THE MAINTENANCE OF POLYGENIC VARIATION IN FINITE POPULATIONS

Models of the maintenance of genetic variance in a polygenic trait have usually assumed that population size is infinite and that selection is weak. Consequently, they will overestimate the amount of variation maintained in finite populations. I derive approximations for the equilibrium genetic variance, in finite populations under weak stabilizing selection for triallelic loci and for an infinite “rare alleles” model. These are compared to results for neutral characters, to the “Gaussian allelic” model, and to Wright's approximation for a biallelic locus under arbitrary selection pressures. For a variety of parameter values, the three-allele, Gaussian, and Wrightian approximations all converge on the neutral model when population size is small. As expected, far less equilibrium genetic variance can be maintained if effective population size, N, is on the order of a few hundred than if N is infinite. All of the models predict that comparisons among populations with N less than about 10⁴ should show substantial differences in . While it is easier to maintain absolute when alleles interact to yield dominance or overdominance for fitness, less additivity also makes more susceptible to differences in N. I argue that experimental data do not seem to reflect the predicted degree of relationship between N and . This calls into question the ability of mutation-selection balance or simple balancing selection to explain observed . The dependence of on N could be used to test the adequacy of mutation-selection balance models.     

MAINTENANCE OF POLYGENIC VARIATION IN SPATIALLY STRUCTURED POPULATIONS: ROLES FOR LOCAL MATING AND GENETIC REDUNDANCY

Although heritable genetic variation is critical to the evolutionary process, we know little about how it is maintained. Obviously, mutation-selection balance must play a role, but there is considerable doubt over whether it can account for heritabilities as high as 0.5, which are commonly found in natural populations. Most models of mutation-selection balance assume panmictic populations. In this paper we use Monte Carlo simulations to examine the effect of isolation by distance on the variation maintained by mutation in a polygenic trait subject to optimizing selection. We show that isolation by distance can substantially increase the total variation maintained in continuous populations over a wide range of dispersal patterns, but only if more than one genotype produces the optimal phenotype (genetic redundancy). Isolation by distance alone has only a slight effect on the variation maintained in the total population for neutral alleles. The combined effect of isolation by distance and genetic redundancy, however, allows the maintenance of substantial variation despite strong stabilizing selection. The mechanism is straightforward. Isolation by distance allows mutation and drift to operate independently in different parts of the population. Because of their independent evolutionary histories, different parts of the population independently draw from the available set of redundant genotypes. Because the genotypes are redundant, selection does not discriminate among them, and they will persist until eliminated by drift. The population as a whole maintains many distinct genotypes. We show that this process allows mutation to maintain high levels of variation, even under strong stabilizing selection, and that over a moderate range of dispersal patterns the amount of variation maintained in the entire population is independent of both the strength of selection and the variance of the dispersal distance. Furthermore, we show that individual heterozygosity is increased in locally mating populations when selection is strong. Finally, our simulations provide a rough picture of how selection and the dispersal pattern influence the spatial distribution of genetic and phenotypic variation.     

中国赤蜂属一新种(膜翅目:蜜蜂总科, 条蜂科)

本文记述采自我国新疆的条蜂属一新种。模式标本保存于中国科学院动物研究所。 角条蜂Anthophora antennalis新种 雄虫 体长8毫米,黑色,头部(图1)唇基、上唇(基部两侧圆形褐色斑)、上颚(端部黑褐色)、颜侧(触角窝以下)、额唇基区、触角柄节及梗节的前表面均黄色;触角鞭节上表面红褐色,第1节基部及末节黑色;触角下表面褐色;各基跗节黑褐色,2-4跗节褐色;翅基片红褐色;胫节距浅黄色;腹部1—5节背板端缘黄褐色。头部明显横宽(长比宽为5:7);上颚无内齿;上唇横宽(长比宽为3:4),刻点粗而不均匀;唇基隆起较弱(图2),刻点     

VARIATION IN POPULATION GROWTH RATE IN THE WOODLAND ANNUAL IMPATIENS PALLIDA (BALSAMINACEAE)

Variation in population growth rate over environmental gradients was determined for the annual Impatiens pallida (Balsaminaceae), by monitoring age- and size-specific survivorship and fecundity in five populations of this summer-flowering and primarily woodland species. All I. pallida seedlings emerged within a few days of each other and a size hierarchy was established within a month, and remained unchanged thereafter. Light and initial seedling density together explained 67% of the variance in mean adult plant size. As a result of differences among populations in the amount of disturbance, survivorship to the time of floral bud production ranged from 39% to 93% of the initial seedling total. Survivorship during the reproductive period was most affected by plant size and soil moisture. For plants surviving to flowering time, the probability of setting seed, the type of seed and the number of seeds produced per plant were significantly positively correlated with plant size. More than 82% of all seeds were produced by plants greater than or 1 m tall. Cleistogamy was the major form of reproduction in 4 out of 5 populations monitored. The net reproductive rate (R₀) differed greatly among populations, ranging from 1.23 to 16.27. Population growth rate increased with increasing resource availability and decreasing disturbance during the growing season. The magnitude of R₀ depended primarily on 1) timing, intensity and frequency of disturbance, 2) length of the reproductive period, and 3) population size structure.     

