Statistical assessment of population variability: a methodological approach

We have implemented a multivariate statistical methodology to assess the degree and pattern of cranial variability in skeletal samples. Specifically, the method is designed to test whether variability in a skeletal sample exceeds "normal within-group variability" defined in the present instance as variability present among crania from a cemetery associated with a village. It involves comparing a covariance matrix derived from a sample of unknown composition to one representing "normal within-group variability." The method has been applied to two Plains Indian craniometric samples. The Leavenworth site (39CO9) represents the remnants of previously autonomous Arikara Indian villages devastated by epidemic diseases in the late 1700s. The Bad River 2 Phase is an archaeological designation grouping together closely related sites in the Bad-Cheyenne region of South Dakota dating from 1740-1795 AD. We were able to show substantial heterogeneity among crania from Leavenworth. District burial areas at Leavenworth account for some of the heterogeneity, supporting the notion that they represent an attempt to maintain former social distinctions. We were unable to differentiate among sites within the Bad River 2 Phase, suggesting that it is a valid biological unit.     

Variability within the chemical analysis of horticultural substrates

Summary The variability within the chemical analysis of a horticultural substrate is described by the variance components, which are isolated in a hierarchical model, consisting of samples, analysts, subsamples and chemical determinations. It is shown that the samples contribute to the larger part of the total variability, although the variance component due to the analysts should not be neglected and differences between analysts are persistent. The increase of precision in function of the number of samples is shown.     

Comparison of four simple methods for estimating sexual dimorphism in fossils

Estimating sexual dimorphism in skeletal and dental features of fossil species is difficult when the sex of individuals cannot be reliably determined. Several different methods of estimating dimorphism in this situation have been suggested: extrapolation from coefficients of variation, division of a sample about the mean or median into two subsamples which are then treated as males and females, and finite mixture analysis (specifically for estimating the maximum dimorphism that could be present in a unimodal distribution). The accuracy of none of these methods has been thoroughly investigated and compared in a controlled manner. Such analysis is necessary because the accuracy of all methods is potentially affected by fluctuations in either sample size, sex ratio, or the magnitude of intrasexual variability. Computer modeling experiments show that the mean method is the least sensitive to fluctuations in these parameters and generally provides the best estimates of dimorphism. However, no method can accurately estimate low to moderate levels of dimorphism, particularly if intrasexual variability is high and sex ratios are skewed. © 1994 Wiley-Liss, Inc.     

Detection of Cryptosporidium oocysts in water: effect of the number of samples and analytic replicates on test results

Due to the small number of Cryptosporidium oocysts in water, the number of samples taken and the analyses performed can affect the results of detection. In this study, 42 water samples were collected from one watershed during 20 storm events over 1 year, including duplicate or quadruplicate samples from 16 storm events. Ten samples from four events had three to eight subsamples. They were processed by EPA method 1623, and Cryptosporidium oocysts present were detected by immunofluorescent microscopy or PCR. Altogether, 24 of 39 samples (47 of 67 samples and subsamples) analyzed by microscopy were positive for Cryptosporidium. In contrast, 36 of 42 samples (62 of 76 samples and subsamples) were positive by PCR, including 10 microscopy-negative samples (13 microscopy-negative samples and subsamples). Six of the 24 microscopy-positive samples were negative by PCR, and all samples had one or less oocyst in a 0.5-ml packed pellet volume calculated. Discordant results were obtained by microscopy and PCR from six and three of the storm events, respectively, with multiple samples. Discordant microscopy or PCR results were also obtained among subsamples. Most of the 14 Cryptosporidium genotypes were found over a brief period. Cryptosporidium-positive samples had a mean of 1.9 genotypes per sample, with 39 of the 62 positive samples/subsamples having more than one genotype. Samples/subsamples with more than one genotype had an overall PCR-positive rate of 73%, compared to 34% for those with one genotype. The PCR amplification rate of samples was affected by the volume of DNA used in PCR.     

