Effect of sampling scale on the assessment of epiphytic bacterial populations

Bacterial populations on above-ground plant surfaces were estimated at three different biological scales, including leaflet disks, entire leaflets, and whole plants. The influence of sample scale on the estimation of mean bacterial population size per unit and per gram and on the variability among sampling units was quantified at each scale. Populations were highly variable among sampling units at every scale examined, suggesting that there is no optimal scale at which sample variance is reduced. The distribution of population sizes among sample units was sometimes, but not consistently, described by the lognormal. Regardless of the sampling scale, expression of population sizes on a per gram basis may not reduce variance, because population size was not generally a function of sample unit weight within any single sampling scale. In addition, the data show that scaling populations on a per gram basis does not provide a useful means of comparing population estimates from samples taken at different scales. The implications of these results for designing sampling strategies to address specific issues in microbial ecology are discussed. Correspondence to: L.L. Kinkel     

Estimation,variance and optimal sampling of gene diversity

An extension of Nei's analysis of diversity in a subdivided population is proposed for a haploid locus. The differentiation G _STbecomes a natural extension of Wright's F _STand generalizes Weir and Cockerham's parameter of co-ancestry by relaxing the assumption of identical correlation for all the alleles. Inter- and intrapopulation variances of the estimated diversities and differentiation are derived. Finally, the optimal sampling strategy for measuring G _STwhen a fixed number of individuals can be analysed is considered. It is shown that, at a given locus, there is a unique sample size per population which yields the smallest variance of G _ST,regardless of the number of populations studied. These theoretical developments are illustrated with an analysis of chloroplast DNA diversity in a forest tree. The results emphasize the necessity of sampling many populations, rather than many individuals per population, for an accurate measurement of the subdivision of gene diversity at a single locus.     

Adaptive Cluster Sampling in the Context of Restoration

Abundance is an important population state variable for monitoring restoration progress. Efficient sampling often proves difficult, however, when populations are sparse and patchily distributed, such as early after restoration planting. Adaptive cluster sampling (ACS) can help by concentrating search effort in high density areas, improving the encounter rate and the ability to detect a population change over time. To illustrate the problem, I determined conventional design sample sizes for estimating abundance of 12 natural populations and 24 recently planted populations (divided among two preserves) of Lupinus perennis L. (wild blue lupine). I then determined the variance efficiency of ACS relative to simple random sampling at fixed effort and cost for 10 additional planted populations in two habitats (field vs. shrubland). Conventional design sample sizes to estimate lupine stem density with 10% or 20% margins of error were many times greater than initial sample size and would require sampling at least 90% of the study area. Differences in effort requirements were negligible for the two preserves and natural versus planted populations. At fixed sample size, ACS equaled or outperformed simple random sampling in 40% of populations; this shifted to 50% after correcting for travel time among sample units. ACS appeared to be a better strategy for inter‐seeded shrubland habitat than for planted field habitat. Restoration monitoring programs should consider adaptive sampling designs, especially when reliable abundance estimation under conventional designs proves elusive.     

THE HERITABLE BASIS OF VARIATION IN LARVAL DEVELOPMENTAL PATTERNS WITHIN POPULATIONS OF THE WOOD FROG (RANA SYLVATICA)

This study compares the heritable basis of variation in larval developmental patterns of mountain and lowland populations of the wood frog, Rana sylvatica. Additive genetic variances, heritabilities, and genetic correlations for larval developmental time and size at metamorphosis are estimated from half-sib and full-sib crosses. Considerable additive-genetic variances and high heritabilities are revealed for developmental time in both the mountain and the lowland population. There was a high level of additive-genetic variance and high heritability for body size at metamorphosis in the mountain population, but these were very low in the lowland population. The genetic correlations between developmental rate and larval body size are negative for the mountain population and near zero for the lowland population. It is argued that the differences in genetic structure between these two populations reflect differences in the selective regimes of their respective environments.     

