Inferring Speciation and Extinction Rates under Different Sampling Schemes

Large-scale phylogenies provide a valuable source to study background diversification rates and investigate if the rates have changed over time. Unfortunately most large-scale, dated phylogenies are sparsely sampled (fewer than 5% of the described species) and taxon sampling is not uniform. Instead, taxa are frequently sampled to obtain at least one representative per subgroup (e.g. family) and thus to maximize diversity (diversified sampling). So far, such complications have been ignored, potentially biasing the conclusions that have been reached. In this study I derive the likelihood of a birth-death process with non-constant (time-dependent) diversification rates and diversified taxon sampling. Using simulations I test if the true parameters and the sampling method can be recovered when the trees are small or medium sized (fewer than 200 taxa). The results show that the diversification rates can be inferred and the estimates are unbiased for large trees but are biased for small trees (fewer than 50 taxa). Furthermore, model selection by means of Akaike's Information Criterion favors the true model if the true rates differ sufficiently from alternative models (e.g. the birth-death model is recovered if the extinction rate is large and compared to a pure-birth model). Finally, I applied six different diversification rate models – ranging from a constant-rate pure birth process to a decreasing speciation rate birth-death process but excluding any rate shift models – on three large-scale empirical phylogenies (ants, mammals and snakes with respectively 149, 164 and 41 sampled species). All three phylogenies were constructed by diversified taxon sampling, as stated by the authors. However only the snake phylogeny supported diversified taxon sampling. Moreover, a parametric bootstrap test revealed that none of the tested models provided a good fit to the observed data. The model assumptions, such as homogeneous rates across species or no rate shifts, appear to be violated.

This study aimed at establishing a core collection based on the analysis of data from simple sequence repeat (SSR) alleles and morphological and agronomical traits (MOR) of the primary core collection from apricot germplasm resources. The index of genetic diversity, and frequency ratios of retention and loss of the alleles were studied between cluster and random sampling methods at five sampling ratios. The results demonstrate that the cluster sampling method preceded random sampling, and cluster sampling of SSR combined with MOR at the rate of 80% was the best sampling strategy among all the sampling methods. Based on this sampling strategy, 120 accessions were selected as the core collection of apricot, which retained 100% alleles in the primary core collection and 100% phenotypic characters. The core collection developed had also been evaluated by using the data of six quantitative traits, which showed that the established core collection could well represent the genetic diversity of the original collection of 1501 apricot accessions.

The underlying objective of epidemiological investigations is to extrapolate results from a sample to the relevant population. The simplest way of achieving this is to adopt a sampling strategy in which each individual in the population has the same chance of being selected--that is, to employ an 'equal probability of selection method' (epsem). The easiest ways of achieving this are to use simple random sampling or stratified random sampling with a constant sampling fraction. These strategies are often impracticable, however, particularly in large investigations covering a wide geographical area where resource implications dictate a more complex approach such as multi-stage or cluster sampling. Following detailed definitions and appropriate illustrations of these terms, the main purpose of this paper is to provide a working guide of how to achieve epsem using these various random sampling techniques. In brief, for multi-stage sampling with the rare feature of equal-sized first stage units, epsem is achieved by applying the above simple or stratified approaches to the first stage units. Even in the more realistic scenario of unequal first stage units, the same options apply provided that a fixed proportion of second stage units are to be selected (cluster sampling is in fact just one example of this, with 100% sampling of second stage units). If on the other hand a fixed number of second stage units are to be selected then for epsem the first stage units should be selected with each one having a probability proportionate to its size.

Several total-evidence dating studies under the fossilized birth-death (FBD) model have produced very old age estimates, which are not supported by the fossil record. This phenomenon has been termed "deep root attraction (DRA)." For two specific data sets, involving divergence time estimation for the early radiations of ants, bees, and wasps (Hymenoptera) and of placental mammals (Eutheria), it has been shown that the DRA effect can be greatly reduced by accommodating the fact that extant species in these trees have been sampled to maximize diversity, so-called diversified sampling. Unfortunately, current methods to accommodate diversified sampling only consider the extreme case where it is possible to identify a cut-off time such that all splits occurring before this time are represented in the sampled tree but none of the younger splits. In reality, the sampling bias is rarely this extreme and may be difficult to model properly. Similar modeling challenges apply to the sampling of the fossil record. This raises the question of whether it is possible to find dating methods that are more robust to sampling biases. Here, we show that the skyline FBD (SFBD) process, where the diversification and fossil-sampling rates can vary over time in a piecewise fashion, provides age estimates that are more robust to inadequacies in the modeling of the sampling process and less sensitive to DRA effects. In the SFBD model we consider, rates in different time intervals are either considered to be independent and identically distributed or assumed to be autocorrelated following an Ornstein-Uhlenbeck (OU) process. Through simulations and reanalyses of Hymenoptera and Eutheria data, we show that both variants of the SFBD model unify age estimates under random and diversified sampling assumptions. The SFBD model can resolve DRA by absorbing the deviations from the sampling assumptions into the inferred dynamics of the diversification process over time. Although this means that the inferred diversification dynamics must be interpreted with caution, taking sampling biases into account, we conclude that the SFBD model represents the most robust approach currently available for addressing DRA in total-evidence dating.

