Empirical comparison of distance equations using discrete traits

The use of the Grewal-Smith statistic in measuring biological distance among skeletal population samples has been questioned since it was first applied to human populations. Recently, in an attempt to stabilize the variance of the Grewal-Smith statistic for use with non-metric analysis, Sjøvold ('73) and Green and Suchey ('76) have introduced corrections and alternative transformations which may enhance the meaning of biological distance among population samples. Their recommendations improve the statistics for specific variable ranges; i.e., small sample size and low trait frequencies. Thirteen equations representing Grewal-Smith, Freeman-Tukey, Anscombe, and Bartlett transformations and/or corrections, were compared using rank order correlation statistics on actual biological distances generated by real population data as presented in existing literature. Results from testing these actual distance models show little variation between equations based on the populational data sets used. Based on these findings, the distance model resulting from the Grewal-Smith statistic is not inferior to the more sophisticated models, although the latter may be superior by allowing specific improvements for small sample size and/or low trait frequencies.     

Implications of variation in worker body size for the honey bee recruitment system

Honey bee scouts seek food from flowers, return to the colony, and may perform a dance used to recruit dance followers to the flowers. Variation in body size of workers may result in the communication of misinformation because some information acquired by the scout and signaled to recruits is affected by body size. I tested two predictions of this hypothesis. (1) Recruitment communication takes place between bees of similar size despite the withincolony size distribution. (2) There is an inverse relationship between the size variation of foraging honey bees (Apis mellifera)and the rate at which nectar is returned to the colony. A positive relationship was found between the size of a dancer and that of its dance followers, which together comprise a dance group. There was less variation in size within dance groups than among groups. These two factors effectively lower the difference in size between signal sender and signal receiver and may enhance the flow of accurate size-dependent information. Also, an inverse relationship between size variation and rate of nectar intake was detected in each of six colonies using partial correlation analysis. This may be due to communication of misinformation when size variance is higher. The relationship was statistically significant in two colonies and the combined results were significant. The results of the first study suggest the generally weak relationships found in this second study.     

Body size and host range in European Heteroptera

We used data on body size and host range of phytophagous Heteroptera in central Europe, an inverse measure of specialisation, to analyse the relationship of body size vs specialisation: 1) we found a clear positive relationship between body size and host range using species as independent data points. 2) However, a nested analysis of variance shows that most of the variance in body size occurred at higher taxonomic levels whereas most of the variance in host specialisation occurred between species. This suggests different phylogenetic inertia of body size and specialisation. Nevertheless, using means of different higher taxonomic levels there is still a significant positive correlation between body size and host range. 3) With more sophisticated methods of correcting for the phylogenetic relatedness between species, the positive correlation between body size and host range still holds, despite the different assumptions of each method. Thus, the relationship between body size and host range is a very robust pattern in true bugs.     

Easy determination of ploidy level in Arabidopsis thaliana plants by means of pollen size measurement

Summary Cytogenetic examination of transgenic Arabidopsis thaliana (L.) Heynh. plants obtained by Agrobacterium-mediated gene transfer to cotyledon- and root-explants or by direct gene transfer into protoplasts revealed a high percentage of tetraploid or aneuploid transformants. Depending on the transformation procedure used, 13% (root explant transformation), 33% (cotyledon explant transformation), or 38% (direct gene transfer) of the transformants showed aberrant ploidy levels. A good correlation between the ploidy level of a plant and the size of its pollen grains was observed. This allows quick and simple testing of the ploidy level of transgenic Arabidopsis plants.Abbreviations AM Arabidopsis medium - ANOVA analysis of variance - DAPI 4,6-Diamidino-2-phenylindole - PEG polyethyleneglycol     

Univariate estimates of sexual dimorphism: The effects of intrasexual variability

