Effects of reducing sample size on density estimates of citrus rust mite (Acari: Eriophyidae) on citrus fruit: simulated sampling

The consequence of reducing sample size on the accuracy and precision of estimates of citrus rust mite, Phyllocoptruta oleivora (Ashmead), densities on oranges was investigated. The sample unit was a 1-cm2 surface area on fruit. Sampling plans consisting of 360, 300, 200, 160, 80, 48, 36, or 20 samples per 4 ha were evaluated through computer simulations by using real count data from 32 data sets of 600 sample units per 4 ha. The original and reduced sampling plans were hierarchical with different numbers of sample areas per 4 ha, trees per area, fruit per tree, and samples per fruit. Individual estimates (n=100 simulations per data set) using each plan were sometimes considerably below or above target densities. In an original set of count data with a mean of six mites per cm2, simulations of 36 samples per 4 ha produced individual estimates ranging from one to 16 mites per cm2, whereas 80 samples per 4 ha produced estimates ranging from two to 10 mites per cm2. The plans consisting of 36 or more samples were projected to provide precision levels of 0.25 (SEM/mean) or better at densities of five or more mites per cm2 based on log-data, a projection that needs to be verified under real-grove situations. Each plan consistently provided mite detection in these sampling simulations except those consisting of 20 or 36 samples, which sometimes failed to detect mites when the target density was less than five mites per cm2. The study provided insight into the probable precision, accuracy and detection thresholds for eight candidate sampling plans varying from relatively low to high resource input.     

Effects of sampling and sub-sampling variation using the STAR-AQEM sampling protocol on the precision of macroinvertebrate metrics

As part of the extensive field sampling programme within the European Union STAR project, replicate macroinvertebrate samples were taken using the STAR-AQEM sampling method at each of 2–13 sites of varying ecological quality within each of 15 stream types spread over 12 countries throughout Europe. The STAR-AQEM method requires the sub-sampling and taxonomic identification of at least one-sixth of the sample and at least 700 individuals. Replicate sub-samples were also taken at most of these sites. Sub-sampling effects caused more than 50% of the overall variance between replicate samples values for 12 of the 27 macroinvertebrate metrics analysed and was generally greatest for metrics that depend on the number of taxa present. The sampling precision of each metric was estimated by the overall replicate sampling variance as a percentage P_samp of the total variance in metric values within a stream type. Average over all stream types, the three Saprobic indices had the lowest percentage sampling variances with median values of only 3–6%. Most of the metrics had typical replicate sampling variances of 8–18% of the total variability within a stream type; this gives rise to estimated rates of mis-classifying sites to ecological status class of between 22 and 55% with an average of about 40%. This suggests that the precision of such metrics based on the STAR-AQEM method is only sufficient to indicate gross changes in the ecological status of sites, but there will be considerable uncertainty in the assignment of sites to adjacent status classes. These estimates can be used to provide information on the effects of STAR-AQEM sampling variation on the expected uncertainty in multi-metric assessments of the ecological status of sites in the same or similar stream types, where only one sample has been taken at a point in time and thus there is no replication.     

The effect of fixed‐count subsampling on macroinvertebrate biomonitoring in small streams

• 1 When rigorous standards of collecting and analysing data are maintained, biological monitoring adds valuable information to water resource assessments. Decisions, from study design and field methods to laboratory procedures and data analysis, affect assessment quality. Subsampling ‐ a laboratory procedure in which researchers count and identify a random subset of field samples ‐ is widespread yet controversial. What are the consequences of subsampling?
• 2 To explore this question, random subsamples were computer generated for subsample sizes ranging from 100 to 1000 individuals as compared with the results of counting whole samples. The study was done on benthic invertebrate samples collected from five Puget Sound lowland streams near Seattle, WA, USA. For each replicate subsample, values for 10 biological attributes (e.g. total number of taxa) and for the 10‐metric benthic index of biological integrity (B‐IBI) were computed.
• 3 Variance of each metric and B‐IBI for each subsample size was compared with variance associated with fully counted samples generated using the bootstrap algorithm. From the measures of variance, we computed the maximum number of distinguishable classes of stream condition as a function of sample size for each metric and for B‐IBI.
• 4 Subsampling significantly decreased the maximum number of distinguishable stream classes for B‐IBI, from 8.2 for fully counted samples to 2.8 classes for 100‐organism subsamples. For subsamples containing 100–300 individuals, discriminatory power was low enough to mislead water resource decision makers.

     

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.     