ALLOZYMIC VARIATION IN LOCAL APOMICTIC POPULATIONS OF LEMNA MINOR (LEMNACEAE)

Flowering occurrence and allozymic variation were studied in eight local populations of Lemna minor in eastern Ontario, Canada. After 2 years of survey, not a single flower was observed. This absence of flowering suggests the possibility of loss of sexual reproduction. This may have had no net adverse effect on fitness given the simple life history and prolific vegetative propagation in L. minor. However, the absence of sexual reproduction may limit genotypic diversity. The allozymic analysis detected 18 loci from 13 enzyme systems. Large deviations from Hardy-Weinberg equilibrium were common because of an excess of homozygotes for several enzyme systems. The genotypic diversity within these eight populations had a mean D value of 0.973 with an average number of genotypes per population of 19.6. These results suggest that genotypic diversity within these populations is not severely limited by the rarity of sexual reproduction. The mean genotypic distance index (D₁₄ = 0.801) suggests a high degree of differentiation between populations. The mean number of populations per genotype was 1.78. Using a Mantel test, the genotypic distance matrix was not significantly related to the population-to-population distance matrix (t = -0.161, P = 0.413). Although rare events of sexual reproduction may help maintain genetic variation, somatic mutations and multiple origins of clones may be important factors maintaining genetic diversity both within and between populations of L. minor.     

VARIATION IN LEAFLET MORPHOLOGY AMONG POPULATIONS OF CARIBBEAN CYCADS (ZAMIA)

Caribbean cycads (Zamia L.) are well known for variation in leaflet morphology. Here, I examine the variation in leaflet morphology among five populations of Zamia in Florida. Variables measured were leaflet length and width, leaflet length: width ratio, leaflet surface area, rachis and petiole lengths, number of leaflets per leaf, and total leaf area. In addition to comparisons among the Florida populations, these populations are compared with three previously studied populations in Puerto Rico (Newell, 1986). For the most part, the populations exhibited significant differences in all variables. In spite of the extensive morphological variation in this group of plants, leaflet morphology has long been important in Zamia taxonomy. The Florida populations would be considered by some to be either one, two, or three different species. The Florida and Puerto Rico populations together might be considered as few as one species or as many as five species. Based upon the data presented here, the five Florida populations appear to represent a single species; and the three Puerto Rico populations appear to represent two additional species. Further clarification of the taxonomy of Caribbean Zamia will require additional characters such as cone morphology and protein or DNA patterns.     

SEXUALITY, INCOMPATIBILITY, SIZE VARIATION, AND PREFERENTIAL POLYANDRY IN NATURAL POPULATIONS AND CLONES OF SELLAPHORA PUPULA (BACILLARIOPHYCEAE)

The capitate and rectangular demes of the freshwater epipelic diatom Sellaphora pupula (Kütz.) Mereschk. are dioecious, the first such report for any freshwater diatom. Sexual differentiation, which is probably determined genetically, involves recognition at the cell surface as well as differences in gamete behavior (one gametangium produces an active "male" gamete, the other a passive "female" gamete). In culture, successful sexual reproduction occurs only when compatible clones are mixed. All cells of a clone behave identically in interclonal crosses, being either male or female, regardless of the stage of the life cycle, in contrast to the sequential hermaphroditism of centric diatoms. Males and females have identical frustule morphology. As in other diatoms, there is an upper size threshold for sexual reproduction, below which cells become progressively easier to sexualize. In culture, sexual interactions occur in cells much smaller than those ever seen in natural populations, so that in nature the sexual size range is effectively open. Natural populations almost always contain sexualizable cells; often, most of the cells are below the upper sexual size threshold. Male gametangia are, on average, slightly larger than females in the capitate deme, which may be produced by preferential polyandry, depleting the population of males and making them younger at mating. Rarely, selfing occurs producing zygotes, but these abort before producing initial cells. The sizes of the gametangia and initial cells are correlated but this does not invalidate the use of "cardinal points" of the life cycle in taxonomy. No interbreeding occurs between the rectangular and capitate demes. However, when males of one deme are mixed with females of the other, there is a stimulation of activity, as during the early stages of pairing in compatible intrademic crosses.     

中国水域江豚种群遗传变异的研究

运用ＰＣＲ产物的银染测序技术,测定了中国水域江豚长江豚长江种群、黄海种群和南海种群共１２头个休的２个长度分别为３１７ｂｐ和２４５ｂｐ的ｍｔＤＮＡ控制区序列,并以此分析了江豚种遗传变异。结果表明：中国水域江豚各种群的控制区序列所定义的单倍型互不相同,无共有的单保型。以２个ｍｔＤＮＡ控制区片段的核苷酸序旬,以及把２个片段合并后产生的较大片段的序列,用ＭＥＧＡ软件中的ＵＰＧＭＡ法构建的系统树把江豚聚类为     