The difference between male and female values of quantitative traits depends on the distribution of the variables within each sex, increasing with the rise in the difference between male and female average values and with the decrease of the dispersion of measurements in both sexes. This paper deals with the sensitivity of some widely used indices (relative difference between male and female mean values (MDI), Student's t, and the so-called Bennett-Chakraborty-Majumder D coefficient) with respect to intrasexual variability. The Kolmogorov-Smirnov distance (KS) is suggested here as a further index of dimorphism, although it is not usually utilized for this purpose. The theoretical approach is accompanied by the analysis of empirical data (metric variables obtained from a sample of present Sardinians) and by computer simulations under various assumptions. Indices based on the difference between male and female average values are not able to evaluate fully the various aspects of dimorphism. Student's t proved to be an adequate measure of whole sex differences, both in real and in simulated samples, as intrasexual variability is included in its formulation. The D index also proved to be a good measure of undivided sexual dimorphism, as it is the result of formal examination, and from application to empirical or to simulated cases. The Kolmogorov-Smirnov distance gave the best performance both in formal examination and in the whole simulation results, as it takes into account intrasexual variability, and is applicable to any kind of distribution. In simulated cases it was sensitive to variations of means and variances, and it was able to evaluate variance dimorphism. Since the last three indices measure the combined effect of size and variance dimorphism, the joint use of the MDI index is suggested in order to isolate the relative contribution of the difference between the means. Am J Phys Anthropol 109:501–508, 1999. © 1999 Wiley-Liss, Inc.     

Interpretation of scale in paired quadrat variance methods

Question: Previous interpretations of the variance plot of paired quadrat variance method (PQV) have been incomplete. The objective of this study was to clarify the interpretation of PQV, and to shed additional light on how different quadrat variance methods can be used, in concert, to measure scale in transect data. Methods: We used artificial and real data to examine how the PQVmethod elucidates spatial pattern. Two‐term local quadrat variance (TTLQV) and new local variance (NLV) methods, together with their three‐term counterparts, were also applied to the same data sets, and the results from all methods were compared. Results: When the mean gap size equalled the mean patch size along a transect, the first peak of the variance of PQV, NLV and TTLQV corresponded with the gap size (or patch size). However, if the mean gap size and patch size were unequal, the variance plot of PQV displayed a flat‐topped plateau, in which the first inflection represented the mean size of the smaller phase and the second inflection represented the mean size of the larger phase; TTLQV showed a clear peak and NLV displayed a distinct first peak while the second inflection was dampened. The results also indicated than the three‐term versions of quadrat variance methods did not consistently outperform their two‐term counterparts, and often confused the interpretation of scale. Conclusions: The quadrat variance methods associated with the patch‐gap measurements were able to efficiently detect not only the size of patches, but also the size of gaps.     

Aspects of Diversity Measurement for Microbial Communities

A useful measure of diversity was calculated for microbial communities collected from lake water and sediment samples using the Shannon index (H′) and rarefaction [E(S)]. Isolates were clustered by a numerical taxonomy approach in which limited (<20) tests were used so that the groups obtained represented a level of resolution other than species. The numerical value of diversity for each sample was affected by the number of tests used; however, the relative diversity compared among several sampling locations was the same whether 11 or 19 characters were examined. The number of isolates (i.e., sample size) strongly influenced the value of H′ so that unequal sized samples could not be compared. Rarefaction accounts for differences in sample size inherently so that such comparisons are made simple. Due to the type of sampling carried out by microbiologists, H′ is estimated and not determined and therefore requires a statement of error associated with it. Failure to report error provided potentially misleading results. Calculation of the variance of H′ is not a simple matter and may be impossible when handling a large number of samples. With rarefaction, the variance of E(S) is readily determined, facilitating the comparison of many samples.     

