A statistical analysis of subsampling and an evaluation of the Folsom plankton splitter

Subsampling techniques are important for the determination of precise plankton density estimates. A binomial model of random subsampling, and its Poisson extension, were developed for the purpose of evaluating the performance of compartment-type plankton subsamplers. Two approaches were used to assess the performance of the Folsom plankton splitter on an extensive series of nearshore Lake Michigan crustacean zooplankton samples collected between 1974 and 1979. First, Folsom subsamples were observed to be significantly (p < 0.05) more variable than expected from the random model of subsampling. Second, a random effects ANOVA model was used to compare fractions of the total variance in density estimates that were attributable to subsampling and sampling phases of a specially designed study. Departures from randomness in subsampling were sufficiently small that an analysis of optimal allocation of effort between subsampling and sampling phases, based on the ANOVA model, indicated that only one to three subsamples needed to be examined per sample.     

Using Fecal DNA and Closed-Capture Models to Estimate Feral Horse Population Size

Accurate population estimates provide the foundation for managing feral horses (Equus caballus ferus) across the western United States. Certain feral horse populations are protected by the Wild and Free-Roaming Horses and Burros Act of 1971 and managed by the Bureau of Land Management (BLM) or the United States Forest Service on designated herd management areas (HMAs) or wild horse territories, respectively. Horses are managed to achieve an appropriate management level (AML), which represents the number of horses determined by BLM to contribute to a thriving natural ecological balance and avoid deterioration of the range. To achieve AML for each HMA, BLM resource managers need accurate and precise population estimates. We tested the use of non-invasive fecal samples in a genetic capture-recapture framework to estimate population size in a closed horse population at the Little Book Cliffs HMA, Colorado, USA, with a known size of 153 individuals. We collected 1,957 samples over 3 independent sampling periods in 2014 and amplified them at 8 microsatellite loci. We applied mark-recapture models to determine population size using 954 samples that amplified at all 8 loci. We subsampled and reanalyzed our dataset to simulate different data collection protocols and evaluated effects on accuracy and precision of estimates using N-mixture modeling, full likelihood closed-capture modeling, and capwire single-occasion modeling that used data from all 3 sampling periods. Our model results were accurate and precise for analyses that used data from all 3 occasions; however, capwire single-occasion modeling was not accurate when we analyzed each sampling period separately. For all subsampling analysis scenarios, reducing sample size decreased precision, whether by reducing number of field staff, field days, or geographic areas surveyed on each period. Reducing spatial coverage of the survey area did not result in accurate population estimates and only marginally lowered the number of samples that would need to be collected to maintain accuracy. Because laboratory analysis contributes the greatest expense for this method ($80 U.S./sample), reducing fecal sample size is advantageous. Our results demonstrate that non-invasive sampling combined with good survey design and careful genetic and capture-recapture analyses can provide an alternative method to estimate the number of feral horses in a closed population. This method may be especially appropriate in situations where aerial inventories are not practical or accurate because of low sighting conditions. But the higher costs associated with laboratory sample analyses may reduce the method's feasibility compared to helicopter surveys. © 2021 The Wildlife Society. This article has been contributed to by US Government employees and their work is in the public domain in the USA.     

Estimating processing time of stream benthic samples

Multiple regression analysis was used to generate equations relating time required to sort and tabulate benthic invertebrates to size characteristics of benthic samples collected from a 5th-order river and a 3rd-order woodland stream. Number of invertebrates in a sample was the primary determinant of sample sorting time. Amount of detritus, occurrence of filamentous algae (Cladophora) and source stream contributed significant but minor additional variability to estimates (cumulativeR ² = 0.95). When number of animals was excluded as a variable, amount of detritus and presence/absence ofCladophora alone could be used to predict sorting time (R ² = 0.81). A typical sample containingCladophora required 29% longer to sort than samples containing equivalent amounts of organic material but noCladophora. The influence of sampler size and subsampling on processing and sorting time are considered. A general equation was derived to provide guidelines for selecting a size of stream sampler that subsequently minimizes total processing time required to estimate density of benthos with acceptable, constant precision. Overall sample processing and sorting time are reduced by using a smaller sampler or by subsampling only if benthic densities of animals are high. Use of regression equations to anticipate processing and sorting time required for a particular sampling program permits development of more efficient designs.     

