Seasonality of rates: testing for seasonal variation when the population at risk is variable

We present what appears to be the first Bayesian procedure to analyze the seasonal variation of rates from data that generally have small amplitude and small sample size, with a possibly variable population at risk. Such data are pertinent both to the medical and the social sciences, for example. Our procedure is easy to apply and versatile, because it can be used to assess various usual patterns of seasonal variation. To illustrate the application of our procedure, we provide three examples with different seasonal patterns. Based on real data, the examples are enhanced by tables and graphics that elucidate the procedure’s application.

Hematocrit (Hct) values in healthy adult populations exhibit seasonal variation, with the lowest values occurring in the summer. The extent to which environmental temperature contributes to the seasonal trend in deferral rates for unacceptable Hct in the American Red Cross was further analyzed. A centralized database of donations during 2002 to 2004, constituting 24.3 million donor presentations, was further characterized. Data on mean monthly temperature in the United States were obtained for the same period from a government agency. Multivariate regression analyses were performed to determine the relationship between Hct deferral rates among blood donors and environmental temperature and donor characteristics. Hct deferral rates were associated with mean monthly temperature in the United States (R(2) = 0.77). The relationship between the Hct deferral rate and environmental temperature was strongest in the region of the country with the highest seasonal variation in temperature, followed by regions with intermediate and low seasonal variation in temperature, respectively. The seasonal pattern in Hct deferral rates occurred in both sexes and across all age groups, with significantly higher Hct deferral rates occurring in June through August compared to other quarters (p < 0.0007). There is a significant seasonal pattern in Hct deferral rates that is associated with environmental temperature. The relationship between Hct deferral rates and temperature is strongest in areas of the country with greater temperature variability. The effect of seasonality on Hct deferrals should be taken into account for donor counseling, recruitment, and retention efforts.

Autotrophic respiration may regulate how ecosystem productivity responds to changes in temperature, atmospheric [CO2] and N deposition. Estimates of autotrophic respiration are difficult for forest ecosystems, because of the large amount of biomass, different metabolic rates among tissues, and seasonal variation in respiration rates. We examined spatial and seasonal patterns in autotrophic respiration in a Pinus strobus ecosystem, and hypothesized that seasonal patterns in respiration rates at a common temperature would vary with [N] for fully expanded foliage and fine roots, with photosynthesis for foliage, and with growth for woody tissues (stems, branches, and coarse roots). We also hypothesized that differences in [N] would largely explain differences in maintenance or dormant‐season respiration among tissues.For April–November, mean respiration at 15 °C varied from 1.5 to 2.8 μmol kg−1 s−1 for fully expanded foliage, 1.7–3.0 for growing foliage, 0.8–1.6 for fine roots, 0.6–1.1 (sapwood) for stems, 0.5–1.8 (sapwood) for branches, and 0.2–1.5 (sapwood) for coarse roots. Growing season variation in respiration for foliage produced the prior year was strongly related to [N] (r2 = 0.94), but fine root respiration was not related to [N]. For current‐year needles, respiration did not covary with [N]. Night‐time foliar respiration did not vary in concert with previous‐day photosynthesis for either growing or fully expanded needles. Stem growth explained about one‐third of the seasonal variation in stem respiration (r2 = 0.38), and also variation among trees (r2 = 0.43). We did not determine the cause of seasonal variation in branch and coarse root respiration, but it is unlikely to be directly related to growth, as the pattern of respiration in coarse roots and branches was not synchronized with stem growth. Seasonal variations in temperature‐corrected respiration rates were not synchronized among tissues, except foliage and branches. Spatial variability in dormant‐season respiration rates was significantly related to tissue N content in foliage (r2 = 0.67), stems (r2 = 0.45), coarse roots (r2 = 0.36), and all tissues combined (r2 = 0.83), but not for fine roots and branches. Per unit N, rates for P. strobus varied from 0.22 to 3.4 μmol molN−1 s−1 at 15 °C, comparable to those found for other conifers. Accurate estimates of annual autotrophic respiration should reflect seasonal and spatial variation in respiration rates of individual tissues.