Assessing genetic diversity of Elymus sibiricus (Poaceae: Triticeae) populations from Qinghai-Tibet Plateau by ISSR markers

Inter-simple sequence repeats (ISSR) markers were used to assess the genetic diversity and population structure in eight populations of Elymus sibiricus L. from the southeast of Qinghai-Tibet Plateau of China. Of the 100 primers screened, 13 produced highly reproducible ISSR bands. Using these primers, 193 discernible DNA fragments were generated with 149 (77.2%) being polymorphic, indicating considerable genetic variation at the species level. In contrast, there were relatively low levels of polymorphism at the population level with the percentage of polymorphic bands (PPB) ranging from 44.04 to 54.92%. The mean gene diversity (H_E) was estimated to be 0.181 within populations (range 0.164–0.200), and 0.274 at the species level. A high level of genetic differentiation among populations was detected based on Nei's genetic diversity analysis (33.1%), Shannon's index analysis (34.5%), Bayesian method (33.2%) and AMOVA analysis (42.5%). No significant statistical differences (analysis of molecular variance [AMOVA], P = 0.08) in ISSR variation were found between the sample collection regions. However, among populations (42.5% of the variance) and within populations (57.5% of the variance), there were significant differences (P < 0.001). Populations shared high levels of genetic identity. This pattern of genetic variation was different from that for most of inbreeding Triticeae species reported. In addition, a geographical pattern of population differentiation, where the populations from south and north of sampling sites were clearly separated from each other, was revealed by both the cluster and principal coordinates analyses. Generally, the result of this study indicates that E. sibiricus contains high molecular variation in its populations. The implications of these results for the conservation of the species are discussed.     

Comparative population structure of two dominant species,Shinkaia crosnieri (Munidopsidae: Shinkaia) and Bathymodiolus platifrons (Mytilidae: Bathymodiolus), inhabiting both deep‐sea vent and cold seep inferred from mitochondrial multi‐genes

Deep‐sea hydrothermal vents and cold seeps, limited environments without sunlight, are two types of extreme habitat for marine organisms. The differences between vents and cold seeps may facilitate genetic isolation and produce population heterogeneity. However, information on such chemosynthetic fauna taxa is rare, especially regarding the population diversity of species inhabiting both vents and cold seeps. In this study, three mitochondrial DNA fragments (the cytochrome c oxidase submit I (COI), cytochrome b gene (Cytb), and 16S) were concatenated as a mitochondrial concatenated dataset (MCD) to examine the genetic diversity, population structure, and demographic history of Shinkaia crosnieri and Bathymodiolus platifrons. The genetic diversity differences between vent and seep populations were statistically significant for S. crosnieri but not for B. platifrons. S. crosnieri showed less gene flow and higher levels of genetic differentiation between the vent and seep populations than B. platifrons. In addition, the results suggest that all the B. platifrons populations, but only the S. crosnieri vent populations, passed through a recent expansion or bottleneck. Therefore, different population distribution patterns for the two dominant species were detected; a pattern of population differentiation for S. crosnieri and a homogeneity pattern for B. platifrons. These different population distribution patterns were related to both extrinsic restrictive factors and intrinsic factors. Based on the fact that the two species were collected in almost identical or adjacent sampling sites, we speculated that the primary factors underlying the differences in the population distribution patterns were intrinsic. The historical demographics, dispersal ability, and the tolerance level of environmental heterogeneity are most likely responsible for the different distribution patterns.     

GENETIC FINGERPRINT-INFERRED POPULATION SUBDIVISION AND SPATIAL GENETIC TESTS FOR ISOLATION BY DISTANCE AND ADAPTATION IN THE COASTAL PLANT LIMONIUM CAROLINIANUM