The Influence of Mark-Recapture Sampling Effort on Estimates of Rock Lobster Survival

Five annual capture-mark-recapture surveys on Jasus edwardsii were used to evaluate the effect of sample size and fishing effort on the precision of estimated survival probability. Datasets of different numbers of individual lobsters (ranging from 200 to 1,000 lobsters) were created by random subsampling from each annual survey. This process of random subsampling was also used to create 12 datasets of different levels of effort based on three levels of the number of traps (15, 30 and 50 traps per day) and four levels of the number of sampling-days (2, 4, 6 and 7 days). The most parsimonious Cormack-Jolly-Seber (CJS) model for estimating survival probability shifted from a constant model towards sex-dependent models with increasing sample size and effort. A sample of 500 lobsters or 50 traps used on four consecutive sampling-days was required for obtaining precise survival estimations for males and females, separately. Reduced sampling effort of 30 traps over four sampling days was sufficient if a survival estimate for both sexes combined was sufficient for management of the fishery.     

When can noninvasive samples provide sufficient information in conservation genetics studies?

Noninvasive sampling, of faeces and hair for example, has enabled many genetic studies of wildlife populations. However, two prevailing problems common to these studies are small sample sizes and high genotyping errors. The first problem stems from the difficulty in collecting noninvasive samples, particularly from populations of rare or elusive species, and the second is caused by the low quantity and quality of DNA extracted from a noninvasive sample. A common question is therefore whether noninvasive sampling provides sufficient information for the analyses commonly conducted in conservation genetics studies. Here, we conducted a simulation study to investigate the effect of small sample sizes and genotyping errors on the precision and accuracy of the most commonly estimated genetic parameters. Our results indicate that small sample sizes cause little bias in measures of expected heterozygosity, pairwise F_ST and population structure, but a large downward bias in estimates of allelic diversity. Allelic dropouts and false alleles had a much smaller effect than missing data, which effectively reduces sample size further. Overall, reasonable estimates of genetic variation and population subdivision are obtainable from noninvasive samples as long as error rates are kept below a frequency of 0.2. Similarly, unbiased estimates of population clustering can be made with genotyping error rates below 0.5 when the populations are highly differentiated. These results provide a useful guide for researchers faced with studying the conservation genetics of small, endangered populations from noninvasive samples.     

A computer simulation study on the number of loci and trees required to estimate genetic variability in cacao (Theobroma cacao L.)

Current methods for measures of genetic diversity of populations and germplasm collections are often based on statistics calculated from molecular markers. The objective of this study was to investigate the precision and accuracy of the most common estimators of genetic variability and population structure, as calculated from simple sequence repeat (SSR) marker data from cacao (Theobroma cacao L.). Computer simulated genomes of replicate populations were generated from initial allele frequencies estimated using SSR data from cacao accessions in a collection. The simulated genomes consisted of ten linkage groups of 100 cM in length each. Heterozygosity, gene diversity and the F statistics were studied as a function of number of loci and trees sampled. The results showed that relatively small random samples of trees were needed to achieve consistency in the observed estimations. In contrast, very large random samples of loci per linkage group were required to enable reliable inferences on the whole genome. Precision of estimates was increased by more than 50% with an increase in sample size from one to five loci per linkage group or 50 per genome, and up to 70% with ten loci per linkage group, or equivalently, 100 loci per genome. The use of fewer, highly polymorphic loci to analyze genetic variability led to estimates with substantially smaller variance but with an upward bias. Nevertheless, the relative differences of estimates among populations were generally consistent for the different levels of polymorphism considered.     

Phanerozoic marine diversity: rock record modelling provides an independent test of large-scale trends

Sampling bias created by a heterogeneous rock record can seriously distort estimates of marine diversity and makes a direct reading of the fossil record unreliable. Here we compare two independent estimates of Phanerozoic marine diversity that explicitly take account of variation in sampling—a subsampling approach that standardizes for differences in fossil collection intensity, and a rock area modelling approach that takes account of differences in rock availability. Using the fossil records of North America and Western Europe, we demonstrate that a modelling approach applied to the combined data produces results that are significantly correlated with those derived from subsampling. This concordance between independent approaches argues strongly for the reality of the large-scale trends in diversity we identify from both approaches.     

