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We introduce a class of discrete single species models with distributed delay in the reproductive process and a cohort dependent survival function that accounts for survival pressure during that delay period. These delay recurrences track the mature population for species in which individuals reach maturity after at least τ and at most τ+τM breeding cycles. Under realistic model assumptions, we prove the existence of a critical delay threshold, τ˜c. For given delay kernel length τM, if each individual takes at least τ˜c time units to reach maturity, then the population is predicted to go extinct. We show that the positive equilibrium is decreasing in both τ and τM. In the case of a constant reproductive rate, we provide an equation to determine τ˜c for fixed τM, and similarly, provide a lower bound on the kernel length, τ˜M for fixed τ such that the population goes extinct if τM≥τ˜M. We compare these critical thresholds for different maturation distributions and show that if all else is the same, to avoid extinction it is best if all individuals in the population have the shortest delay possible. We apply the model derivation to a Beverton-Holt model and discuss its global dynamics. For this model with kernels that share the same mean delay, we show that populations with the largest variance in the time required to reach maturity have higher population levels and lower chances of extinction.

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OBJECTIVES: To evaluate the incidence rate of Duchenne muscular dystrophy (DMD) in the male newborns in the Ningxia region and establish a critical threshold for screening DMD in newborns to distinguish between the normal population and affected individuals. METHODS: A total of 10 000 male newborns were screened using immunofluorescence analysis of creatine kinase isoenzyme concentrations in heel spot dried blood specimens. Newborns with the concentrations higher than the critical threshold were recalled for serum creatine kinase measurements. Genetic testing was performed to confirm diagnosis in cases showing abnormalities. RESULTS: Among the screened 10 000 male newborns, two were confirmed to have DMD through genetic testing, resulting in a preliminary estimated incidence rate of 1/5 000 for male newborns in the Ningxia region. The critical threshold for creatine kinase isoenzyme concentration in newborns in this region was determined to be 468.57 ng/mL. CONCLUSIONS: Screening for DMD in newborns is feasible in the Ningxia region. Early screening, diagnosis, and treatment of DMD can improve the quality of life for affected individuals and help families make informed decisions regarding further pregnancies.

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Organic materials containing humic acids (HAs) play important roles in regulating the bioavailability of cadmium (Cd) in soils and thus its accumulation in crops. The effects of the two active components of HAs, humic acid (HA) and fulvic acid (FA), in organic materials and their different ratios (HA/FA) on Cd uptake and accumulation in rice were investigated using a field plot experiment, and their relationships with the Cd fractions and availability in paddy soil as influenced by the use of these organic materials were analyzed in combination with the fractionation method of chemical continuous extraction. The results showed that the effects of HAs on Cd availability in soil and Cd accumulation in rice grains were controlled by the ratios of the active components in the organic materials. The treatments with an HA/FA ratio ≥ 4/6 had a passivating effect on soil Cd, resulting in a significant reduction in Cd availability. Compared with that in the control without the application of HAs (CK), rice grain Cd concentration was reduced by 15.2%-33.3%, whereas those with an HA/FA ratio ≤ 2/8 activated Cd in soil, and the available Cd content was significantly increased. Compared with that in CK, rice grain Cd concentration was increased by 24.2%-42.4%. The ratios of HA/FA in HAs affected the morphological transformation of soil Cd. Compared with the CK treatment, the treatments with ratios of HA/FA ≥ 4/6 promoted the transformation of soil Cd from the exchangeable form (EX-Cd) with high activity to the carbonate bound form (CA-Cd) and Fe and Mn oxide-bound forms (FM-Cd) with low activity, whereas those with ratios of HA/FA ≤ 2/8 showed the opposite effects. The effects of HA and FA on soil pH and available sulfur concentration differed. Soil pH had a significant positive correlation with HA addition but a negative correlation with FA addition, and soil available sulfur content had a significant positive correlation with FA addition at the rice tillering stage. Therefore, to ensure the quality and safety of rice, organic materials with an HA/FA ratio ≥ 4/6 should be selected. The results provided a scientific basis for the directed utilization of organic materials containing HAs.

