Herbivores and the Spatial Distributions of the Phytoplankton. II. Estimating Grazing in Planktonic Environments

Large errors are made when laboratory measurements of the ingestion rate of herbivorous zoo-plankton are used to estimate grazing in planktonic environments. The errors arise because the spatial heterogeneity in natural plankton distributions is greater than the heterogeneity present in laboratory experiments. Two probability models are developed for extrapolating laboratory measurements of ingestion to planktonic environments. Both models require sample statistics of the plankton distributions, and these are estimated from sampling studies of the small scale distribution of marine plankton. One model predicts laboratory measurements overestimate the ration obtained by an individual copepod by 30 %. A second model predicts errors exceeding ±50 % are possible when laboratory measurements are used to estimate the grazing by a population of cope-pods.     

Interaction among Non-toxic Phytoplankton,Toxic Phytoplankton and Zooplankton: Inferences from Field Observations

We explore the mutual dependencies and interactions among different groups of species of the plankton population, based on an analysis of the long-term field observations carried out by our group in the North–West coast of the Bay of Bengal. The plankton community is structured into three groups of species, namely, non-toxic phytoplankton (NTP), toxic phytoplankton (TPP) and zooplankton. To find the pair-wise dependencies among the three groups of plankton, Pearson and partial correlation coefficients are calculated. To explore the simultaneous interaction among all the three groups, a time series analysis is performed. Following an Expectation Maximization (E-M) algorithm, those data points which are missing due to irregularities in sampling are estimated, and with the completed data set a Vector Auto-Regressive (VAR) model is analyzed. The overall analysis demonstrates that toxin-producing phytoplankton play two distinct roles: the inhibition on consumption of toxic substances reduces the abundance of zooplankton, and the toxic materials released by TPP significantly compensate for the competitive disadvantages among phytoplankton species. Our study suggests that the presence of TPP might be a possible cause for the generation of a complex interaction among the large number of phytoplankton and zooplankton species that might be responsible for the prolonged coexistence of the plankton species in a fluctuating biomass.     

Estimation of the biomass of plankton

Summary A mathematical function is demonstrated in the numbers of individuals of the various species in a planktonic biocoenosis. The logarithms of the numbers form a Gauss or normal probability curve. A similar probability relation is found in the volumes of the individuals of the various species as well as in the biomass of the various populations.This relationship in the numbers is caused by the effect of the numerous ecological factors influencing the rate of proliferation of the various plankton species. The cause of this relationship concerning the volumes of the various species is not understood. The relationship between the various biomasses is the mathematical product of number and mean volume.An approximate hyperbolic function can be derived from the population volumes and with the aid of a simple equation the plankton biomass is calculated. A modus operandi is given to abbreviate the work necessary to determine the plankton biomass with Lohmann's method. Only ten or twenty of the most dominant populations out of all species present in a plankton sample, have to be counted and measured.The biomasses of the populations in various plankton samples may easily be compared using the hyperbolic or the probability relationship.The biomasses of plankton in various habitats may easily be compared in a graphic way. The logarithms of the biomasses found during the year follow a probability curve and may be plotted and compared on a cumulative logarithmic probability graph.The number of organisms of each species to be counted depends on the degree of accuracy and has to be about a hundred. A chance determined spread is always found in plankton counts.The spatial distribution of most plankters shows a very broad spread. Therefore, sampling at ten places and working with the mean of the ten samples is compulsory.Some gregariously living zooplankters form bunches in the water. A reliable mean may be calculated using the hyperbolic function which seems to describe their densities at the various places.From the existing methods of collection of plankton the rotary, electric pump is chosen. A translucent hose with a special and moving mouth is let down into the water. First the water passes through the plankton-net and after that through the pump and the water-meter. A series of 7 samples of increasing decimal volumes is drawn in this way. From these samples the plankton is concentrated and fractionated by means of two sedimentation chambers, four small plankton sieves and three plankton nets. The sieves and nets have various standardized meshes.Square counting chambers of 10 cm² area are used. These chambers have a thin glass bottom and a broad rim. The sedimentation chambers and the small plankton sieves fit on and into the chambers thus minimizing the loss of organisms.The plankton organisms are enumerated by means of an inverted microscope projecting the image on a ground glass which makes counting easier. Only those organisms seen within a measured square on the ground glass are counted.By standardization of the sample volumes, the magnifications of the microscope and the dimensions of the squares the conversion factors are so simple that only zeros or a decimal point have to be placed in the number counted to obtain the result.International standardization of the method of estimation of the biomass of plankton and the expression of the results is proposed.     