Detection of Cryptosporidium Oocysts in Water: Effect of the Number of Samples and Analytic Replicates on Test Results

Due to the small number of Cryptosporidium oocysts in water, the number of samples taken and the analyses performed can affect the results of detection. In this study, 42 water samples were collected from one watershed during 20 storm events over 1 year, including duplicate or quadruplicate samples from 16 storm events. Ten samples from four events had three to eight subsamples. They were processed by EPA method 1623, and Cryptosporidium oocysts present were detected by immunofluorescent microscopy or PCR. Altogether, 24 of 39 samples (47 of 67 samples and subsamples) analyzed by microscopy were positive for Cryptosporidium. In contrast, 36 of 42 samples (62 of 76 samples and subsamples) were positive by PCR, including 10 microscopy-negative samples (13 microscopy-negative samples and subsamples). Six of the 24 microscopy-positive samples were negative by PCR, and all samples had one or less oocyst in a 0.5-ml packed pellet volume calculated. Discordant results were obtained by microscopy and PCR from six and three of the storm events, respectively, with multiple samples. Discordant microscopy or PCR results were also obtained among subsamples. Most of the 14 Cryptosporidium genotypes were found over a brief period. Cryptosporidium-positive samples had a mean of 1.9 genotypes per sample, with 39 of the 62 positive samples/subsamples having more than one genotype. Samples/subsamples with more than one genotype had an overall PCR-positive rate of 73%, compared to 34% for those with one genotype. The PCR amplification rate of samples was affected by the volume of DNA used in PCR.     

Hypoplastic area method for analyzing dental enamel hypoplasia

Most analyses of dental enamel hypoplasia compare frequencies of disturbed tooth types, which do not account for variability in the area of affected enamel. An alternate methodology, hypoplastic area, is presented here that accounts for this variability by combining acute and continuous enamel hypoplasia into an interval-level variable. The method compares samples based on individuals, by multiple tooth type variables, or by a single value rather than by tooth types. Use of the hypoplastic area method is illustrated by analyzing human skeletal dentitions in three archaeological samples: Meroitic Nubians from Semna South, Sudan; Anasazi from Navajo Reservoir, New Mexico; and Mogollon from Grasshopper Pueblo, Arizona. Both univariate and multivariate statistical tests are employed to assess variation in defects between individuals and samples. By incorporating measurements of continuous defects, the hypoplastic area method provides information beyond that of frequency data in comparing levels of stress. Flexibility of the method is also discussed. © 1995 Wiley-Liss, Inc.     

A method for subsampling unsorted benthic macroinvertebrates by weight

A simple method for subsampling unsorted benthic macroinvertebrates by weight is described for different types of samples obtained from lentic and lotic environments. It is especially useful for samples containing large amounts of filamentous algae that preclude the use of conventional subsampling methods. The method provided random dispersions of individuals in the original samples. Overall variability of the subsamples was low for artificial substrate and catastrophic drift samples. Variability was higher for regular drift samples, which had the lowest numbers of individuals of the three sample types. The method produced considerable savings in time spent sorting. Subsampling approaches for community level studies are discussed.     

‘Electronic subsampling’ of macrobenthic samples: how many individuals are needed for a valid assessment result?

We developed and tested an `electronic subsampling technique' with benthic invertebrate samples taken in three German stream types to investigate, how strongly the number of individuals analysed influences the results. For each of 152 samples (`reference samples') 100 subsamples of the sizes 100, 200, 300, 500 and 700 individuals were generated randomly. To evaluate subsample deviation from the reference sample 45 metrics were calculated. In general, the variability of metric results increases with decreasing subsample size. Individual metrics show different sensitivity to decreasing subsample size. Three of the metrics tested (German Saprobic Index, German Fauna Index and Ecological Quality Index using Macroinvertebrates) are part of the German AQEM assessment system, for which they are transferred into quality classes. More than 40% of the 100-individuals subsamples are classified into a different quality class compared to the reference samples, but less than 20% for 700-individual subsamples. A certainty >20% is obtained with a subsample size of 300 individuals in lowland streams, whereas 700 individuals are needed to achieve the same level of confidence in mountain streams. Metrics, which rely on absolute abundances or abundance classes (e.g. BMWP, number of taxa) show higher sensitivity to a changing number of individuals than metrics, which depend on relative abundances (e.g. [%] Lithal preferences, [%] of Gatherers/collectors). Thus, the reliability of the metrics is related to subsample size, stream type and metric type.     