Background: Immunization averts a large number of children in each year. The burden of vaccine preventable diseases remains high in developing countries compared to developed countries. To overcome from this burden different types of immunization programs have been implemented. For better immunization coverage in developing countries, considerable progress is to be made to improve the knowledge and awareness regarding importance of vaccines. In this study a compara-tive study of immunization coverage under two sampling methods has been performed. Methods: In this study variance and design effect of proportion of children vaccinated against different types of vaccines (BCG, OPV, DPT, Hepatitis B, Hib, Measles and MMR) are estimated under two stage (30 × 30) cluster and systematic sampling for comparison of these two survey sampling methods. Also the homogeneity of clusters has been tested by using chi-square test. Results: It is observed that BCG, OPV and DPT vaccination coverage is more than 90% whereas Hepatitis B, Measles, Hib and MMR vaccination coverage is between 50% - 64% only. Here systematic random sampling is more complicated than two stage (30 × 30) cluster sampling. Also the result shows that the clusters are homogeneous with respect to proportion of children vaccinated. Conclusion: There is no significant difference between the two survey methodologies regarding the point estimation of vaccination coverage but estimation of variances of vaccination coverage is less in two stage (30 × 30) cluster sampling than that of the systematic sampling. Also the clusters are homogeneous. Very less improvement has been observed in case of fully vaccination coverage than the previous study. From the study it can be said that two stage (30 × 30) cluster sampling will be preferred to systematic sampling and simple random sampling method.

Random sampling and reconstruction of concentrated signals in a reproducing kernel space

Objective To estimate the prevalence of psoriasis in resident population in Hainan province through a large-scale,multi-center epidemiological survey.Methods Ten small towns or communities were selected from each of 18 cities or counties in Hainan province as survey sites.Multi-stage sampling strategies (including stratified sampling,simple random sampling and cluster sampling) were used in this study.After respondents signed an informed consent form,investigators completed a registration form containing information regarding clinical features of psoriasis,environmental factors,character trait,aggravating factors,trauma history,infection history,etc.Statistical analysis was carried out by the EpiData 3.1 and SPSS 17.0 software.Results This study recruited 35 314 subjects,and 30 935 responded with a return rate of 87.60％.The ratio of man to women was 1.2 ∶ 1,with an average age of (33.86 ± 17.78) years.Forty-six cases of psoriasis were confirmed in these respondents.The overall and standardized prevalence rate of psoriasis was 1.49‰ and 1.42‰ respectively.A significant increase was observed in the standardized prevalence rate of psoriasis in males compared with females (1.85‰ vs.0.84‰,x2 =6.86,P ＜ 0.01).The average age of onset was (33.49 ± 14.61) years,and the most common clinical type was psoriasis vulgaris (82.60％,38/46).Anxiety was the risk factor of psoriasis.The impact of psoriasis on the quality of life included barriers to social (89.13％) and physical activity (73.91％) as well as psychological disorders (86.97％).Conclusions The prevalence rate of psoriasis in resident population in Hainan province is lower than the national average level in China.It seems that multiple factors are implicated in the initiation and progression of psoriasis. Key words: Psoriasis; Epidemiology; Hainan

According to Weibull distribution timing truncation test, considering that it is difficult to have a strictly defined complete failure samples in engineering practice, so the life sampling schemes of censored failure samples are discussed. Here, we have considered random right censored samples with different censored ratios. Compared with other sampling studies, this paper is not limited to explore more sampling theories, but uses SPSS software to give the specific operation processes of three sampling schemes: simple random sampling, two-stage sampling and Bayes sampling considering the minimum total cost, as well as the discussion on the verification analysis of the sampling accuracy. In order to simplify the estimation of Weibull distribution parameters, the estimated parameters are obtained by the probability plot analysis of Minitab software, thus the error between the sample’s MTBF (Mean Time Between Failure) and the overall MTBF is calculated. The sensitivity of Weibull distribution parameters is obtained by Minitab software. Finally, according to the accuracy of the three sampling schemes with different censored ratios, the optimal life sampling decision is obtained, which may provide sampling reference for the decision makers.