Quantitative trait locus mapping based on resampling in a vast maize testcross experiment and its relevance to quantitative genetics for complex traits

From simulation studies it is known that the allocation of experimental resources has a crucial effect on power of QTL detection as well as on accuracy and precision of QTL estimates. In this study, we used a very large experimental data set composed of 976 F(5) maize testcross progenies evaluated in 19 environments and cross-validation to assess the effect of sample size (N), number of test environments (E), and significance threshold on the number of detected QTL, the proportion of the genotypic variance explained by them, and the corresponding bias of estimates for grain yield, grain moisture, and plant height. In addition, we used computer simulations to compare the usefulness of two cross-validation schemes for obtaining unbiased estimates of QTL effects. The maximum, validated genotypic variance explained by QTL in this study was 52.3% for grain moisture despite the large number of detected QTL, thus confirming the infinitesimal model of quantitative genetics. In both simulated and experimental data, the effect of sample size on power of QTL detection as well as on accuracy and precision of QTL estimates was large. The number of detected QTL and the proportion of genotypic variance explained by QTL generally increased more with increasing N than with increasing E. The average bias of QTL estimates and its range were reduced by increasing N and E. Cross-validation performed well with respect to yielding asymptotically unbiased estimates of the genotypic variance explained by QTL. On the basis of our findings, recommendations for planning of QTL mapping experiments and allocation of experimental resources are given.     

Comparison of point counts and territory mapping for detecting effects of forest management on songbirds

Point counts are commonly used to assess changes in bird abundance, including analytical approaches such as distance sampling that estimate density. Point‐count methods have come under increasing scrutiny because effects of detection probability and field error are difficult to quantify. For seven forest songbirds, we compared fixed‐radii counts (50 m and 100 m) and density estimates obtained from distance sampling to known numbers of birds determined by territory mapping. We applied point‐count analytic approaches to a typical forest management question and compared results to those obtained by territory mapping. We used a before–after control impact (BACI) analysis with a data set collected across seven study areas in the central Appalachians from 2006 to 2010. Using a 50‐m fixed radius, variance in error was at least 1.5 times that of the other methods, whereas a 100‐m fixed radius underestimated actual density by >3 territories per 10 ha for the most abundant species. Distance sampling improved accuracy and precision compared to fixed‐radius counts, although estimates were affected by birds counted outside 10‐ha units. In the BACI analysis, territory mapping detected an overall treatment effect for five of the seven species, and effects were generally consistent each year. In contrast, all point‐count methods failed to detect two treatment effects due to variance and error in annual estimates. Overall, our results highlight the need for adequate sample sizes to reduce variance, and skilled observers to reduce the level of error in point‐count data. Ultimately, the advantages and disadvantages of different survey methods should be considered in the context of overall study design and objectives, allowing for trade‐offs among effort, accuracy, and power to detect treatment effects.     

Drift and upstream movement in Yuccabine Creek,an Australian tropical stream

Drift and upstream movement were monitored over 14 months in a seasonal upland tropical stream in northeastern Australia. There were distinct seasonal pulses in the drift with variable peak levels in the summer wet season and low more stable levels during the dry season. Drift density ranged from 0.36 to 3.98 animals per m³ (monthly mean = 1.26). There was no correlation between drift density and either benthic density or stream discharge. In the absence of catastrophic drift, drift was dispersive, not depletive in the wet season. A total of 121 taxa were caught in the 14 drift samples. Most taxa had nocturnal maximum drift levels with a peak immediately after sunset, a pattern apparently related to level of light and not temperature. Compensation for drift by upstream-moving nymphs and larvae was least during the wet season and increased during the dry season to a peak of 27% by numbers. Mean compensation was 8.2%. It is suggested that apart from in the wet season when an animal may drift substantial distances, most riffle animals will spend their larval lives in one small stretch of stream.     

The drift distances and time spent in the drift by freshwater shrimps, Gammarus pulex, in a small stony stream, and their implications for the interpretation of downstream dispersal