Phylogenomic Subsampling and the Search for Phylogenetically Reliable Loci

Phylogenomic subsampling is a procedure by which small sets of loci are selected from large genome-scale data sets and used for phylogenetic inference. This step is often motivated by either computational limitations associated with the use of complex inference methods or as a means of testing the robustness of phylogenetic results by discarding loci that are deemed potentially misleading. Although many alternative methods of phylogenomic subsampling have been proposed, little effort has gone into comparing their behavior across different data sets. Here, I calculate multiple gene properties for a range of phylogenomic data sets spanning animal, fungal, and plant clades, uncovering a remarkable predictability in their patterns of covariance. I also show how these patterns provide a means for ordering loci by both their rate of evolution and their relative phylogenetic usefulness. This method of retrieving phylogenetically useful loci is found to be among the top performing when compared with alternative subsampling protocols. Relatively common approaches such as minimizing potential sources of systematic bias or increasing the clock-likeness of the data are found to fare worse than selecting loci at random. Likewise, the general utility of rate-based subsampling is found to be limited: loci evolving at both low and high rates are among the least effective, and even those evolving at optimal rates can still widely differ in usefulness. This study shows that many common subsampling approaches introduce unintended effects in off-target gene properties and proposes an alternative multivariate method that simultaneously optimizes phylogenetic signal while controlling for known sources of bias.     

An empirical exploration of data quality in DNA-based population inventories

I present data from 21 population inventory studies - 20 of them on bears - that relied on the noninvasive collection of hair, and review the methods that were used to prevent genetic errors in these studies. These methods were designed to simultaneously minimize errors (which can bias estimates of abundance) and per-sample analysis effort (which can reduce the precision of estimates by limiting sample size). A variety of approaches were used to probe the reliability of the empirical data, producing a mean, per-study estimate of no more than one undetected error in either direction (too few or too many individuals identified in the laboratory). For the type of samples considered here (plucked hair samples), the gain or loss of individuals in the laboratory can be reduced to a level that is inconsequential relative to the more universal sources of bias and imprecision that can affect mark-recapture studies, assuming that marker systems are selected according to stated guidelines, marginal samples are excluded at an early stage, similar pairs of genotypes are scrutinized, and laboratory work is performed with skill and care.     

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.     

Use of resampling to assess optimal subgroup composition for estimating genetic parameters from progeny trials

Estimations of genetic parameters of wood traits based on reduced sample populations are widely reported in the literature, but few investigations have considered the consequences of these small populations on the precision of parameter estimates. The purpose of this study was to determine an optimal strategy for sampling subgroups, by varying either the number of families or the number of individuals (trees) per family, and by verifying the accuracy of certain genetic parameters (across-trials analysis). To achieve this, simulations were conducted using random resampling without replacement (k?=?1,000/pair of varying factors) on datasets containing 10-year total height of two coniferous species (Larix laricina and Picea mariana), as well as pilodyn measurements of wood density evaluated on a 26-year-old population of P. mariana. SAS® 9.2 Macro Language and Procedures were used to estimate confidence intervals of several genetic parameters with different reduced samplings. Simulation results show that reducing the number of trees per family per site had more impact on the magnitude and precision of genetic parameter estimates than reducing the number of families, especially for half-sib heritability and type B genetic correlations for height and wood density. A priori determination of an optimal subsampling strategy to evaluate the accuracy of genetic parameters should become common practice before assessing wood traits, in tree breeding studies or when planning juvenile retrospective progeny trials for forest tree species.     

Eliminating autocorrelation reduces biological relevance of home range estimates

1. Destructive subsampling or restrictive sampling are often standard procedures to obtain independence of spatial observations in home range analyses. We examined whether home range estimators based upon kernel densities require serial independence of observations, by using a Monte Carlo simulation, antler flies and snapping turtles as models.
2. Home range size, time partitioning and total straight line distances travelled were tested to determine if subsampling improved kernel performance and estimation of home range parameters.
3. The accuracy and precision of home range estimates from the simulated data set improved at shorter time intervals despite the increase in autocorrelation among the observations.
4. Subsampling did not reduce autocorrelation among locational observations of snapping turtles or antler flies, and home range size, time partitioning and total distance travelled were better represented by autocorrelated observations.
5. We found that kernel densities do not require serial independence of observations when estimating home range, and we recommend that researchers maximize the number of observations using constant time intervals to increase the accuracy and precision of their estimates.     

Evolutionary Relationship of DNA Sequences in Finite Populations

With the aim of analyzing and interpreting data on DNA polymorphism obtained by DNA sequencing or restriction enzyme technique, a mathematical theory on the expected evolutionary relationship among DNA sequences (nucleons) sampled is developed under the assumption that the evolutionary change of nucleons is determined solely by mutation and random genetic drift. The statistical property of the number of nucleotide differences between randomly chosen nucleons and that of heterozygosity or nucleon diversity is investigated using this theory. These studies indicate that the estimates of the average number of nucleotide differences and nucleon diversity have a large variance, and a large part of this variance is due to stochastic factors. Therefore, increasing sample size does not help reduce the variance significantly. The distribution of sample allele (nucleomorph) frequencies is also studied, and it is shown that a small number of samples are sufficient in order to know the distribution pattern.     