Species diversity patterns are governed by complex interactions among biotic and abiotic factors over time and space, but are essentially the result of the diversification dynamics (differential speciation and extinction rates) over the long‐term evolutionary history of a clade. Previous studies have suggested that temporal variation in global temperature drove long‐term diversity changes in Crocodylia, a monophyletic group of large ectothermic organisms. We use a large database of crocodylian fossil occurrences (192 spp.) and body mass estimations, under a taxic approach, to characterize the global diversification dynamics of crocodylians since the Cretaceous, and their correlation with multiple biotic and abiotic factors in a Bayesian framework. The diversification dynamic of crocodylians, which appears to have originated in the Turonian (c. 92.5 Ma), is characterized by several phases with high extinction and speciation rates within a predominantly low long‐term mean rate. Our results reveal long‐term diversification dynamics of Crocodylia to be a highly complex process driven by a combination of biotic and abiotic factors which influenced the speciation and extinction rates in dissimilar ways. Higher crocodylian extinction rates are related to low body mass disparity, indicating selective extinctions of taxa at both ends of the body mass spectrum. Speciation rate slowdowns are noted when the diversity of the clade is high and the warm temperate climatic belt is reduced. Our finding supports the idea that temporal variations of body mass disparity, self‐diversity, and the warm climate belt size provided more direct mechanistic explanations for crocodylian diversification than do proxies of global temperature.

Ecologists rely on field surveys to monitor long‐term ecological change but finite sampling and the prevalence of rare species mean that surveys inevitably miss some species present at a given location. These ‘phantom species’ produce pseudo‐turnover by inflating observed rates of local colonization and extinction in resurvey studies, especially among rare species. In this paper, we quantify the probability that pseudo‐turnover occurs due to imprecise plot relocation and/or shifts in where individuals are located. Using sampling models derived from the binomial distribution, we estimate probabilities of missing species as a function of local abundance and sampling intensity. Spatially explicit simulations confirm that our binomial model is robust to non‐random sampling schemes and clumped species distributions. False absences decline predictably as species abundance and sampling intensity increase allowing us to statistically adjust naïve estimates of colonization and extinction for expected rates of pseudo‐turnover. To illustrate the model's real‐world utility, we analyze apparent colonizations and extinctions for 331 species distributed over 83 sites in southern Wisconsin forests surveyed in both the 1950s and 2000s. Limited sampling in the 1950s means expected rates of pseudo‐colonization are appreciable. Accounting for pseudo‐turnover thus reduces estimated community‐wide colonization rates by 51% compared to naïve (observed) rates. More complete sampling in the 2000s limited overestimates of local extinction to 14%. We distinguish three zones of inference based on sampling intensity and species abundance where: 1) naïve estimates approximate true values of turnover, 2) adjustments are important, and 3) species are too rare relative to sampling to reliably infer turnover. Accounting for phantom species substantially improves our ability to accurately estimate local colonization and extinction rates, enhancing our ability to infer community dynamics and monitor long‐term ecological change.

Data on the lateral variability of soil loss from Submediterranean rangelands are presented. Modified Gerlach troughs were used to measure both rill and interrill erosion. Random, systematic, stratified random, and cluster sampling methods were tested for various numbers of plots and plot widths in order to find the method that gives the most accurate estimate of soil loss. If both the rill and interrill subpopulations are sampled, random sampling and stratified random sampling give almost identical standard errors. Cluster sampling yields larger errors and is therefore less effective. Systematic sampling, however, allows one to choose more accurate samples of an economical size, but its efficacy depends largely on the number of rills in the study area. The smallest standard errors are obtained by measuring the total rill erosion and by sampling only the interrill subpopulation. When this procedure is applied, the four sampling methods turn out to be equally accurate.

