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INTRODUCTION: Hyperpolarization-activated cyclic nucleotide-gated (HCN) ion channels mediate repetitive action potential firing in the heart and nervous system. The HCN2 isoform is expressed in nociceptors, and preclinical studies suggest a critical role in neuropathic pain. Ivabradine is a nonselective HCN blocker currently available for prescription for cardiac indications. Mouse data suggest that ivabradine in high concentrations is equianalgesic with gabapentin. We sought to translate these findings to patients with chronic peripheral neuropathic pain. OBJECTIVES: We sought to translate these findings to patients with chronic peripheral neuropathic pain. METHODS: We adopted an open-label design, administering increasing doses of ivabradine to target a heart rate of 50 to 60 BPM, up to a maximum of 7.5 mg twice daily. All participants scored their pain on an 11-point numerical rating scale (NRS). RESULTS: Seven (7) participants received the drug and completed the study. There was no significant treatment effect on the primary endpoint, the difference between the mean score at baseline and at maximum dosing (mean reduction = 0.878, 95% CI = -2.07 to 0.31, P = 0.1). Exploratory analysis using linear mixed models, however, revealed a highly significant correlation between ivabradine dose and pain scores (χ2(1) = 74.6, P < 0.001), with a reduction of 0.12 ± 0.01 (SEM) NRS points per milligram. The 2 participants with painful diabetic neuropathy responded particularly well. CONCLUSION: This suggests that ivabradine may be efficacious at higher doses, particularly in patients with diabetic neuropathic pain. Importantly, participants reported no adverse effects. These data suggest that ivabradine, a peripherally restricted drug (devoid of central nervous system side effects), is well tolerated in patients with chronic neuropathic pain. Ivabradine is now off-patent, and its analgesic potential merits further investigation in clinical trials.
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Populations of migratory waterbirds are facing dramatic declines worldwide due to illegal hunting, habitat loss and climate change. Conservation strategies to reverse these trends are imperative, especially in tropical developing countries, which almost invariably allocate insufficient levels of investment for environmental protection. Here, we compared the effectiveness of sustainable-use Protected Areas (PAs) and Community-based Conservation (CBC) arrangements for the conservation of migratory waterbirds that breed on seasonal riverine sandy beaches in Brazilian Amazonia. We modeled local population responses of four migratory waterbird species on 155 beaches along a ~1,600 km section of a major tributary of the Amazon, as a function of community enforcement, official protection status, human pressure and landscape features. We show that 21 community-protected beaches within the study area host more than 80% of all sampled birds. Black Skimmers showed the most dramatic response, with breeding numbers 135-fold larger in CBC arrangements compared to beaches with no official protection status. The same pattern was observed for nesting Large-Billed and Yellow-Billed Terns. For the Near Threatened Orinoco Goose, PA status was the strongest predictor of local population size. These dramatic results demonstrate the value of protected refugia, achieved through the concerted action of participating local communities, to support breeding populations of key waterbird species. This highly-effective and low-cost conservation model can potentially be replicated in other regions of the developing world experiencing increasingly intensive exploitation of riverine natural resources.
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Charadriiformes/fisiologia , Pesquisa Participativa Baseada na Comunidade/métodos , Conservação dos Recursos Naturais/métodos , Migração Animal/fisiologia , Animais , Biodiversidade , Aves , Brasil , Cruzamento , Charadriiformes/metabolismo , Pesquisa Participativa Baseada na Comunidade/tendências , Ecossistema , Humanos , Densidade Demográfica , Dinâmica Populacional , Refúgio de Vida Selvagem , Estações do Ano , Áreas AlagadasRESUMO
OBJECTIVES: To assess the effectiveness of radiofrequency denervation (RD) of lumbosacral anatomical targets for the management of chronic back pain. DESIGN: Systematic review and meta-analysis of randomised controlled trials (RCTs). METHODS: A database search (Medline, Medline in Process, Embase, CINHAL and the Cochrane library) was conducted from January 2014 to April 2019 for placebo or no-treatment controlled trials of RD for the management of chronic back pain. Included trials were quality assessed using the Cochrane Risk-of-Bias Tool and the quality of outcomes assessed using the Grading of Recommendations, Assessment, Development and Evaluations (GRADE) approach. Meta-analysis was conducted to calculate mean difference (MD) in post-treatment Pain Score. RESULTS: Nineteen RCTs were included in the review. There appears to be short-term pain relief (1-3 months) provided by RD of the sacroiliac joint (five trials, MD -1.53, CI -2.62 to 0.45) and intervertebral discs (four trials, MD -0.98, CI -1.84 to 0.12), but the placebo effect is large and additional intervention effect size is small (<1 on an 11 point (0-10) Pain Scale). Longer-term effectiveness (>6 months) is uncertain. CONCLUSIONS: RD of selected lumbosacral targets appears to have a small, short-term, positive effect for the management of patients with chronic back pain. However, the quality of evidence for the majority of outcomes is low or very low quality and there is still a degree of uncertainty, particularly around the duration of effect.