Optimal sampling of a population to determine QTL location, variance, and allelic number

In a population intended for breeding and selection, questions of interest relative to a specific segregating QTL are the variance it generates in the population, and the number and effects of its alleles. One approach to address these questions is to extract several inbreds from the population and use them to generate multiple mapping families. Given random sampling of parents, sampling strategy may be an important factor determining the power of the analysis and its accuracy in estimating QTL variance and allelic number. We describe appropriate multiple-family QTL mapping methodology and apply it to simulated data sets to determine optimal sampling strategies in terms of family number versus family size. Genomes were simulated with seven chromosomes, on which 107 markers and six QTL were distributed. The total heritability was 0.60. Two to ten alleles were segregating at each QTL. Sampling strategies ranged from sampling two inbreds and generating a single family of 600 progeny to sampling 40 inbreds and generating 40 families of 15 progeny each. Strategies involving only one to five families were subject to variation due to the sampling of inbred parents. For QTL where more than two alleles were segregating, these strategies did not sample QTL alleles representative of the original population. Conversely, strategies involving 30 or more parents were subject to variation due to sampling of QTL genotypes within the small families obtained. Given these constraints, greatest QTL detection power was obtained for strategies involving five to ten mapping families. The most accurate estimation of the variance generated by the QTL, however, was obtained with strategies involving 20 or more families. Finally, strategies with an intermediate number of families best estimated the number of QTL alleles. We conclude that no overall optimal sampling strategy exists but that the strategy adopted must depend on the objective.Communicated by P. Langridge     

Effect of sampling scale on the assessment of epiphytic bacterial populations

Bacterial populations on above-ground plant surfaces were estimated at three different biological scales, including leaflet disks, entire leaflets, and whole plants. The influence of sample scale on the estimation of mean bacterial population size per unit and per gram and on the variability among sampling units was quantified at each scale. Populations were highly variable among sampling units at every scale examined, suggesting that there is no optimal scale at which sample variance is reduced. The distribution of population sizes among sample units was sometimes, but not consistently, described by the lognormal. Regardless of the sampling scale, expression of population sizes on a per gram basis may not reduce variance, because population size was not generally a function of sample unit weight within any single sampling scale. In addition, the data show that scaling populations on a per gram basis does not provide a useful means of comparing population estimates from samples taken at different scales. The implications of these results for designing sampling strategies to address specific issues in microbial ecology are discussed. Correspondence to: L.L. Kinkel     

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.     

The program structure does not reliably recover the correct population structure when sampling is uneven: subsampling and new estimators alleviate the problem

Inferences of population structure and more precisely the identification of genetically homogeneous groups of individuals are essential to the fields of ecology, evolutionary biology and conservation biology. Such population structure inferences are routinely investigated via the program structure implementing a Bayesian algorithm to identify groups of individuals at Hardy–Weinberg and linkage equilibrium. While the method is performing relatively well under various population models with even sampling between subpopulations, the robustness of the method to uneven sample size between subpopulations and/or hierarchical levels of population structure has not yet been tested despite being commonly encountered in empirical data sets. In this study, I used simulated and empirical microsatellite data sets to investigate the impact of uneven sample size between subpopulations and/or hierarchical levels of population structure on the detected population structure. The results demonstrated that uneven sampling often leads to wrong inferences on hierarchical structure and downward‐biased estimates of the true number of subpopulations. Distinct subpopulations with reduced sampling tended to be merged together, while at the same time, individuals from extensively sampled subpopulations were generally split, despite belonging to the same panmictic population. Four new supervised methods to detect the number of clusters were developed and tested as part of this study and were found to outperform the existing methods using both evenly and unevenly sampled data sets. Additionally, a subsampling strategy aiming to reduce sampling unevenness between subpopulations is presented and tested. These results altogether demonstrate that when sampling evenness is accounted for, the detection of the correct population structure is greatly improved.     

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.     