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PURPOSE: This study aimed to examine if peripheral fatigue is adjusted during knee extensor (KE) exercise in order not to surpass a critical threshold patient with type 1 diabetes (T1D) and the consequences of this mechanism on the force-duration relationship. METHODS: Eleven T1D individuals randomly performed two different sessions in which they performed 60 maximum voluntary contractions (MVC; 3 s contraction, 2 s relaxation). One trial was performed in the non-fatigued state (CTRL) and another after fatiguing neuromuscular stimulation of the KE (FNMES). Peripheral and central fatigue were quantified by the difference between pre and post exercise in quadriceps voluntary activation (ΔVA) and potentiated twitch (ΔPtw). Critical torque (CT) was determined as the average force of the last 12 contractions, whereas W' was calculated as the area above the CT. RESULTS: Although FNMES led to a significant decrease in potentiated twitch (Ptw) before performing the 60-MVCs protocol (p < 0.05), ΔVA (∼ -7.5%), ΔPtw (∼ -39%), and CT (∼816 N) post-MVCs were similar between the two conditions. The difference in W' between CTRL and FNMES was correlated with the level of pre-fatigue induced in FNMES (r2 = 0.60). In addition, W' was correlated with ΔPtw (r2 = 0.62) in the CTRL session. CONCLUSION: Correlative results in the present study indicate that regulating peripheral fatigue mechanisms at a critical threshold limit W'. Additionally, peripheral fatigue during KE exercise is limited to an individual threshold in T1D patients.

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Telomere length and telomere shortening are thought to be critical cellular attributes and processes that are related to an individual's life span and fitness. The general pattern across most taxa is that after birth telomere length gradually decreases with age. Telomere protection and restoration mechanisms are usually assumed to reduce the rate of shortening or at most keep telomere length constant. However, here we have compiled a list of 26 articles showing that there is an increasing number of studies reporting apparent elongation of telomeres (i.e., a net increase in TL from timet to timet+1) often in a considerable proportion of the individuals studied. Moreover, the few studies which have studied telomere elongation in detail show that increases in telomere length are unlikely to be due to measurement error alone. In this article, we argue that episodes of telomere elongation deserve more attention as they could reflect individual strategies to optimise life histories and maximise fitness, which may not be reflected in the overall telomere dynamics patterns. We propose that patterns of telomere (net) elongation may be partly determined by other factors than those causing telomere shortening, and therefore deserve analyses specifically targeted to investigate the occurrence of telomere elongation. We elaborate on two ecological hypotheses that have been proposed to explain patterns of telomere elongation (the 'excess resources elongation' and the 'last resort elongation' hypothesis) and we discuss the current evidence for (or against) these hypotheses and propose ways to test them.

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Since certain prey hide from predators to protect themselves within their habitats, predators are forced to change their diet due to a lack of prey for consumption, or on the contrary, subsist only with alternative food provided by the environment. Therefore, in this paper, we propose and mathematically contrast a predator-prey, where alternative food for predators is either considered or not when the prey population size is above the refuge threshold size. Since the model with no alternative food for predators has a Hopf bifurcation and a transcritical bifurcation, in addition to a stable limit cycle surrounding the unique interior equilibrium, such bifurcation cases are transferred to the model when considering alternative food for predators when the prey size is above the refuge. However, such a model has two saddle-node bifurcations and a homoclinic bifurcation, characterized by a homoclinic curve surrounding one of the three interior equilibrium points of the model.