A similarity measure sensitive to the contribution of rare species and its use in investigation of variation in marine benthic communities

Summary We propose a new measure of similarity, the normalized expected species shared or NESS. The measure is based on the expected number of species shared between random samples of size, m, drawn from a population. The NESS measure is shown to be a generalization of Morisita's similarity and is demonstrated to be less biased than other commonly used measures. The contribution of dominant and rare species is explicit according to the sample size, m, chosen. For large m, NESS is sensitive to the less common species in the populations to be compared.The NESS measure has been used to cluster a 2-year sequence of subtidal benthic samples taken after a severe disturbance. The NESS measure is responsive to the less common species so that both a temporal progression in community recovery and seasonal variation are revealed.Contribution No. 3699 from the Woods Hole Oceanographic Institution     

Of beta diversity,variance, evenness,and dissimilarity

The amount of variation in species composition among sampling units or beta diversity has become a primary tool for connecting the spatial structure of species assemblages to ecological processes. Many different measures of beta diversity have been developed. Among them, the total variance in the community composition matrix has been proposed as a single‐number estimate of beta diversity. In this study, I first show that this measure summarizes the compositional variation among sampling units after nonlinear transformation of species abundances. Therefore, it is not always adequate for estimating beta diversity. Next, I propose an alternative approach for calculating beta diversity in which variance is substituted by a weighted measure of concentration (i.e., an inverse measure of evenness). The relationship between this new measure of beta diversity and so‐called multiple‐site dissimilarity measures is also discussed.     

The Role of Life Cycle and Migration in Selection for Variance in Offspring Number

For two genotypes that have the same mean number of offspring but differ in the variance in offspring number, naturalselection will favor the genotype with lower variance. In such cases, the average growth rate is not sufficient as a measure of fitness or as a predictor of fixation probability. However, the effect of variance in offspring number on the fixationprobability of mutant strategies has been calculated under several scenarios with the general conclusion that variance in offspring number reduces fitness in proportion to the inverse of the population size [Gillespie, J., Genetics 76:601–606, 1974; Proulx, S.R., Theor. Popul. Biol. 58:33–47, 2000]. This relationship becomes more complicated under a metapopulation scenario where the “effective” population size depends on migration rate, population structure, and lifecycle. It is shown that in a life cycle where reproduction and migration (the birth-migration-regulation life cycle, or BMR)occur prior to density regulation within every deme, the fitness of a strategy depends on migration rate. When migration rates are near zero, the fitness of the strategy is determined by the size of individual demes, so that the strategy favoredin small populations tends to be fixed. As migration rate increases and approaches panmixis between demes, the fitness ofa reproductive strategy approaches what its value would be in a single, panmictic deme with a population size correspondingtothe census size of the metapopulation. Interestingly, when the life cycle is characterized by having density regulation in each deme prior to migration (the BRM life cycle) the fixation probability of a strategy is independent of migration rate. These results are found to be qualitatively consistent with the individual-based simulation results in Shpak [Theor. Biosci.124:65–85, 2005]. An erratum to this article can be found at     

Investigations into parametric analysis of data from in vivo micronucleus assays by comparison with non-parametric methods

Data from micronucleus assays of 6 compounds were analysed by 3 non-parametric and 3 parametric methods. Two of the latter involved transformation of the data so several transformation strategies were investigated. It was concluded that the non-parametric Kolmogorov-Smirnov two-sample test was the most reliable method of analysis. None of the parametric solutions was entirely satisfactory. The Bayesian solution to the Behrens-Fisher problem of normal distributions with differing variances was an acceptable compromise after the data had been transformed by the inverse hyperbolic sine method applicable to negative binomials.     

Comparison of adjustment methods for stratified two‐sample tests in the context of ROC analysis

We compare several nonparametric and parametric weighting methods for the adjustment of the effect of strata. In particular, we focus on the adjustment methods in the context of receiver‐operating characteristic (ROC) analysis. Nonparametrically, rank‐based van Elteren's test and inverse‐variance (IV) weighting using the area under the ROC curve (AUC) are examined. Parametrically, the stratified t‐test and IV AUC weighted method are applied based on a binormal monotone transformation model. Stratum‐specific, pooled, and adjusted estimates are obtained. The pooled and adjusted AUCs are estimated. We illustrate and compare these weighting methods on a multi‐center diagnostic trial and through extensive Monte‐Carlo simulations.     