Evaluation of a pumping system for sampling zooplankton

This study describes the sampling efficiency of a plankton pumpdesigned to operate from a moving research vessel. The samplingefficiency of the pump was evaluated by comparing the catchper unit volume of several planktonic taxa sampled simultaneouslywith the pump and with a modified Gulf V plankton sampler ora tube sampler. The estimates of plankton density obtained withthe pump sampler corresponded well with those obtained withthe modified plankton net and tube sampler. We conclude thatthe use of a plankton pump in zooplankton sampling gives resultscomparable to those found with traditional sampling, exceptthat the results were biased for the sampling of rotifers andcopepod eggs.     

Sampling strategy optimization to increase statistical power in landscape genomics: A simulation‐based approach

An increasing number of studies are using landscape genomics to investigate local adaptation in wild and domestic populations. Implementation of this approach requires the sampling phase to consider the complexity of environmental settings and the burden of logistical constraints. These important aspects are often underestimated in the literature dedicated to sampling strategies. In this study, we computed simulated genomic data sets to run against actual environmental data in order to trial landscape genomics experiments under distinct sampling strategies. These strategies differed by design approach (to enhance environmental and/or geographical representativeness at study sites), number of sampling locations and sample sizes. We then evaluated how these elements affected statistical performances (power and false discoveries) under two antithetical demographic scenarios. Our results highlight the importance of selecting an appropriate sample size, which should be modified based on the demographic characteristics of the studied population. For species with limited dispersal, sample sizes above 200 units are generally sufficient to detect most adaptive signals, while in random mating populations this threshold should be increased to 400 units. Furthermore, we describe a design approach that maximizes both environmental and geographical representativeness of sampling sites and show how it systematically outperforms random or regular sampling schemes. Finally, we show that although having more sampling locations (between 40 and 50 sites) increase statistical power and reduce false discovery rate, similar results can be achieved with a moderate number of sites (20 sites). Overall, this study provides valuable guidelines for optimizing sampling strategies for landscape genomics experiments.     

Comparison of sleds versus plankton nets for sampling fish larvae and eggs

Fish larvae and fish eggs were sampled from the inshore waters of eastern Lake Michigan from 1978 through 1980, using a benthic sled and a plankton net towed within 0.5 m of the lake bottom. Differences between estimates of ichthyoplankton abundance based on the benthic sled and those based on the plankton net towed near bottom were examined along with interactions between gear, bottom depth, and time of day. Time of day was determined to be an important factor in comparing these two gear, but data were inconclusive as to the effect of depth on gear differences. Abundance of fish eggs calculated using sled tow data was significantly higher than that for the plankton net. For nighttime collections, density of alewife Alosa pseudoharengus larvae sampled in the plankton net significantly exceeded that for the sled, whereas density of spottail shiner Notropis hudsonius larvae based on sled data was significantly higher than that based on the plankton net for day sampling. Overall, the plankton net appeared to be adequate for sampling abundance of alewife larvae, while the sled was preferred for sampling fish eggs, spottail shiner larvae, and the following less common, but apparently demersal larvae: trout-perch Percopsis omiscomaycus, johnny darter Etheostoma nigrum, ninespine stickleback Pungitius pungitius, and slimy sculpin Cottus cognatus.     

Internal seiches in Lake Constance: influence on plankton abundance at a fixed sampling site

During thermal stratification, pronounced internal seiches occurin Lake Constance with periods of 4–6 days The amplitudesreach 12 m at the sampling site in berlinger See (northwesternpart of Lake Constance). Seiches change the thickness of thewarm and generally biologically rich epilimnion and, thus, alsothe areal abundance of planktonic organisms at a fixed samplingsite. The potential impact of seiche-dnven changes of epilimneticthickness on observed plankton abundance was calculated usingcontinuously recorded temperature profiles and weekly verticalprofiles of plankton biomass. Observed plankton biomass wasrecalculated by taking into account the effect of changing layerthickness in order to give a more realistic picture of biomasschanges caused by waxing and waning of populations Our calculationsimply that changes of strata thickness do not mask the generalseasonal trend in population dynamics (e g. spring bloom andclear water phase), estimates of average yearly standing stockare not significantly affected if sampling is done at leastweekly. However, changes of strata thickness can alter arealplankton abundance at the sampling site by a factor of 2 within2 days During pronounced seiches, areal abundance of phytoplankton,which generally exhibit a stronger vertical gradient than-mostother plankton, may be changed by a factor of 3–4 withinhours Hence, at our sampling site, the impact of changes instrata thickness cannot be ignored for detailed analysis ofpopulation dynamics of autotrophs involving comparisons betweensingle observations     

