Statistics of Natural Populations. III. Sequential Sampling Plans for the Estimation of Gene Frequencies

Biometrics ◽  
1986 ◽  
Vol 42 (1) ◽  
pp. 45 ◽  
Author(s):  
Marc J. Sobel ◽  
Jonathan Arnold ◽  
Milton Sobel
Keyword(s):  
Sequential Sampling ◽  
Natural Populations ◽  
Gene Frequencies ◽  
Sampling Plans

NUMERICAL ANALYSIS OF RANDOM DRIFT IN A CLINE

Genetics ◽  
1980 ◽  
Vol 94 (2) ◽  
pp. 497-517
Author(s):  
Thomas Nagylaki ◽  
Bradley Lucier
Keyword(s):  
Natural Populations ◽  
The Other ◽  
Random Genetic Drift ◽  
Gene Frequencies ◽  
Random Drift ◽  
Linear Habitat ◽  
Asymptotic Formulae ◽  
A Chain ◽  
Average Position ◽  
Uniform Population

ABSTRACT The equilibrium state of a diffusion model for random genetic drift in a cline is analyzed numerically. The monoecious organism occupies an unbounded linear habitat with constant, uniform population density. Migration is homogeneouq symmetric and independent of genotype. A single diallelic locus with a step environment is investigated in the absence of dominance and mutation. The flattening of the expected cline due to random drift is very slight in natural populations. The ratio of the variance of either gene frequency to the product of the expected gene frequencies decreases monotonically to a nonzero constant. The correlation between the gene frequencies at two points decreases monotonically to zero as the separation is increased with the average position fixed; the decrease is asymptotically exponential. The correlation decreases monotonically to a positive constant depending on the separation as the average position increasingly deviates from the center of the cline with the separation fixed. The correlation also decreases monotonically to zero if one of the points is fixed and the other is moved outward in the habitat, the ultimate decrease again being exponential. Some asymptotic formulae are derived analytically.—The loss of an allele favored in an environmental pocket is investigated by simulating a chain of demes exchanging migrants, the other assumptions being the same as above. For most natural populations, provided the allele would be maintained in the population deterministically, this process is too slow to have evolutionary importance.

scholarly journals Sequential Sampling for Estimation and Classification of the Incidence of Hop Powdery Mildew II: Cone Sampling

Plant Disease ◽  
2007 ◽  
Vol 91 (8) ◽  
pp. 1013-1020 ◽  
Author(s):  
David H. Gent ◽  
William W. Turechek ◽  
Walter F. Mahaffee
Keyword(s):  
Powdery Mildew ◽  
Binomial Distribution ◽  
Disease Incidence ◽  
Sequential Sampling ◽  
Model Construction ◽  
Data Sets ◽  
Data Set ◽  
Sampling Plans ◽  
Simulated Sampling

Sequential sampling models for estimation and classification of the incidence of powdery mildew (caused by Podosphaera macularis) on hop (Humulus lupulus) cones were developed using parameter estimates of the binary power law derived from the analysis of 221 transect data sets (model construction data set) collected from 41 hop yards sampled in Oregon and Washington from 2000 to 2005. Stop lines, models that determine when sufficient information has been collected to estimate mean disease incidence and stop sampling, for sequential estimation were validated by bootstrap simulation using a subset of 21 model construction data sets and simulated sampling of an additional 13 model construction data sets. Achieved coefficient of variation (C) approached the prespecified C as the estimated disease incidence, [Formula: see text], increased, although achieving a C of 0.1 was not possible for data sets in which [Formula: see text] < 0.03 with the number of sampling units evaluated in this study. The 95% confidence interval of the median difference between [Formula: see text] of each yard (achieved by sequential sampling) and the true p of the original data set included 0 for all 21 data sets evaluated at levels of C of 0.1 and 0.2. For sequential classification, operating characteristic (OC) and average sample number (ASN) curves of the sequential sampling plans obtained by bootstrap analysis and simulated sampling were similar to the OC and ASN values determined by Monte Carlo simulation. Correct decisions of whether disease incidence was above or below prespecified thresholds (pt) were made for 84.6 or 100% of the data sets during simulated sampling when stop lines were determined assuming a binomial or beta-binomial distribution of disease incidence, respectively. However, the higher proportion of correct decisions obtained by assuming a beta-binomial distribution of disease incidence required, on average, sampling 3.9 more plants per sampling round to classify disease incidence compared with the binomial distribution. Use of these sequential sampling plans may aid growers in deciding the order in which to harvest hop yards to minimize the risk of a condition called “cone early maturity” caused by late-season infection of cones by P. macularis. Also, sequential sampling could aid in research efforts, such as efficacy trials, where many hop cones are assessed to determine disease incidence.