This paper examines two wild populations of Limonium carolinianum for population genetic subdivision and spatial patterns of genetic variation in an attempt to simultaneously test for both the action of local adaptation to tidal gradients and isolation by distance (IBD). A VNTR (variable number of tandem repeats) genetic “fingerprinting” marker was used to infer relatedness among mapped plants in two populations. Band sharing within and between populations estimated F'_ST, an approximate measure of F_ST. Regression models were used to analyze the relationship between band sharing and spatial separation in tidal elevation and horizontal distance, as well as the relationship of fecundity differences with band sharing and spatial distance. Populations differed in band size frequency distributions and mean number of bands per profile and, therefore, likely differed in effective population size. F'_ST was estimated at 0.0678 and was significantly greater than F'_ST among randomly constructed subpopulations. Band sharing decreased 0.13% per meter in one population but showed no significant relation to distance in the other. In the population with significant IBD band sharing increased with increasingly different tidal elevation, contrary to an adaptive hypothesis, possibly due to directional gene flow or drift. Deme sizes were approximately 25 meters and greater than 100 meters, spanning larger areas than the entire environmental gradient. Fecundity differences were not associated with spatial parameters or band sharing. Unequal potential maternal fecundity measured as variance in number of seeds per maternal family was a significant source of genetic sampling variance. The VNTR marker employed is capable of detecting adaptation as identity by descent in ecological time and is an appropriate method for estimating the net evolutionary fate of polygenic traits. The results show that the net balance between selection along an environmental gradient and the effects of IBD and unequal maternal fecundity favor genetic differentiation by random processes in populations of Limonium.     

Variance of Neutral Genetic Variances within and between Populations for a Quantitative Character

The variances of genetic variances within and between finite populations were systematically studied using a general multiple allele model with mutation in terms of identity by descent measures. We partitioned the genetic variances into components corresponding to genetic variances and covariances within and between loci. We also analyzed the sampling variance. Both transient and equilibrium results were derived exactly and the results can be used in diverse applications. For the genetic variance within populations, sigma 2 omega, the coefficient of variation can be very well approximated as [formula: see text] for a normal distribution of allelic effects, ignoring recurrent mutation in the absence of linkage, where m is the number of loci, N is the effective population size, theta 1(0) is the initial identity by descent measure of two genes within populations and t is the generation number. The first term is due to genic variance, the second due to linkage disequilibrium, and third due to sampling. In the short term, the variation is predominantly due to linkage disequilibrium and sampling; but in the long term it can be largely due to genic variance. At equilibrium with mutation [formula: see text] where u is the mutation rate. The genetic variance between populations is a parameter. Variance arises only among sample estimates due to finite sampling of populations and individuals. The coefficient of variation for sample gentic variance between populations, sigma 2b, can be generally approximated as [formula: see text] when the number of loci is large where S is the number of sampling populations.     

Accounting for missing data in the estimation of contemporary genetic effective population size (Ne)

Theoretical models are often applied to population genetic data sets without fully considering the effect of missing data. Researchers can deal with missing data by removing individuals that have failed to yield genotypes and/or by removing loci that have failed to yield allelic determinations, but despite their best efforts, most data sets still contain some missing data. As a consequence, realized sample size differs among loci, and this poses a problem for unbiased methods that must explicitly account for random sampling error. One commonly used solution for the calculation of contemporary effective population size (N_e) is to calculate the effective sample size as an unweighted mean or harmonic mean across loci. This is not ideal because it fails to account for the fact that loci with different numbers of alleles have different information content. Here we consider this problem for genetic estimators of contemporary effective population size (N_e). To evaluate bias and precision of several statistical approaches for dealing with missing data, we simulated populations with known N_e and various degrees of missing data. Across all scenarios, one method of correcting for missing data (fixed‐inverse variance‐weighted harmonic mean) consistently performed the best for both single‐sample and two‐sample (temporal) methods of estimating N_e and outperformed some methods currently in widespread use. The approach adopted here may be a starting point to adjust other population genetics methods that include per‐locus sample size components.     

TYPE I ERROR RATES FOR TESTING GENETIC DRIFT WITH PHENOTYPIC COVARIANCE MATRICES: A SIMULATION STUDY

Studies of evolutionary divergence using quantitative genetic methods are centered on the additive genetic variance–covariance matrix ( G ) of correlated traits. However, estimating G properly requires large samples and complicated experimental designs. Multivariate tests for neutral evolution commonly replace average G by the pooled phenotypic within‐group variance–covariance matrix ( W ) for evolutionary inferences, but this approach has been criticized due to the lack of exact proportionality between genetic and phenotypic matrices. In this study, we examined the consequence, in terms of type I error rates, of replacing average G by W in a test of neutral evolution that measures the regression slope between among‐population variances and within‐population eigenvalues (the Ackermann and Cheverud [AC] test) using a simulation approach to generate random observations under genetic drift. Our results indicate that the type I error rates for the genetic drift test are acceptable when using W instead of average G when the matrix correlation between the ancestral G and P is higher than 0.6, the average character heritability is above 0.7, and the matrices share principal components. For less‐similar G and P matrices, the type I error rates would still be acceptable if the ratio between the number of generations since divergence and the effective population size (t/N_e) is smaller than 0.01 (large populations that diverged recently). When G is not known in real data, a simulation approach to estimate expected slopes for the AC test under genetic drift is discussed.     

