Testing for Compensation in a Multi-species Community

Abstract The dynamics of a community are said to be compensatory if aggregate biomass is less variable over time than the biomass of the individual components of the system. In broad terms, the presence of compensation reflects interactions between components that tend to stabilize the overall community. A common quantitative measure used to detect compensation is the ratio of the temporal variance of total biomass to the sum of the biomass variances of the components, with a ratio less than 1 indicative of compensation. The purpose of this note is to describe a test for compensation when the variance ratio is estimated from biomass time series data. The test involves a bootstrap procedure that accounts for serial correlation in biomass. Failure to account for positive serial correlation can lead to spurious detection of compensation. The test is illustrated using biomass data for fish stocks on Georges Bank.     

Robust estimation and inference for bivariate line-fitting in allometry

In allometry, bivariate techniques related to principal component analysis are often used in place of linear regression, and primary interest is in making inferences about the slope. We demonstrate that the current inferential methods are not robust to bivariate contamination, and consider four robust alternatives to the current methods -- a novel sandwich estimator approach, using robust covariance matrices derived via an influence function approach, Huber's M-estimator and the fast-and-robust bootstrap. Simulations demonstrate that Huber's M-estimators are highly efficient and robust against bivariate contamination, and when combined with the fast-and-robust bootstrap, we can make accurate inferences even from small samples.     

Potential use of DNA barcoding for the identification of Salvia based on cpDNA and nrDNA sequences

An effective DNA marker for authenticating the genus Salvia was screened using seven DNA regions (rbcL, matK, trnL–F, and psbA–trnH from the chloroplast genome, and ITS, ITS1, and ITS2 from the nuclear genome) and three combinations (rbcL + matK, psbA–trnH + ITS1, and trnL–F + ITS1). The present study collected 232 sequences from 27 Salvia species through DNA sequencing and 77 sequences within the same taxa from the GenBank. The discriminatory capabilities of these regions were evaluated in terms of PCR amplification success, intraspecific and interspecific divergence, DNA barcoding gaps, and identification efficiency via a tree-based method. ITS1 was superior to the other marker for discriminating between species, with an accuracy of 81.48%. The three combinations did not increase species discrimination. Finally, we found that ITS1 is a powerful barcode for identifying Salvia species, especially Salvia miltiorrhiza.     

Detecting local diversity‐dependence in diversification

Whether there are ecological limits to species diversification is a hotly debated topic. Molecular phylogenies show slowdowns in lineage accumulation, suggesting that speciation rates decline with increasing diversity. A maximum‐likelihood (ML) method to detect diversity‐dependent (DD) diversification from phylogenetic branching times exists, but it assumes that diversity‐dependence is a global phenomenon and therefore ignores that the underlying species interactions are mostly local, and not all species in the phylogeny co‐occur locally. Here, we explore whether this ML method based on the nonspatial diversity‐dependence model can detect local diversity‐dependence, by applying it to phylogenies, simulated with a spatial stochastic model of local DD speciation, extinction, and dispersal between two local communities. We find that type I errors (falsely detecting diversity‐dependence) are low, and the power to detect diversity‐dependence is high when dispersal rates are not too low. Interestingly, when dispersal is high the power to detect diversity‐dependence is even higher than in the nonspatial model. Moreover, estimates of intrinsic speciation rate, extinction rate, and ecological limit strongly depend on dispersal rate. We conclude that the nonspatial DD approach can be used to detect diversity‐dependence in clades of species that live in not too disconnected areas, but parameter estimates must be interpreted cautiously.     

Robust One-Way ANOVA under Possibly Non-Regular Conditions

Consider the one-way ANOVA problem of comparing the means m₁, m₂, …, m_c of c distributions F₁(x) = F(x — m₁), …, F_c(x) = F(x — m_c). Solutions are available based on (i) normal-theory procedures, (ii) linear rank statistics and (iii) M-estimators. The above model presupposes that F₁, F₂, …, F_c have equal variances (= homoscedasticity). However practising statisticans content that homoscedasticity is often violated in practice. Hence a more realistic problem to consider is F₁(x) = F((x — m₁)/σ₁), …, F_c(x) = F((x — m_c)/σ_c), where F is symmetric about the origin and σ₁, …, σ_c are unknown and possibly unequal (= heteroscedasticity). Now we have to compare m₁, m₂, …, m_c. At present, nonparametric tests of the equality of m₁, m₂, …, m_c are available. However, simultaneous tests for paired comparisons and contrasts and do not seem to be available. This paper begins by proposing a solution applicable to both the homoscedastic and the heteroscedastic situations, assuming F to be symmetric. Then the assumptions of symmetry and the identical shapes of F₁, …, F_c are progressively relaxed and solutions are proposed for these cases as well. The procedures are all based on either the 15% trimmed means or the sample medians, whose quantiles are estimated by means of the bootstrap. Monte Carlo studies show that these procedures tend to be superior to the Wilcoxon procedure and Dunnett's normal theory procedure. A rigorous justification of the bootstrap is also presented. The methodology is illustrated by a comparison of mean effects of cocaine administration in pregnant female Sprague-Dawley rats, where skewness and heteroscedascity are known to be present.     

