Relative efficiency of unequal versus equal cluster sizes in cluster randomized trials using generalized estimating equation models

There is growing interest in conducting cluster randomized trials (CRTs). For simplicity in sample size calculation, the cluster sizes are assumed to be identical across all clusters. However, equal cluster sizes are not guaranteed in practice. Therefore, the relative efficiency (RE) of unequal versus equal cluster sizes has been investigated when testing the treatment effect. One of the most important approaches to analyze a set of correlated data is the generalized estimating equation (GEE) proposed by Liang and Zeger, in which the “working correlation structure” is introduced and the association pattern depends on a vector of association parameters denoted by ρ. In this paper, we utilize GEE models to test the treatment effect in a two‐group comparison for continuous, binary, or count data in CRTs. The variances of the estimator of the treatment effect are derived for the different types of outcome. RE is defined as the ratio of variance of the estimator of the treatment effect for equal to unequal cluster sizes. We discuss a commonly used structure in CRTs—exchangeable, and derive the simpler formula of RE with continuous, binary, and count outcomes. Finally, REs are investigated for several scenarios of cluster size distributions through simulation studies. We propose an adjusted sample size due to efficiency loss. Additionally, we also propose an optimal sample size estimation based on the GEE models under a fixed budget for known and unknown association parameter (ρ) in the working correlation structure within the cluster.     

Population genetic structure and germplasm conservation of Stipa purpurea on Qinghai-Tibetan Plateau under grazing

At what intensity the grazing should be practiced on the Qinghai-Tibetan Plateau in China is always confusing farmers, scientists and policy makers for a long time owing to its geographical exception. In order to develop a strategy for sustainable grazing management, we used the dominant Stipa purpurea as a model species to detect genetic diversity and fine spatial structure under different grazing intensities. Intra-population neutral genetic diversity in non-grazed population was significantly higher than three grazed populations; however, the highest value among grazed populations appeared in the moderately grazed population. A relatively low degree of genetic differentiation among populations by AMOVA analysis and a high level of gene flow existed among populations (Gst = 0.2649, Nm = 1.3875 〉 1). The genetic ‘patch’ size increased from 4 m to 16 m and subpopulation number within the S. purpurea populations ranged from 7 to 5 with increasing grazing intensity, therefore grazing will be beneficial to reduce the fragmentation and to increase the population-level adaptation. Though enclosure or no grazing is the best protection of plant germplasm like wind-pollination S. purpurea, moderate grazing is better strategy for grassland use on the Qinghai-Tibetan Plateau.     

Divergent growth of Norway spruce on Babia Góra Mountain in the western Carpathians

Growth divergence – i.e. the expression of divergent growth trends of neighboring trees – has certain implications for dendrochronological research, for instance in the context of climate reconstructions but also in terms of estimating net ecosystem productivity. Thus, understanding the underlying mechanisms is essential to extend our fundamental dendroecological knowledge. In this context, the Picea genus plays an important role since several of its species were reported to exhibit growth divergence. Here, we investigate a well sampled Norway spruce (Picea abies (L.) Karst) data set for growth divergence comprising ring-width and Blue Intensity measurements from seven sites on Babia Góra Mountain, at the border between Poland and Slovakia. By means of Principal Component Gradient Analysis, inter-series correlations, and climate growth relationships, we are able to show that I) Norway spruce on Babia Góra expressed growth divergence since the 1970s, II) the definition of groups increased the strength of population signals and the stability of climate-growth relationships, and III) Blue Intensity appeared as a more robust proxy for environmental conditions. We discuss soil heterogeneity, genetics, and air pollution as possible underlying mechanisms, thereby indicating further research avenues to obtain a better understanding of growth divergence.     

Aggregating land use quantity and intensity to link water quality in upper catchment of Miyun Reservoir

Eutrophication resulting from nutrient enrichment decreases water quality and harms ecosystem structure and function, and its degree is significantly affected by land use in the catchment. Quantifying the relationship between eutrophication and land use can help effectively manage land use to improve water quality. Previous studies principally utilized land use quantity as an indicator to link water quality parameters, but these studies lacked insight into the impact of land use intensity. Taking the upper catchment of Miyun Reservoir as a case study, we developed a method of aggregating land use quantity and intensity to build a new land use indicator and tested its explanatory power on water quality. Six nutrient concentrations from 52 sub-watersheds covering the whole catchment were used to characterize the spatial distribution of eutrophication. Based on spatial techniques, empirical conversion coefficients, remote sensing data, and socio-economic statistical data, land use intensity was measured and mapped visually. The new land use indicator was calculated and linked to nutrient concentrations by Pearson correlation coefficients. Results demonstrated that our new indicator incorporating intensity information can quantify the different nutrient-exporting abilities of different land use areas. Compared to traditional indicators that only incorporate land use quantity, most Pearson correlation coefficients between the new indicator and water nutrient concentrations increased. This new information enhanced the explanatory power of land use on water nutrient concentrations, and so will be able to help us understand the impact of land use on water quality and guide decision making for better land use management.     