1. The objectives were (i) to determine experimentally and to model the relationship between mean water velocity and both the mean distance travelled, and the mean time spent, in the drift by freshwater shrimps, Gammarus pulex; (ii) to develop a drift distance–water velocity model from the experimental study, and validate it with field data; (iii) to examine the relationship between drift rate, water velocity and benthic density with the latter expressed as a mean value for the whole stream and a mean value corrected for the distance travelled in the drift. 2. In field experiments at 10 water velocities (0.032–0.962 m s^?1), the significant relationship between the mean drift distance and mean water velocity was described both by a power function (power, 0.96) and a linear relationship. The mean drift time was fairly constant at 8.3 s (95% CL ± 0.4). A simple model estimated the drift distance and time spent in the drift by different percentages of the drifting invertebrates. This model predicted correctly the positive relationship between drift rate and water velocity for field data over a year. 3. The relationship between drift rate per hour and the independent variables, water velocity and benthic density, was well described by a multiple‐regression model. Adding temperature and date did not improve model fit. Variations in water velocity and benthic density explained 96% of the variation in nocturnal drift rate (65% to velocity, 31% to benthic density), but only 40% of the variation in diurnal drift rate (29% to velocity, 11% to benthic density). Correcting benthic density for the drift distances did not improve model fit. 4. The significance of this study is that it developed models to predict drift distances and time, values being similar to those obtained in another, larger stream. It also illustrated the importance of spatial scale in the interpretation of drift by showing that when drift distances were taken into account, the impact of drift on the population was higher (4–10% lost day^?1) than when drift distances were ignored (usually < 3% lost day^?1), especially at a local level.     

The interaction among evolutionary forces in the pathogenic fungus Mycosphaerella graminicola

The population genetic dynamic of a species is driven by interactions among mutation, migration, drift, mating system, and selection, but it is rare to have sufficient empirical data to estimate values for all of these forces and to allow comparison of the relative magnitudes of these evolutionary forces. We combined data from a mark-release-recapture experiment, extensive population surveys, and computer simulations to evaluate interactions among these evolutionary forces in the pathogenic fungus Mycosphaerella graminicola. The results from these studies showed that, on average, the immigration rate was 0.027, the fraction of outcrossing individuals was 0.035, and the selection coefficient associated with immigrants was 0.106 each generation. We also estimated that effective population sizes for this fungus were larger than 24,000 and the mutation rate for the RFLP markers used in surveys and field experiments was approximately 4 x 10(-5). Computer simulations based on these estimates indicate that, on average, the global population of M. graminicola has reached equilibrium. Population genetic parameters including number of alleles, gene diversity, and population subdivision estimated from the computer simulations were surprisingly close to empirical estimates. Simulations also revealed that random drift is the major evolutionary force decreasing genetic variation in this fungus, followed by natural selection. The major force adding to genetic variation was mutation, followed by gene flow and sexual recombination. Gene flow played the leading role in decreasing population subdivision while natural selection was the major factor increasing population subdivision.     

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.     

Spatial and temporal distribution patterns of drifting pupal exuviae of Chironomidae (Diptera) in streams of tropical northern Australia

1. Periodic collecting of floating cast pupal cuticles of chironomids (exuviae) in two tropical northern Australian streams demonstrates (i) spatial heterogeneity in species composition across a wide stream, (ii) temporal heterogeneity in the maximum abundance of each species, and that (iii) species accumulate as a function of sample size and duration of sampling, 2. Spatial heterogeneity is ascribed to variation in larval microhabitat across the wide stream, combined with short exuvial drift duration and restricted upstream mixing. 3. Temporal heterogeneity is ascribed to diel periodicity in adult emergence and, as with spatial heterogeneity, to the short floating life. 4. The consequences of spatial and temporal variation for the sampling of exuvial drift are discussed in relation to the objectives of particular programmes. Thus, if the objective is assessment of chironomid species composition for inventory purposes such as faunistics or conservation, the large sample sizes attained by 24-h sampling are necessary and appropriate. However, for rapid assessment that requires comparable samples at different sites, species numbers may be optimized by temporally and spatially restricted sampling of the maximal emergence period, which in this study is at dusk, or by subsampling from a 24-h sample.     

Seasonal and diel periodicity in the drift of aquatic insects in a subtropical Florida stream

A study of insect drift was conducted in a small, subtropical Florida stream from December 1971 to December 1972 to describe the seasonal and diel periodicity and to determine factors influencing behavioural drift. Paired samples of 2 h duration beginning 15 min after sunset were taken biweekly, and hourly collections over a 24-h period were made quarterly. Benthic invertebrates were collected on each date from three habitats (riffle, pool and aquatic vegetation) and temperature, dissolved oxygen and current velocity were measured. Drift rates ranged from 100 to 2125 organisms/m². h (0·03 to 0·49 organisms/m³) and were greatest in winter and early spring; minimal rates occurred in the summer months. The following six taxa, in order of relative abundance, comprised 87% of the drift: Baetis intercalaris, Cheumatopsyche sp., Stenonema exiguum, Chironomidae, Stenelmis fuscata and Simulium sp. Total drift showed no significant correlation with temperature, dissolved oxygen or mean benthic abundance and only slight correlation with current velocity (r=0·34). Stepwise, multiple regression analyses indicated that riffle density and mean size of drifting organisms were important factors influencing the drift rates of B. intercalaris (R=0·67) and S. exiguum (R=0·82); mean size, riffle density and water temperature influenced the drift of Cheumatopsyche sp. (R=0·78). The other taxa of drifting insects showed no significant correlation with the variables measured. Diel (24 h) studies of the major taxa showed marked differences in the periodicity, both within and between taxa, indicating the need for long-term studies with frequent sample intervals in subtropical habitats. A new drift pattern for the family Chironomidae, alternans type, was observed for late instars of Polypedilum halterale.     

