A model-based method for estimating effective dispersal distance in tropical plant populations

Dispersal is a key mechanism to help populations propagate across space and thus is important in helping to understand spatial patterns. However, it is often difficult to quantify empirically as it requires intensive and detailed field study. Here we describe a method for estimating the effective dispersal distance of tropical plant populations. The method integrates a simple spatially explicit, individual-based dynamic model and spatial statistical analysis. The model is partly parameterized from spatial point pattern data as well as time series data from a 50 ha tropical forest plot in Barro Colorado Island (BCI) in Panama. Correlation between our estimated dispersal distances and those from inverse modeling based on field studies to date on BCI raises some questions about the match between our methods and those previously used. The method we propose can be generalized to any population for which spatial point pattern data are available. Additional field studies would be useful to further validate our method.     

Using genetic markers to estimate the pollen dispersal curve

Pollen dispersal is a critical process that shapes genetic diversity in natural populations of plants. Estimating the pollen dispersal curve can provide insight into the evolutionary dynamics of populations and is essential background for making predictions about changes induced by perturbations. Specifically, we would like to know whether the dispersal curve is exponential, thin-tailed (decreasing faster than exponential), or fat-tailed (decreasing slower than the exponential). In the latter case, rare events of long-distance dispersal will be much more likely. Here we generalize the previously developed TWOGENER method, assuming that the pollen dispersal curve belongs to particular one- or two-parameter families of dispersal curves and estimating simultaneously the parameters of the dispersal curve and the effective density of reproducing individuals in the population. We tested this method on simulated data, using an exponential power distribution, under thin-tailed, exponential and fat-tailed conditions. We find that even if our estimates show some bias and large mean squared error (MSE), we are able to estimate correctly the general trend of the curve - thin-tailed or fat-tailed - and the effective density. Moreover, the mean distance of dispersal can be correctly estimated with low bias and MSE, even if another family of dispersal curve is used for the estimation. Finally, we consider three case studies based on forest tree species. We find that dispersal is fat-tailed in all cases, and that the effective density estimated by our model is below the measured density in two of the cases. This latter result may reflect the difficulty of estimating two parameters, or it may be a biological consequence of variance in reproductive success of males in the population. Both the simulated and empirical findings demonstrate the strong potential of TWOGENER for evaluating the shape of the dispersal curve and the effective density of the population (d(e)).     

A new method for estimating the effective population size from allele frequency changes

A new procedure is proposed for estimating the effective population size, given that information is available on changes in frequencies of the alleles at one or more independently segregating loci and the population is observed at two or more separate times. Approximate expressions are obtained for the variances of the new statistic, as well as others, also based on allele frequency changes, that have been discussed in the literature. This analysis indicates that the new statistic will generally have a smaller variance than the others. Estimates of effective population sizes and of the standard errors of the estimates are computed for data on two fly populations that have been discussed in earlier papers. In both cases, there is evidence that the effective population size is very much smaller than the minimum census size of the population.     

A method to determine the mean pollen dispersal of individual plants growing within a large pollen source

Pollen dispersal has been recently focused on as a major issue in the risk assessment of transgenic crop plants. The shape of the pollen dispersal of individual plants is hard to determine since a very large number of plants must be monitored in order to track rare longdistance dispersal events. Conversely, studies using large plots as a pollen source provide a pollen distribution that depends on the shape of the source plot. We report here on a method based on the use of Fourier transforms by which the pollen dispersal of a single, average individual can be obtained from data using large plots as pollen sources, thus allowing the estimation of the probability of long-distance dispersal for single plants. This method is subsequently implemented on simulated data to test its susceptibility to random noise and edge effects. Its conditions of application and value for use in ecological studies, in particular risk assessment of the deliberate release of transgenic plants, are discussed.     