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Dor Lombar/terapia , Terapia por Radiofrequência/normas , Humanos , Dor Lombar/fisiopatologia , Terapia por Radiofrequência/métodosRESUMO
The persistent high deforestation rate and fragmentation of the Amazon forests are the main threats to their biodiversity. To anticipate and mitigate these threats, it is important to understand and predict how species respond to the rapidly changing landscape. The short-eared dog Atelocynus microtis is the only Amazon-endemic canid and one of the most understudied wild dogs worldwide. We investigated short-eared dog habitat associations on two spatial scales. First, we used the largest record database ever compiled for short-eared dogs in combination with species distribution models to map species habitat suitability, estimate its distribution range and predict shifts in species distribution in response to predicted deforestation across the entire Amazon (regional scale). Second, we used systematic camera trap surveys and occupancy models to investigate how forest cover and forest fragmentation affect the space use of this species in the Southern Brazilian Amazon (local scale). Species distribution models suggested that the short-eared dog potentially occurs over an extensive and continuous area, through most of the Amazon region south of the Amazon River. However, approximately 30% of the short-eared dog's current distribution is expected to be lost or suffer sharp declines in habitat suitability by 2027 (within three generations) due to forest loss. This proportion might reach 40% of the species distribution in unprotected areas and exceed 60% in some interfluves (i.e. portions of land separated by large rivers) of the Amazon basin. Our local-scale analysis indicated that the presence of forest positively affected short-eared dog space use, while the density of forest edges had a negative effect. Beyond shedding light on the ecology of the short-eared dog and refining its distribution range, our results stress that forest loss poses a serious threat to the conservation of the species in a short time frame. Hence, we propose a re-assessment of the short-eared dog's current IUCN Red List status (Near Threatened) based on findings presented here. Our study exemplifies how data can be integrated across sources and modelling procedures to improve our knowledge of relatively understudied species.
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The recognition that much biodiversity exists outside protected areas is driving research to understand how animals survive in anthropogenic landscapes. In Madagascar, cacao (Theobroma cacao) is grown under a mix of native and exotic shade trees, and this study sought to understand whether lemurs were present in these agroecosystems. Between November 2016 and March 2017, discussions with farmers, nocturnal reconnaissance surveys and camera traps were used to confirm the presence of lemurs in the Cokafa and Mangabe plantations near Ambanja, north-west Madagascar. Four species of lemur were encountered in nocturnal surveys: Mirza zaza, Phaner parienti, Microcebussp. and Cheirogaleussp. with encounter rates of 1.2, 0.4, 0.4 and 0.3 individuals/km, respectively. The presence of Lepilemur dorsalis was confirmed by camera trap. This is the first time lemurs have been studied in cacao plantations, and understanding how these threatened animals use anthropogenic landscapes is vital for their conservation.
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Biodiversidade , Cacau , Cheirogaleidae , Conservação dos Recursos Naturais , Lemuridae , Animais , Madagáscar , Densidade Demográfica , ÁrvoresRESUMO
Amazonia forest plays a major role in providing ecosystem services for human and sanctuaries for wildlife. However, ongoing deforestation and habitat fragmentation in the Brazilian Amazon has threatened both. The ocelot is an ecologically important mesopredator and a potential conservation ambassador species, yet there are no previous studies on its habitat preference and spatial patterns in this biome. From 2010 to 2017, twelve sites were surveyed, totaling 899 camera trap stations, the largest known dataset for this species. Using occupancy modeling incorporating spatial autocorrelation, we assessed habitat use for ocelot populations across the Brazilian Amazon. Our results revealed a positive sigmoidal correlation between remote-sensing derived metrics of forest cover, disjunct core area density, elevation, distance to roads, distance to settlements and habitat use, and that habitat use by ocelots was negatively associated with slope and distance to river/lake. These findings shed light on the regional scale habitat use of ocelots and indicate important species-habitat relationships, thus providing valuable information for conservation management and land-use planning.
