Sample size in the monitoring of benthic macrofauna in the profundal of lakes: evaluation of the precision of estimates

We discuss here the influence of sample size (number of replicates) on the accuracy and precision of the results when sampling profundal benthos with an Ekman grab according to the Finnish standard, SFS 5076, which is equivalent to the Swedish and Norwegian standards. The aim was to find criteria for choosing a sample size which would avoid any powerful influence of chance on the results without entailing an unreasonable amount of work for monitoring purposes.Lake Haukivesi (area 620 km², total phosphorus 13 µg l^–1 and colour 35 Pt mg l^–1), Lake Paasivesi (116 km², 5 µg l^–1 and 35 Pt mg l^–1) and Lake Puruvesi (322 km², 4 µg l^–1 and 5 Pt mg l^–1) were sampled randomly in June and October 1991. 25 Replicate samples were taken on each occasion from the deep profundal area of each lake, defined here as 60-100% of the maximum depth. The sedimentation areas studied were fairly homogeneous, since the animal communities were not markedly affected by the variations in depth. Distribution estimates for the statistics studied, such as number of individuals, expected number of species, diversity and benthic quality indices, were calculated for a large set of random samples taken from the empirical data by computer (bootstrap sampling). The sample variance, s ², correlated with the mean animal density, m (ind. m^–2), according to the equation s ² = 31.77 m ^1.247. The sample size required to achieve the desired precision in mean animal density (D, expressed as the ratio standard error/mean) can thus be estimated as n = 31.77 m ^–0.753 D ^–2. The number of replicate samples needed to achieve a standard error of 20% of the mean density was 10 in Lake Haukivesi, seven in Lake Paasivesi and 11 in Lake Puruvesi. The accuracy and precision of the estimated number of species, Shannon's diversity and Benthic Quality Index improved markedly as the sample size was increased to 10 replicates. As a compromise between work load and statistical reliability, a figure of 10 replicate Ekman samples is proposed here for the monitoring of profundal benthos. The proposed sample size usually produces individual numbers which are high enough for practical purposes, probably at least 100 individuals, which is recommended as a minimum in the standard. The lower number of replicate samples recommended in recent Finnish handbook, 3–5, usually produces inadequate data, and this may detract from the comparability of the results and leave the changes in profundal communities undetected.     

Pitfalls of hypothesis tests and model selection on bootstrap samples: Causes and consequences in biometrical applications

The bootstrap method has become a widely used tool applied in diverse areas where results based on asymptotic theory are scarce. It can be applied, for example, for assessing the variance of a statistic, a quantile of interest or for significance testing by resampling from the null hypothesis. Recently, some approaches have been proposed in the biometrical field where hypothesis testing or model selection is performed on a bootstrap sample as if it were the original sample. P‐values computed from bootstrap samples have been used, for example, in the statistics and bioinformatics literature for ranking genes with respect to their differential expression, for estimating the variability of p‐values and for model stability investigations. Procedures which make use of bootstrapped information criteria are often applied in model stability investigations and model averaging approaches as well as when estimating the error of model selection procedures which involve tuning parameters. From the literature, however, there is evidence that p‐values and model selection criteria evaluated on bootstrap data sets do not represent what would be obtained on the original data or new data drawn from the overall population. We explain the reasons for this and, through the use of a real data set and simulations, we assess the practical impact on procedures relevant to biometrical applications in cases where it has not yet been studied. Moreover, we investigate the behavior of subsampling (i.e., drawing from a data set without replacement) as a potential alternative solution to the bootstrap for these procedures.     

Multivariate allometry of the robust australopithecine zygomatic foramen: Bootstrap approach to confidence limits

The oddly rounded and disproportionate temporal fossa (or zygomatic foramen) in hyper-robust australopithecine fossils has elicited comment. Is this feature a scaled, positively-allometric version of hominoid anatomy in general or a unique adaptation? Multivariate allometry employing log principal component analysis is directed at the question, but confidence limits of the sampling error associated with these estimates are either dependent upon questionable multivariate theory or else unattainable by theory. The bootstrap method is therefore employed to estimate these aspects of dispersion. The size and shape of the hyper-robust australopithecine zygomatic foramen cannot be explained by simple extrapolation of primate interspecific allometries; although the positively and negatively allometric aspects of scaling are similar, the actual coefficients of scaling are significantly larger in the crucial variable in the australopithecines.     

Quantifying uncertainty in molecular dynamics simulations of grain boundary migration

Molecular dynamics simulations of simple bicrystal systems have been much used as a tool to explore how the migration of grain boundaries varies with their structure and with experimental conditions. In order to permit the exploration of a large parameter space, many studies are forced to rely on a small number of simulations (often a single simulation) for each configuration. The motion of a grain boundary is inherently statistical and any variability in the measured grain boundary velocity should be taken into account in subsequent analysis of trends in grain boundary mobility. Here we present the results of large numbers of simulations of equivalent boundaries, which show that this variability can be large, particularly when small systems are simulated. We show how a bootstrap resampling approach can be used to characterise the statistical uncertainty in boundary velocity using the information present in a single simulation. We show that the approach is robust across a variety of system sizes, temperatures and driving force strengths and types, and provides a good order-of-magnitude measure of the population standard deviation across multiple equivalent simulations.     