A new method for estimating effective population sizes from a single sample of multilocus genotypes

Equations for the effective size ( N_e ) of a population were derived in terms of the frequencies of a pair of offspring taken at random from the population being sibs sharing the same one or two parents. Based on these equations, a novel method (called sibship assignment method) was proposed to infer N_e from the sibship frequencies estimated from a sibship assignment analysis, using the multilocus genotypes of a sample of offspring taken at random from a single cohort in a population. Comparative analyses of extensive simulated data and some empirical data clearly demonstrated that the sibship assignment method is much more accurate [measured by the root mean squared error, RMSE, of 1/(2 N_e )] than other methods such as the heterozygote excess method, the linkage disequilibrium method, and the temporal method. The RMSE of 1/(2 N_e ) from the sibship assignment method is typically a small fraction of that from other methods. The new method is also more general and flexible than other methods. It can be applied to populations with nonoverlapping generations of both diploid and haplodiploid species under random or nonrandom mating, using either codominant or dominant markers. It can also be applied to the estimation of N_e for a subpopulation with immigration. With some modification, it could be applied to monoecious diploid populations with self-fertilization, and to populations with overlapping generations.     

The development of composite dispersal functions for estimating absolute pollen productivity in the Swiss Alps

Considering the complexity of real-world pollen dispersal, a single set of parameters may be inadequate to model pollen dispersal, especially as dispersal occurs on both local and regional scales. Here we combine more than one dispersal function into a composite dispersal function (CDF). The function incorporates multiple parameters and different modes of pollen transportation, and thus has the potential to better simulate the relationship between deposited pollen and the surrounding vegetation than would otherwise be possible. CDFs based on different dispersal functions and combinations of dispersal functions were evaluated using a pollen-trap dataset from the Swiss Alps. Absolute pollen productivity (APP) was estimated at 7,700 ± 2,000 grains cm⁻² year⁻¹ for Larix decidua, 13,500 ± 1,900 grains cm⁻² year⁻¹ for Picea abies and 95,600 ± 17,700 grains cm⁻² year⁻¹ for Pinus cembra (with 95% confidence level). The results are consistent with previous APP estimates made from the same dataset using different methods.     

水稻花粉扩散的模拟研究

水稻花粉扩散可导致基因飘流问题,尤其是转基因水稻,其外源基因的扩散可能会引发一系列的环境安全问题。为了模拟花粉扩散过程,2007年和2009年分别在南京(32°01′N,118°52′E)和溧水(31°35′N,119°11′E),以两优培九为材料,各组织了一次田间试验。通过空气中的花粉扩散浓度的观测和微气象塔梯度环境要素的采集,采用高斯烟羽模型为基础,利用最小二乘法,模拟了水稻花粉的扩散浓度,并利用独立试验数据验证了模型效果。结果表明:花粉释放集中在始花期后第1天到第5天的09:00-11:00,且花粉释放量与开花量显著相关(r=0.880**)。花粉浓度的模拟值和实测值变化趋势一致,其均方根误差和相对误差分别为0.509粒/(m2.d)和3.47%。该花粉扩散模型可以正确反映花粉扩散浓度的分布特征。但在花粉浓度的预测精度上,尤其是预测花粉远距离传播时,仍需要改进。     

一种等分作物花粉扩散圆形源区的方法

【背景】转基因作物花粉在大气中扩散会引起基因漂流,从而可导致不可预知的环境风险,运用模型预测可评估其花粉扩散状况、定量确定可靠的安全扩散距离。为了应用高斯烟羽模型应用于模拟转基因作物花粉在大气中的扩散浓度,提出了一种如何将半径为R的圆形花粉源区划分成许多等面积小面元的方法。【方法】通过数学推导,首次提出了各等面积面元中心点坐标的计算公式。【结果】根据在中国东北地区吉林省公主岭玉米花粉扩散和基因漂流的试验观测资料,将该公式应用到高斯烟羽扩散模型中,模拟了玉米花粉扩散到源区外不同距离处的浓度,对比花粉扩散模拟值与实测值,两者具有较好的一致性,表明应用该公式模拟花粉扩散能取得令人满意的效果。【结论与意义】分析证明这种推导划分半径为R的圆形花粉源区各面元中心点坐标的计算公式是可靠的,该方法可为应用高斯烟羽模型计算花粉源区内不同位置点单个源强对源区外某一距离处的花粉浓度的贡献提供便利。     