Sampling bias in studies of dentoalveolar pathology in past human populations

Two subsamples of 30 subjects drawn from the same skeletal population (Monte d'Argento, Italy, Medieval age) were examined in a parallel blind study of dentoalveolar pathology, tooth wear and calculus, in order to assess the influence of sampling bias on dietary reconstruction. The effect of interobserver error was controlled and random subdivision was performed on a sample homogeneous for age and social condition. In spite of this, appreciable differences in the frequencies of some pathologies and, therefore, in dietary reconstruction were found, thus pointing to potential effectiveness of sampling bias in archaeological partial samples.     

Efficiency of scat-analysis lab procedures for bear dietary studies: The case of the Apennine brown bear

Bear food habits are often quantified using scat analysis, mainly due to its non-invasiveness and because samples are relatively easy to collect. However, lab processing time can be daunting and may end up competing with other field activities. Sub-sampling a bear scat to analyze its contents may reduce the lab processing time, but the number of subsamples per scat is usually chosen arbitrarily. We investigated the effect of the number of subsamples per bear scat on the estimatation of the diet composition of the Apennine brown bear in the Abruzzo Lazio and Molise National Park. Based on a sample of 328 bear scats collected in 2006, and from 5 to 1 subsamples (10 ml) per scat, dietary analysis showed qualitative and quantitative stability at a decreasing number of subsamples, and only food items of negligible importance were occasionally missed using 1–2 subsamples per scat. We concluded that 2 subsamples can be used without significant loss in accuracy, corresponding to a 60% reduction in lab time, and to more than 50 days of lab work for one operator to process our entire bear scat sample. By assessing the effect of sub-sampling a bear scat for dietary analysis, we also present preliminary data on the seasonal food habits of the Apennine brown bear population.     

Changes in articular eminence morphology with dental function

Measurements of mandibular fossa depth and slope of the articular eminence were obtained for human skeletal samples chosen to represent a wide spectrum of subsistence strategies and oral function: hunter-gatherers (Eskimos, Australians), American Indians dependent to a variable extent on maize agriculture, and early twentieth century American whites and blacks. In the Eskimo and Australian samples, a generalized and steady increase in fossa depth and slope was observed with increasing functional age (tooth wear) through wear level 5 (of 8), followed by a levelling off or slight decrease in fossa depth in later wear levels on the anterior teeth and a sharp decrease in fossa depth in later wear levels on the molars. Although much less consistent due in part to extensive and early molar loss, patterns of variation in the remaining samples were characterized overall by a decrease in fossa depth and slope with increasing wear, especially on the molars. Further, in those samples with high incidences of posterior tooth loss, fossa depth was routinely less and the eminence more gently sloped in subsamples having experienced molar loss than in subsamples retaining all their molars. These data provide evidence that the temporomandibular joint (TMJ) undergoes continuous morphological alteration throughout adult life, and that these alterations are probably mediated by dental function. Moreover, they suggest that differences in patterning of such alterations may exist among human groups with contrasting patterns of tooth use.     