Effects of temperature, photoperiod, and light intensity on the calling rhythm in Arctiid moths

Mean times of onset for calling in Haploa clymene (Brown), Spilosoma virginica (Fabricius), Pareuchaetes insulata (Walker), Cycnia tenera (Hübner), and Euchaetes egle (Drury) advance to earlier times in the photoperiod at lower temperatures. Temperature has no apparent effect on the calling period in Pyrrharctia isabella (J. E. Smith), Spilosoma congrua Walker, and Apantesis nais (Drury). The relationship between the temperatures experienced by each of these species as adults and the response of their calling rhythms to temperature is discussed. Lights-on can elicit calling behaviour in C. tenera, although it is not an absolute requirement because calling eventually begins when lights-on is delayed 4 h and calling also begins prior to lights-on at lower temperatures. Calling periods lengthen in C. tenera and S. congrua when the scotophase is prolonged and in S. congrua after the onset of a lower photophase light intensity (40 lux), suggesting that a higher photophase light intensity (450 lux) inhibits calling and thus causes its termination.

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Résumé Aux faibles températures le moment moyen de déclenchement de l'appel apparaît plus tôt au cours de la photopériode chez Haploa clymene Brown, Spilosoma virginica Fab., Pareuchaetes insulata Walk., Cycnia tenera Hübn. et Euchaetes egle Drury. La température n'a apparemment pas d'effet sur le moment où l'appel débute chez Pyrrharctica isabella J.E. Smith, S. congrua Walk. et Apantesis nais Drury.L'analyse porte sur les relations entre les températures subies par les adultes de ces espèces et leurs réactions d'appel aux différentes températures. L'apparition de la lumière peut induire le comportement d'appel chez C. tenera, bien que ce ne soit pas indispensable puisqu'il peut éventuellement commencer à des températures plus basses avant l'illumination quand celle-ci est retardée de 4 heures. Les périodes d'appel sont prolongées avec la scotophase chez C. tenera et S. congrua, et même après l'apparition d'une photophase à faible intensité lumineuse (40 lux), l'appel de S. congrua se poursuit, ce qui suggère que les photophases à intensité lumineuse plus élevée (450 lux) inhibent l'appel et ainsi en provoquent la fin.

     

A Comparison of Bone Mineral Density and Its Predictors in HIV-Infected and HIV-Uninfected Older Men

ObjectiveBone health in older individuals with HIV infection has not been well studied. This study aimed to compare bone mineral density (BMD), trabecular bone score (TBS), and bone markers between HIV-infected men and age- and body mass index (BMI)-matched HIV-uninfected men aged ≥60 years. We investigated the associations of risk factors related to fracture with BMD, TBS, and bone markers in HIV-infected men.MethodsThis cross-sectional study included 45 HIV-infected men receiving antiretroviral therapy and 42 HIV-uninfected men. Medical history, BMD and TBS measurements, and laboratory tests related to bone health were assessed in all the participants. HIV-related factors known to be associated with bone loss were assessed in the HIV-infected men.ResultsThe mean BMD, TBS, and osteopenia or osteoporosis prevalence were similar among the cases and controls. The HIV-infected men had significantly higher mean N-terminal propeptide of type 1 procollagen and C-terminal cross-linking telopeptide of type I collagen levels. Stepwise multiple linear regression analysis demonstrated that low BMI (lumbar spine, P = .015; femoral neck, P = .018; and total hip, P = .005), high C-terminal cross-linking telopeptide of type I collagen concentration (total hip, P = .042; and TBS, P = .010), and low vitamin D supplementation (TBS, P = .035) were independently associated with low BMD and TBS.ConclusionIn older HIV-infected men with a low fracture risk, the mean BMD and TBS were similar to those of the age- and BMI-matched controls. The mean bone marker levels were higher in the HIV group. Traditional risk factors for fracture, including low BMI, high C-terminal cross-linking telopeptide of type I collagen level, and low vitamin D supplementation, were significant predictors of low BMD and TBS.     