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The flood pulse is the main factor structuring and differentiating the ecological communities of Amazonian unflooded (terra firme) and seasonally-flooded (várzea) forests as they require unique adaptations to survive the prolonged annual floods. Therefore, várzea and terra firme forests hammer out a spatio-temporal mosaic of resource availability, which may result in landscape scale seasonal movements of terrestrial vertebrates between adjacent forest types. Yet the lateral movements of terrestrial vertebrates between hydrologically distinct neighbouring forest types exhibiting staggered resource availability remains poorly understood, despite the important implications of this spatial dynamic for the ecology and conservation of forest wildlife. We examined the hypothesis of terrestrial fauna seasonal movements between two adjacent forest types at two contiguous sustainable-use forest reserves in Western Brazilian Amazonia. We used camera trapping data on the overall species richness, composition, and abundance of nine major vertebrate trophic guilds to infer on terrestrial vertebrate movements as a function of seasonal changes in floodplain water level. Species richness differed in neighboring terra firme forests between the high-and low-water phases of the flood pulse and terra firme forests were more species rich than várzea forests. There were clear differences in species composition between both forest types and seasons. Generalized Linear Models showed that water level was the main factor explaining aggregate abundance of all species and three trophic guilds. Our results indicate that the persistence of viable populations of large terrestrial vertebrates adjacent to major Amazonian rivers requires large, well-connected forest landscapes encompassing different forest types to ensure large-scale lateral movements by forest wildlife.
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The degree to which terrestrial vertebrate populations are depleted in tropical forests occupied by human communities has been the subject of an intense polarising debate that has important conservation implications. Conservation ecologists and practitioners are divided over the extent to which community-based subsistence offtake is compatible with ecologically functional populations of tropical forest game species. To quantify depletion envelopes of forest vertebrates around human communities, we deployed a total of 383 camera trap stations and 78 quantitative interviews to survey the peri-community areas controlled by 60 semi-subsistence communities over a combined area of over 3.2 million hectares in the Médio Juruá and Uatumã regions of Central-Western Brazilian Amazonia. Our results largely conform with prior evidence that hunting large-bodied vertebrates reduces wildlife populations near settlements, such that they are only found at a distance to settlements where they are hunted less frequently. Camera trap data suggest that a select few harvest-sensitive species, including lowland tapir, are either repelled or depleted by human communities. Nocturnal and cathemeral species were detected relatively more frequently in disturbed areas close to communities, but individual species did not necessarily shift their activity patterns. Group biomass of all species was depressed in the wider neighbourhood of urban areas rather than communities. Interview data suggest that species traits, especially group size and body mass, mediate these relationships. Large-bodied, large-group-living species are detected farther from communities as reported by experienced informants. Long-established communities in our study regions have not "emptied" the surrounding forest. Low human population density and low hunting offtake due to abundant sources of alternative aquatic protein, suggest that these communities represent a best-case scenario for sustainable hunting of wildlife for food, thereby providing a conservative assessment of game depletion. Given this 'best-case' camera trap and interview-based evidence for hunting depletion, regions with higher human population densities, external trade in wildlife and limited access to alternative protein will likely exhibit more severe depletion.
