicated experimental populations of the annual plant Clarkia pulchella to evaluate the existence of a causal relationship between loss of genetic variation and population survival probability. Two treatments differing in the relatedness of the founders, and thus in the genetic effective population size (N_e), were maintained as isolated populations in a natural environment. After three generations, the low N_e treatment had significantly lower germination and survival rates than did the high N_e treatment. These lower germination and survival rates led to decreased mean fitness in the low N_e populations: estimated mean fitness in the low N_e populations was only 21% of the estimated mean fitness in the high N_e populations. This inbreeding depression led to a reduction in population survival: at the conclusion of the experiment, 75% of the high N_e populations were still extant, whereas only 31% of the low N_e populations had survived. Decreased genetic effective population size, which leads to both inbreeding and the loss of alleles by genetic drift, increased the probability of population extinction over that expected from demographic and environmental stochasticity alone. This demonstrates that the genetic effective population size can strongly affect the probability of population persistence.     

EFFECTIVE POPULATION SIZE AND GENETIC DRIFT IN TRISTYLOUS EICHHORNIA PANICULATA (PONTEDERIACEAE)

Populations of the tristylous, annual Eichhornia paniculata are markedly differentiated with respect to frequency of mating types. This variation is associated with evolutionary changes in mating system, from predominant outcrossing to high self-fertilization. To assess the potential influence of genetic drift acting on this variation, we estimated effective population size in 10 populations from northeastern Brazil using genetic and demographic methods. Effective size (N_e) was inferred from temporal changes in allele frequency at two to eight isozyme loci and also calculated using five demographic variables: 1) the number of flowering individuals (N); 2) temporal fluctuations in N; 3) variance in flower number; 4) frequency of mating types; and 5) selfing rate. Average N_e based on isozyme data was 15.8, range 3.4–70.6, and represented a fraction (mean N_e/N = 0.106) of the census number of individuals (mean N = 762.8; range: 30.5–5,040). Temporal variation in N and variance in flower number each reduced N_e to about a half of N whereas mating type frequencies and selfing rate caused only small reductions in N_e relative to N. All estimates of N_e based on demographic variables were considerably larger than those obtained from genetic data. The two kinds of estimates were in general agreement, however, when all demographic variables were combined into a single measure. Monte Carlo simulations indicated that effective size must be fewer than about 40 for drift to overcome the frequency-dependent selection that maintains the polymorphism for mating type. Applying the average N_e/N value to 167 populations censused in northeastern Brazil indicated that 72% had effective sizes below this number. This suggests that genetic drift is likely to play a dominant role in natural populations of E. paniculata.     

SIZE STRUCTURE AND DYNAMICS IN A POPULATION OF SARGASSUM MUTICUM (PHAEOPHYCEAE)

Sargassum muticum (Yendo) Fensholt is an introduced brown seaweed with a very distinctive seasonal growth cycle on European shores. The present study links the dynamics of a population of S. muticum with the seasonal growth cycle of the species and the density-dependent processes operating throughout this cycle. Results indicate that both growth cycle and intraspecific competition influenced the structure and population dynamics. Size inequality increased during the slow growth phase (autumn–winter) of the 2-year study. Mechanisms generating inequality of size could be the existence of asymmetric competition and the inherent differences in growth rates between old (regenerated) and new thalli (recruits). Inequality of size distributions decreased progressively during the last months of the growth phase (spring–summer) and could be related to a process of self-thinning. There was a negative biomass–density relationship (as a measure of biomass accumulation-driven mortality) that confirms the importance of self-thinning as a major demographic factor in the S. muticum population.     

不同水分条件下春小麦种群中个体大小不整齐性及遗传学分析

种群内个体大小不整齐性是种群数量结构的主要指标。本文研究了不同水分条件下,３个品种春小麦种群个体大小不整齐性的建立及变化规律。对春小麦种群不整齐性的遗传学分析表明：遗传结构与随机环境修饰对种群数量结构形成的相对重要性,因水分条件不同而异。种群不整齐性在自然选择中的作用可用下列简单模型表示：ＧＳ０＝ＳＨ×ｈ２ＳＨＧＳ０：自然选择强度;ＳＨ：大小不整齐性;ｈ２ＳＨ：不整齐性的遗传力。     

THE INFLUENCE OF POPULATION SIZE AND ISOLATION ON GENE FLOW BY POLLEN IN SILENE ALBA

In a series of experiments conducted over two seasons, we used arrays of experimental populations to examine the effects of flower number and distance between patches on gene flow by pollen. For this study we used the dioecious, short-lived perennial plant Silene alba (Caryophyllaceae). This species lives in disturbed roadside and agricultural habitats and displays a weedy population dynamic with high colonization and extinction rates. The motivation for the study was to understand what factors may be influencing genetic connectedness among newly colonized populations within a regional metapopulation. By using experimental populations composed of genotypes homozygous at a diagnostic locus, it was possible to identify explicitly pollen movement into a focal patch as a function of flower number and distance to the nearest neighboring patch. Overall, the mean immigration rate (measured as the fraction of seeds sired by males outside the focal patch) at 20 m was just over 47%, whereas at 80 m immigration rates were less than 6%. In addition, by knowing the context in which each of these gene-flow events occurred, it was possible to understand some of the factors that influenced the exchange of genes. Both the number of flowers in the focal population (target) and in the neighboring populations (source) had a significant effect on the frequency of gene flow. Our experimental data also demonstrate that factors that influence gene flow at one spatial scale may not act in the same way at another. Specifically, the influence of target size and the relative size of the target and source patches on rates of gene flow depended on whether the patches were separated by 20 m or 80 m. These data suggest that the patterns of gene flow within a metapopulation system can be complex and may vary within a growing season.