Unbiased Confidence Intervals for the Odds Ratio of Two Independent Binomial Samples with Application to Case–Control Data

The problem of confidence interval construction for the odds ratio of two independent binomial samples is considered. Two methods of eliminating the nuisance parameter from the exact likelihood, conditioning and maximization, are described. A conditionally exact tail method exists by putting together upper and lower bounds. A shorter interval can be obtained by simultaneous consideration of both tails. We present here new methods that extend the tail and simultaneous approaches to the maximized likelihood. The methods are unbiased and applicable to case-control data, for which the odds ratio is important. The confidence interval procedures are compared unconditionally for small sample sizes in terms of their expected length and coverage probability. A Bayesian confidence interval method and a large-sample chi2 procedure are included in the comparisons.     

Evaluation of exact and asymptotic interval estimators in logistic analysis of matched case-control studies.

We compare six methods for constructing confidence intervals for a single parameter in stratified logistic regression. Three of these are based on inversion of standard asymptotic tests--namely, the Wald, the score, and the likelihood ratio tests. The other three are based on the exact distribution of the sufficient statistic for the parameter of interest. These include the traditional exact method of constructing confidence intervals, and two others, the mid-P and mean-P methods, which are modifications of this procedure that aim at reducing the conservative bias of the exact method. Using efficient algorithms, the six methods are compared by determination of their exact coverage levels in a series of conditional sample spaces. An incident case-control study of lung cancer in women is used to further illustrate the differences among the various methods. Computation of coverage functions is seen as a useful graphical diagnostic tool for assessing the appropriateness of different methods. The mid-P and the score methods are seen to have better coverage properties than the other four.     

Exact unconditional inference for risk ratio in a correlated 2 x 2 table with structural zero

In this article, we consider small-sample statistical inference for rate ratio (RR) in a correlated 2 x 2 table with a structural zero in one of the off-diagonal cells. Existing Wald's test statistic and logarithmic transformation test statistic will be adopted for this purpose. Hypothesis testing and confidence interval construction based on large-sample theory will be reviewed first. We then propose reliable small-sample exact unconditional procedures for hypothesis testing and confidence interval construction. We present empirical results to evince the better confidence interval performance of our proposed exact unconditional procedures over the traditional large-sample procedures in small-sample designs. Unlike the findings given in Lui (1998, Biometrics 54, 706-711), our empirical studies show that the existing asymptotic procedures may not attain a prespecified confidence level even in moderate sample-size designs (e.g., n = 50). Our exact unconditional procedures on the other hand do not suffer from this problem. Hence, the asymptotic procedures should be applied with caution. We propose two approximate unconditional confidence interval construction methods that outperform the existing asymptotic ones in terms of coverage probability and expected interval width. Also, we empirically demonstrate that the approximate unconditional tests are more powerful than their associated exact unconditional tests. A real data set from a two-step tuberculosis testing study is used to illustrate the methodologies.     

Small-sample confidence limits for parameters under inequality constraints with application to quantal bioassay

A family of methods is presented for constructing confidence limits for the parameters of a collection of distributions when a simple ordering is assumed among the parameters. The methods are shown to yield confidence limits that are exact or conservative for finite samples. For discrete distributions, one of the methods produces confidence limits that are at least as tight as the limits produced by a commonly used single-sample procedure. Confidence limits are demonstrated for a binomial quantal bioassay problem assuming a nondecreasing dose-response function. Results of a simulation study show that competing asymptotic methods can produce serious discrepancies between nominal and actual coverage probabilities for binomial samples of sizes up to 30, and demonstrate that the new approach can be competitive with the asymptotic methods when the latter maintain their nominal error rates.     