EXPERIMENTAL MOLECULAR EVOLUTION OF BACTERIOPHAGE T7

We present an analysis of molecular evolution in a laboratory-generated phylogeny of the bacteriophage T7, a virus of 40 kilo-base pairs of double-stranded DNA. The known biology of T7 is used in concert with observed changes in restriction sites and in DNA sequences to produce a model of restriction-site convergence and divergence in the experimental lineages. During laboratory propagation in the presence of a mutagen, the phage lineages changed an estimated 0.5%-1.5% in base pairs; most change appears to have been G → A or C → T, presumably because of the mutagen employed. Some classes of restriction-site losses can be explained adequately as simple outcomes of random processes, given the mutation rate and the bias in mutation spectrum. However, some other classes of sites appear to have undergone accelerated rates of loss, as though the losses were selectively favored. Overall, the wealth of knowledge available for T7 biology contributes only modestly to these explanations of restriction-site evolution, but rates of restriction-site gains remain poorly explained, perhaps requiring an even deeper understanding of T7 genetics than was employed here. Having measured these properties of molecular evolution, we programmed computer simulations with the parameter estimates and pseudo-replicated the empirical study, thereby providing a data base for statistical evaluation of phylogeny reconstruction methods. By these criteria, replicates of the experimental phylogeny would be correctly reconstructed over 97% of the time for the three methods tested, but the methods differed significantly both in their ability to recover the correct topology and in their ability to predict branch lengths. More generally, the study illustrates how analyses of experimental evolution in bacteriophage can be exploited to reveal relationships between the basics of molecular evolution and abstract models of evolutionary processes.     

BOOTSTRAP CORRECTION FOR DIURNAL ACTIVITY CYCLE IN CENSUS DATA FOR ANTARCTIC SEALS1

Antarctic phocid seals and particularly the crabeater (Lobodon carcinophagus) have been observed to display a diurnal cycle in their propensity to haul out on pack ice where they are visible for census. The fact that they are not visible for much of the 24-h period means that density estimates made over broad geographic areas at various times of the day statistically confound this cycle with geographic variability. Limitation of census observations to times of peak haulout results in extreme logistical difficulties and/or considerable reduction in sample size upon which to base population estimates. Reduced sample size results in high variability in population estimates and broad confidence bands. To develop a model with which to correct density estimates for variability due to diurnal cycle, a series of stationary censuses at fixed locations in the Antarctic continental ice pack was made over significant fractions of several days. A unimodal polynomial model for the observed density variation in any one location was statistically significant; a similar model combining multiple locations with densities standardized to peak daily values was also significant. The latter model was used to make corrections for time of day to density estimates in three test data sets taken over broad geographic areas of the Antarctic. Statistical simulation (bootstrap) methods were used to determine if variances of corrected density estimates were lower than those based on uncorrected observations taken only during the peak haulout times of the day. Results were that 95% interval estimates for corrected densities were narrowed to between 40% and 61% of the uncorrected estimates. While there are additional possible sources of variation in haulout tendency, pending further data collection and analyses, the model developed represents a considerably more precise methodology than either averaging over haulout variability or limiting observations to peak daily periods.     

The genetics of adaptive shape shift in stickleback: pleiotropy and effect size

The distribution of effect sizes of genes underlying adaptation is unknown ( Orr 2005 ). Are suites of traits that diverged under natural selection controlled by a few pleiotropic genes of large effect (major genes model), by many independently acting genes of small effect (infinitesimal model), or by a combination, with frequency inversely related to effect size (geometric model)? To address this we carried out a quantitative trait loci (QTL) study of a suite of 54 position traits describing body shapes of two threespine stickleback species: an ancestral Pacific marine form and a highly derived benthic species inhabiting a geologically young lake. About half of the 26 detected QTL affected just one coordinate and had small net effects, but several genomic regions affected multiple aspects of shape and had large net effects. The distribution of effect sizes followed the gamma distribution, as predicted by the geometric model of adaptation when detection limits are taken into account. The sex‐determining chromosome region had the largest effect of any QTL. Ancestral sexual dimorphism was similar to the direction of divergence, and was largely eliminated during freshwater adaptation, suggesting that sex differences may provide variation upon which selection can act. Several shape QTL are linked to Eda, a major gene responsible for reduction of lateral body armor in freshwater. Our results are consistent with predictions of the geometric model of adaptation. Shape evolution in stickleback results from a few genes with large and possibly widespread effects and multiple genes of smaller effect.