Knowledge of the abundance of animal populations is essential for their management and conservation. Determining reliable measures of abundance is, however, difficult, especially with wide‐ranging species such as cheetah Acinonyx jubatus. This study generated a correction factor to calculate true cheetah density from spoor survey data and subsequently tested its accuracy using the following season's data. Data were collected from October 2005 to December 2006 on a known population of wild, free‐ranging cheetah in the Jwana Game Reserve, Botswana. The cheetahs in the area were captured, tagged and photographed. The reserve was divided into twelve 9 km transects covering all vegetation types and prey densities. The total sampling distance was 8226 km, with a spoor density of 2.32 individual cheetah spoor per 100 km2. To determine a precise and accurate spoor density, it was necessary to sample for a longer period during the dry season (April–September) than during the wet season (October–March). This difference may be due to cheetah behavioural changes with seasonal variations in habitat and prey. The true density was 5.23 cheetahs per 100 km2 ranging from 3.33 to 7.78 at the low and high points of the population, respectively. A positive linear correlation between spoor and true density was observed. This relationship differed in the wet and dry season and required refinement with the following season's data. Correction factors may be viable, but require further testing taking the behavioural responses to seasonal, habitat and prey variations into consideration.

The study was conducted to analyze spatial and temporal variations of lightning activity over Sri Lanka and the surrounding coastal belt region bounded by 5.75–10.00 N and 79.50–89.00 E. Flash data collected by the Lightning Imaging Sensor (LIS) on NASA’s Tropical Rainfall Measuring Mission (TRMM) satellite from 1998 to 2014 and the Lightning Imaging Sensor placed on the International Space Station (ISS) from 2018 to 2021 were used for the study. The Mann-Kendall test and Sen’s slope estimator were applied to annual and seasonal lightning data from 1998 to 2014 to identify the trends in the TRMM dataset. A positive slope of 0.23 was obtained for annual flash densities, while a slope of 0.956 was obtained for First Inter-Monsoon (FIM) seasonal data. Considering the ISS data, the annual variation of lightning activity in 2020 displays the lowest flash density, whereas the highest is represented in 2019 with a value of 10.48 flashes km−2 year−1. The highest mean flash density is observed in Colombo in 2019 at a value of 34.85 flashes km−2 year−1. Overall, April displayed the highest annual flash distribution from 2018 to 2021, whereas the second peak was mostly viewed around September and November. All districts have displayed a significant amount of lightning during April for the period 2018 to 2021. FIM displayed the highest lightning distribution over the country. When considering the seasonal variation, districts belonging to the wet zone and intermediate zone displayed most flashes during the FIM.

Considerations of sample size in medical research

Insect communities vary seasonally with changing climatic conditions and related changes in resource availability, strength of competition, or pressure by natural antagonists. But seasonal dynamics, particularly in tropical mountain ecosystems, are not well understood. We monitored cavity-nesting Hymenoptera communities on Mt. Kilimanjaro, Tanzania, to analyse temporal patterns of nest-building activity, ecological rates, and life-history traits in relation to seasonal climatic variation and elevation. We installed trap nests on 25 study sites in natural and disturbed habitat types covering the colline (&lt;1,300&nbsp;m) and submontane zones (≥1,300&nbsp;m a.s.l). We analysed patterns of seasonality in the cavity-nesting ecology of Hymenoptera at three different trophic levels –bees, caterpillar-hunting wasps and spider-hunting wasps– over a complete annual period, covering two rainy and two dry seasons. Nest-building activity showed strong seasonal trends in all three investigated trophic levels and peaked at the end of the short rainy season at low elevations. Nest-building activity was considerably higher and seasonal trends were better synchronised between the different trophic levels in the colline zone at low elevations. We also detected seasonal patterns for parasitism and natural mortality rates, sex ratio, and development time, which varied with trophic level and between elevation levels. Climate and flower abundance were important predictors for seasonal patterns in nest-building activity, ecological rates and life-history traits. These results reveal that seasonal trends in nest-building activity of lowland Hymenoptera seem to be linked to changes in climate and resource availability that reflect the seasonal patterns in plant growth and flowering documented in lowland savanna ecosystems. Higher resource availability also increased the sex ratio in bees towards the more costly females and enhanced their survival rates. These spatiotemporal links between climate, resources, ecological rates, and life-history traits indicate high sensitivity of plant-host-antagonist interactions to environmental changes.