Carbon and nutrient physiology in shrubs at the upper limits: a multispecies study

高山分布上限灌木的碳与养分生理碳水化合物不足是高山林线树种生长限制假说之一,国内外以碳水化合物为基础的高山林线研究已有很多,而与高山林线相比,人们对碳水化合物在灌丛线形成中的作用知之甚少。除此之外,土壤养分亦被视为限制高山树种向上分布的重要因素之一。本研究将探究欧亚多种高山灌木不同器官中非结构性碳水化合物(NSCs)、氮(N)和磷(P)在不同季节及高低海拔上的含量变化规律。研究结果显示,除了与夏季相比冬季细根中具有较低的P含量以外,不同海拔与季节对灌木不同器官中的N和P含量均无显著影响。冬季灌木枝条中的NSCs和可溶性糖含量显著高于夏季。海拔与季节对细根中NSCs、淀粉、可溶性糖和糖与淀粉比值的影响均有显著的交互作用。在冬季,灌木细根中的可溶性糖与淀粉含量在海拔上限处要显著低于其在低海拔处;而在夏季,这些指标在高低海拔间均无显著差异。本研究结果表明,与高山林线树种相似,海拔分布上限的灌木冬季细根中较低的非结构性碳水化合物含量可能限制了灌木的向上分布。     

林地土壤水源涵养多因素复合模拟研究——以苕溪流域为例

为了研究不同植被覆盖度、不同林相及不同林种林下土壤水源涵养的特性,以浙江省苕溪流域上游区为例,采用野外不同林种土壤持水能力定时定点实测取样、室内不同植被覆盖度(0,15%,30%,45%,60%,75%,90%)、不同林相(上层覆盖、下层覆盖、上下层覆盖)的物理模型人工模拟降雨试验方法,通过不同深度土壤水分含量测试、产汇流和入渗系数计算,探索了林地不同经营管理方式下土壤涵养水源的特性,结果表明:(1)地表入渗系数随植被覆盖度的增加而增大,随坡长增加入渗系数的增长比率增加,降雨过程中植被覆盖度对入渗系数的影响比坡长的影响大。(2)不同林相的模拟试验结果表明,地表入渗系数排序为上下层覆盖上层覆盖下层覆盖裸地。随着产流历时增加,林下土层的蓄水量呈线型增加,与裸坡比较,累积蓄水量增加百分数为:上层覆盖为23%,下层覆盖为29%,上下层覆盖为37%。(3)通过监测不同林地不同深度土壤含水率的变化,并与裸地进行对比得出不同林地涵养水源能力的强弱。其蓄水能力排序分别为板栗林茶园竹林。研究结果为林地管理、林相培育和林下土壤持水能力的提高具有科学方法论上的支撑和生产实践方面的借鉴。     

Confidence Intervals for Microbial Density Using Serial Dilutions with MPN Estimates

An alteration to Woodward's methods is recommended for deriving a 1 — α confidence interval for microbial density using serial dilutions with most-probable-number (MPN) estimates. Outcomes of the serial dilution test are ordered by their MPNs. A lower limit for the confidence interval corresponding to an outcome y is the density for which y and all higher ordered outcomes have total probability α/2. An upper limit is derived in the analogous way. An alteration increases the lowest lower limits and decreases the highest upper limits. For comparison, a method that is optimal in the sense of null hypothesis rejection is described. This method ranks outcomes dependent upon the microbial density in question, using proportional first derivatives of the probabilities. These and currently used methods are compared. The recommended method is shown to be more desirable in certain respects, although resulting in slightly wider confidence intervals than De Man's (1983) method.     

Asymmetric boundary shifts of tropical montane Lepidoptera over four decades of climate warming