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Distribuição Animal , Conservação dos Recursos Naturais , Dieta Paleolítica/estatística & dados numéricos , População Rural/estatística & dados numéricos , Animais , Animais Selvagens , Biomassa , Peso Corporal , Brasil , Feminino , Florestas , Humanos , Masculino , Densidade Demográfica , Características de Residência , VertebradosRESUMO
OBJECTIVES: To improve awareness and recognition of chronic bacterial prostatitis (CBP) and chronic prostatitis/chronic pelvic pain syndrome (CP/CPPS) among non-specialists and patients. To provide guidance to healthcare professionals treating patients with CBP and CP/CPPS, in both non-specialist and specialist settings. To promote efficient referral of care between non-specialists and specialists and the involvement of the multidisciplinary team (MDT). PATIENTS AND METHODS: The guideline population were men with CBP or CP/CPPS (persistent or recurrent symptoms and no other urogenital pathology for ≥3 of the previous 6 months). Consensus recommendations for the guidelines were based on a search to identify literature on the diagnosis and management of CBP and CP/CPPS (published between 1999 and February 2014). A Delphi panel process was used where high-quality, published evidence was lacking. RESULTS: CBP and CP/CPPS can present with a wide range of clinical manifestations. The four main symptom domains are urogenital pain, lower urinary tract symptoms (LUTS - voiding or storage symptoms), psychological issues and sexual dysfunction. Patients should be managed according to their individual symptom pattern. Options for first-line treatment include antibiotics, α-adrenergic antagonists (if voiding LUTS are present) and simple analgesics. Repeated use of antibiotics, such as quinolones, should be avoided if there is no obvious symptomatic benefit from infection control or cultures do not support an infectious cause. Early use of treatments targeting neuropathic pain and/or referral to specialist services should be considered for patients who do not respond to initial measures. An MDT approach (urologists, pain specialists, nurse specialists, specialist physiotherapists, general practitioners, cognitive behavioural therapists/psychologists, and sexual health specialists) is recommended. Patients should be fully informed about the possible underlying causes and treatment options, including an explanation of the chronic pain cycle. CONCLUSION: Chronic prostatitis can present with a wide variety of signs and symptoms. Identification of individual symptom patterns and a symptom-based treatment approach are recommended. Further research is required to evaluate management options for CBP and CP/CPPS.
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Dor Crônica , Dor Pélvica , Prostatite , Dor Crônica/diagnóstico , Dor Crônica/terapia , Consenso , Humanos , Masculino , Dor Pélvica/diagnóstico , Dor Pélvica/terapia , Prostatite/diagnóstico , Prostatite/terapiaRESUMO
We coupled dynamic optimization and bioenergetics models to assess the assumption that lake trout (Salvelinus namaycush) depth distribution is structured by temperature, food availability, and predation risk to maximize reproductive mass by autumn spawning. Because the model uses empirical daily thermal-depth profiles recorded in a small boreal shield lake (lake 373 at the Experimental Lakes Area, northwestern Ontario) during 2 years of contrasting thermal stratification patterns, we also assessed how climate-mediated changes in lakes may affect the vertical distribution, growth, and fitness of lake trout, a cold-water top predator. The depths of acoustic-tagged lake trout were recorded concurrently with thermal-depth profiles and were compared to model output, enabling an assessment of model performance in relation to the observed fish behavior and contrasting thermal conditions. The depths and temperatures occupied by simulated fish most closely resembled those of the tagged fish when risk of predation was included in the model, indicating the model may incorporate the most important underlying mechanisms that determine lake trout depth. Annual differences suggest less use of shallow (warm), productive habitats, resulting in markedly less reproductive mass, during the year with the warm stratification pattern. Mass for reproduction may be lower in warmer conditions because of reduced reproductive investment, yet survival may be inadvertently higher because risky surface waters may be avoided more often in warmer, shallower, and metabolically costly conditions. At a minimum our study suggests that lake trout reproductive mass and fitness may be expected to change under the anticipated longer and warmer stratification patterns.
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Ecossistema , Metabolismo Energético , Modelos Teóricos , Truta/crescimento & desenvolvimento , Animais , Mudança Climática , Feminino , Lagos , Masculino , Ontário , Reprodução , Estações do Ano , TemperaturaRESUMO
BACKGROUND: There is a lack of information about the prevalence, manifestations, and management of chronic pain in children in the UK. We surveyed consultants with an interest in chronic pain management and general practitioners (GPs) in the UK in order to understand their perspective on chronic pain in children. METHODS: We conducted a postal survey of clinicians with an interest in chronic pain management and GPs in the UK. The survey contained questions relating to the following aspects of managing children with chronic pain: (i) clinicians' training and experience; (ii) available resources; (iii) perceived prevalence, presentation, and referral patterns; (iv) interventions; and (v) outcomes. RESULTS: 472 pain clinicians and 131 GPs were contacted. The response rates were 55% and 61% respectively. Of the respondents, 77% of pain clinicians and 95% of GPs acknowledged a lack of adequate training for managing children with chronic pain. 57% of the pain clinicians and 63% of the GPs reported that the prevalence of chronic pain in children was <5%. In the comments section, 22% of those respondents who frequently manage children with chronic pain reported an increase in the incidence of this problem over the last 5 years. The common chronic pain syndromes in children were reported to be: musculoskeletal and limb pain, recurrent abdominal and pelvic pain, and headache. 15% of the respondents advised that children with chronic pain would be best managed in specialist pediatric centers and 75% opined that majority of children with chronic pain have a fair to good prognosis. CONCLUSIONS: More information is required about prevalence, manifestations and long-term effects of chronic pain in children in the UK. There is a need for increasing training and resources amongst GPs and pain clinicians for managing chronic pain in the pediatric age group.