Comparison of genetic (co)variance matrices within and between Scabiosa canescens and S. columbaria

In the current study, we used bootstrap analyses and the common principal component (CPC) method of Flury (1988) to estimate and compare the G ‐matrix of Scabiosa columbaria and S. canescens populations. We found three major patterns in the G ‐matrices: (i) the magnitude of the (co)variances was more variable among characters than among populations, (ii) different populations showed high (co)variance for different characters, and (iii) there was a tendency for S. canescens to have higher genetic (co)variances than S. columbaria. The hypothesis of equal G ‐matrices was rejected in all comparisons and there was no evidence that the matrices differed by a proportional constant in any of the analyses. The two ‘species matrices’ were found to be unrelated, both for raw data and data standardized over populations, and there was significant between‐population variation in the G ‐matrix in both species. Populations of S. canescens showed conservation of structure (principal components) in their G ‐matrices, contrasting with the lack of common structure among the S. columbaria matrices. Given these observations and the results from previous studies, we propose that selection may be responsible for some of the variation between the G ‐matrices, at least in S. columbaria and at the between‐species level.     

Impact of precocious male parr on the effective size of a wild population of Atlantic salmon

1. There is growing evidence that sexually mature but morphologically juvenile males of Atlantic salmon (precocious or mature male parr) actively participate in reproduction and, therefore, in the genetic composition of the populations of this species. The impact of mature male parr on the effective population size (N_e) of such populations has been previously studied under experimental settings, but no studies have been performed directly on natural populations. 2. Continuous monitoring and sampling of all sea returns is possible in the Lérez River (northwest of Spain). From demographic data on variances of reproductive success and genetic data from six microsatellite marker loci we carried out parentage assignment and assessed the impact of male parr on demographic and genetic estimates of N_e in two consecutive years. 3. Our results reveal that: (i) approximately 60% of the total sire paternity is attributable to mature parr; (ii) mature parr decrease the variance of reproductive success of males by a threefold factor and increase the effective population size of males by a 10‐fold factor; (iii) however, they do not substantially affect the variance of reproductive success and the effective size of females; (iv) mature parr increase two‐to threefold the overall effective size of the population but the ratio N_e/N, where N is the population size including or not mature parr in each case, is not affected.     

Age-related variation in genetic control of height growth in Douglas-fir

Summary The development of genetic variances in height growth of Douglas-fir over a 53-year period is analyzed and found to fall into three periods. In the juvenile period, variances in environmental error increase logarithmically, genetic variance within populations exists at moderate levels, and variance among populations is low but increasing. In the early reproductive period, the response to environmental sources of error variance is restricted, genetic variance within populations disappears, and populational differences strongly emerge but do not increase as expected. In the later period, environmental error again increases rapidly, but genetic variance within populations does not reappear and population differences are maintained at about the same level as established in the early reproductive period. The change between the juvenile and early reproductive periods is perhaps associated with the onset of ecological dominance and significant allocations of energy to reproduction.This paper is published with the approval of the Director of Research, North Carolina Agricultural Experiment Station, as No. 3361 of the Journal Series. The computing services in this project were supported by NIH Grant GM-11 546, held by the Institute of Statistics, North Carolina State University at Raleigh.     