scholarly journals Spatial distribution pattern and sequential sampling plans for Bactrocera oleae (Gmelin) (Dip: Tephritidae) in olive orchards

2016 ◽  
Vol 48 (1) ◽  
pp. 23
Author(s):  
A. Arbab ◽  
F. Mirphakhar
Keyword(s):  
Spatial Distribution ◽  
Sample Size ◽  
Sequential Sampling ◽  
Bactrocera Oleae ◽  
Sampling Plans ◽  
Optimum Sample Size ◽  
Precision Level ◽  
The Individual ◽  
Optimum Sample ◽  
Basic Distribution

The distribution of adult and larvae <em>Bactrocera oleae</em> (Diptera: Tephritidae), a key pest of olive, was studied in olive orchards. The first objective was to analyze the dispersion of this insect on olive and the second was to develop sampling plans based on fixed levels of precision for estimating <em>B. oleae</em> populations. The Taylor’s power law and Iwao’s patchiness regression models were used to analyze the data. Our results document that Iwao’s patchiness provided a better description between variance and mean density. Taylor’s <em>b</em> and Iwao’s <em>β</em> were both significantly more than 1, indicating that adults and larvae had aggregated spatial distribution. This result was further supported by the calculated common <em>k</em> of 2.17 and 4.76 for adult and larvae, respectively. Iwao’s a for larvae was significantly less than 0, indicating that the basic distribution component of <em>B. oleae</em> is the individual insect. Optimal sample sizes for fixed precision levels of 0.10 and 0.25 were estimated with Iwao’s patchiness coefficients. The optimum sample size for adult and larvae fluctuated throughout the seasons and depended upon the fly density and desired level of precision. For adult, this generally ranged from 2 to 11 and 7 to 15 traps to achieve precision levels of 0.25 and 0.10, respectively. With respect to optimum sample size, the developed fixed-precision sequential sampling plans was suitable for estimating flies density at a precision level of D=0.25. Sampling plans, presented here, should be a tool for research on pest management decisions of <em>B. oleae</em>.

Sequential Sampling Plans for Colorado Potato Beetle (Coleoptera: Chrysomelidae) in Eggplant

1998 ◽  
Vol 27 (1) ◽  
pp. 33-38 ◽  
Author(s):  
George C. Hamilton ◽  
James H. Lashomb ◽  
Salvatore Arpaia ◽  
Robert Chianese ◽  
Mark Mayer
Keyword(s):  
Colorado Potato Beetle ◽  
Sequential Sampling ◽  
Sampling Plans ◽  
Potato Beetle

scholarly journals Enzyme variability in the Drosophila willistoni Group. V. Genic variation in natural populations of Drosophila equinoxialis

1972 ◽  
Vol 20 (1) ◽  
pp. 19-42 ◽  
Author(s):  
Francisco J. Ayala ◽  
Jeffrey R. Powell ◽  
Martin L. Tracey
Keyword(s):  
Genetic Variation ◽  
Allelic Variation ◽  
Natural Populations ◽  
Starch Gel Electrophoresis ◽  
Gene Frequencies ◽  
Group V ◽  
Neutral Genetic Variation ◽  
Starch Gel ◽  
Genic Variation ◽  
Standard Techniques

SUMMARYWe have studied genetic variation at 27 loci in 42 samples from natural populations of a neotropical species, Drosophila equinoxialis, using standard techniques of starch-gel electrophoresis to detect allelic variation in genes coding for enzymes. There is considerarle genetic variability in D. equinoxialis. We have found allelic variation in each of the 27 loci, although not in every population. On the average, 71% of the loci are polymorphic – that is, the most common allele has a frequency no greater than 0·95 – in a given population. An individual is heterozygous on the average at 21·8% of its loci.The amount of genetic variation fluctuates widely from locus to locus. At the Mdh-2 locus arout 1% of the individuals are heterozygotes; at the other extreme more than 56% of the individuals are heterozygous at the Est-3. At any given locus the configuration of allelic frequencies is strikingly similar from locality to locality. At each and every locus the same allele is generally the most common throughout the distribution of the species. Yet differences in gene frequencies occur between localities. The pattern of genetic variation is incompatible with the hypothesis that the variation is adaptively neutral. Genetic variation in D. equinoxialis is maintained by balancing natural selection.The amount and pattern of genetic variation is similar in D. equinoxialis and its sibling species, D. willistoni. Yet the two species are genetically very different. Different sets of alleles occur at nearly 40% of the loci.

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