A method for estimating the effective number of loci affecting a quantitative character

A likelihood method is introduced that jointly estimates the number of loci and the additive effect of alleles that account for the genetic variance of a normally distributed quantitative character in a randomly mating population. The method assumes that measurements of the character are available from one or both parents and an arbitrary number of full siblings. The method uses the fact, first recognized by Karl Pearson in 1904, that the variance of a character among offspring depends on both the parental phenotypes and on the number of loci. Simulations show that the method performs well provided that data from a sufficient number of families (on the order of thousands) are available. This method assumes that the loci are in Hardy–Weinberg and linkage equilibrium but does not assume anything about the linkage relationships. It performs equally well if all loci are on the same non-recombining chromosome provided they are in linkage equilibrium. The method can be adapted to take account of loci already identified as being associated with the character of interest. In that case, the method estimates the number of loci not already known to affect the character. The method applied to measurements of crown–rump length in 281 family trios in a captive colony of African green monkeys (Chlorocebus aethiopus sabaeus) estimates the number of loci to be 112 and the additive effect to be 0.26 cm. A parametric bootstrap analysis shows that a rough confidence interval has a lower bound of 14 loci.     

A simple and effective method for isolating RNA from alfalfa pollen

Extraction of RNA from alfalfa pollen using conventional grinding devices resulted in low yields of degraded RNA; degradation appeared to be related to the length of time required to break open the pollen grains with such devices. A glass syringe was modified to provide the restricted, shearing environment necessary for rapidly rupturing this type of tissue. This apparatus would be useful for extracting a variety of molecules from pollen of any species, but is particularly valuable for species which produce low amounts of relatively small pollen grains.     

A new method for estimating age-at-death from the first rib

A new method for estimating adult age-at-death from the first rib was developed as a modification of the Kunos et al. (Am J Phys Anthropol 110 (1999) 303-323) method. Data were collected on three aspects of the first rib (costal face, rib head, and tubercle facet) for 470 known-age males of Balkan ancestry collected as evidence during investigations conducted by the International Criminal Tribunal for the former Yugoslavia (ICTY). Ages-at-death range from 12 to 90 years (mean of 47.7 years). Several variables were extracted from the original study utilizing all three skeletal aspects of the first rib. This list was modified to 11 variables as preliminary tests on seriations of the samples were undertaken. A cumulative probit model with age measured on a log scale was used to calculate the mean and standard deviation of the ages-of-transition for each component. Multivariate analysis of the three components was also performed. The lowest correlation (r = 0.079, controlling for age) was between the geometric shape of the costal face and the surface texture of the tubercle facet. Assuming a correlation of zero, these two traits were used to calculate the highest posterior density regions for estimating individual ages-at-death. Age-at-death estimates generated from 50 and 95% posterior density regions indicate that this method captures age-related change reaching the ninth decade. The Bayesian statistical approach used here produced a valuable and promising new method for estimating age-at-death. Additional research is necessary to determine if these highest posterior density regions produce results highly correlated with age in other samples and its applicability to females.     

A pseudo-likelihood method for estimating effective population size from temporally spaced samples