A model of biocomplexity and its application to the analysis of some terrestrial and marsh eukaryotic microbial communities with an emphasis on amoeboid protists

Biocomplexity theory has become increasingly important in understanding ecosystem dynamics as we realize that the interactions among subunits in a multi-component system often produce elaborate states that are not easily explained in terms of the individual parts of the system. A Euclidean geometric model of biocomplexity is presented and illustrated using protistan communities. The model is based on three quantitative biotic dimensions (indices) for small subsamples (0.01 g) taken from each sample core of substratum: (1) richness of morphospecies expressed as mean count per 0.01 g, (2) spatial diversity of protists expressed as then umber of unique morphospecies (i.e. those occurring in only one of the 0.01-g subsamples and not in any of the other subsamples), and (3) patchiness (non-uniform aggregation) of the distribution of protists across the 0.01-g subsamples. These three indices are mapped into a three-dimensional Euclidean space model, and the position of each point and its geometric distance from the origin are used as a general index of biocomplexity. The usefulness of the model is illustrated by applying it to a range of terrestrial and marsh communities. Within the set of 15 samples examined in this study, the marsh rhizosphere samples are among the most complex.     

Dental pathology of prehistoric residents of Oregon

Dentitions of 208 prehistoric skeletal specimens from five geographic regions of Oregon were studied to describe their dental status. Comparisons were made of the incidence of specific pathologies among regions and between jaws. Maxillary premortem tooth losses were significantly higher than mandibular tooth loss. A relatively high caries incidence occurs in samples from the Willamette Valley and Klamath Basin, where plant foods were used aboriginally to a significant extent. A high frequency of abscesses was recorded in the Klamath Basin and the Lower Columbia River sample, which also showed the highest levels of attrition. Each of the five subsamples shows patterns of dental pathology consistent with former use of natural resources.     

Assessing intrasample variation: analysis of Rapa Nui (Easter Island) museum cranial collections example

Osteological studies both old and new have utilized various Polynesian cranial samples, individually or in combination, to assess the racial composition of prehistoric Polynesians as a group, with regards to other Pacific populations, or to represent the Polynesian peoples as a whole in various multivariate analyses of worldwide populations. However, few of these studies have assessed the degree of intrasample variation produced when data derived from skeletal samples from different Polynesian islands (populations) are pooled to represent "Polynesians" as a whole. A similar argument can be made when data derived from various museum skeletal samples of the same Polynesian population are pooled to produce a larger sample representing that particular Polynesian population (Murrill [1968] Cranial and postcranial skeletal remains from Easter Island; Minneapolis: University of Minnesota Press; Stefan [2002] Am. J. Phys. Anthropol. [Suppl.] 34:147). This study examined Easter Island crania curated at various museums in North America, South America, and Europe to assess whether significant differences exist among the museum collections of Rapa Nui (Easter Island) skeletal material. A NORM statistical program (Schafer and Olsen [1997] NORM, version 1.01; University Park: Pennsylvania State University) for multiple imputation of incomplete multivariate datasets was utilized to estimate missing data. A variance comparison method, which utilizes variance/covariance matrices derived from "hypothesis" and "baseline/reference" samples (Key and Jantz [1990] Hum. Evol. 5:457-469; Key and Jantz [1990] Am. J. Phys. Anthropol. 82:53-59) was used to compare the Rapa Nui museum samples. This method is designed to test whether variability in a "hypothesis" museum sample exceeds "normal within-group variability" represented by the "baseline/reference" sample. The method was applied to six Rapa Nui museum samples (AANMW, MNHN-KB, MNHN-NAE, NHM, MH, and AMNH). The results indicate that the museum "hypothesis," male and female samples, exhibited little intrasample variability from the "baseline/reference" sample (MAPSE), though the samples were collected at different times and by different individuals. These results show the ability of multiple imputation and variance comparison methodologies to predict missing variables while maintaining the inherent variance/covariance structure and to discriminate sample variation in artificially assembled samples.     