Aim To estimate whether species have shifted at equal rates at their leading edges (cool boundaries) and trailing edges (warm boundaries) in response to climate change. We provide the first such evidence for tropical insects, here examining elevation shifts for the upper and lower boundaries shifts of montane moths. Threats to species on tropical mountains are considered. Location Mount Kinabalu, Sabah, Malaysia. Methods We surveyed Lepidoptera (Geometridae) on Mount Kinabalu in 2007, 42 years after the previous surveys in 1965. Changes in species upper and lower boundaries, elevational extents and range areas were assessed. We randomly subsampled the data to ensure comparable datasets between years. Estimated shifts were compared for endemic versus more widespread species, and for species that reached their range limits at different elevations. Results Species that reached their upper limits at 2500–2700 m (n= 28 species, 20% of those considered) retreated at both their lower and upper boundaries, and hence showed substantial average range contractions (?300 m in elevational extent and ?45 km² in estimated range area). These declines may be associated with changes in cloud cover and the presence of ecological barriers (geological and vegetation transitions) which impede uphill movement. Other than this group, most species (n= 109, 80% of the species considered) expanded their upper boundaries upwards (by an average of 152 m) more than they retreated at their lower boundaries (77 m). Main conclusions Without constraints, leading margins shifted uphill faster than trailing margins retreated, such that many species increased their elevational extents. However, this did not result in increases in range area because the area of land available declines with increasing elevation. Species close to a major ecological/geological transition zone on the mountain flank declined in their range areas. Extinction risk may increase long before species reach the summit, even when undisturbed habitats are available.     

Upward shift in elevational plant species ranges in Sikkilsdalen,central Norway

Phytosociological studies can be an important tool to detect temporal vegetation changes in response to global climate change. In this study, we present the results of a resurvey of a plot‐based phytosociological study from Sikkilsdalen, central Norway, originally executed between 1922 and 1932. By using a detailed phytosociological study we are able to investigate several aspects of elevational shifts in species ranges. Here we tested for upward and downward shifts in observed upper and lower distribution limits of species, as well as changes in species optima along an elevational gradient, and related the observed range shifts to species traits that could explain the observed trends. More species shifted upwards than downwards, independently of whether we were investigating shifts in species’ upper or lower distribution ranges or in species optima. However, shifts in species upper range margins changed independently of their lower range margins. Linking different species traits to the magnitude of shifts we found that species with a higher preference for prolonged snow cover shifted upwards more in their upper elevational limits and in their optima than species that prefer a shorter snow cover, whereas no species traits were correlated with the magnitude of changes in lower limits. The observed change in species ranges concord both with studies on other mountains in the region and with studies from other alpine areas. Furthermore, our study indicates that different factors are influencing species ranges at the upper and lower range limits. Increased precipitation rates and increased temperatures are considered the most important factors for the observed changes, probably mainly through altering the pattern in snow cover dynamics in the area.     

Diversity and spatial pattern of coral communities in the Red Sea upper twilight zone

Summary This is the first study based on numerical analysis of the abundance of 11 scleractinian corals of depths at between 100–210 m in the Red Sea twilight zone. Two distinct coral communities were found: a Leptoseris fragilis community at a depth of 100–130 m (zone 1) and a Dendrophillia horsti community below 130 m (zone 2, 3). Population densities and coral coverage are very low; distribution of individuals is highly clumped. Highest observed densities on 100 m² were 2720 individuals for L. fraglis, 2720 for D. horsti and 2260 for Javania insignis. Calculated coverage rates were maximally 3.6% (L. fragilis), 0.08% (D. horsti) and 0.11% (J. insignis). L. fragilis, the only symbiont bearing coral, was very abundant. It has an unusual depth range for a photosynthesising coral. Coral density is only weakly correlated with hard bottom coverage. Species diversity with an average of 8 species is highest at 120–170 m and decreases in shallower and deeper water. The study depth range is a transient zone for coral distribution. It contains the upper distribution limits of a few deep sea corals and the lower ones of several shallower water species. Ahermatypic corals, collected at 160–170 m depth, were transplanted from their original depth to 159, 118, 70 and 40 m; after one year most species survived transplantation far beyond their upper distributional limits. The symbiotic L. fragilis, collected at 120 m, survived transplantation to deep water (159 m) as well as shallow zones (90, 70 and 40 m). The study demonstrates the feasibility of line-transect methods for coral community studies with a submersible.     