Technological advances have steadily increased the detail of animal tracking datasets, yet fundamental data limitations exist for many species that cause substantial biases in home‐range estimation. Specifically, the effective sample size of a range estimate is proportional to the number of observed range crossings, not the number of sampled locations. Currently, the most accurate home‐range estimators condition on an autocorrelation model, for which the standard estimation frame‐works are based on likelihood functions, even though these methods are known to underestimate variance—and therefore ranging area—when effective sample sizes are small.Residual maximum likelihood (REML) is a widely used method for reducing bias in maximum‐likelihood (ML) variance estimation at small sample sizes. Unfortunately, we find that REML is too unstable for practical application to continuous‐time movement models. When the effective sample sizeNis decreased toN ≤ (10), which is common in tracking applications, REML undergoes a sudden divergence in variance estimation. To avoid this issue, while retaining REML’s first‐order bias correction, we derive a family of estimators that leverage REML to make a perturbative correction to ML. We also derive AIC values for REML and our estimators, including cases where model structures differ, which is not generally understood to be possible.Using both simulated data and GPS data from lowland tapir (Tapirus terrestris), we show how our perturbative estimators are more accurate than traditional ML and REML methods. Specifically, when(5) home‐range crossings are observed, REML is unreliable by orders of magnitude, ML home ranges are ~30% underestimated, and our perturbative estimators yield home ranges that are only ~10% underestimated. A parametric bootstrap can then reduce the ML and perturbative home‐range underestimation to ~10% and ~3%, respectively.Home‐range estimation is one of the primary reasons for collecting animal tracking data, and small effective sample sizes are a more common problem than is currently realized. The methods introduced here allow for more accurate movement‐model and home‐range estimation at small effective sample sizes, and thus fill an important role for animal movement analysis. Given REML’s widespread use, our methods may also be useful in other contexts where effective sample sizes are small.

Nitric oxide and ozone concentrations have been measured in situ from a high-altitude research aircraft. Data which show the variations of NO and O3 with the time of year are presented for altitudes of 18.3 and 21.3 km. The extreme values of the observed NO concentrations at 21.3 km are 1.2 billion per cu cm in summer and 0.2 billion per cu cm in winter. At 18.3 km the extreme values are 1.6 billion per cu cm in summer and 0.1 billion per cu cm in winter. The smoothed NO seasonal data show a variation of about a factor of 2.5 at 21.3 km and a factor of 4 at 18.3 km. The ozone data show the generally expected magnitude and seasonal variation. We have used a photochemical model employing the measured ozone concentrations, the mean solar zenith angle, and seasonal HNO3 data reported by others to predict the seasonal NO variation at 20 km. The result is a summer-to-winter NO ratio of 2.5 which is in fair agreement with the observed ratios.

Regression and correlation analyses were used to predict responses of phytoplankton biomass (chlorophyll) (microg L(-1)) to nitrate (NO(3)) (mg L(-1)), phosphate (PO(4)) (mg L(-1)) and ammonium (NH(4)) (mg L(-1)) dynamics in the shallow hypertrophic Lake Manyas, Turkey. Nutrient concentrations showed a descending gradient with distance, while chlorophyll concentrations showed an ascending gradient with the distance from the Siğirci Inlet to the Karadere Outlet. Higher nutrient concentrations did always not coincide with higher chlorophyll concentrations. The results showed that regression models developed using seasonal data were more accurate in predicting chlorophyll concentrations than those developed using the pooled data from whole year (based on R (2) and the difference between the measured and predicted values). The findings also revealed that within a single large shallow lake, chlorophyll-nutrient relationships might show significant variations spatially. The objective of this study was to determine the seasonal and spatial variations in the relationships between chlorophyll, nitrate, phosphate and ammonium in the shallow hypertrophic Lake Manyas, Turkey.