To explore the situation and the affect factors of myopia and scientificalness and effectiveness of eye exercises about primary and middle school students. Through the random cluster sampling method, 20 000 students of 90 schools including key and non-key primary or junior or senior school in country and city of shandong, qinghai, yunnan, Shanghai and wenzhou were random selected. Primary students is 11 246 junior students is 3673 senior students is 4220.We surveyed related situation of eye exercises, myopia. a total of 19 139 valid questionnaires were received. By random sampling stratification method, freshmen were selected and retrospective surveyed. 929 freshmen have normal vision when they graduated primary school. 338 freshmen have normal vision when they graduated primary school.2 groups are considered analysis object, and Myopic students of the former in junior school stages and the latter in senior school stages are considered case group, normal vision are considered control group, and then through the Logistic multiple stepwise regression analysis, a regression analysis model is established. This survey show that myopia prevalence was 13.7% of primary students, 42.9% of junior students, 69.7% of senior students. According to the significant P < 0.001, Rsquare = 0.14, the result shows that the model has the significant statistical significance. Among the influence factors, whether to long-term excessive use eye is the most significant, and following by outdoor activities and gender. A chi-square test χ(2) = 0.371 and P = 0.543 show that doing eye exercises was not statistically significant to prevalence of myopia. The influence factors are changed, and the preventive methods should be adjusted with the social environment.

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&lt;p&gt;Although not as efficient as simple random sampling, cluster sampling has been regarded as a&lt;br /&gt; valid sampling technique when the researcher is attempting to save cost. In order to do so, it is&lt;br /&gt; necessary that random selection occurs in all stages of sampling. This simulation study&lt;br /&gt; examines purposeful selection of cluster sampling in the second stage of a two stage cluster&lt;br /&gt; design.&lt;/p&gt;

The topic of this thesis is the latitudinal diversity gradient: the general increase in numbers of species from high latitudes towards the equator. Although it is a well-documented and very general pattern, there is little consensus among biologists as to the causes of high tropical species richness. In Chapter 1 I give an overview of the latitudinal diversity gradient and hypotheses proposed to explain it, and outline a framework for developing and testing hypotheses. The emphasis in this thesis is on non-equilibrium hypotheses, and in particular on the idea that rates of species diversification are higher at low latitudes. In Chapter 2 I directly test the hypothesis that rates of species diversification increase towards the equator, using the phylogenetic method of sister-group comparisons. For birds and butterflies, 1 show that there does indeed appear to be an increase in rates of diversification towards lower latitudes. One possible explanation for this pattern links climatic conditions at low latitudes to faster speciation, via a causal chain which includes a higher rate of molecular evolution. In Chapter 3 I test the prediction that rates of molecular evolution are faster at low latitudes, using phylogenies reconstructed from DNA sequence data for birds. Although the results provide no evidence for a latitudinal effect on rates of cytb and ND2 evolution in birds, this chapter demonstrates a way in which further tests on a wider range of genes and taxa can be carried out as more sequence data becomes available. If rates of diversification are higher in the tropics, this may result from latitudinal gradients in life history traits which could influence rates of speciation or extinction. However, previous attempts to test for such patterns have rarely controlled for phylogenetic relationships among species, and have never controlled for geographic range overlap. In Chapter 4 I present a method for analyzing latitudinal variation in life history traits which takes both of these problems into account. For birds, this method indicates strong latitudinal variation in geographic range size and clutch size, less strong variation in body size and niche width, and no variation in the strength of sexual selection. While this does not prove that life history plays a part in generating the latitudinal diversity gradient, a robust demonstration of latitudinal variation in life history traits is an important prerequisite for any hypotheses which link life history with high tropical species richness. Speciation and extinction rates are believed to vary with species' life history and ecology. If speciation or extinction rates also vary with latitude, we should expect species with certain traits to show stronger latitudinal diversity gradients than others. We should also expect to see latitudinal variation in the macroecological structure of species assemblages. Chapters 5 and 6 confirm these expectations. In Chapter 5 I show that smaller-bodied bird species have steeper latitudinal diversity gradients than larger species. This is reflected in systematic latitudinal variation in the shape of body size frequency distributions, usually thought to be relatively consistent across regions. In Chapter 6 I show that body size - abundance relationships in the Australian marsupial fauna differ considerably between temperate and tropical subsets of the fauna. Whereas the temperate species display the typical negative relationship, the tropical species show no significant relationship. This pattern is consistent with the explanation that extinction rates vary with respect to body size, abundance and the latitude in which a species occurs. Together, the results of the analyses presented in this thesis provide evidence in favour of the non-equilibrium view that there are more species in the tropics because rates of species diversification are higher. It seems likely that this is due to latitudinal variation in environmental conditions, leading to latitudinal variation in species' life histories and the structure of species assemblages, and to latitudinal variation in rates of speciation or extinction. However, it is still difficult to judge whether it is variation in speciation rate (cradle model) or extinction rate (museum model) which is of primary importance, or if both are equally important. Further work on this question, applying the large-scale comparative methodology used here, will be necessary to progress towards a full understanding of the high species richness of the tropics.