Acclimation effects on critical and lethal thermal limits of workers of the Argentine ant, Linepithema humile

For the Argentine ant Linepithema humile, bioclimatic models often predict narrower optimal temperature ranges than those suggested by behavioural and physiological studies. Although water balance characteristics of workers of this species have been thoroughly studied, gaps exist in current understanding of its thermal limits. We investigated critical thermal minima and maxima and upper and lower lethal limits following acclimation to four temperatures (15, 20, 25, 30 degrees C; 12L:12D photoperiod) in adult workers of the Argentine ant, L. humile, collected from Stellenbosch, South Africa. At an ecologically relevant rate of temperature change of 0.05 degrees Cmin(-1), CTMax varied between 38 and 40 degrees C, and CTMin varied between 0 and 0.8 degrees C. In both cases the response to acclimation was weak. A significant time by exposure temperature interaction was found for upper and lower lethal limits, with a more pronounced effect of acclimation at longer exposure durations. Upper lethal limits varied between 37 and 44 degrees C, whilst lower lethal limits varied between -4 and -10.5 degrees C, with an acclimation effect more pronounced for upper than lower lethal limits. A thermal envelope for workers of the Argentine ant is provided, demonstrating that upper thermal limits do likely contribute to distributional limits, but that lower lethal limits and limits to activity likely do not, or at least for workers who are not exposed simultaneously to the demands of load carriage and successful foraging behaviour.     

Confidence intervals for directly standardized rates using mid‐p gamma intervals

Directly standardized rates continue to be an integral tool for presenting rates for diseases that are highly dependent on age, such as cancer. Statistically, these rates are modeled as a weighted sum of Poisson random variables. This is a difficult statistical problem, because there are k observed Poisson variables and k unknown means. The gamma confidence interval has been shown through simulations to have at least nominal coverage in all simulated scenarios, but it can be overly conservative. Previous modifications to that method have closer to nominal coverage on average, but they do not achieve the nominal coverage bound in all situations. Further, those modifications are not central intervals, and the upper coverage error rate can be substantially more than half the nominal error. Here we apply a mid‐p modification to the gamma confidence interval. Typical mid‐p methods forsake guaranteed coverage to get coverage that is sometimes higher and sometimes lower than the nominal coverage rate, depending on the values of the parameters. The mid‐p gamma interval does not have guaranteed coverage in all situations; however, in the (not rare) situations where the gamma method is overly conservative, the mid‐p gamma interval often has at least nominal coverage. The mid‐p gamma interval is especially appropriate when one wants a central interval, since simulations show that in many situations both the upper and lower coverage error rates are on average less than or equal to half the nominal error rate.     

Importance of abiotic stress as a range-limit determinant for European plants: insights from species responses to climatic gradients

Aim We examined whether species occurrences are primarily limited by physiological tolerance in the abiotically more stressful end of climatic gradients (the asymmetric abiotic stress limitation (AASL) hypothesis) and the geographical predictions of this hypothesis: abiotic stress mainly determines upper‐latitudinal and upper‐altitudinal species range limits, and the importance of abiotic stress for these range limits increases the further northwards and upwards a species occurs. Location Europe and the Swiss Alps. Methods The AASL hypothesis predicts that species have skewed responses to climatic gradients, with a steep decline towards the more stressful conditions. Based on presence–absence data we examined the shape of plant species responses (measured as probability of occurrence) along three climatic gradients across latitudes in Europe (1577 species) and altitudes in the Swiss Alps (284 species) using Huisman–Olff–Fresco, generalized linear and generalized additive models. Results We found that almost half of the species from Europe and one‐third from the Swiss Alps showed responses consistent with the predictions of the AASL hypothesis. Cold temperatures and a short growing season seemed to determine the upper‐latitudinal and upper‐altitudinal range limits of up to one‐third of the species, while drought provided an important constraint at lower‐latitudinal range limits for up to one‐fifth of the species. We found a biome‐dependent influence of abiotic stress and no clear support for abiotic stress as a stronger upper range‐limit determinant for species with higher latitudinal and altitudinal distributions. However, the overall influence of climate as a range‐limit determinant increased with latitude. Main conclusions Our results support the AASL hypothesis for almost half of the studied species, and suggest that temperature‐related stress controls the upper‐latitudinal and upper‐altitudinal range limits of a large proportion of these species, while other factors including drought stress may be important at the lower range limits.     