Estimation of the Allele Number in a Natural Population by the Method of Isofemale Lines

The number of alleles present in a natural population of unknown structure is estimated using a sequential sampling procedure applied to isofemale lines. Two questions are raised: how many individuals per isofemale line must be assayed and how many isofemale lines must be sampled to get an adequate sample to estimate the number of alleles, at a given risk, of the natural population? On the one hand, we show that when wild females are inseminated once, only two individuals per line are required. On the other hand, the number of isofemale lines that must be sampled depends on the risk chosen of losing an allele, on the number of alleles present in the population and on their drawing probabilities. When the population structure is known, an accurate answer can be provided. For an unknown population structure, one general sequential sampling previously described by J. Rouault and P. Capy is proposed to estimate the number of alleles in the population from data on isofemale lines.     

Sample design effects in landscape genetics

An important research gap in landscape genetics is the impact of different field sampling designs on the ability to detect the effects of landscape pattern on gene flow. We evaluated how five different sampling regimes (random, linear, systematic, cluster, and single study site) affected the probability of correctly identifying the generating landscape process of population structure. Sampling regimes were chosen to represent a suite of designs common in field studies. We used genetic data generated from a spatially-explicit, individual-based program and simulated gene flow in a continuous population across a landscape with gradual spatial changes in resistance to movement. Additionally, we evaluated the sampling regimes using realistic and obtainable number of loci (10 and 20), number of alleles per locus (5 and 10), number of individuals sampled (10–300), and generational time after the landscape was introduced (20 and 400). For a simulated continuously distributed species, we found that random, linear, and systematic sampling regimes performed well with high sample sizes (>200), levels of polymorphism (10 alleles per locus), and number of molecular markers (20). The cluster and single study site sampling regimes were not able to correctly identify the generating process under any conditions and thus, are not advisable strategies for scenarios similar to our simulations. Our research emphasizes the importance of sampling data at ecologically appropriate spatial and temporal scales and suggests careful consideration for sampling near landscape components that are likely to most influence the genetic structure of the species. In addition, simulating sampling designs a priori could help guide filed data collection efforts     

二化螟种群密度的克力格估值及其模拟抽样

为设计可靠合理的二化螟幼虫种群密度抽样方案,从二化螟幼虫空间分布原始总体出发,另构建了一个随机总体和一个顺序总体,采用无放回随机抽样、间隔变程以上无放回随机抽样和基于克力格估值且初始点随机的顺序抽样对3总体进行了模拟抽样比较．结果表明,间隔变程以上随机抽样对原始总体平均数的估计优于随机抽样,且随总体聚集程度增加,间隔变程以上随机抽样愈优;正确识别种群空间格局极为重要,对聚集分布总体采用随机抽样和对随机分布总体采用间隔变程以上随机抽样均将降低抽样估计精度．针对随机抽样在应用上的局限性,提出了一种基于地统计学克力格估值、初始点随机的顺序抽样方案：它以初始点随机保证随机性,以顺序抽样保证可操作性,以二化螟种群空间分布的区域变量属性保证克力格样本较调查样本对局域样本和总体的平均数估计为优;且聚集范围一定时,总体聚集强度愈大,克力格样本局域估计和全局估计愈优于调查样本;取样间隔(以变程为标准)极为重要,样方的空间布局要平衡考虑相互独立的样方对数和变程范围内的样方对数。     

Associated LAH Numbers,Factorial Series Distributions and Unbiased Estimation of a Size Parameter

A finite population consists of kN individuals of N different categories with k individuals each. It is required to estimate the unknown parameter N, the number of different classes in the population. A sequential sampling scheme is considered in which individuals are sampled until a preassigned number of repetitions of already observed categories occur in the sample. Corresponding fixed sample size schemes were considered by Charalambides (1981). The sequential sampling scheme has the advantage of always allowing unbiased estimation of the size parameter N. It is shown that relative to Charalambides' fixed sample size scheme only minor adjustments are required to account for the sequential scheme. In particular, MVU estimators of parametric functions are expressible in terms of the C-numbers introduced by Charalambides.     