Testing Equivalence Simultaneously for Location and Dispersion of two Normally Distributed Populations

In clinical trials with an active control usually therapeutical equivalence of a new treatment is investigated by looking at a location parameter of the distributions of the primary efficacy variable. But even if the location parameters are close to each other existing differences in variability may be connected with different risks for under or over treatment in an individual patient. Assuming normally distributed responses a multiple test procedure applying two shifted one-sided t-tests for the mean and accordingly two one-sided F-tests for the variances is proposed. Equivalence in location and variability is established if all four tests lead to a rejection at the (one-sided) level α. A conservative procedure “correcting” the t-tests for heteroscedasticity is derived. The choice of a design in terms of the global level α, the global power, the relevant deviations in the population means and variances, as well as the sample size is outlined. Numerical calculations of the actual level and power for the proposed designs show, that for balanced sample sizes the classical uncorrected one-sided t-tests can be used safely without exaggerating the global type I error probability. Finally an example is given.     

Realized Sampling Variances of Estimates of Genetic Parameters and the Difference between Genetic and Phenotypic Correlations

A data set of 1572 heritability estimates and 1015 pairs of genetic and phenotypic correlation estimates, constructed from a survey of published beef cattle genetic parameter estimates, provided a rare opportunity to study realized sampling variances of genetic parameter estimates. The distribution of both heritability estimates and genetic correlation estimates, when plotted against estimated accuracy, was consistent with random error variance being some three times the sampling variance predicted from standard formulae. This result was consistent with the observation that the variance of estimates of heritabilities and genetic correlations between populations were about four times the predicted sampling variance, suggesting few real differences in genetic parameters between populations. Except where there was a strong biological or statistical expectation of a difference, there was little evidence for differences between genetic and phenotypic correlations for most trait combinations or for differences in genetic correlations between populations. These results suggest that, even for controlled populations, estimating genetic parameters specific to a given population is less useful than commonly believed. A serendipitous discovery was that, in the standard formula for theoretical standard error of a genetic correlation estimate, the heritabilities refer to the estimated values and not, as seems generally assumed, the true population values.     

Experimental studies of adaptive differentiation in Bahamian Anolis lizards

Populations of the lizards Anolis carolinensis and A. sagrei were experimentally introduced onto small islands in the Bahamas. Less than 15 years after introduction, we investigated whether the populations had diverged and, if so, whether differentiation was related to island vegetational characteristics or propagule size. No effect of founding population size was evident, but differentiation of A. sagrei appears to have been adaptive, a direct relationship existed between how vegetationally different an experimental island was from the source island and how much the experimental population on that island had diverged morphologically. Populations of A. carolinensis had also diverged, but were too few for quantitative comparisons. A parallel exists between the divergence of experimental populations of A. sagrei and the adaptive radiation of Anolis lizards in the Greater Antilles; in both cases, relative hindlimb length and perch diameter are strongly correlated. This differentiation could have resulted from genetic change or environmentally-driven phenotypic plasticity. Laboratory studies on A. sagrei from a population in Florida indicate that hindlimb length exhibits adaptive phenotypic plasticity. Further studies are required to determine if the observed differences among the experimental populations are the result of such plasticity. Regardless of whether the differences result from plasticity, genetic change, or both, the observation that anole populations differentiate rapidly and adaptively when exposed to novel environmental conditions has important implications for understanding the adaptive radiation of Caribbean anoles.     

Demographic variance in heterogeneous populations: matrix models and sensitivity analysis

The demographic consequences of stochasticity in processes such as survival and reproduction are modulated by the heterogeneity within the population. Therefore, to study effects of stochasticity on population growth and extinction risk, it is critical to use structured population models in which the most important sources of heterogeneity (e.g. age, size, developmental stage) are incorporated as i‐state variables. Demographic stochasticity in heterogeneous populations has often been studied using one of two approaches: multitype branching processes and diffusion approximations. Here, we link these approaches, through the demographic stochasticity in age‐ or stage‐structured matrix population models. We derive the demographic variance, σ²_d, which measures the per capita contribution to the variance in population growth increment, and we show how it can be decomposed into contributions from transition probabilities and fertility across ages or stages. Furthermore, using matrix calculus we derive the sensitivity of σ²_d to age‐ or stage‐specific mortality and fertility. We apply the methods to an extensive set of data from age‐classified human populations (long‐term time‐series for Sweden, Japan and the Netherlands; two hunter–gatherer populations, and the high‐fertility Hutterites), and to a size‐classified population of the herbaceous plant Calathea ovandensis. For the human populations our analysis reveals substantial temporal changes in the demographic variance as well as its main components across age. These new methods provide a powerful approach for calculating the demographic variance for any structured model, and for analyzing its main components and sensitivities. This will make possible new analyses of demographic variance across different kinds of heterogeneity in different life cycles, which will in turn improve our understanding of mechanisms underpinning extinction risk and other important biological outcomes.     