Stomatal Behavior and CO(2) Exchange Characteristics in Amphistomatous Leaves

The possibility that differences in stomatal conductance between upper and lower surfaces of amphistomatous leaves are adaptations to differences in CO₂ exchange characteristics for the two surfaces was investigated. The ratio of upper to lower stomatal conductance was found to change little in response to light and humidity for well-watered sunflower (Helianthus annuus L.) plants. Stressing the plants (ψ = −17 bars) and rewatering 1 day before gas exchange measurements reduced upper conductance more severely than lower in both indoor- and outdoor-grown plants, and caused small changes in conductance ratio with light and humidity. A similar pattern was found using outdoor grown sunflower and cocklebur (Xanthium strumarium L.) plants. Calculated intercellular CO₂ concentrations for upper and lower surfaces were always close to identical for a particular set of environmental conditions for both sunflower and cocklebur, indicating that no differences in CO₂ exchange characteristics exist between the two surfaces. By artificially creating a CO₂ gradient across the leaf, the resistance to CO₂ diffusion through the mesophyll was estimated and found to be so low that despite possible nonhomogeneity of the mesophyll, differences in CO₂ exchange characteristics for the two surfaces are unlikely. It is concluded that differences in conductance between upper and lower stomates are not adaptations to differences in CO₂ exchange characteristics.     

Variations in carbon source–sink relationships in subalpine fir across elevational gradients

• Cold‐adapted trees display acclimation in both carbon source and carbon sink capacity to low‐temperature stress at their upper elevational range limits. Hence a balanced carbon source–sink capacity might be required for their persistence and survival at the elevational tree limits.
• The present study examined the spatial dynamics of carbon source–sink relationship in subalpine fir (Abies fargesii) trees along elevational gradients in the northern slope of the temperate region and in the southern slope of the subtropics in terms of climate in the Qinling Mountain range, north‐central China.
• The results showed that non‐structural carbohydrate (NSC) concentrations in both the source and sink tissues increased with the increase in elevation. The ratio of carbon source–sink displayed a consistent decreasing trend with the increase in elevation and during growing season, showing that it was lowest at a ratio of 2.93 in the northern slope and at a ratio of 2.61 in the southern slope at the upper distribution elevations in the late growing season. Such variations of carbon source–sink ratio might be attributable to the balance between carbon source and sink activities, which changed seasonally across the elevational distribution range.
• We concluded that a ratio of carbon source–sink of at least 2.6 might be essential for subalpine fir trees to persist at their upper range limits. Therefore, a sufficient source–sink ratio and a balanced source–sink relationship might be required for subalpine fir trees to survive and develop at their upper elevational distribution limits.

     

Determination of the upper and lower limits of the mechanistic stoichiometry of incompletely coupled fluxes. Stoichiometry of incompletely coupled reactions