The Discovery of Single-Nucleotide Polymorphisms—and Inferences about Human Demographic History

A method of historical inference that accounts for ascertainment bias is developed and applied to single-nucleotide polymorphism (SNP) data in humans. The data consist of 84 short fragments of the genome that were selected, from three recent SNP surveys, to contain at least two polymorphisms in their respective ascertainment samples and that were then fully resequenced in 47 globally distributed individuals. Ascertainment bias is the deviation, from what would be observed in a random sample, caused either by discovery of polymorphisms in small samples or by locus selection based on levels or patterns of polymorphism. The three SNP surveys from which the present data were derived differ both in their protocols for ascertainment and in the size of the samples used for discovery. We implemented a Monte Carlo maximum-likelihood method to fit a subdivided-population model that includes a possible change in effective size at some time in the past. Incorrectly assuming that ascertainment bias does not exist causes errors in inference, affecting both estimates of migration rates and historical changes in size. Migration rates are overestimated when ascertainment bias is ignored. However, the direction of error in inferences about changes in effective population size (whether the population is inferred to be shrinking or growing) depends on whether either the numbers of SNPs per fragment or the SNP-allele frequencies are analyzed. We use the abbreviation "SDL," for "SNP-discovered locus," in recognition of the genomic-discovery context of SNPs. When ascertainment bias is modeled fully, both the number of SNPs per SDL and their allele frequencies support a scenario of growth in effective size in the context of a subdivided population. If subdivision is ignored, however, the hypothesis of constant effective population size cannot be rejected. An important conclusion of this work is that, in demographic or other studies, SNP data are useful only to the extent that their ascertainment can be modeled.     

Subsampling Hair Samples Affects Accuracy and Precision of DNA-Based Population Estimates

ABSTRACT Variance in population estimates is affected by the number of samples that are chosen to genotype when multiple samples are available during a sampling period. Using genetic data obtained from noninvasive hair-snags used to sample black bears (Ursus americanus) in the Northern Lower Peninsula of Michigan, USA, we developed a bootstrapping simulation to determine how precision of population estimates varied based on the number of samples genotyped. Improvements in precision of population estimates were not monotonic over all samples sizes available for genotyping. Estimates of cost, both financially and in terms of bias associated with increasing genotyping error and benefits in terms of greater estimate precision, will vary by species and field conditions and should be determined empirically.     

Inference of the distribution of fitness effects of mutations is affected by single nucleotide polymorphism filtering methods,sample size and population structure

The distribution of fitness effects (DFE) of new mutations has been of interest to evolutionary biologists since the concept of mutations arose. Modern population genomic data enable us to quantify the DFE empirically, but few studies have examined how data processing, sample size and cryptic population structure might affect the accuracy of DFE inference. We used simulated and empirical data (from Arabidopsis lyrata) to show the effects of missing data filtering, sample size, number of single nucleotide polymorphisms (SNPs) and population structure on the accuracy and variance of DFE estimates. Our analyses focus on three filtering methods—downsampling, imputation and subsampling—with sample sizes of 4–100 individuals. We show that (1) the choice of missing-data treatment directly affects the estimated DFE, with downsampling performing better than imputation and subsampling; (2) the estimated DFE is less reliable in small samples (<8 individuals), and becomes unpredictable with too few SNPs (<5000, the sum of 0- and 4-fold SNPs); and (3) population structure may skew the inferred DFE towards more strongly deleterious mutations. We suggest that future studies should consider downsampling for small data sets, and use samples larger than 4 (ideally larger than 8) individuals, with more than 5000 SNPs in order to improve the robustness of DFE inference and enable comparative analyses.     

An evaluation of the methods to estimate effective population size from measures of linkage disequilibrium

In 1971, John Sved derived an approximate relationship between linkage disequilibrium (LD) and effective population size for an ideal finite population. This seminal work was extended by Sved and Feldman (Theor Pop Biol 4, 129, 1973) and Weir and Hill (Genetics 95, 477, 1980) who derived additional equations with the same purpose. These equations yield useful estimates of effective population size, as they require a single sample in time. As these estimates of effective population size are now commonly used on a variety of genomic data, from arrays of single nucleotide polymorphisms to whole genome data, some authors have investigated their bias through simulation studies and proposed corrections for different mating systems. However, the cause of the bias remains elusive. Here, we show the problems of using LD as a statistical measure and, analogously, the problems in estimating effective population size from such measure. For that purpose, we compare three commonly used approaches with a transition probability‐based method that we develop here. It provides an exact computation of LD. We show here that the bias in the estimates of LD and effective population size are partly due to low‐frequency markers, tightly linked markers or to a small total number of crossovers per generation. These biases, however, do not decrease when increasing sample size or using unlinked markers. Our results show the issues of such measures of effective population based on LD and suggest which of the method here studied should be used in empirical studies as well as the optimal distance between markers for such estimates.     