ALLOZYME VARIATION AMONG POPULATIONS OF BIOMPHALARIA CAMERUNENSIS (BOETTGER, 1941) (GASTROPODA: PLANORBIDAE) IN CAMEROON

Allozyme electrophoresis was used to study genetic diversityamong populations of the freshwater, hermaphroditic snail Biomphalariacamerunensis in Cameroon. Five of 19 loci studied in 15 enzymesystems were polymorphic. Intrapopulation variation was evidentin 8 of 12 populations sampled and heterozygotes were presentin 6 of these. Two populations with large sampled sets werepanmictic. Although results for the remaining 4 populationswith heterozygotes present were inconclusive, our findings supportthe hypothesis that Biomphalaria are out-breeders. The allelesfor two loci, asparate aminotransferase-1 (AAT-1) and 6-phosphogluconatedehydrogenase (6-PGD), showed distribution patterns that suggestthey may be limited by climate or habitat. The slow migratingAAT-1 was the only allele found in the mountainous regions ofthe southwest. This region falls under the Cameroon-type climateand is the wettest region in the country. The faster allelewas restricted to the lowland rain forest of the south. For6-PGD the fast allele was found throughout the range of B. camerunensis,but the slower allele was found only in the mountainous regionswithin the Cameroon-type climate. (Received 27 April 1989; accepted 9 September 1989)     

ALLOZYME VARIATION AMONG POPULATIONS OF BIOMPHALARIA PFEIFFERI (KRAUSS, 1848) (GASTROPODA: PLANORBIDAE) IN CAMEROON

Allozyme electrophoresis was used to study genetic diversityamong the freshwater, hermaphroditic snail Biomphalaria pfeifferiin Cameroon. Four of 19 loci studied were polymorphic. The allozymesfor two loci, aspartate aminotransferase-1 (AAT-1) and isocitratedehydrogenase (IDH), showed distribution patterns related toclimatic zones. AAT-1¹⁰⁰ and IDH¹⁰⁰ occurred predominantly inthe Tropical Climatic Zone, located in the northern half ofthe country. AAT-1¹⁴⁰ and IDH⁹⁰ were common in the EquatorialZone. Intrapopulation variations occurred in 5 of 19 populationsampled. Only one population, polymorphic for AAT-1 locus, waspanmictic. The other 4 populations were not in Hardy-Weinbergequilibrium. The deficiency of heterozygotes in those populationsis unusual for a member of the genus Biomphalaria and may bedue to a predominance of self-fertilization. Other explanationsinclude ecological factors or the presence of segregated sub-populationsthat do not outcross. This latter hypothesis is supported bythe total absence of heterozygotes for PGM alleles. (Received 24 August 1989; accepted 14 September 1989)     

ALLOZYME VARIATION AMONG POPULATIONS OF BULINUS FORSKALII (EHRENBERG, 1831) (GASTROPODA: PLANORBIDAE) IN CAMEROON

Allozyme electrophoresis was used to study genetic diversityamong populations of the freshwater, hermaphroditic snail Bulinusforskalii in Cameroon. Three of 15 loci studied in 13 enzymesystems were polymorphic. Intrapopulation variation occurredin 8 of 32 populations sampled and heterozygotes were presentin 2 of these. Neither of these populations were in Hardy-Weinbergequilibrium. These findings are in agreement with reports thathave demonstrated a low genetic diversity in this very widelydistributed, eurytopic species and that have indicated thisspecies reproduces principally by self-fertilization. The restricteddistributions of rarer alleles in three loci may be due to anarrower habitat range for those phenotypes. For isocitratedehydrogenase and phosphoglucoisomerase, the faster alleleswere found throughout the range of B. forskalii extending fromthe Sahelian regions of the north to rain forest of the south.The slower, rarer alleles for these loci were restricted tothe equatorial rain forest regions. For hydroxybutyrate dehydrogenase,the opposite was true for the rarer allele, which was restrictedto a small region in the arid, tropical climate. (Received 27 April 1989; accepted 5 September 1989)     

THE RELATIONSHIPS BETWEEN SEASONAL VARIATION IN LIGHT INTENSITY,RAMET SIZE,AND SEXUAL REPRODUCTION IN NATURAL AND EXPERIMENTAL POPULATIONS OF ASTER ACUMINATUS (COMPOSITAE)

We conducted experiments to evaluate the effects of different patterns of seasonal light availability on ramet size and sexual reproduction in the understory herb, Aster acuminatus. In April 1982, 200 potted rhizomes were divided equally between a high light and a shaded site. Twice during the growing season subsets of pots were reciprocally transferred between the sites, resulting in eight different light treatments. There was significant variation among treatments in mean ramet weight (0.41–1.21 g), height (15.0–23.4 cm), number of flowers (0.4–7.9) and percentage of ramets flowering (14–95). Periods of high light increased ramet height, weight, rhizome production and flowering, but high light earlier in the season increased ramet height more than did high light later in the season, while high light later had pronounced effects on the other three traits. Measurements taken in nine natural patches experiencing different patterns of seasonal light availability are consistent with the experimental results. The results provide new insights into the general phenomenon of size-dependent reproduction in herbs and illustrate how the phenology of biomass allocation can affect growth and reproduction.