Estimation of the spatial autocorrelation function: consequences of sampling dynamic populations in space and time

The estimation of spatial autocorrelation in spatially- and temporally-referenced data is fundamental to understanding an organism's population biology. I used four sets of census field data, and developed an idealized space-time dynamic system, to study the behavior of spatial autocorrelation estimates when a practical method of sampling is employed. Estimates were made using both a classical geostatistical approach and a recently developed non-parametric approach. In field data, the estimate of the local spatial autocorrelation (i.e. autocorrelation as the distance between pairs of sampling points approaches 0), was greatly affected by sample size, while the range of spatial dependence (i.e. the distance at which the autocorrelation becomes negligible) was fairly stable. Similar patterns were seen in the theoretical system, as well as greater variability in local spatial autocorrelation during the invasion stage of colonization. When sampling for the purposes of quantifying spatial patterns, improved estimates of spatial autocorrelation may be obtained by increasing the number of pairs of points that are close in space at the expense of attempting to cover the entire region of interest with equidistant sampling points. Also, results from the theoretical space-time system suggested that greater resolution in sampling may be required in newly establishing populations relative to those already established.     

Estimation of Finite and Closed Population Size: An Inverse Sampling Approach with Unequal Recapture Probability

Based on capture-mark-recapture sampling methods the problem of estimating unknown population size was considered. The sampling started with the assumption that at the beginning of the experiment all the individuals were unmarked, and the unmarked individuals caught in each sample will be marked and returned to the original population before the next sample is drawn. It is also assumed that the population is closed by birth, death, emigration and immigration. Using a general inverse sampling approach, the unknown population size N is estimated by a maximum likelihood estimator (MLE), and a simple form for approximate MLE is obtained. The probability function for S (the minimum number of samples required to be drawn to have L (L ≥ 1) samples, each of which contains at least one marked individual) and the form for E[S] are also obtained. In addition, corrections and improvements of some previous works in this field are given.     

Cascading tripartite binomial classification plans to monitor European red mite (Acari,Tetranychidae) through a season; development and evaluation of a new methodology for pest monitoring

A monitoring protocol that schedules future sample bouts based on the outcome of density classification and expected population growth has been developed and applied to monitoring European red mite (Panonychus ulmi Koch) through a growing season. The monitoring protocol is based on concatenating through time tripartite sequential classification sampling plans that use binomial counts in lieu of complete enumeration. Binomial counts are scored positive when the number of organisms (mites) on a sample unit (leaves) exceeds a tally number. At each sample occasion the monitoring procedure leads to one of three possible decisions; intervene when the density is high, sample at the next sample occasion (after one week) when the density is intermediate, and sample at the second next sample occasion (after two weeks) when the density is low. Evaluation of the monitoring protocol under field conditions showed that the protocol with constituent tally 0 binomial count sampling plans was quite successful in timing intervention at the moment when population densities were about to exceed an established threshold that dictated intervention. The performance of this monitoring protocol and another protocol in which constituent sampling plans used binomial counts with a tally number of 4 were compared using simulation. Sampling plans that used a tally number of 4 were more precise than plans that used a tally number of 0. However, the overall performance of the monitoring protocol based on tally 0 sampling plans did not greatly differ from the monitoring protocol based on tally 4 sampling plans. Simulated performance of the tally 0 protocol was corroborated by field evaluation. The monitoring protocol based on tripartite classification required 30 to 45 percent fewer sample bouts than a protocol based on conventional sequential classification at weekly intervals. The monitoring protocol based on tripartite classification was also better able to schedule intervention when needed compared to a protocol based on conventional classification at two week intervals. Using the tally 0 protocol and current thresholds forP. ulmi, cumulative mite density was kept below 300 mite-days per leaf, which is well below levels regarded damaging. A tally 0 protocol with raised thresholds, developed on the basis of this finding, gave the best simulated performance of all protocols evaluated.     

The use of simultaneous sampling bottle and vertical net collections to describe the dynamics of a zooplankton population

Simultaneous collections of zooplankton were made at four stations in the Plover Clove Reservoir using Friedinger sampling bottles and vertical Nakai plankton net hauls. Comparison of the results obtained revealed certain obvious numerical and spatial anomalies, and it is suggested that these result from inherent characteristics of the two types of apparatus together with behavioural responses and physical attributes of the individual zooplankton species. Statistical correlation between these two methods was generally good in terms of the seasonal patterns of distribution of the population, but in terms of depth distribution and the relative abundance of the individual species of the population few significant correlations resulted. It is therefore suggested that unless merely seasonal trends are required, it is advisable to use more than one sampling apparatus to obtain valid data concerning the overall dynamics of such a zooplankton population.Department of Botany, University of Hong Kong