Longitudinal analysis of pre- and post-treatment measurements with equal baseline assumptions in randomized trials

For continuous variables of randomized controlled trials, recently, longitudinal analysis of pre- and posttreatment measurements as bivariate responses is one of analytical methods to compare two treatment groups. Under random allocation, means and variances of pretreatment measurements are expected to be equal between groups, but covariances and posttreatment variances are not. Under random allocation with unequal covariances and posttreatment variances, we compared asymptotic variances of the treatment effect estimators in three longitudinal models. The data-generating model has equal baseline means and variances, and unequal covariances and posttreatment variances. The model with equal baseline means and unequal variance–covariance matrices has a redundant parameter. In large sample sizes, these two models keep a nominal type I error rate and have high efficiency. The model with equal baseline means and equal variance–covariance matrices wrongly assumes equal covariances and posttreatment variances. Only under equal sample sizes, this model keeps a nominal type I error rate. This model has the same high efficiency with the data-generating model under equal sample sizes. In conclusion, longitudinal analysis with equal baseline means performed well in large sample sizes. We also compared asymptotic properties of longitudinal models with those of the analysis of covariance (ANCOVA) and t-test.     

PHENOTYPIC EVOLUTION BY NEUTRAL MUTATION

A general model is developed for predicting the genetic variance within populations and the rate of divergence of population mean phenotypes for quantitative traits under the joint operation of random sampling drift and mutation in the absence of selection. In addition to incorporating the dominance effects of mutant alleles, the model yields some insight into the effects of linkage and the mating system on the mutational production of quantitative-genetic variation. Despite these additional and potentially serious complications, it is found that, for small populations, the simple predictions obtained by previous investigators using additive-genetic models hold reasonably well. Even after accounting for dominance and linkage, the equilibrium level of genetic variance is unlikely to be much less than 2NV_m or to be more than 4NV_m, where N is the effective population size and V_m is the new variance from mutation appearing each generation. The rate of increase of the between-line variance per generation ultimately equals 2V_m regardless of population size, although the time to attain the asymptotic rate is proportional to N. Expressions are presented for the rate of approach to the equilibrium level of genetic variance and for the expected variance of the within-population and between-population genetic variances. The relevance of the derived model, which amounts to a generalization of the neutral theory to the phenotypic level, is discussed in the context of the detection of natural selection, the maintenance of pure lines for biomedical and agricultural purposes, the development of genetic conservation programs, and the design of indices of morphological distance between species.     

Interpopulation differences in pupal size and fecundity are not associated with occurrence of outbreaks in Epirrita autumnata (Lepidoptera, Geometridae)

Abstract.

• 1 Among-population differences in pupal mass were studied in a geometrid, Epirrita autumnata. Some Epirrita autumnata populations regularly reach outbreak densities while others are never known to do so. Because adults do not feed, pupal mass of females correlates strongly with fecundity.
• 2 Larvae were collected from twelve field sites. Ten of our sample populations originated within the outbreak range of the species and represented different phases of outbreaks. Two populations originated outside the outbreak range.
• 3 Pupal mass of field-collected E. autumnata varied significantly among populations. The peak phase populations had the smallest pupae and the biggest were found in low density populations outside the outbreak range.
• 4 Offspring of moths from each population were reared under identical conditions in two larval densities. Significant differences were not found in pupal mass among populations. That is, the inherent size, correlated with fecundity of moths, was not different between populations originating within and outside the outbreak range, nor among collections from different densities or phases of the outbreaks.
• 5 Rearing density did not interact in a consistent way with population.
• 6 As far as size and fecundity are concerned, the results do not support Chitty's hypothesis that differences in genetic composition of the population at low and high density phases generate cyclic fluctuations of population density.
• 7 Because no hereditary or maternal differences were found in size and fecundity between E.autumnata originating within and outside the outbreak range, variation in reproductive capacity cannot explain why outbreaks occur only in some populations.