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Ecosystem services (ESs) have been widely used for ecological protection and land spatial planning. Natural and anthropogenic drivers exhibit a strong dynamic coupling relationship with ESs. However, current ESs-related research focused on mapping the ESs spatially or investing the trade-offs and synergies relationship between ES, ignoring the nonlinear response of ESs to natural and anthropogenic drivers. Here we aimed to investigate the nonlinear effect of 14 potential drivers (8 natural and 6 anthropogenic) on the total value of six typical ESs (ESV). Taking Beijing-Tianjin-Hebei urban agglomeration (BTH) in China as an example, we established 14 constrain lines and identified critical thresholds through the restricted cubic splines (RCS) regression. We found strong non-linear impacts of natural and anthropogenic drivers on ESV and critical thresholds existed among all the 14 constrain lines. The RCS plots showed that the overall ESV was kept at a high level before or after certain thresholds (e.g., altitude >687 m, slope >13.4°, NDVI >0.7, distance from water <31.2 km, etc.). We categorized these threshold combinations and found the potentially high ES delivery areas were mainly distributed in the Yanshan Mountian, accounting for approximately 5% of the total BTH region. These critical thresholds offer a new method to delineate conservation and restoration priority areas.

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The decision to delay or cancel spraying insecticides against pest aphids is dependent on the ratio of prey/predator, which reflects how well the predator can suppress the aphid population increase in the field. It is challenging to estimate the ratio of prey/predator due to the multiple factors involved in the interaction between prey and predator. Cotton aphid (Aphis gossypii Glover) is a serious pest, widely distributed in cotton-growing areas around the world. We combined different ratios of aphids with aphid oligophagous ladybird beetles (Coccinella septempunctata Linnaeus) under laboratory and garden conditions to investigate the critical threshold for prey/predator which effectively reduced the cotton aphid population increase. Two kinds of modeling were developed to understand the relationships between the ratio of prey/predator and the PGR (population growth rate), and with the effectiveness of biocontrol (EBC). We found the critical values of PGR should be less than -0.0806 (predators artificially released after 5 days) and then less than -0.075 (predators released after 10 days) if EBC is less than 50%. We recommend that the ratio of prey/predator should be less than 450 for the effective biocontrol of cotton aphids at the cotton seedling stage. These values can be reference indices for the management of aphids in mid-summer.

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While most cases of pancreatitis in dogs are thought to be idiopathic, potential risk factors are identified. In this article we provide a state-of-the-art overview of suspected risk factors for pancreatitis in dogs, allowing for improved awareness and detection of potential dog-specific risk factors, which might guide the development of disease prevention strategies. Additionally, we review important advances in our understanding of the pathophysiology of pancreatitis and potential areas for therapeutic manipulation based thereof. The outcome of pathophysiologic mechanisms and the development of clinical disease is dependent on the balance between stressors and protective mechanisms, which can be evaluated using the critical threshold theory.

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Cancer is a serious threat to human health and life. Using anti-tumor drugs is one of the important ways for treating cancer. A large number of experiments have shown that the hormesis appeared in the dose-response relationship of various anti-tumor drugs. Modeling this phenomenon will contribute to finding the appropriate dose. However, few studies have used dynamical models to quantitatively explore the hormesis phenomenon in anti-tumor drug dose-response. In this study, we present a mathematical model and dynamical analysis to quantify hormesis of anti-tumor drugs and reveal the critical threshold of antibody dose. Firstly, a dynamical model is established to describe the interactions among tumor cells, natural killer cells and M2-polarized macrophages. Model parameters are fitted through the published experimental data. Secondly, the positivity of solution and bounded invariant set are given. The stability of equilibrium points is proved. Thirdly, through bifurcation analysis and numerical simulations, the hormesis phenomenon of low dose antibody promoting tumor growth and high dose antibody inhibiting tumor growth is revealed. Furthermore, we fit out the quantitative relationship of the dose-response of antibodies. Finally, the critical threshold point of antibody dose changing from promoting tumor growth to inhibiting tumor growth is obtained. These results can provide suggestions for the selection of appropriate drug dosage in the clinical treatment of cancer.

