Given Level Of Precision Research Articles

Distribution and analysis of cabbage root fly pupal populations

SUMMARYThe distribution of cabbage root fly pupae around roots of brassica plants was studied from 1971 to 1977.Different distributions of the first and overwintering generations of pupae demonstrated that the two should be considered separately. The number of plant roots to be sampled for a given level of precision was greater for the first than for the overwintering generation. Sampling plans for the range of pupal populations normally encountered during the two generations are illustrated. They were unaffected by changes in plant species, plant cultivar and plant density and were also suitable for use in both untreated and insecticide‐treated crops. No attempts were made to obtain a plan for the second generation of pupae because of the difficulty in accurately predicting the occurrence of this generation in the field. Taylor's power law gave a good description of the distribution of pupae. Although many factors changed between generations the value of the power remained constant at 1–3, apparently the index of aggregation characteristic of the pupal stage of the cabbage root fly in Canada as well as in England.

Sampling Intensity, Informational Content of Samples, and Precision in Estimating Within-Tree Populations of Dendroctonus frontalis12

The practice of quantitatively sampling within-tree populations of Dendroctonus frontalis was investigated by comparing the relationships between sampling intensity, informational content of samples, and precision in estimation. Random and stratified random sampling plans were compared and contrasted to selective or purposeful sampling using the tree geometry model-probability density function (TG-PDF) estimation procedure. The random techniques required large quantities of data and were therefore less suitable than the TG-PDF procedure. The latter procedure incorporates knowledge of the vertical distribution of the D. frontalis life stages and therefore required much less data for a given level of precision. The TG-PDF procedure was evaluated on the basis of precision obtained in using the technique on different numbers of sample levels and the position of the sample levels. Precision as judged by the refined standard deviation of the estimate σ R increased as the number of levels sampled increased. For a given number of levels, the refined σ R , which associates covariables with the sample levels, always produced a better estimate than the basic standard deviation σ B which assumed equal information from each sample level. Positioning of sample levels along the infested bole influenced the precision obtained. Dispersing the sample levels over the infested bole while avoiding the extremes generally resulted in better precision for each life stage. The precision in estimation was best where the informational content C of the individual levels was similar. The optimal location for sample levels varied with the life stage being sampled. Generally 2 or 3 levels provided an adequate estimate for most sampling requirements. The emerging adult life stage was the most variable and therefore the more difficult and costly to sample.

Treatment Designs to Estimate Optimum Plant Density for Maximum Corn Grain Yield1

AbstractUse of an exponential regression model relating corn (Zea mays L.) grain yield to plant density allows estimation of the optimum density for producing maximum yield. The experimenter's choice of treatment design (i.e. the particular plant densities included in an experiment) has an important influence on the precision of the estimated optimum density. The best treatment designs provide the greatest precision with a given number of replications, or, alternatively, provide a given level of precision with the smallest number of replications.Expression of yield as a proportion of maximum yield and plant densities as proportions of the optimum density greatly simplifies the evaluation of treatment designs with respect to their ability to provide precise estimates of the optimum density. A total of 375 three, four, and five density treatment designs were evaluated on the dimensionless proportional scale in order to determine those which provide the greatest precision. Maximum allowable relative errors for the best three, four, and five density treatment designs are reported for each of 15 combinations of minimum and maximum densities expressed on a proportional scale. The best treatment designs contain unequally incremented densities and provide considerably more precise estimates of the optimum density than do designs with equally incremented densities.

The distribution and analysis of cabbage root fly egg populations

SUMMARYThe distribution of the egg stage of the cabbage root fly around brassica plants was studied at Wellesbourne on 0.05–0.4 ha plots during 1970 and 1971.The three generations of flies occurred at similar times in both years and the numbers of eggs collected generally decreased from the first to the third generation. Differences between generations demonstrated that each generation should be treated separately. The number of plant samples required for a given level of precision increased from the first to the third generation, indicating that experiments relying on egg counts should be planned to coincide with the first generation whenever possible. A sampling plan for the range of oviposition normally encountered during the three generations is illustrated for both one‐ and five‐plant samples. For the same level of precision, estimates of the populations from five‐plant samples required only 50% to 80% of the time of those from one‐plant samples. When aestivation occurs the peak of oviposition in the second generation is difficult to determine, and designed experiments should not be undertaken. The negative binomial distribution failed to describe the clumping of the eggs for a complete generation, since a common k could not be fitted to the data. The distribution of the eggs was best described by Taylor's power law which showed that although sampling factors changed with generation, the value of the power did not. A value of 1.4 appears to be the index of aggregation characteristic of the egg stage of this species.

The development of sampling techniques for populations of the tarnished plant bug, Lygus lineolaris (hemiptera: Miridae)

SummaryThe relationship of ‘mean crowding’ to mean density showed that counts of nymphs and adults of the tarnished plant bug, Lygus lineolaris (Beauv.), on birdsfoot trefoil were aggregated and that the index of basic contagion approached zero for each developing stage. Aggregation increased gradually from the first to the fourth instar and then decreased through the adult stage. The mortality process from the first to the fifth instar was inversely density dependent.Inter‐sample variance was the major source of population variance although significant variance was occasionally associated with blocks and plots owing to heterogeneity of the host stand. The most appropriate sample unit was a 3 sq. ft. area of foliage and substrate. This was divided into four quarters; application of the variance component technique indicated that in most cases one quarter drawn at random was optimal for sampling different stages. The number of samples required to attain a given level of precision varied inversely with population density. The cost function for sampling was determined for specified levels of precision.