Закон больших чисел при нарушениях статистической устойчивости

Понятие сходимости последовательности случайных величин обобщено на случай сходимости последовательности гиперслучайных величин. Показано, что закон больших чисел имеет место не только при наличии сходимости выборочного среднего к фиксированному числу, но и тогда, когда такой сходимости нет. Установлено, что выборочное среднее случайной величины может сходиться к фиксированному числу, стремиться к плюс бесконечности, минус бесконечности или флуктуировать в пределах определенного интервала, а выборочное среднее гиперслучайной величины может сходиться к фиксированной величине, множеству фиксированных величин (множеству чисел), флуктуировать в непересекающихся интервалах, флуктуировать в пределах одного интервала или стремиться к плюс или минус бесконечности.Поняття збіжності послідовності випадкових величин узагальнено на випадок збіжності послідовності гіпервипадкових величин. Показано, що закон великих чисел має місце не тільки у разі, коли є збіжність вибіркового середнього до фіксованого числа, але й коли такої збіжності немає. Встановлено, що вибіркове середнє випадкових величин може збігатись до фіксованого числа, прямувати до плюс чи мінус нескінченності або флуктувати в межах інтервалу, а вибіркове середнє гіпервипадкової величини може збігатись до фіксованого числа, множини фіксованих чисел, флуктувати в межах інтервалів, що не перетинаються, флуктувати в межах одного інтервалу або прямувати до плюс чи мінус нескінченності.The term sequence convergence of random quantities has been generalized to the sequence convergence of hyper-random quantities. It has been shown that the low of large numbers for random sequence is correct not only when the average tends to fixed number but in case of the absence of the convergence. It has been found that the average of random variables can approach to the fixed number, tend to plus or minus infinity or fluctuate within the interval and the average of hyper-random variable can approach to the fixed number, to the set of fix numbers, fluctuate within the of disjoint intervals, fluctuate within the single interval or tend to plus or minus infinity

Long‐term follow‐up of stereotactic radiosurgery for head and neck malignancies

BackgroundStereotactic radiosurgery is widely applied to deliver additional dose to head and neck tumors. However, its safety and efficacy remains equivocal.MethodsOne hundred eighty‐four patients with primary head and neck cancers treated between January 1990 and August 2012 with Gamma Knife stereotactic radiosurgery were retrospectively reviewed.ResultsTwo hundred fifteen sites were treated with Gamma Knife stereotactic radiosurgery among 184 patients. Fifty‐one percent of patients received concurrent external beam radiotherapy (EBRT), 72% had prior surgery, and 46% received chemotherapy. Most (44%) had squamous cell carcinoma and most patients (65%) were treated for recurrent disease. With a median follow‐up of 17.3 months, 12‐month local control was 82%. Late effects occurred in 59 patients with the most common being temporal lobe necrosis (15 patients).ConclusionRadiosurgery can provide tumor control for patients with head and neck cancers involving the skull base. Long‐term follow‐up is important in survivors to identify late effects. © 2014 Wiley Periodicals, Inc. Head Neck 37: 1557–1562, 2015Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/115998/1/hed23798.pd

Congruent responses to weather variability in high arctic herbivores

Assessing the role of weather in the dynamics of wildlife populations is a pressing task in the face of rapid environmental change. Rodents and ruminants are abundant herbivore species in most Arctic ecosystems, many of which are experiencing particularly rapid climate change. Their different life-history characteristics, with the exception of their trophic position, suggest that they should show different responses to environmental variation. Here we show that the only mammalian herbivores on the Arctic islands of Svalbard, reindeer (Rangifer tarandus) and sibling voles (Microtus levis), exhibit strong synchrony in population parameters. This synchrony is due to rain-on-snow events that cause ground ice and demonstrates that climate impacts can be similarly integrated and expressed in species with highly contrasting life histories. The finding suggests that responses of wildlife populations to climate variability and change might be more consistent in Polar regions than elsewhere owing to the strength of the climate impact and the simplicity of the ecosystem

Contrasting effects of summer and winter warming onbody mass explain population dynamics in a food-limitedArctic herbivore