Effects of plant spacing and interplanting with oilseed rape on colonisation of dwarf hops by the damson-hop aphid, Phorodon humuli

The pattern of colonisation of dwarf hops (Humulus lupulus) by damson-hop aphid (Phorodon humuli (Schrank)) migrating from Prunus spp. was investigated at six plant spacings and where some of the hops were replaced by oilseed rape (Brassica napus L.), a non-host of the aphid. The number of migrant aphids that accumulated on hop stems (bines) increased with increasing bine size and density. The numbers of aphids that colonised hops interplanted with oilseed rape reflected the density of the hop plants only and not the overall plant density. As the physical size of the wind shadow within which flying aphids can manoeuvre and land was unimportant unless provided by a host plant, the finding supports the theory that flying aphids respond to olfactory stimuli associated with their hosts. Variation in bine height (as a measure of plant size) explained 29–93% of the variance in aphid counts during the 3 years' study and bine density 1–14%. Standardising the data as the numbers of aphids per metre of bine and taking a square-root transformation of these standardised counts improved the precision of the analyses and, by stabilising variances, facilitated comparisons between years as growth became more vigorous as the plants matured. Each year, the rate of increase in numbers of aphids settling on plots of hops declined curvilinearly with increasing bine density. Maximum colonisation by P. humuli occurred at a bine density of five per metre row, a density similar to that used commercially by growers of dwarf hops.     

Resolution of patch capacitance recordings and of fusion pore conductances in small vesicles

We investigated the noise levels in cell-attached patch capacitance recordings with a lock-in amplifier. The capacitance noise level decreases with increasing sine wave frequency up to 20-40 kHz. With a 20-mV rms sine wave the rms noise level above 8 kHz is <50 aF. With increasing sine wave amplitudes a further reduction down to 14 aF could be achieved. Capacitance measurements with a lock-in amplifier may also be used to measure the conductance of fusion pores connecting the vesicular lumen to the extracellular space. It is estimated that at noise levels of 14 aF fusion pore conductances between 20 pS and 700 pS may be resolved in vesicles with 380-aF capacitance by using a 50-kHz sine wave. This corresponds to vesicles with a approximately 110-nm diameter. It is suggested that with low-noise techniques fusion pores may be detectable in vesicles approaching the size of large synaptic vesicles.     

Inbreeding and the genetic variance in floral traits of Mimulus guttatus

The additive genetic variance, V(A), is frequently used as a measure of evolutionary potential in natural plant populations. Many plants inbreed to some extent; a notable observation given that random mating is essential to the model that predicts evolutionary change from V(A). With inbreeding, V(A) is not the only relevant component of genetic variation. Several nonadditive components emerge from the combined effects of inbreeding and genetic dominance. An important empirical question is whether these components are quantitatively significant. We use maximum likelihood estimation to extract estimates for V(A) and the nonadditive 'inbreeding components' from an experimental study of the wildflower Mimulus guttatus. The inbreeding components contribute significantly to four of five floral traits, including several measures of flower size and stigma-anther separation. These results indicate that inbreeding will substantially alter the evolutionary response to natural selection on floral characters.     

Modelling reproductive effort in sub-and maritime Antarctic mosses

A comparison is made of the reproductive effort (RE), considered as the investment in sporophyte relative to gametophyte biomass, of eight species of moss occurring at sub-and maritime Antarctic sites. Six of the species showed smaller sporophytes and game-tophytes at the climatically more extreme maritime Antaretic sites and one species showed no size difference between regions. The remaining species, although showing no regional difference, showed some evidence of a reverse pattern, with higher altitude samples having greater biomass than lower altitude samples. Spore counts indicated a measure of compensation in maritime Antarctic samples, with no significant decrease in spore output in several species despite smaller sporophyte biomass. The relationship between sporophyte (S) and gametophyte (G) biomass within samples was described by an allometric curve (S=aG ^b ) which gave a better fit than a straight line for six species. This form of model allows comparisons of patterns of RE to be made between samples with non-or partially overlapping size distributions, even when the relationship involves size-dependence. An allometric curve was not appropriate for describing samples of one species (Andreaea regularis), and insufficient data were available to identify any relationship in Polytrichum alpinum. The exponent (b) differed between species, but there were no statistically significant differences between exponents from samples of the same species. Samples of two species could further be described by the same coefficient (a), indicating that they lie on the same curve. However, samples of three species from sub-Antarctic South Georgia gave significantly higher coefficients, indicating increased RE relative to maritime Antarctic 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.     