A comparative study of four dredges used for sampling benthic macroinvertebrates in rivers

SUMMARY. After considering the large number of dredges described in the literature, four light-weight dredges were chosen for manual operation from a small boat or the bank: Irish triangular dredge, small Fast dredge, medium-sized and large Naturalist's dredges. The dredges were tested in a series of trials at three sites in two rivers. A stratified random sample (number of sampling units, n = 5) was taken at each site and the modal particle sizes at sites 1–3 were 1–2 mm (fine gravel), 64–128 mm (larger stones) and 128–256 mm, respectively. The dredges usually took a similar range of stone sizes at each site but the design of the Fast dredge excluded larger stones (>16 mm). The Irish dredge sometimes failed to operate correctly. Variations in the volume of substrata taken with each dredge were large, both between sampling units in the same sample and between samples. The latter differences were partially due to the increase in the modal size of the stones, especially between sites 1 and 2, the different sampling areas of the dredges and the depth of penetration into the substratum. Penetration depth was probably greatest for the two Naturalist's dredges, smaller for the Fast dredge and smallest for the Irish dredge. In field trials, the relative abundances of major taxa were similar for most dredges at each site; major exceptions were the Fast dredge at site 2 and the Irish dredge at site 3. There was a high variability between sampling units in the same sample and therefore a lack of precision in the estimates of the mean number of invertebrates per sample. Therefore, the dredges cannot be used as quantitative samplers for the estimation of population density. Their adequacy as qualitative samplers for the estimation of total number of taxa per sample varied considerably and maximum estimates of their efficiencies for a small sample (n= 5) were <40% for the Irish and Fast dredges, >57% for the medium-sized Naturalist's dredge and >76% for the large Naturalist's dredge. There was a clear relationship between the number of taxa and the number of invertebrates taken at each site and this relationship was well described by a power law with an exponent within the range 0.18–0.53. The number of sampling units in the sample had no significant effect on the power-law equations for each site. The power-law equation was very similar for most of the dredges at each site, the only major exception being the Fast dredge at site 1. The implications of this relationship are discussed.     

Are sample sizes usually at least an order of magnitude too low for reliable estimates of leaf asymmetry?

Estimates of leaf size and asymmetry for individual trees are often obtained using sample sizes that are too small to take into account the possibility that size and asymmetry may be affected by the position of the leaf on the tree. This issue was addressed by exploring variation in leaf size and asymmetry within an individual of Alder (Alnus glutinosa). We found differences between branches for leaf size and for signed asymmetry but not for unsigned asymmetry. We also found that the size of a leaf was not correlated with its position on a branch and that the asymmetry of a leaf was not correlated with either its position on a branch or with the asymmetry of its neighbour. Repeated subsampling of a sample of 870 leaves showed that a subsample size approaching 500 leaves was required for consistently reliable estimates of the standard deviation of unsigned asymmetry. Smaller subsamples were required for consistently reliable estimates of mean unsigned asymmetry and of the mean and standard deviation of leaf size, but subsamples of less than 100 leaves provided consistently reliable estimates only of mean leaf size. For this species, reliable estimates of an individual's level of asymmetry are obtained only if several hundred leaves are sampled over several branches, but it is not necessary to sample the same sequence of leaves from each branch.     

Gluttonous predators: how to estimate prey size when there are too many prey

Prey size is an important factor in food consumption. In studies of feeding ecology, prey items are usually measured individually using calipers or ocular micrometers. Among amphibians and reptiles, there are species that feed on large numbers of small prey items (e.g. ants, termites). This high intake makes it difficult to estimate prey size consumed by these animals. We addressed this problem by developing and evaluating a procedure for subsampling the stomach contents of such predators in order to estimate prey size. Specifically, we developed a protocol based on a bootstrap procedure to obtain a subsample with a precision error of at the most 5%, with a confidence level of at least 95%. This guideline should reduce the sampling effort and facilitate future studies on the feeding habits of amphibians and reptiles, and also provide a means of obtaining precise estimates of prey size.