A Direct Assessment of the Role of Genetic Drift in Determining Allele Frequency Variation in Populations of EUPHYDRYAS EDITHA

Estimates of allele frequencies at six polymorphic loci were collected over eight generations in two populations of Euphydryas editha. We have estimated, in addition, the effective population size for each generation for both populations with results from mark-recapture and other field data. The variation in allele frequencies generated by random genetic drift was then studied using computer simulations and our direct estimates of effective population size. Substantial differences between observed values and computer-generated expected values assuming drift alone were found for three loci (Got, Hk, Pgi) in one population. These observations are consistent with natural selection in a variable environment.     

Determining Consistency of Spatial Dispersion of Nematodes in Small Plots

Nematode population densities in field plots were estimated by collecting samples consisting of 12 soil cores. Plots encompassed a variety of plant hosts and sampling dates, and provided data on the population densities of seven species of plant-parasitic nematodes. Three separate samples were collected per plot on each sampling date to obtain estimates of the mean and variance of numbers for each species. For each nematode species, these estimates were used to derive the Taylor''s Power Law regression over plots having identical hosts and sampling dates. For some nematode species, comparisons of regression equations among different sampling dates on the same host revealed similarities in values of a and b from Taylor''s Power Law. Parameters of Taylor''s Power Law relationships were used to develop sampling plans and to obtain estimates of sample precision. Precision estimates from specific and general sampling plans are illustrated for Belonolaimus longicaudatus.     

Estimates and comparisons of the effects of sampling variation using ‘national’ macroinvertebrate sampling protocols on the precision of metrics used to assess ecological status

The Water Framework Directive (WFD) of the European Union requires all member countries to provide information on the level of confidence and precision of results in their river monitoring programmes to assess the ecological status class of river sites. As part of the European Union project STAR, the overall effects of sampling variation for a wide range of commonly used metrics and sampling methods were assessed. Replicate samples were taken in each of two seasons at 2–6 sites of varying ecological status class within each of 18 stream types spread over 12 countries, using both the STAR-AQEM method and a national sampling method or, where unavailable, the RIVPACS sampling protocol. The sampling precision of a combination of sampling method and metric was estimated by expressing the replicate sampling variance as a percentage P_samp of the total variance in metric values with a stream type; low values of P_samp indicate high precision. Most metrics had percentage sampling variances less than 20% for all or most stream types and methods. Most national methods including RIVPACS had sampling precisions at least as good as those for the STAR-AQEM method as used in their country at the same sites; the main exceptions were the national methods used in Latvia and Sweden. The national methods used in the Czech Republic, Denmark, France, Poland and the RIVPACS method used in the UK and Austria all had percentage sampling variances of less than 10% for the majority of metrics assessed. In contrast, none of the metrics had percentage sampling variances less than 10% when based on either the Italian (IBE) method, which used bank-side sorting, or the Latvian national method which identifies only a limited set of taxa. P_samp was lowest on average for the two stream types sampled in the Czech Republic using either the PERLA national method or the STAR-AQEM method. Averaged over all stream types and methods, the three Saprobic-based metrics had the lowest average percentage sampling variances (3–6%) amongst the 26 metrics assessed. These estimates of sampling standard deviation can be used to help assess the uncertainty in single or multi-metric systems for estimating site ecological status using the general STAR Bioassessment Guidance Software (STARBUGS) developed within the STAR project.     