-The cumulative effects of climate warming on herbivore vital rates and population dynamics are hard to predict, given that the expected effects differ between seasons. In the Arctic, warmer summers enhance plant growth which should lead to heavier and more fertile individuals in the autumn. Conversely, warm spells in winter with rainfall (rain-on-snow) can cause ‘icing’, restricting access to forage, resulting in starvation, lower survival and fecundity. As body condition is a ‘barometer’ of energy demands relative to energy intake, we explored the causes and consequences of variation in body mass of wild female Svalbard reindeer (Rangifer tarandus platyrhynchus) from 1994 to 2015, a period of marked climate warming. Late winter (April) body mass explained 88% of the between-year variation in population growth rate, because it strongly influenced reproductive loss, and hence subsequent fecundity (92%), as well as survival (94%) and recruitment (93%). Autumn (October) body mass affected ovulation rates but did not affect fecundity. April body mass showed no long-term trend (coefficient of variation, CV = 8.8%) and was higher following warm autumn (October) weather, reflecting delays in winter onset, but most strongly, and negatively, related to ‘rain-on-snow’ events. October body mass (CV = 2.5%) increased over the study due to higher plant productivity in the increasingly warm summers. Density-dependent mass change suggested competition for resources in both winter and summer but was less pronounced in recent years, despite an increasing population size. While continued climate warming is expected to increase the carrying capacity of the high Arctic tundra, it is also likely to cause more frequent icing events. Our analyses suggest that these contrasting effects may cause larger seasonal fluctuations in body mass and vital rates. Overall our findings provide an important ‘missing’ mechanistic link in the current understanding of the population biology of a keystone species in a rapidly warming Arctic. Keywords: climate change, density dependence, extreme events, icing, nutrition, primary production, Rangifer, reindeer, Svalbard, weathe

Low Spatial Habitat Overlap of Herbivores in the High Arctic Tundra

Herbivores play a crucial role in shaping tundra ecosystems through their effects on vegetation, nutrient cycling, and soil abiotic factors. Understanding their habitat use, co-occurrence, and overlap is therefore essential for informing ecosystem-based management and conservation. In the High Arctic, only a marginal proportion of the land area is vegetated, and climate change is impacting herbivore population sizes and their habitats. In this study, we assessed the spatial habitat overlap of a vertebrate herbivore community based on: 1) regional predictive summer habitat suitability models for the resident Svalbard reindeer (Rangifer tarandus platyrhynchus), resident Svalbard rock ptarmigan (Lagopus muta hyperborea), and the migratory pink-footed goose (Anser brachyrhynchus), and 2) presence of fecal pellets, reflecting the annual habitat use of reindeer, ptarmigan, and geese, including the pink-footed goose and barnacle goose (Branta leucopsis). Our findings revealed that only small proportions of the available land cover (∼ 12,516 km2; all land area excluding glaciers and freshwater) are suitable for each of the species (habitat suitability [HS] \u3e 0.5): reindeer (22 %), ptarmigan (11 %), and pink-footed goose (4 %). Overlapping suitable habitat [HS \u3e 0.5] for reindeer and goose accounted for only 3 % of the total vegetated area (∼ 8848 km2) and was primarily found in heath and moist habitats dominated by mosses, graminoids, and herbaceous plants. The overlapping suitable habitat for reindeer and ptarmigan covered 8 % of the vegetated area, in higher elevation ridges with vegetation on drier substrates. The shared habitat for ptarmigan and goose, and all three species of herbivores, was less than 1 % of the vegetated area. Additionally, an assessment of fecal pellets suggested that the highest overlap in habitat use among reindeer and goose occurred in bird cliff moss tundra, followed by moss tundra and heath habitats. The small proportion of the vegetated area suitable for all three herbivores indicates a high degree of habitat differentiation. Therefore, different habitats need to be considered for the management and conservation of resident and migratory herbivore species in this High Arctic Archipelago. Moreover, our results underscore the importance of the small but productive parts of the landscape that were used by all herbivores

Maximum Host Survival at Intermediate Parasite Infection Intensities

BACKGROUND: Although parasitism has been acknowledged as an important selective force in the evolution of host life histories, studies of fitness effects of parasites in wild populations have yielded mixed results. One reason for this may be that most studies only test for a linear relationship between infection intensity and host fitness. If resistance to parasites is costly, however, fitness may be reduced both for hosts with low infection intensities (cost of resistance) and high infection intensities (cost of parasitism), such that individuals with intermediate infection intensities have highest fitness. Under this scenario one would expect a non-linear relationship between infection intensity and fitness. METHODOLOGY/PRINCIPAL FINDINGS: Using data from blue tits (Cyanistes caeruleus) in southern Sweden, we investigated the relationship between the intensity of infection of its blood parasite (Haemoproteus majoris) and host survival to the following winter. Presence and intensity of parasite infections were determined by microscopy and confirmed using PCR of a 480 bp section of the cytochrome-b-gene. While a linear model suggested no relationship between parasite intensity and survival (F = 0.01, p = 0.94), a non-linear model showed a significant negative quadratic effect (quadratic parasite intensity: F = 4.65, p = 0.032; linear parasite intensity F = 4.47, p = 0.035). Visualization using the cubic spline technique showed maximum survival at intermediate parasite intensities. CONCLUSIONS/SIGNIFICANCE: Our results indicate that failing to recognize the potential for a non-linear relationship between parasite infection intensity and host fitness may lead to the potentially erroneous conclusion that the parasite is harmless to its host. Here we show that high parasite intensities indeed reduced survival, but this effect was masked by reduced survival for birds heavily suppressing their parasite intensities. Reduced survival among hosts with low parasite intensities suggests costs of controlling parasite infections; however, the nature of such costs remains to be elucidated

