Evaluation of statistical precision and design of efficient sampling for the population estimation based on frequency of occurrence

The binomial sampling to estimate population density of an organism based simply upon the frequency of its occurrence among sampled quadrats is a labour-saving technique which is potentially useful for small animals like insects and has actually been applied occasionally to studies of their populations. The present study provides a theoretical basis for this convenient technique, which makes it statistically reliable and tolerable for consistent use in intensive as well as preliminary population censuses. Firs, the magnitude of sampling error in relation to sample size is formulated mathematically for the estimate to be obtained by this indirect method of census, using either of the two popular models relating frequency of occurrence (p) to mean density (m), i.e. the negative binomial model, p=1−(1+m/k)^−k, and the empirical model, p=1−exp(−am^b). Then, the equations to calculate sample size and census cost that are necessary to attain a given desired level of precision in the estimation are derived for both models. A notable feature of the relationship of necessary sample size (or census cost) to mean density in the frequency method, in constrast to that in the ordinary census, is that it shows a concave curve which tends to rise sharply not only towards lower but also towards higher levels of density. These theoretical results make it also possible to design sequential estimation procedures based on this convenient census technique, which may enable us with the least necessary cost to get a series of population estimates with the desired precision level. Examples are presented to explain how to apply these programs to acutal censuses in the field.     

A statistical model of the reproduction of aphids

1. The logistic function has been generally used to describe the reproductive process of a “population” of animal. However, this model can not give us any information about the reproductive process of “individuals” in the population. In this study a statistical model on the basis of the reproduction of individuals of barley aphid is presented to find the proportion of the mature individuals, the heterogeneity in reproductive ability of the aphids, etc.
2. The model is constructed as follows:
3. The probability that j insects are found on a plant at time t₀ is represented as Q(j).
4. The probability that h individuals of j have reproductive ability, say, mature individuals, in the period t₀ to t₁ is represented as B(h/j)=_jC_hw^h(1−w)^j−h, where w is the proportion of mature individuals.
5. In a population with a homogeneous reproductive ability, the probability that each parent lays i offspring in the period t₀ to t₁ is represented as P(i/m)=e^−mmⁱ/i!, where m is mean. And, in a population, m changes according to the gamma distribution. Hence the probability that a parent lays i offspring between t₀ and t₁ is represented as , where p and k are parameters of negative binomial distribution. The probability that h parents on a plant lays s offspring is represented as .
6. From the assumptions mentioned above, the probability that s offspring are to be found at time t₁ on a plant with the original j individuals at time t₀ is represented by
7. The experimental populations were demonstrated to fit well to the model.

     

The spatial distribution pattern of the brown planthopperNilaparvata lugens Stål (Homoptera: Delphacidae) in west Java,Indonesia

Spatial distribution pattern of the brown planthopper (BPH) was analyzed at 9 experimental fields in the northern part of West Java during two consecutive rice cropping seasons, i.e., wet and dry seasons. The population of each developmental stage and wing form of BPH at each location showed consistent departure from the random (Poisson) distribution, the variances of the densities in most cases exceeding their means. Namely, the distribution pattern of BPH per hill of rice plant was found to have a general tendency to be aggregated or contagious and to fit fairly well to the negative binomial model. The tendency for aggregation was further confirmed by both the β-values of -m regression being larger than unity and the C_A-values being larger than zero for each developmental stage. Although significant variations in the distribution pattern as measured by β- or C_A-value were observed between different developmental stages, between wing forms and among locations, the degree of aggregation for a given developmental stage at each experimental field remained fairly stable throughout the crop period, despite wide temporal changes in population density. Possible factors to explain these characteristics of the spatial distribution pattern of the BPH in West Java were discussed with reference to the process generating it.     

Scale dependence of vegetation-environment correlations: A case study of a North Carolina piedmont woodland

Abstract. Vegetation and its correlation with environment has been traditionally studied at a single scale of observation. If different ecological processes are dominant at different spatial and temporal scales, the results obtained from such observations will be specific to the single scale of observation employed and will lack generality. Consequently, it is important to assess whether the processes that determine community structure and function are similar at different scales, or whether, how rapidly, and under what circumstances the dominant processes change with scale of observation. Indeed, early work by Greig-Smith and associates (Greig-Smith 1952; Austin & Greig-Smith 1968; see Greig-Smith 1979; Kershaw & Looney 1985; Austin & Nicholls 1988) suggested that plant-plant interactions are typically important at small scales, but that the physical environment dominates at large scales. Using a gridded and mapped 6.6 ha portion of the Duke Forest on the North Carolina piedmont for a case study, we examined the importance of scale in vegetation studies by testing four hypotheses. First, we hypothesized that the correlation between vegetation composition and environment should increase with increasing grain (quadrat) size. Our results support this hypothesis. Second, we hypothesized that the environmental factors most highly correlated with species composition should be similar at all grain sizes within the 6.6-ha study area, and should be among the environmental factors strongly correlated with species composition over the much larger extent of the ca. 3500 ha Duke Forest. Our data are not consistent with either portion of this hypothesis. Third, we hypothesized that at the smaller grain sizes employed in this study (< 256 m²), the composition of the tree canopy should contribute significantly to the vegetation pattern in the under-story. Our results do not support this hypothesis. Finally, we predicted that with increased extent of sampling, the correlation between environment and vegetation should increase. Our data suggest the opposite may be true. This study confirms that results of vegetation analyses can depend greatly on the grain and extent of the samples employed. Whenever possible, sampling should include a variety of grain sizes and a carefully selected sample extent so as to ensure that the results obtained are robust. Application of the methods used here to a variety of vegetation types could lead to a better understanding of whether different ecological processes typically dominate at different spatial scales.     