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Analgesia , Medicina de Família e Comunidade , Dor , Inquéritos e Questionários , Anestesiologia/educação , Criança , Doença Crônica , Medicina de Família e Comunidade/educação , Pesquisas sobre Atenção à Saúde , Humanos , Dor/epidemiologia , Dor/etiologia , Manejo da Dor , Prevalência , Prognóstico , Encaminhamento e Consulta/estatística & dados numéricos , Reino Unido/epidemiologiaRESUMO
While aquatic environments have long been thought to be more moderate environments than their terrestrial cousins, environmental data demonstrate that for some systems this is not so. Numerous important environmental parameters can fluctuate dramatically, notably dissolved oxygen, turbidity and temperature. The roles of dissolved oxygen and turbidity on predator-prey interactions have been discussed in detail elsewhere within this issue and will be considered only briefly here. Here, we will focus primarily on the role of temperature and its potential impact upon predator-prey interactions. Two key properties are of particular note. For temperate aquatic ecosystems, all piscine and invertebrate piscivores and their prey are ectothermic. They will therefore be subject to energetic demands that are significantly affected by environmental temperature. Furthermore, the physical properties of water, particularly its high thermal conductivity, mean that thermal microenvironments will not exist so that fine-scale habitat movements will not be an option for dealing with changing water temperature in lentic environments. Unfortunately, there has been little experimental analysis of the role of temperature on such predator-prey interactions, so we will instead focus on theoretical work, indicating that potential implications associated with thermal change are unlikely to be straightforward and may present a greater threat to predators than to their prey. Specifically, we demonstrate that changes in the thermal environment can result in a net benefit to cold-adapted species through the mechanism of predator-prey interactions.
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Meio Ambiente , Cadeia Alimentar , Efeito Estufa , Animais , Peixes/fisiologia , Água Doce , Temperatura Alta , Modelos Biológicos , Densidade DemográficaRESUMO
Many soft tissue complaints are associated with the development of neuropathic pain. This pain is produced by pathophysiological processes that are different to the processes involved in the generation of the inflammatory or nociceptive pain more commonly encountered in soft tissue disorders. One of the consequences of this is that neuropathic pain can often be less responsive to standard analgesic therapies. The use of alternative analgesic strategies may be necessary if we are to treat neuropathic pain successfully. This chapter aims to outline some of the clinical features associated with neuropathic pain, the aetiological factors leading to its development and the evidence base (or lack) behind current treatment strategies. It will try to provide a rational approach to the management of neuropathic pain in patients with soft tissue disorders, particularly focusing on pharmacological management. Neuropathic pain is the focus of much current research activity, particularly pharmacological research, and this chapter will attempt to identify gaps in our clinical knowledge and highlight opportunities for further research.
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Doenças Musculoesqueléticas/complicações , Neuralgia/tratamento farmacológico , Neuralgia/etiologia , Analgésicos Opioides/uso terapêutico , Anticonvulsivantes/uso terapêutico , Antidepressivos/uso terapêutico , Humanos , Neuralgia/fisiopatologia , PrognósticoRESUMO
1. The importance of body size and growth rate in ecological interactions is widely recognized, and both are frequently used as surrogates for fitness. However, if there are significant costs associated with rapid growth rates then its fitness benefits may be questioned. 2. In replicated whole-lake experiments, we show that a domestic strain of rainbow trout (artificially selected for maximum intrinsic growth rate) use productive but risky habitats more than wild trout. Consequently, domestic trout grow faster in all situations, experience greater survival in the absence of predators, but have lower survival in the presence of predators. Therefore, rapid growth rates are selected against due to increased foraging effort (or conversely, lower antipredator behaviour) that increases vulnerability to predators. In other words, there is a behaviourally mediated trade-off between growth and mortality rates. 3. Whereas rapid growth is beneficial in many ecological interactions, our results show the mortality costs of achieving it are large in the presence of predators, which can help explain the absence of an average phenotype with maximized growth rates in nature.