A pseudo maximum likelihood method is proposed to estimate effective population size (Ne) using temporal changes in allele frequencies at multi-allelic loci. The computation is simplified dramatically by (1) approximating the multi-dimensional joint probabilities of all the data by the product of marginal probabilities (hence the name pseudo-likelihood), (2) exploiting the special properties of transition matrix and (3) using a hidden Markov chain algorithm. Simulations show that the pseudo-likelihood method has a similar performance but needs much less computing time and storage compared with the full likelihood method in the case of 3 alleles per locus. Due to computational developments, I was able to assess the performance of the pseudo-likelihood method against the F-statistic method over a wide range of parameters by extensive simulations. It is shown that the pseudo-likelihood method gives more accurate and precise estimates of Ne than the F-statistic method, and the performance difference is mainly due to the presence of rare alleles in the samples. The pseudo-likelihood method is also flexible and can use three or more temporal samples simultaneously to estimate satisfactorily the NeS of each period, or the growth parameters of the population. The accuracy and precision of both methods depend on the ratio of the product of sample size and the number of generations involved to Ne, and the number of independent alleles used. In an application of the pseudo-likelihood method to a large data set of an olive fly population, more precise estimates of Ne are obtained than those from the F-statistic method.     

A new approach for estimating the crosslink density of covalently crosslinked ionic polysaccharide gels

For an ideal polysaccharide gel with a known total polymer chain contour length, crosslinks all of the same functionality and elastic chains all with the same contour length and stiffness, the gel crosslink density can readily be determined from measurements of the maximum volume of the swollen gel (Moe et al., (1991) Food Hydrocolloids, 5, (1/2), 119–123. In the case of randomly crosslinked polysaccharide gels, where the chain contour length between two adjacent crosslinks may vary greatly, it is often much more difficult to determine the crosslink density. This paper reports on an attempt to extend the use of maximum gel volume measurements to estimate crosslink density for the latter type of gel. This is done by calculating the maximum swelling volume for polymer networks with four-functional crosslinks, known elastic chain mean contour length and standard deviation. The numerical analysis involves the calculation of the equilibrium force at each crosslink as the network expands. This allows a detailed study of how the distribution of individual polymer chain contour lengths affects the maximum swelling volume. The computer simulation results are compared with the results from experimental measurements of the maximum volume of swollen covalently crosslinked sodium alginate gels.     

A new method for estimating joint parameters from motion data

Joint centers and axes of rotation (joint parameters) are central to all branches of movement analysis. In gait analysis, the standard protocol used to determine hip and knee joint parameters is prone to errors arising from palpation, anthropometric regression equations, and misplaced alignment devices. Several alternative methods have been proposed, but to date none have been shown to be accurate and reliable enough for use in the clinical setting. This article describes a new method for joint parameter estimation. The new method can be summarized as follows: (i) the motions of two adjacent segments spanning a single joint are tracked, (ii) the axis of rotation between every pair of observed segment configurations is computed, (iii) the most likely intersection of all axes (effective joint center) and most likely orientation of the axes (effective joint axis) is found. Initial validation of the method was conducted on a hinged mechanical analog and a single healthy adult subject. For the analog, the center was found to be within 3.8 mm of the geometric center and 2.0 degrees of the geometric axis (standard deviation). For the adult subject, hip centers varied on the order of 1-3 mm, knee centers by 3-9 mm, and knee axes by 2.0 degrees. The results suggest that the new method is an objective, precise, and practical alternative to the standard clinical approach.     

棉铃虫羽化高峰期有效积温预测法的校正

为减小年际间气温变化对昆虫有效积温预测误差的影响,以新疆石河子垦区121团棉铃虫Helicoverpa armigera(Hübner)羽化高峰期为例,利用single sine模型分别计算12年2种有效积温范围(10～30℃和10～35℃)的累计有效积温值,并获得其多年平均值,依此进行棉铃虫羽化高峰期预测;通过当年与12年(有效积温>0日期至羽化高峰日期)平均气温之差,对预测误差进行校正。结果表明:当年平均气温与12年平均值差值越大,预测误差也越大;各代直线回归校正模型均达到显著水平(P<0.05);2种有效积温范围下,校正后各代平均预测误差天数均有所减少,对越冬代误差校正效果最优,校正后各代历史符合率分别为83.33%、100%、100%和100%、100%、93.33%。该校正方法能够显著提高预测准确度,尤其适用于年际间棉铃虫发育期间平均气温变化较大的代别和地区,同时可为多种害虫预测误差校正提供了依据。