It is well understood that for conventional survey designs the set of unordered distinct units in a sample is a minimally sufficient statistic. This means that for inferential statistic of the sample, the value of the...It is well understood that for conventional survey designs the set of unordered distinct units in a sample is a minimally sufficient statistic. This means that for inferential statistic of the sample, the value of the sampled units rather than the sample design is important. Sampling rare populations presents distinct challenges. Examples of rare populations are in biology with rare and endangered animals where there are only a few remaining individuals, or in social science, with the low incidence of people from an unusually high (or low) income group. Sampling rare populations tends to result in the case that many of the sample units do not contain information on the characteristic of interest (e.g., the rare animal, or people from the unusual income group). For finite rare populations the set of unordered distinct rare-units in a sample is a minimally sufficient statistic. In an example case study of a rare buttercup, the properties of the minimal sufficient estimator are explored. We compare the efficiency of the estimator for the population total based on the minimally sufficient statistic, with the standard estimator for a range of sample sizes. The variance of the minimally sufficient estimator was always smaller than the variance of the sufficient estimator. For rare populations where non-rare units can be distinguished from rare units because they have the same fixed value, the minimal sufficient statistic is the rare units, if any, in the sample.展开更多
The objective of this study was to determine the efficiency of biological nitrogen fixation (BNF) of local Bradyrhizobium isolates in soil of various fertility levels using 15N dilution technique. Local isolates wer...The objective of this study was to determine the efficiency of biological nitrogen fixation (BNF) of local Bradyrhizobium isolates in soil of various fertility levels using 15N dilution technique. Local isolates were obtained from cowpea rhizosphere in fields of different Iraqi provinces. Six isolates were selected in this study, which was conducted as a pot experiment under greenhouse conditions. Effects of the following fertility levels were evaluated: at F1, 0 mg N, P and K was added; at F2, 25 mg N/kg soil, 10 mg P/kg soil and 25 mg K/kg soil were added, respectively; the other two levels were F3 at which 50, 20 and 50 mg/kg soil and at F4 75, 30 and 75 mg/kg soil for N, P and K, respectively, were added. Urea, labeled with 15N 10% access atom (aa), was used as a source of N. The highest BNF was observed under the lowest fertility level, i.e., F1. BNF across all isolates was markedly decreased with the increase of nutrient application to soil, being totally eliminated at the highest fertility level F4. Numbers of nodules per plant root of all isolates were the least under the zero nutrients application and the highest nodules number were found under the highest levels of N, P and K application. Number of nodules does not necessarily reflect the best BNF efficiency of all isolates. However, fertility levels were of significant effect on average nodule number of all isolates. The lowest plant dry weight was under the first fertility level F1 irrelevant of Rhizobium isolates. In general, the highest plant dry weight was under the second soil fertility level F2.展开更多
文摘It is well understood that for conventional survey designs the set of unordered distinct units in a sample is a minimally sufficient statistic. This means that for inferential statistic of the sample, the value of the sampled units rather than the sample design is important. Sampling rare populations presents distinct challenges. Examples of rare populations are in biology with rare and endangered animals where there are only a few remaining individuals, or in social science, with the low incidence of people from an unusually high (or low) income group. Sampling rare populations tends to result in the case that many of the sample units do not contain information on the characteristic of interest (e.g., the rare animal, or people from the unusual income group). For finite rare populations the set of unordered distinct rare-units in a sample is a minimally sufficient statistic. In an example case study of a rare buttercup, the properties of the minimal sufficient estimator are explored. We compare the efficiency of the estimator for the population total based on the minimally sufficient statistic, with the standard estimator for a range of sample sizes. The variance of the minimally sufficient estimator was always smaller than the variance of the sufficient estimator. For rare populations where non-rare units can be distinguished from rare units because they have the same fixed value, the minimal sufficient statistic is the rare units, if any, in the sample.
文摘The objective of this study was to determine the efficiency of biological nitrogen fixation (BNF) of local Bradyrhizobium isolates in soil of various fertility levels using 15N dilution technique. Local isolates were obtained from cowpea rhizosphere in fields of different Iraqi provinces. Six isolates were selected in this study, which was conducted as a pot experiment under greenhouse conditions. Effects of the following fertility levels were evaluated: at F1, 0 mg N, P and K was added; at F2, 25 mg N/kg soil, 10 mg P/kg soil and 25 mg K/kg soil were added, respectively; the other two levels were F3 at which 50, 20 and 50 mg/kg soil and at F4 75, 30 and 75 mg/kg soil for N, P and K, respectively, were added. Urea, labeled with 15N 10% access atom (aa), was used as a source of N. The highest BNF was observed under the lowest fertility level, i.e., F1. BNF across all isolates was markedly decreased with the increase of nutrient application to soil, being totally eliminated at the highest fertility level F4. Numbers of nodules per plant root of all isolates were the least under the zero nutrients application and the highest nodules number were found under the highest levels of N, P and K application. Number of nodules does not necessarily reflect the best BNF efficiency of all isolates. However, fertility levels were of significant effect on average nodule number of all isolates. The lowest plant dry weight was under the first fertility level F1 irrelevant of Rhizobium isolates. In general, the highest plant dry weight was under the second soil fertility level F2.