Skeletal morphology of two controversial Poecilosclerid genera (Porifera,Demospongiae):Discorhabdella andCrambe

The generaDiscorhabdella andCrambe are characterized by bearing uncommon spicule types, i.e. pseudoastrose acanthostyles and sphaeroclones, respectively. They have traditionally been considered to be unrelated taxa, but the present reexamination made evident that an important amount of skeletal features are shared by both. Some of these morphological features, such as the ornamentation on the point of the ectosomal subtylostyles, are reported for the first time. The study also revealed that a tuberose nature of the tyles of the main choanosomal megascleres could be a common ancestral condition in both genera. The morphology of the multi-toothed anchorate chelae showed a gradual transition across the species, suggesting that the morphological diversity in chelae was generated in these genera through a “palmate-anchorate-arcuate” evolutionary sequence. However, the forward or backward direction of this sequence remained unclear from the available evidence. Important levels of skeletal variability were found to affect many of the skeletal characters, especially in the genusCrambe. In some cases, this variability transgressed the limits theoretically defining a species, making evident that the traditional procedure just based on comparison of the skeletons becomes unreliable when tackling the taxonomy of these genera. Most of the skeletal variability seemed to correspond to genetic polymorphisms, except in the case ofC. acuata. In this taxon, the skeletal variability could be a result of the existence of a cryptic species, originated by a misconceived synonymy betweenC. acuata andC. chelastra. Besides the skeletal variability, the obscure taxonomic meaning of many skeletal features favored the existence of conflicting taxonomic proposals for the suprageneric location of these genera, depending on the author’s criteria. This study made evident that any subsequent attempt of phylogenetic inference should be based on an unweighted analysis of the available skeletal information.     

Temporal aspects of biological distance: serial correlation and trend in a prehistoric skeletal lineage

A number of previous studies have examined biological variability within individual human skeletal samples, using internal chronology as an explanatory source for variation. In this paper time series and matrix comparison methods are used to examine temporal serial correlation and trend of biological characteristics within a skeletal sample. These methods follow appropriately upon the assumption that the processes of genetic drift and migration lead to temporal autocorrelation of the mean genotype within individual genetic lineages. In the current analysis, using skeletal material from the Pete Klunk Mound Group, temporal serial correlation is demonstrated between samples from different mounds. This indicates that a previous provisional archaeological ordering of the mounds is probably correct. Absence of temporal trend for any of the nonmetric traits examined here suggests a lack of directional evolutionary forces operating on these traits.     

Log-linear analysis of dental caries occurrence in four skeletal series.

Four skeletal series (Corinth, Greece; Gran Quivira, New Mexico; Semna South, Sudanese Nubia, and a large group from scattered sites in England) were coded for sex, jaw, tooth group, dental attrition, dental caries, site and time period. Through thec concepts of a basal level of caries and a cariosity gradient, a single model was found which best described the occurrence of this disease in these samples. All factors were found to contribute significantly to the model. Within the possible subsamples the general characteristics are that the profiles of males, of the mandibulae and of those with light attrition are more likely to have lower overall dental caries levels and to be relatively more carious in the back of the mouth than the front when compared to the pooled sample of all teeth and caries. The opposite is also found to be generally true; the teeth of females, maxillae and heavy attrition are associated with more caries, especially toward the front of the mouth. These results imply that samples appearing otherwise homogeneous display much variation. They also reveal distinct regularities in the reactions of diverse human groups to dental caries.     

L'ipotesi dell'effetto del campo geomagnetico e la variabilità tra le ripetizioni in prove di germinazione ed accrescimento in Triticum