Lakes and wetlands provide top-priority hotspots that play a key role in maintaining and protecting threatened and migratory waterfowl. Identifying seasonal and spatial variations in aquatic bird communities and their responses to environmental factors is vital conservation efforts. However, there is a lack of information on waterfowl in Mongolian lakes and their associated wetlands. The purpose of this study was to investigate the spatial–seasonal changes in waterfowl assemblage structures in Mongolian lakes, as well as to determine how they respond to various environmental factors (lake surface area, elevation, and geographical distribution). Statistical analyses were performed using seasonal data (May, July, and September) for 28 waterfowl collected from 54 lakes across the country between 2016 and 2018. Seasonal heterogeneity in species richness and abundance was observed in lakes in each geographical region (Eastern, Central, and Western Mongolia). The composition of waterfowl in the lake was also relatively similar between May and September compared to July. This was due to the overlapping migration seasons in spring and autumn. Regionally, the number of waterfowl was much higher in the Eastern Mongolian lakes, followed by Central Mongolian lakes and then Western Mongolian lakes. This is likely due to differences in habitat availability and water levels between the regions. Eastern Mongolian lakes tend to have more wetlands and shallow water habitats, while Central and Western Mongolian lakes tend to have deeper open-water habitats. These differences in habitat types could contribute to the observed differences in waterfowl abundance among the regions. Additionally, some small lakes and the group of small lakes supported a greater abundance and diversity of waterfowl compared to some medium-sized and large lakes, suggesting that they are important for conservation. Indices of diversity (H’) and species dominance (D’) showed positive and negative correlations with lake surface area, respectively. Perhaps the increased surface area of the lake decreases the habitat overlap for designated waterfowl due to habitat heterogeneity. Accordingly, the indices (H’ and EH) increased as the waterfowl species composition became relatively equivalent in large lakes. Overall, spatial variations among the lakes were primarily attributable to the individual features of the lakes (shallowness, small lake groupings, and surface area), and seasonal variation in the lakes depended majorly on the compositional changes of the waterfowl due to migration.

Internal variations of the troposphere–stratosphere coupled system with intraseasonal and interannual timescales are investigated in a parameter sweep experiment with a simple global circulation model under a periodic annual forcing. In order to examine the role of forced planetary waves in the variations, the amplitude of a sinusoidal surface topography is chosen as an experimental parameter; 100-yr integrations are performed for each of 10 topographic amplitudes from 0 to 3000 m. The extratropical stratospheric circulation depends on the topographic amplitude in its mean seasonal march and intraseasonal and interannual variations. In the run without the topography, the stratospheric circulation is basically driven thermally and hardly shows interannual variation in any seasons. In the runs in which the topography is included, on the other hand, the stratospheric circulation is dynamically active and shows large interannual variation in different seasons, that is, spring for small topographic amplitudes (around 500 m) and winter for large amplitudes (around 1000 m). The mean seasonal march and interannual variation in these runs of small and large amplitudes resemble those in the Southern and Northern Hemispheres, respectively. In this study, the annual forcing is introduced only in the stratosphere while the tropospheric condition is kept constant in time, in order to investigate downward influence from the stratosphere to the troposphere in the seasonal march. The annual response of the atmosphere can significantly penetrate into the troposphere, depending on the topographic amplitude. The downward penetration is significant for the amplitudes of planetary and synoptic-scale waves, while it is negligible for zonal mean quantities. The empirical orthogonal function and lag correlation analyses show that a sequence of variability associated with stratospheric sudden warmings (SSWs) in the run of the topographic amplitude of 1000 m is characterized by poleward and downward propagation of anomalies of the zonal mean zonal wind and the planetary wave amplitude. Preconditioning for and the aftereffect of SSWs extend through both the stratosphere and troposphere. One month before SSWs, the polar night jet and the tropospheric jet shift poleward while planetary waves amplify in the troposphere and stratosphere. The anomalies of the zonal wind and wave amplitude further propagate poleward and downward for several months after SSWs.