A rationale is formulated for the design of experiments to determine the upper and lower limits of the mechanistic stoichiometry of any two incompletely coupled fluxes J1 and J2. Incomplete coupling results when there is a branch at some point in the sequence of reactions or processes coupling the two fluxes. The upper limit of the mechanistic stoichiometry is given by the minimum value of dJ2/dJ1 obtained when the fluxes are systematically varied by changes in steps after the branch point. The lower limit is given by the maximum value of dJ2/dJ1 obtained when the fluxes are varied by changes in steps prior to the branch point. The rationale for determining these limits is developed from both a simple kinetic model and from a linear nonequilibrium thermodynamic treatment of coupled fluxes, using the mechanistic approach [Westerhoff, H. V. & van Dam, K. (1979) Curr. Top. Bioenerg. 9, 1-62]. The phenomenological stoichiometry, the flux ratio at level flow and the affinity ratio at static head of incompletely coupled fluxes are defined in terms of mechanistic conductances and their relationship to the mechanistic stoichiometry is discussed. From the rationale developed, experimental approaches to determine the mechanistic stoichiometry of mitochondrial oxidative phosphorylation are outlined. The principles employed do not require knowledge of the pathway or the rate of transmembrane leaks or slippage and may also be applied to analysis of the stoichiometry of other incompletely coupled systems, including vectorial H+/O and K+/O translocation coupled to mitochondrial electron transport.     

Thermal acclimation capacity of Jack Beardsley mealybug (Pseudococcus jackbeardsleyi) to survive in a warming world

The study of thermal tolerance and acclimation capacity in Jack Beardsley mealybug, Pseudococcus jackbeardsleyi Gimpel and Miller is the crucial step in determining their abilities to cope with climate change. Thus, the aim of this research was to determine the effects of acclimation temperatures on the changes in thermal tolerance of P. jackbeardsleyi. The influences of acclimation temperature at moderate (25?°C) and high (35?°C) temperatures on their lower and upper thermal limits were measured composed of critical thermal minimum (CT_min), maximum (CT_max), chill coma temperature (CCT) and heat coma temperature (HCT) for first instar nymphs and adults. The important information derived from this study revealed that the upper thermal limits of adults are constrained to a relative narrow range that will make them sensitive to relative small changes in temperatures, whilst all mean upper thermal indices at 35?°C were significantly higher than at 25?°C for nymphs. For this highlight notice, nymphs have more potential to change their upper thermal limits which will allow them to withstand high temperatures in the field. These results are a sign to warn us that P. jackbeardsleyi could become highly noxious which cause severe outbreaks damage to the crops in the tropics under global warming.     

Conditional Inference Following Group Sequential Testing

The work of Fisher (1959) and Buehler (1959) discuss the importance of conditioning on recognizable subsets of the sample space. The stopping time yields an easily identifiable partition of the sample space when considering group sequential testing. We first present confidence intervals that are correct when conditioning on the subset of data for which a trial stopped at a particular analysis. These intervals have very desirable properties for observations that are highly unusual (given any value of the mean). In addition, they provide insight into how information about the mean is distributed between the two sufficient statistics. We then use conditional coverage probabilities to compare the sample mean, stagewise, and repeated confidence intervals. We find that none of these intervals outperforms the others when conditioning on stopping time, and no interval is a uniformly acceptable performer.     

Thermal tolerance ranges and climate variability: A comparison between bivalves from differing climates

The climate variability hypothesis proposes that in variable temperate climates poikilothermic animals have wide thermal tolerance windows, whereas in constant tropical climates they have small thermal tolerance windows. In this study we quantified and compared the upper and lower lethal thermal tolerance limits of numerous bivalve species from a tropical (Roebuck Bay, north western Australia) and a temperate (Wadden Sea, north western Europe) tidal flat. Species from tropical Roebuck Bay had higher upper and lower lethal thermal limits than species from the temperate Wadden Sea, and Wadden Sea species showed an ability to survive freezing temperatures. The increased freezing resistance of the Wadden Sea species resulted in thermal tolerance windows that were on average 7 °C greater than the Roebuck Bay species. Furthermore, at a local-scale, the upper lethal thermal limits of the Wadden Sea species were positively related to submersion time and thus to encountered temperature variation, but this was not the case for the Roebuck Bay species. A review of previous studies, at a global scale, showed that upper lethal thermal limits of tropical species are closer to maximum habitat temperatures than the upper lethal thermal limits of temperate species, suggesting that temperate species are better adapted to temperature variation. In this study, we show for the first time, at both local and global scales, that the lethal thermal limits of bivalves support the climate variability effect in the marine environment.