Further Study on the Statistical Test to Detect Spatial Pattern

In the study of spatial patterns, the statistic I' = (n — 1)s²/x was commonly used. In this paper, we found that x — s² has an approximated normal distribution with zero mean if the x_i's (i = 1 to n) are independent identically distributed Poisson variables. Based on this conclusion, the hypothesis that a point pattern is completely random can be tested directly. And a method for the test of spatial patterns was proposed which can be sued as an alternative to the Chi-square based dispersion index test.     

Intraspecific spatial niche differentiation: Evidence from Phyllostachys edulis

Interspecific niche differentiation has attracted much more attention than intraspecific niche differentiation. If the intraspecific competition of invasive species is greater than the interspecific competition, it should reduce the invasive abilities of invasive species. Thus, it is important to understand how invasive species avoid or reduce the intraspecific competition. Phyllostachys edulis in southern China is more competitive than many trees. After it invades a community, it can displace other trees. In the current study, we tested whether the different aged bamboo plants (aged two to eight in two-yr increments) exhibited spatial segregation (spatial niche differentiation). The study was performed in the Ecological Station of Dagang Mountain (114°30′～114°45′E, 27°30′～27°50′N), about 200 km east from Nanchang City, Jiangxi province, China. We recorded the planar coordinates of all the plants with diameter at breast height (DBH) ?3 cm. We used the conditional probability (type-specific probability) surface to show the spatial niche differentiation. We also compared the DBH of four aged groups of bamboo plants. We used the Shapiro–Wilk test to test the normality of DBHs of each age group. If DBHs did not follow the Normal distribution, we used the Weibull function to fit these data. Then we used the Kolmogorov–Smirnov test to test whether any two aged groups of DBHs came from the same population. At the end, we used the generalized additive models (GAMs) and a local regression model (LOESS) to explore whether there is a correlation between DBHs and the corresponding planar coordinates. We found that there was significant spatial segregation in four aged groups based on the statistical test. Bamboo plants may reduce their intraspecific competition by spatial niche differentiation. We found that the DBHs approximated the Weibull distribution, and there were very weak relationships between the DBHs and the spatial locations. We concluded that different aged bamboo plants exhibited spatial segregation and may reduce their intraspecific competition by spatial niche differentiation.     

On A Statistical Test to Detect Spatial Pattern

In the analysis of spatial patterns, the most extensively used index of dispersion is s²/m in which s² and m are respectively the sample variance and sample mean of the count x in each sample unit. For statistical testing, the statistic I' = (n — 1) s²/m has been introduced since it has an approximate X distribution under the null hypothesis that individuals are distributed randomly. The main problem with the use of index I' is that the random distribution and the superdispersed distribution are not distinguished. In this paper, we have tried to induce a new statistical method for the detection of spatial pattern, based on the special characteristic of Poisson distribution that both of the m and s² are the unbiased estimates of the parameter.     

The Consideration of Latency Periods in Cumulative Damage Models

The cumulative damage model as outlined in previous papers is unable to reproduce latency periods, particularly after short-term exposures. A refinement being straightforward within the present frame of point process theory is proposed using displacement processes applied to the single damages. For the displacement distribution, the lognormal distribution has been suggested. As in the previous model, exact formula for the behaviour of the survival function after the onset and the cessation of an additional exposure can be derived. Qualitative examinations demonstrate that the thus extended model shows the relevant features known from reports on shortterm exposures. Fitting the model to data of follow-up studies should provide a measure for the impact of an environmental exposure and the parameters for the distribution of the related latency period.     

Organization and evolution of mitochondrial gene clusters in human

Currently, the spatial patterns of mitochondrial genes and how the genomic localization of (pseudo)genes originated from mitochondrial DNA remain largely unexplained. The aim of this study was to elucidate the organization of mitochondrial (pseudo)genes given their evolutionary origin. We used a keyword finding method and a bootstrapping method to estimate parameter values that represent the distribution pattern of mitochondrial genes in the nuclear genome. Almost half of mitochondrial genes showing physical clusters were located in the pericentromeric and subtelomeric regions of the chromosome. Most interestingly, the size of these clusters ranged from 0.085 to 3.2 Mb (average ± SD 1.3 ± 0.73 Mb), which coincides with the size of the evolutionary pocket, or the average size of evolutionary breakpoint regions. Our findings imply that the localization of mitochondrial genes in the human genome is determined independent of adaptation.     

The Multiple Poisson Distribution,Its Characteristics and a Variety of Forms

The multiple Poisson distribution, known under different names, such as generalized Poisson, compound Poisson, composed Poisson, stuttering Poisson, Poisson power series, Poisson-stopped sum distribution, etc., plays an important role in discrete distribution theory. Here we want to show its basic characteristics, the variety of its forms and specify the generalizing distributions.