Abstract

The geomagnetic field effect hypothesis and the variability among replications in germination and growth tests in Triticum. – During previous eperiments on germination and growth of Triticum, we have often found many cases of heteroscedasticity and of statistically significant differences among contemporary replications (i.e. germinators). In such experiments all the caryopses were oriented in the same way inside the germinators, whilst the germinators were randomly set inside the thermostats: therefore the seeds of different germinators might result differently oriented. Some researchers report that seeds differently oriented according to the lines of force of the geomagnetic field, may respond with different germination, growth rates and growth directions of shoots and roots (magnetotropism). The present investigation was designed to ascertain if these effects might be responsible of the variability among the contemporary replications. The different caryopses orientation within laboratory geomagnetic field, does not give evidence of any effect on germination, growth rate and direction. The caryopses show no germination sensibility neither related to different age, light and temperature conditions, neither to different cultivars, neither to varying orientation from the geomagnetic North every 15° and to varying time of ? preorientation ? in dry conditions. Differences between the variability of randomly and North oriented subsamples are not observed. No statistically significant differences are observed among shoots and roots lenghts of seedlings from differently oriented caryopses neither in different environmental conditions, nor as function of the orientation (24 angles of 15°), nor after different preorientations, nor after repeating the test on 608 subsamples (12.000 seedlings). Therefore the variability among contemporary replications is not imputable to the geomagnetic field. The variability and the distributions structure analysis suggest that both the heteroscedasticity and the significant differences among the replications may be due to an interaction among the caryopses inside the germinators through the substrate. This is probably related to the cultivar characteristics. We emphasize that an accurate evaluation of the variability is particularly necessary in germination and growth tests.     

Validation of Bioelectrical Impedance Analysis in Adolescents Across Different Ethnic Groups

Adolescent obesity is difficult to assess in multi‐ethnic populations using BMI, due to variability in the BMI–fatness relationship. We aimed to describe body composition (BC), and to validate leg–leg bioelectrical impedance analysis (BIA), in adolescents from different ethnic groups using deuterium (D₂O) as the reference method. Measurements were made of weight, height, total body water (TBW), and BIA (TANITA TBF‐300) in 110 white, 170 Asian, and 102 black adolescents aged 11–15 years. TBW was converted to lean mass (LM) using assumed hydration of lean tissue. General linear models were used to compare BC by D₂O between the ethnic groups. BC values from D₂O were compared with TANITA values, and used to generate ethnic‐specific prediction equations in the whole sample, and also in equation‐generation (group 1) and cross‐validation (group 2) subsamples. Ethnic variability in BMI did not reflect variability in adiposity. Asians had less LM than white and black adolescents, and less fat mass (FM) than white girls. TANITA in‐built equations did not predict BC accurately across ethnic groups, with significant bias in white and Asian males, and Asian and black females. The new equation generated from the entire sample removes ethnic‐specific mean biases. The group 1 equation showed no significant bias in any ethnic group when tested in group 2. We found significant variability in BC between ethnic groups that was not reflected by BMI. Manufacturers' equations are unsuitable for predicting BC in multi‐ethnic populations, and our new equations are recommended.     

Improved protocol for isolation of Campylobacter spp. from retail broiler meat and use of pulsed field gel electrophoresis for the typing of isolates

To improve the detection of Campylobacter spp. in retail broiler meat, a reference method (R subsamples) based on the enrichment of 25 g of meat in Bolton broth at 42 °C under microaerobiosis was compared with an alternative method (A subsamples) consisting in the rinsing of meat samples for 30 s in buffered peptone water with antimicrobials with incubation at 42 °C under aerobiosis. One piece of meat (breasts, tenderloins and thighs) was rinse in experiment 1 (A1) and two pieces in experiment 2 (A2). Campylobacter spp. were isolated on agar plates and identified by PCR. Retail samples in Alabama had less prevalence (P ≤ 0.05) than samples in the state of Washington. The percentage of positive was higher (P ≤ 0.05) in A than in R subsamples and rinsing two pieces of meat yielded the highest percentage of positive subsamples. R subsamples showed variations in the prevalence by product. However, A subsamples had similar prevalence of positives among products compare to the result from reference method. More Campylobacter coli isolates were collected in A2 subsamples. Pulse field gel electrophoresis (PFGE) was used as subtyping method to study the genome similarity among the isolates from all methods. A larger diversity of isolates were detected by PFGE in A2 subsamples. Denaturing gradient gel electrophoresis analysis suggested that the initial bacterial populations of the meat samples impact the final bacterial profile after enrichment. Rinsing broiler meats was less time consuming, required less sample preparation and was more sensitive than the reference method for the isolation of naturally occurring Campylobacter spp. This new method could help with epidemiological and intervention studies to control Campylobacter spp.