Investigating effects of parasite infection on body condition of the Kafue lechwe (Kobus leche kafuensis) in the Kafue basin

<p>Abstract</p> <p>Background</p> <p>The Kafue lechwe (<it>Kobus leche Kafuensis</it>), a medium-sized semi-aquatic antelope, is endemic to the Kafue basin of Zambia. The population of the Kafue lechwe has significantly dropped in the last decades leading to its subsequent inclusion on the red list of endangered species. In order to save the remaining population from extinction, it has become increasingly important that the impact of parasite infection and infestation on the Kafue lechwe is investigated.</p> <p>Findings</p> <p>Endoparasites accounted for the majority of parasites observed from a study of 40 Kafue lechwe occurring in the the Kafue basin. <it>Amphistoma spp. </it>were present in all animals examined, while <it>Fasciola gigantica </it>had a prevalence rate of 0.525 (95% CI: 0.36 to 0.69) and species of <it>Schistosoma </it>0.3 (95% CI: 0.15 to 0.45). Among the ectoparasites, <it>Strobiloestrous vanzyli</it>, had a prevalence rate of 0.15 (95% CI: 0.03 to 0.27), while <it>Rhipicephalus appendiculatus </it>had a prevalence of 0.075 (3/40). Our findings indicate that body condition was not influenced by the parasitic infestation in Kafue lechwe. There was no association between sex and parasitic burden (odds ratio = 0.3, 95% CI: 0.8-1.3). However, an association between age and parasitic burden was observed as older animals above 15 years were more likely to get parasite infections than those aged between 1-5 years (odds ratio = 1.5, 95% CI: 1.1-2.4).</p> <p>Conclusion</p> <p>Overall, there was no evidence that parasitic infections and infestations adversely affected the lechwe population on the Kafue basin. These findings indicate that ecto- and endo-parasite infestation might not play a significant role in reducing the Kafue lechwe population on the Kafue basin.</p

Coping with unpredictability: Dopaminergic and neurotrophic responses to omission of expected reward in Atlantic salmon (Salmo salar L.).

Comparative studies are imperative for understanding the evolution of adaptive neurobiological processes such as neural plasticity, cognition, and emotion. Previously we have reported that prolonged omission of expected rewards (OER, or 'frustrative nonreward') causes increased aggression in Atlantic salmon (Salmo salar). Here we report changes in brain monoaminergic activity and relative abundance of brain derived neurotrophic factor (BDNF) and dopamine receptor mRNA transcripts in the same paradigm. Groups of fish were initially conditioned to associate a flashing light with feeding. Subsequently, the expected food reward was delayed for 30 minutes during two out of three meals per day in the OER treatment, while the previously established routine was maintained in control groups. After 8 days there was no effect of OER on baseline brain stem serotonin (5-HT) or dopamine (DA) activity. Subsequent exposure to acute confinement stress led to increased plasma cortisol and elevated turnover of brain stem DA and 5-HT in all animals. The DA response was potentiated and DA receptor 1 (D1) mRNA abundance was reduced in the OER-exposed fish, indicating a sensitization of the DA system. In addition OER suppressed abundance of BDNF in the telencephalon of non-stressed fish. Regardless of OER treatment, a strong positive correlation between BDNF and D1 mRNA abundance was seen in non-stressed fish. This correlation was disrupted by acute stress, and replaced by a negative correlation between BDNF abundance and plasma cortisol concentration. These observations indicate a conserved link between DA, neurotrophin regulation, and corticosteroid-signaling pathways. The results also emphasize how fish models can be important tools in the study of neural plasticity and responsiveness to environmental unpredictability

Demographic and reproductive associations with nematode infection in a long-lived mammal

Infection by macroparasites, such as nematodes, varies within vertebrate host systems; elevated infection is commonly observed in juveniles and males, and, for females, with different reproductive states. However, while such patterns are widely recognized in short-lived model systems, how they apply to long-lived hosts is comparatively understudied. Here, we investigated how infection varies with host age, sex, and female reproduction in a semi-captive population of individually marked Asian elephants Elephas maximus. We carried out 1,977 faecal egg counts (FECs) across five years to estimate nematode loads for 324 hosts. Infection patterns followed an established age-infection curve, whereby calves (5 years) exhibited the highest FECs and adults (45 years) the lowest. However, males and females had similar FECs across their long lifespan, despite distinct differences in life-history strategy and clear sexual dimorphism. Additionally, although mothers invest two years in pregnancy and a further three to five years into lactation, nematode load did not vary with four different measures of female reproduction. Our results provide a much-needed insight into the host-parasite dynamics of a long-lived host; determining host-specific associations with infection in such systems is important for broadening our knowledge of parasite ecology and provides practical applications for wildlife medicine and management