Determination of nitrie in human blood by combination of a specific sample preparation with high-performance anion-exchange chromatography and electrochemical detection

All photometric or HPLC methods described to date have been unable to detect nitrite, a reliable marker of NO synthase activity, in human blood because of its rapid metabolism within the erythrocytes. We now elaborate on method to prevent nitrite degradation during sample preparation which in combination with high-performance anion-exchange chromatography and electrochemical detection allows a sensitive measurement of nitrite. A linear current response in the concentration range of 10–1000 nmol/l nitrite was observed yielding a correlation coefficient of 0.99. In addition, the combination of the electrochemical with a UV detector allowed us to simultaneously quantify nitrate one analytical run, which is the end product of NO/nitrite metabolism. Basal levels for nitrate and nitrite in human blood were determined with 25±4 μmol/l and 578±116 nmol/l (n=8), respectively and thus were in the same concentration range as expected from NO measurement in saline perfused isolated organs or cultured endothelial cells. Therefore, the presented method may be used to assess activity of endothelial constitutive NO synthase in humans under physiological and pathophysiological conditions.     

菜蚜二项式抽样设计及其精度分析

１９９０～１９９２年间对杭州市郊区青菜上桃蚜（Ｍｙｚｕｓｐｅｒｓｉｃａｅ）、萝卜蚜（Ｌｉｐａｐｈｉｓｅｒｙｓｉｍｉ）及其混合种群的田间近１００组调查数据,利用每样方（株）虫口不超过数阈值Ｔ（分别为０、１、５、１０、２０、３０、４０）头蚜虫的植株比例（ＰＴ）与种群密度（ｍ,头·株－１）的关系,通过拟合经验公式ｌｎ（ｍ）＝ａ＋ｂｌｎ［－ｌｎ（ＰＴ）］而设计的二项式抽样．通过对三者不同数阈值（Ｔ）的回归决定系数（ｒ２）、种群密度的回归估计方差（Ｖａｒ（ｍ））、抽样精度（以ｄ表示）和实际应用等的比较,结果表明当桃蚜种群处于较高密度即ｍ≥１０时,其理想的Ｔ值为３０;当萝卜蚜种群处于较高密度即ｍ≥５时,其理想的Ｔ值为１０;而它们的混合种群未得到其理想的Ｔ值．数阈值Ｔ为３０和１０可分别用于桃蚜和萝卜蚜的二项式抽样设计．而传统的二项式抽样即０～１抽样由于应用于小白菜上菜蚜的抽样设计时产生很大的误差,不宜采用．     

Selection studies in sugarcane (Saccharum sp. hybrids)

Summary An approximate method to determine sample size for the estimation of population variance, ², is given. The estimate of ² is denoted as s² . Based on the assumption of a normal distribution for (s²/²–1), the sample size is approximately equal to 20,000 z² _p,/k²; where z is a standard normal deviate, p is the probability that s² ( 100¦s² – ²¦/²) is less than, or equal to, a critical value k, and k (measured as gDs²) is the desired precision of s² .The expected value of s², with respect to sample size, and the expected cumulative frequencies of s² over sample size for various k values are given. Their goodness of fit to the observed results was satisfactory except for populations that were different from normal. The observed values were taken from a study on four yield components in five sugarcane polycross progenies, grown in two contrasting environments over 2 years in three selection stages.The expected s² was found to be independent of the population coefficient of variance.Research suppoted in part by USDA, ARS, grant #12-14-5001-34. Published with the approval of the Director as Paper No. 412 in the Journal Series of the Experiment Station, Hawaiian Sugar Planters' Association.     

Ecological studies of collembolan populations in a pine forest soil IV. Comparison of distribution patterns

The distribution pattern of ten species of Collembola was studied during the four years period from July 1971 to May 1975 in a pine forest soil. The distribution patterns were analysed for two scales of distribution, i. e., the distribution over the plot of 10×10 m² and the micro-distribution within a block sample consisting of 36 contigious units each 2×2 cm² in area, by applying the -m regression method. The fundamental pattern which appeared was quite similar for the species examined and individuals were aggregated in response to the heterogeneity of habitat conditions. The causes of aggregations were discussed with regard to some environmental factors. The relative abundances of 10 species within the collembolan community was examined in relation to the habitat utilization and the relative abundance was not related to the degree of aggregation but rather to the area occupied by individuals. This suggests that the more numerically abundant species tend to occupy broader micro-habitat. Biological meaning of aggregation was discussed in connection with the population biology and community organization of collembola.