ABSTRACTAimA species' rate of climatic niche evolution may reflect its ability to survive changing climates. Yet large‐scale studies of these rates remain limited. Here, we assessed global patterns in climatic niche rates among angiosperms and explored the potential drivers shaping these patterns.LocationGlobal.Time PeriodCurrent.Major Taxa StudiedAngiosperms.MethodsWe estimated broad‐scale climatic niches for 231,567 angiosperm species based on distributional data from over 1100 sources. By integrating a published phylogeny of angiosperms, we estimated rates of climatic niche change for each extant species as the difference between its current and ancestral niche divided by the species' age. Global patterns were analysed by averaging rates for all the species found in each geographic unit. We used multiple statistical models to explore the relative contributions of niche width and climatic seasonality to shaping these geographic patterns of niche evolution. We analysed patterns of niche evolution and their underlying drivers separately for temperature‐related and precipitation‐related niches and for different directions of niche evolution (i.e., increases and decreases in species' temperature and precipitation niche values when compared to their most recent ancestors).ResultsRates for temperature variables increased with latitude, whereas rates for precipitation variables decreased with latitude. These opposing patterns in temperature and precipitation rates were related to opposing latitudinal patterns in climatic seasonality and species' niche widths for temperature and precipitation. Rates also differed for different directions of niche evolution, with different patterns associated with changes to warmer vs. cooler climates and wetter vs. drier climates.Main ConclusionsOur results revealed large‐scale geographic patterns in rates of climatic niche change for temperature and precipitation for the largest clade of angiosperms and their underlying drivers. These findings may have important implications for species' abilities to respond to recent climate change.

Following Bees and Wasps up Mt. Kilimanjaro: From Diversity and Traits to hidden Interactions of Species

294 Background: Economic evaluations in oncology aim to assess the value of new therapies in the long term based on clinical trial data that often have restricted follow-up times (&lt; 5 years) and small sample sizes (&lt; 500 patients). This requires the use of extrapolation assumptions on long-term survival that go beyond the observed data. In this analysis, differences in survival extrapolation methods are tested in samples of sizes and follow-up reflecting typical clinical trials against a background of known survival in prostate cancer from a US based cancer registry. Methods: Data from the National Cancer Institute's Surveillance Epidemiology and End Results (SEER) registry on long-term survival in patients with stage IV prostate cancer were employed. The data set comprised those patients diagnosed between 1988 and 2003, with follow-up data available until 2012. Additional survival for those who received surgery (compared to those who did not), was estimated based on extrapolations using standard parametric statistical models (exponential, Weibull, log-logistic, log-normal, Gamma) fitted to the observed data. Survival analyses were run for 5 sample size scenarios (n = 27,670, 1000, 500, 200, 50) and 6 follow-up scenarios (follow-up years = 25, 20, 10, 5, 2, 1) yielding 30 combination scenarios. Performance of the methods was tested relative to the maximum follow-up, maximum sample size scenario (i.e. reference case) from the SEER registry. Results: Log-logistic and log-normal models were associated with flat tails which led to inflated survival estimations. For scenarios with smaller sizes, gamma models often did not converge. Exponential models were the most frequently reported as best model fit (in approximately 50% of scenarios). Also, gains in OS were consistent when exponential models were selected, and closely matched gain in OS from the reference case. Conclusions: Since clinical trials in oncology are often associated with small patient sample sizes and restricted follow-up, selecting an exponential model may lead to the most consistent and stable results based on the experiment constructed here. Further research should confirm these results for other types of cancer.