Evolutionary rescue by beneficial mutations in environments that change in space and time

A factor that may limit the ability of many populations to adapt to changing conditions is the rate at which beneficial mutations can become established. We study the probability that mutations become established in changing environments by extending the classic theory for branching processes. When environments change in time, under quite general conditions, the establishment probability is approximately twice the ‘effective selection coefficient’, whose value is an average that gives most weight to a mutant''s fitness in the generations immediately after it appears. When fitness varies along a gradient in a continuous habitat, increased dispersal generally decreases the chance a mutation establishes because mutations move out of areas where they are most adapted. When there is a patch of favourable habitat that moves in time, there is a maximum speed of movement above which mutations cannot become established, regardless of when and where they first appear. This critical speed limit, which is proportional to the mutation''s maximum selective advantage, represents an absolute constraint on the potential of locally adapted mutations to contribute to evolutionary rescue.     

Competitive and facilitative relationships among three shrub species,and the role of browsing intensity and rooting depth in the Succulent Karoo,South Africa

Abstract. The nearest‐neighbour technique is used to infer competition and facilitation between the three most abundant species in a semi‐arid region of western South Africa. Relationships among the shrubs Leipoldtia schultzei and Ruschia robusta, which are leaf‐succulent members of the Mesembryanthemaceae (‘mesembs’) and Hirpicium alienatum a non‐succulent Asteraceae, were compared on two adjacent sites with different histories of browsing intensity. Competition was more prevalent and more important than facilitation. The only evidence for facilitation was found at the heavily‐browsed site where the palatable Hirpicium was larger under the unpalatable Leipoldtia. Generally the prevalence and importance of competition was reduced at the heavily‐browsed site. Strong evidence was obtained for intraspecific competition in each of the three species; also, competition was evident between the two mesembs, where Leipoldtia was competitively dominant over Ruschia, although neither species inhibited Hirpicium. Minimal competition between the mesembs and the asteraceous shrub was interpreted in terms of differentiation in rooting depth, and competition within the mesembs, in terms of overlap in rooting depth. The mesembs had the bulk of their roots in the top 5 cm of soil, while the asteraceous shrub had the bulk of its roots, and all its fine roots, at greater depths. The shallow‐rooted morphology of the mesembs is well adapted to utilize small rainfall events, which occur frequently in the Succulent Karoo, and do not penetrate the soil deeply. Modifications of existing methods are applied for analysing nearest‐neighbour interactions.     

Effects of grazing intensity and grazing exclusion on litter decomposition in the temperate steppe of Nei Mongol,China

Aims Grazing intensity and grazing exclusion affect ecosystem carbon cycling by changing the plant community and soil micro-environment in grassland ecosystems. The aims of this study were: 1) to determine the effects of grazing intensity and grazing exclusion on litter decomposition in the temperate grasslands of Nei Mongol; 2) to compare the difference between above-ground and below-ground litter decomposition; 3) to identify the effects of precipitation on litter production and decomposition. Methods We measured litter production, quality, decomposition rates and soil nutrient contents during the growing season in 2011 and 2012 in four plots, i.e. light grazing, heavy grazing, light grazing exclusion and heavy grazing exclusion. Quadrate surveys and litter bags were used to measure litter production and decomposition rates. All data were analyzed with ANOVA and Pearson’s correlation procedures in SPSS. Important findings Litter production and decomposition rates differed greatly among four plots. During the two years of our study, above-ground litter production and decomposition in heavy-grazing plots were faster than those in light-grazing plots. In the dry year, below-ground litter production and decomposition in light-grazing plots were faster than those in heavy-grazing plots, which is opposite to the findings in the wet year. Short-term grazing exclusion could promote litter production, and the exclusion of light-grazing could increase litter decomposition and nutrient cycling. In contrast, heavy-grazing exclusion decreased litter decomposition. Thus, grazing exclusion is beneficial to the restoration of the light-grazing grasslands, and more human management measures are needed during the restoration of heavy-grazing grasslands. Precipitation increased litter production and decomposition, and below-ground litter was more vulnerable to the inter-annual change of precipitation than above-ground litter. Compared to the light-grazing grasslands, heavy-grazing grasslands had higher sensitivity to precipitation. The above-ground litter decomposition was strongly positively correlated with the litter N content (R² = 0.489, p < 0.01) and strongly negatively correlated with the soil total N content (R² = 0.450, p < 0.01), but it was not significantly correlated with C:N and lignin:N. Below-ground litter decomposition was negatively correlated with the litter C (R² = 0.263, p < 0.01), C:N (R² = 0.349, p < 0.01) and cellulose content (R² = 0.460, p < 0.01). Our results will provide a theoretical basis for ecosystem restoration and the research of carbon cycling.