Monitoring vegetation change caused by trampling: a study in the Cairngorms,Scotland

Summary

A study was made in the Cairngorms, Scotland to make recommendations for a monitoring scheme capable of detecting changes in the vegetation caused by recreational pressure following the development of a funicular railway. Four methods were used in field trials to assess percentage cover of plant species and gravel, rock and bare ground, where appropriate, in two vegetation types (open and closed). The methods used were visual estimates in 50 × 40 cm quadrats (Q), the mean of visual estimates in twenty 10 × 10 cm sub-quadrats of the 50 × 40 cm quadrats (Q₂₀), a modified point intercept method (RL) and photography. Variances between observers and between-quadrats were estimated for the different methods. The sampling design for detecting change was based on a model of variance, constructed from field trial data.

Between-observer and between-quadrat variances were related to mean percentage cover and approximated to a binomial distribution. The between-quadrat variance was larger than observer variance. The Q₂₀ method achieved appreciably better precision than the other methods. Analysis of half of the 10 × 10 cmsub-quadrats (1/2Q₂₀) selected in a checker board design achieved a relative efficiency of 78% compared with the Q₂₀. This result suggests that comparable precision to the Q₂₀ method could be achieved by choosing about 14 sub-quadrats in a larger quadrat, thus saving some time. Variation between quadrats also suggested that the Q₂₀ method was the one of choice for maximising precision. The precision of the photographic method was based on fewer data points, so is less accurate than other estimates.

Minimum sample sizes were estimated for detecting a 10% relative change of a species in open vegetation with 30% cover (i.e. a change from 30% to <27 or to >33% cover). With a 10 % Type II error rate and 5 % Type I error rate the minimum sample sizes were 47 quadrats for Q, 18 for Q ₂₀, 43 for RL, and 23 for the means of ten 10 × 10 cm sub-quadrats in open vegetation.

The most time-efficient field recording appeared to be the use of Q despite the required sample size being 2.6 times higher than that of Q₂₀. The far lower time requirement per quadrat, however, compensated for the higher numbers. The number of quadrats would depend on the specified change in percentage cover and on the statistical significance level used. For example, to detect a 10% absolute change in cover (i.e. from 30% to either <20 % or >40 % cover) at 95 % probability the net effective recording time is estimated at 5 h per vegetation type while to detect a 5 % change at 99 % probability would require c. 25 h. Larger samples may be required for other species or for species with a low initial cover.     

Relationship between microbial activity of stream sediments,determined by three different methods,and abiotic variables

Microbial activity of stream sediments has been determined by three distinct methods: phosphatase levels, maximum uptake velocity of radiolabeled glucose, and carbon dioxide production rates. These methods have been applied to different types of sediment (mud, sand, gravel) from the same stream and to 5 samples from two different streams for comparison. Temperature, discharge, and 8 other abiotic variables for each sample were also determined. The 3 activity methods correlated closely with each other and were measured with a similar precision. Phosphatase activity could be predicted for all sites from bulk density. The largest proportion of the variance associated with carbon dioxide production was explained by variations in percent of organic matter, but the relationship did not hold for all streams. Maximum uptake velocity, compared with the other 2 activity measurements, was poorly explained by any of the abiotic variables.     

Assessment of Stream Restoration: Sources of Variation in Macroinvertebrate Recovery throughout an 11‐Year Study of Coal Mine Drainage Treatment

Stream restoration researchers have a complex array of alternative assessment methodologies using macroinvertebrates. We examined sources of variation among three field sampling methods and five metrics in three networked streams impacted by a circumneutral coal mine discharge treated midway through an 11‐year study. Constructed wetlands captured the primary stressor, 700 kg iron/day. Before pollution abatement, copious iron hydroxide smothered downstream sites for decades. Two second‐order streams and one fourth‐order receiving stream, each with matching locations upstream and downstream, were monitored midsummer from 1994 to 2004. We compared taxa density (TD) (number/sample), abundance, expected taxa richness (ETR), U.S. regional pollution tolerance values (RTV), and community similarity (CS) indices from 3 to 11 replicate samples/site using grab samples (i.e. D‐nets, rock washes) and incubated leaf packs. Variation due to sampling method, metric, location, and year significantly influenced outcomes when analyzed using regression and analysis of variance. TD, RTV, and CS indicated biological recovery lagged 6 years behind chemical improvement; ETR and abundance showed more severe, persistent impairment in the two, highly impacted second‐order streams compared to the fourth‐order stream. Incubated leaf packs offered a preview of stream recovery in downstream sites, providing clean food (leaves) and substrate (mesh) and attracted more taxa and abundance than grab samples. In light of the worldwide distribution of coal mining often accompanied by metal hydroxide deposits into streams, we suggest restoration project managers use a variety of sampling methods, metrics, and models to evaluate remediation of physical as well as chemical impairment from mining.     

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.     

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.