Large dam reservoirs are probably long-period oscillators of fish diversity

Long‐term fish population time series obtained annually in a backwater (upstream) and a tailwater (downstream) site of the large lowland Jeziorsko Reservoir, Poland, were analysed and compared to detect impoundment influence on the fluctuation of fish population density and on the fluctuation of a fish diversity measure. The partial‐rate correlation function (PRCF) of all constantly occurring fish species displayed negative first‐order feedback of past density on present density, both upstream and downstream. Weak and irregular cyclic patterns were observed in the autocorrelation function (ACF) of populations of several species upstream and of two species downstream. Most fish species exhibited no significant concordant variations between the two sites, but there were no data supporting different regulation. Probably, different exogenous (environmental) factors control fishes at the two sites. The ACFs of the time series of the exponential of Shannon entropy (N₁ diversity measure) obtained at the Jeziorsko tailwater site, and in the main body of the smaller ?ímov Reservoir, Czech Republic, revealed strong fluctuation patterns. The fluctuation was well fitted by a sine‐wave model of a 9 year period at the ?ímov, although it co‐occurred with a positive linear trend. A sine‐wave model also fitted well with the trend at the Jeziorsko tailwater site, where, however, only one 16·5 year period occurred; hence, it is indicative of cyclicity. The results indicate that dam reservoirs may be oscillators of fish diversity and that part of the literature controversy over the effect of a reservoir on fish populations may be due to a too short sampling period: it is shown that both increase and decrease in diversity may be observed on the basis of samples selected from one diversity time series obtained at the tailwater.     

Meta-analysis of the difference of medians

We consider the problem of meta-analyzing two-group studies that report the median of the outcome. Often, these studies are excluded from meta-analysis because there are no well-established statistical methods to pool the difference of medians. To include these studies in meta-analysis, several authors have recently proposed methods to estimate the sample mean and standard deviation from the median, sample size, and several commonly reported measures of spread. Researchers frequently apply these methods to estimate the difference of means and its variance for each primary study and pool the difference of means using inverse variance weighting. In this work, we develop several methods to directly meta-analyze the difference of medians. We conduct a simulation study evaluating the performance of the proposed median-based methods and the competing transformation-based methods. The simulation results show that the median-based methods outperform the transformation-based methods when meta-analyzing studies that report the median of the outcome, especially when the outcome is skewed. Moreover, we illustrate the various methods on a real-life data set.     

Quantitative-genetic analysis of wing form and bilateral asymmetry in isochromosomal lines ofDrosophila subobscura using Procrustes methods

Fluctuating asymmetry (FA) is often used as a measure of underlying developmental instability (DI), motivated by the idea that morphological variance is maladaptive. Whether or not DI has evolutionary potential is a highly disputed topic, marred by methodological problems and fuzzy prejudices. We report here some results from an ongoing study of the effects of karyotype, homozygosity and temperature on wing form and bilateral asymmetry using isochromosomal lines ofDrosophila subobscura. Our approach uses the recently developed methodologies in geometric morphometrics to analyse shape configurations of landmarks within the standard statistical framework employed in studies of bilateral asymmetries, and we have extended these methods to partition the individual variation and the variation in asymmetries into genetic and environmental causal components. The analyses revealed temperaturedependent expression of genetic variation for wing size and wing shape, directional asymmetry (DA) of wing size, increased asymmetries at suboptimal temperature, and a transition from FA to DA in males as a result of increase in the rearing temperature. No genetic variation was generally detected for FA in our samples, but these are preliminary results because no crosses between lines were carried out and, therefore, the contribution of dominance was not taken into account. In addition, only a subset of the standing genetic variation was represented in the experiments.