Biogeographical boundaries and Monmonier's algorithm: a case study in the northern Neotropics

Aim  To use Monmonier's algorithm, a spatially explicit technique, to elucidate positions of biogeographical boundaries in the northern Neotropics.
Location  The northern Neotropics (Isthmus of Tehuantepec, Mexico, south to trans-Andean Colombia).
Methods  We compiled avifaunal lists for 36 forested sites from the literature, museum records, field notes, and web sources. We constructed distance matrices as inverse Jaccard's similarity, used Monmonier's algorithm to place biogeographical boundaries, and created bootstrap matrices to determine the relative strength of boundaries.
Results  Biogeographical boundaries with the best support separated lowland (< 1000 m) and montane sites and areas with a distinct historical background, such as seaways, suture zones, volcanic peaks, and former islands.
Main conclusions  Monmonier's algorithm used with distance (dissimilarity) data effectively identified biogeographical boundaries consistent with historical processes and with past research. Montane sites tended to be circumscribed by sharp boundaries, emphasizing their isolation and higher endemism. Lowland sites, by contrast, tended to be homogeneous, suggesting that dispersal has played a much larger role at low elevations. Former seaways, as in the Nicaraguan Depression and extended Bay of Urabá, yielded boundaries, but typically for highland avifauna only. In addition to providing a rigorous (bootstrap support) and heuristic (direct mapping) means of locating biotic boundaries, Monmonier's algorithm can be a valuable tool for conservation planning.     

Aphanomyces astaci mtDNA: insights into the pathogen’s differentiation and its genetic diversity from other closely related oomycetes

The causative agent of crayfish plague, Aphanomyces astaci (Saprolegniales, Oomycota), is one of the 100 world’s worst invasive alien species and represents a major threat to freshwater crayfish species worldwide. A better understanding of the biology and epidemiology of A. astaci relies on the application of efficient tools to detect the pathogen and assess its genetic diversity. In this study, we validated the specificity of two recently developed PCR-based approaches used to detect A. astaci groups. The first relies on the analysis of mitochondrial ribosomal rnnS (small) and rnnL (large) subunit sequences and the second, of sequences obtained by using genotype-specific primers designed from A. astaci whole genome sequencing. For this purpose, we tested the specificity against 76 selected isolates, including other oomycete species and the recently described species Aphanomyces fennicus, which, when used in nrITS-based specific tests for A. astaci, is known to result in a false positive. Under both approaches, we were able to efficiently and accurately identify A. astaci and its genetic groups in both pure cultures and clinical samples. We report that sequence analysis of the rnnS region alone is sufficient for the identification of A. astaci and a partial characterization of haplogroups. In contrast, the rnnL region alone is not sufficiently informative for A. astaci identification as other oomycete species present sequences identical to those of A. astaci.     

Crockett's Test of Fit for the Bivariate Poisson

An improved version of the test of CROCKETT (1979) for testing for the bivariate Poisson distribution is given and evaluated.     

Inference on Risk Rates Based on Mortality Data Under Censoring and Competing Risks Using Parametric Models

In this paper we consider the competing risks model where the risks may not be independent. We assume both fixed and random censoring. The random censoring mechanism could have either a parametric or a non-parametric form. The life distributions and the parametric censoring distribution considered are exponential or Weibull. The expressions for the asymptotic confidence intervals for various parameters of interest under different models, using the estimated Fisher information matrix and parametric bootstrap techniques have been derived. Monte Carlo simulation studies for some of these cases have been carried out.     

Intercalibration of hydroacoustic and mark–recapture methods for assessing the spawning population size of a threatened fish species

Hydroacoustic counting and a three-year mark–recapture study with passive integrated transponders (PIT tags) were used to estimate the size of a spawning population of nase Chondrostoma nasus , a threatened potamodromous cyprinid that undertakes annual spawning migrations into a tributary of the Danube River. In 2005, the estimates of the size of the spawning population from the hydroacoustic counts ( N = 2234, 95% CL 1929–2538) and from the Jolly–Seber model ( N = 1198, 95% CL 461–5842) corresponded well. Estimates from the jackknife-estimator based on the hydroacoustic counts yielded slightly higher values ( N = 2783, 95% CL 2529–3037), but were still in the same order of magnitude as those from the hydroacoustic and mark–recapture approach. At low run-size, hydroacoustic counting was more time consuming and technically demanding than mark–recapture studies. At the same time, it was non-invasive, provided real-time data on a fine temporal scale, and estimates showed less variability than the Jolly–Seber model. Mark–recapture of fish in spawning streams involved substantial disturbance at a sensitive stage of the life cycle. Hence, hydroacoustics is highly suited for population estimates of threatened potamodromous fishes, where interference needs to be minimized.