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Animais Domésticos/crescimento & desenvolvimento , Animais Selvagens/crescimento & desenvolvimento , Comportamento Animal/fisiologia , Tamanho Corporal/fisiologia , Oncorhynchus mykiss/crescimento & desenvolvimento , Animais , Animais Domésticos/fisiologia , Animais Selvagens/fisiologia , Evolução Biológica , Ecossistema , Mortalidade , Oncorhynchus mykiss/fisiologia , Assunção de Riscos , Análise de Sobrevida , Fatores de TempoRESUMO
Given limited food, prey fishes in a temperate climate must take risks to acquire sufficient reserves for winter and/or to outgrow vulnerability to predation. However, how can we distinguish which selective pressure promotes risk-taking when larger body size is always beneficial? To address this question, we examined patterns of energy allocation in populations of age-0 trout to determine if greater risk-taking corresponds with energy allocation to lipids or to somatic growth. Trout achieved maximum growth rates in all lakes and allocated nearly all of their acquired energy to somatic growth when small in early summer. However, trout in low-food lakes took greater risks to achieve this maximal growth, and therefore incurred high mortality. By late summer, age-0 trout allocated considerable energy to lipids and used previously risky habitats in all lakes. These results indicate that: (i) the size-dependent risk of predation (which is independent of behaviour) promotes risk-taking behaviour of age-0 trout to increase growth and minimize time spent in vulnerable sizes; and (ii) the physiology of energy allocation and behaviour interact to mediate growth/mortality trade-offs for young animals at risk of predation and starvation.
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Ecossistema , Metabolismo Energético/fisiologia , Assunção de Riscos , Seleção Genética , Truta/crescimento & desenvolvimento , Análise de Variância , Animais , Pesos e Medidas Corporais , Água Doce , Funções Verossimilhança , Metabolismo dos Lipídeos , Densidade Demográfica , Estações do AnoRESUMO
Domesticated (farm) salmonid fishes display an increased willingness to accept risk while foraging, and achieve high growth rates not observed in nature. Theory predicts that elevated growth rates in domestic salmonids will result in greater risk-taking to access abundant food, but low survival in the presence of predators. In replicated whole-lake experiments, we observed that domestic trout (selected for high growth rates) took greater risks while foraging and grew faster than a wild strain. However, survival consequences for greater growth rates depended upon the predation environment. Domestic trout experienced greater survival when risk was low, but lower survival when risk was high. This suggests that animals with high intrinsic growth rates are selected against in populations with abundant predators, explaining the absence of such phenotypes in nature. This is, to our knowledge, the first large-scale field experiment to directly test this theory and simultaneously quantify the initial invasibility of domestic salmonid strains that escape into the wild from aquaculture operations, and the ecological conditions affecting their survival.
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Animais Domésticos/crescimento & desenvolvimento , Meio Ambiente , Comportamento Alimentar/fisiologia , Oncorhynchus mykiss/crescimento & desenvolvimento , Assunção de Riscos , Animais , Animais Domésticos/fisiologia , Colúmbia Britânica , Modelos Lineares , Oncorhynchus mykiss/fisiologia , Dinâmica Populacional , Comportamento PredatórioRESUMO
Understanding and predicting the spatial distribution of social foragers among patchily distributed resources is a problem that has been addressed with numerous approaches over the 30 yr since the ideal free distribution (IFD) was first introduced. The two main approaches involve perceptual constraints and unequal competitors. Here we present a model of social foragers choosing among resource patches. Each forager makes a probabilistic choice on the basis of the information acquired through past foraging experiences. Food acquisition is determined by the forager's competitive ability. This model predicts that perceptual constraints have a greater influence on the spatial distribution of foragers than unequal competitive abilities but that competitive ability plays an important role in determining an individual's information state and behavior. Better competitors have access to more information; consequently, we find that competitive abilities and perceptual constraints are integrated through the social environment occupied by individual foragers. Relative competitive abilities influence the forager's information state, and the ability to use information determines the resulting spatial distribution.