Volume estimation of biological objects by systematic sections

The absolute volume of biological objects is often estimated stereologically from an exhaustive set of systematic sections. The usual volume estimator is the sum of the section contents times the distance between sections. For systematic sectioning with a random start, it has been recently shown that is unbiased when m, the ratio between projected object length and section distance, is an integer number (Cruz-Orive 1985). As this quantity is no integer in the real world, we have explored the properties of in the general and realistic situation m . The unbiasedness of under appropriate sampling conditions is demonstrated for the arbitrary compact set in 3 dimensions by a rigorous proof. Exploration of further properties of for the general triaxial ellipsoid leads to a new class of non-elementary real functions with common formal structure which we denote as np-functions. The relative mean square error (CE ²) of in ellipsoids is an oscillating differentiable np-function, which reduces to the known result CE ²= 1/(5m ⁴) for integer m. As a biological example the absolute volumes of 10 left cardiac ventricles and their internal cavities were estimated from systematic sections. Monte Carlo simulation of replicated systematic sectioning is shown to be improved by using m instead of m . In agreement with the geometric model of ellipsoids with some added shape irregularities, mean empirical CE was proportional to m ^–1.36 and m^–1.73 in the cardiac ventricle and its cavity. The considerable variance reduction by systematic sectioning is shown to be a geometric realization of the principle of antithetic variates.     

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.     

Continuous monitoring of lactate during exercise in humans using subcutaneous and transcutaneous microdialysis

We have evaluated the possibility of monitoring the plasma lactate concentration in human volunteers during cycle ergometer exercise using subcutaneous and transcutaneous microdialysis. In transcutaneous microdialysis, the relative increase in dialysate lactate concentration exceeded that of plasma lactate concentration by a factor of 6 during exercise due to exercise-induced lactate secretion in sweat. During exercise the subcutaneous microdialysis dialysate lactate concentration underestimated the plasma lactate concentration possibly due to diffusion limitation or adipose tissue lactate production. While it was demonstrated that microdialysis can be used for on-line lactate monitoring, neither subcutaneous nor transcutaneous dialysate lactate concentration were linearly related to the plasma lactate concentration during exercise, and it was found therefore that it was not possible to monitor directly plasma lactate concentration during exercise.     

The posterior probability distribution of alignments and its application to parameter estimation of evolutionary trees and to optimization of multiple alignments

How to sample alignments from their posterior probability distribution given two strings is shown. This is extended to sampling alignments of more than two strings. The result is first applied to the estimation of the edges of a given evolutionary tree over several strings. Second, when used in conjunction with simulated annealing, it gives a stochastic search method for an optimal multiple alignment.Correspondence to: L. Allison     

寄生蜂种群繁殖分布时间特征的研究

运用１０种寄生蜂的２３张生殖力表资料,分析比较了这些种群繁殖分布的特征．结果表明,寄生蜂种群繁殖具有相似的分布特征,种群繁殖集中分布在生殖头ｄ天内,在生殖头ｄ／２天内繁殖分布更为集中．在生殖头ｄ天内种群繁殖对种群增长的贡献几乎均达到１００％,其中大部分贡献是在生殖头ｄ／２天内实现的．这种繁殖分布特征对于寄生蜂种群内禀增长率的测定和掌握种群数量动态的时间特性十分重要．本文结合Ｉｗａｏ零频率法和Ｇｅｒｒａｒｄ阈限密度法,提出一种改进的种群密度估计方法──“综合阈限密度估计法”,并由此探讨了苹果树上山楂叶螨成螨的密度估计及其抽样技术．采用零样频率来估计成螨的平均密度,并得到用概率保证的理论抽样数模型．比较结果表明,零频率法所需的理论抽样数少于直接计数法．综合阈限密度估计法的拟合效果更为显著．     

山楂叶螨种群空间格局及其应用的研究Ⅱ．成螨种群密度综合估计及其抽样技术

本文结合Ｉｗａｏ零频率法和Ｇｅｒｒａｒｄ阈限密度法,提出一种改进的种群密度估计方法──“综合阈限密度估计法”,并由此探讨了苹果树上山楂叶螨成螨的密度估计及其抽样技术．采用零样频率来估计成螨的平均密度,并得到用概率保证的理论抽样数模型．比较结果表明,零频率法所需的理论抽样数少于直接计数法．综合阈限密度估计法的拟合效果更为显著．     

Evaluation of several methods for estimating phylogenetic trees when substitution rates differ over nucleotide sites

Several maximum likelihood and distance matrix methods for estimating phylogenetic trees from homologous DNA sequences were compared when substitution rates at sites were assumed to follow a gamma distribution. Computer simulations were performed to estimate the probabilities that various tree estimation methods recover the true tree topology. The case of four species was considered, and a few combinations of parameters were examined. Attention was applied to discriminating among different sources of error in tree reconstruction, i.e., the inconsistency of the tree estimation method, the sampling error in the estimated tree due to limited sequence length, and the sampling error in the estimated probability due to the number of simulations being limited. Compared to the least squares method based on pairwise distance estimates, the joint likelihood analysis is found to be more robust when rate variation over sites is present but ignored and an assumption is thus violated. With limited data, the likelihood method has a much higher probability of recovering the true tree and is therefore more efficient than the least squares method. The concept of statistical consistency of a tree estimation method and its implications were explored, and it is suggested that, while the efficiency (or sampling error) of a tree estimation method is a very important property, statistical consistency of the method over a wide range of, if not all, parameter values is prerequisite.     

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     

畜禽遗传资源冷冻保存中的取样方法探讨

本文基于遗传学和数理统计原理,提出了运用冷冻生殖细胞的方法长期保存畜禽遗传资源时,冷冻生殖细胞的4种取样方法,并推证了其误差公式和最低保存数量的估计公式。最后通过实例对公式的实际应用作了说明和讨论分析。