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Chromium (Cr) contamination in paddy soil-rice systems threatens human health through the food chain. This study used a new dataset of 500 paddy soil and plant tissue samples collected in the rice-growing regions of Sindh and Punjab Provinces of Pakistan. Overall, 97.4% of grain samples exceeded the Cr threshold values of 1.0 mg kg-1, determined by the China National Food Standard (CNFS). The Cr in paddy soil, 62.6% samples exceeding the China natural background threshold value (90 mg kg-1) for Cr concentration in paddy soil, and lower than the (pH-dependant > 7.5 threshold value for Cr 350 mg kg-1) as determined by China Environmental Quality Standards (EQSs) for paddy soil (GB15618-2018). Geographically weighted regression (GWR) modelling showed spatially nonstationary correlations, confirming the heterogeneous relationship between dependent (rice grain Cr) and independent paddy soil (pH, SOM, and paddy soil Cr) and plant tissue variables (shoot Cr and root Cr) throughout the study area. The GWR model was then used to determine the critical threshold (CT) for the measured Cr concentrations in the paddy soil system. Overall, 38.4% of paddy soil samples exceeding CT values confirm that the paddy soil Cr risk prevails in the study area. Furthermore, the GWR model was applied to assess the loading capacity (LC), the difference between the CT, and the actual concentration of Cr in paddy soil. Loading capacity identified potential paddy soil Cr pollution risk to rice grain and assessed the risk areas. Overall LC% of samples paddy soil Cr risk areas grade: low-risk grade I (34.6%); moderate-risk grade II (15.8%); high-risk grade III (11.2%); and very high-risk grade IV (38.4%) have been assessed in the study area. The human health index, total hazard quotient (THQ ≪ 1), indicates no potential health risk originating from Cr exposure to the population. However, the excess Cr level in paddy soil and rice grain is still a concern. The current study's results are also valuable for the national decision-making process regarding Cr contamination in the paddy soil-rice system.

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Background and Objectives: Barefoot peak plantar pressures (PPPs) are elevated in diabetes patients with neuropathic foot ulcer (DFU) history; however, there is limited reported evidence for a causative link between high barefoot PPP and DFU risk. We aimed to determine, using a simple mat-based methodology, the site-specific, barefoot PPP critical threshold that will identify a plantar site with a previous DFU. Materials and Methods: In a cross-sectional study, barefoot, site-specific PPPs were measured with normal gait for patients with DFU history (n = 21) and healthy controls (n = 12), using a validated carbon footprint system. For each participant, PPP was recorded at twelve distinct plantar sites (1st-5th toes, 1st-5th metatarsal heads (MTHs), midfoot and heel), per right and left foot, resulting in the analysis of n = 504 distinct plantar sites in the diabetes group, and n = 288 sites in the control group. Receiver operator characteristic curve analysis determined the optimal critical threshold for sites with DFU history. Results: Median PPPs for the groups were: diabetes sites with DFU history (n = 32) = 5.0 (3.25-7.5) kg/cm2, diabetes sites without DFU history (n = 472) = 3.25 (2.0-5.0) kg/cm2, control sites (n = 288) = 2.0 (2.0-3.25) kg/cm2; (p < 0.0001). Diabetes sites with elevated PPP (>6 kg/cm2) were six times more likely to have had DFU than diabetes sites with PPP ≤ 6 kg/cm2 (OR = 6.4 (2.8-14.6, 95% CI), p < 0.0001). PPP > 4.1 kg/cm2 was determined as the optimal critical threshold for identifying DFU at a specific plantar site, with sensitivity/specificity = 100%/79% at midfoot; 80%/65% at 5th metatarsal head; 73%/62% at combined midfoot/metatarsal head areas. Conclusions: We have demonstrated, for the first time, a strong, site-specific relationship between elevated barefoot PPP and previous DFU. We have determined a critical, highly-sensitive, barefoot PPP threshold value of >4.1 kg/cm2, which may be easily used to identify sites of previous DFU occurrence and, therefore, increased risk of re-ulceration. This site-specific approach may have implications for how high PPPs should be investigated in future trials.

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A novel coronavirus has resulted in an outbreak of viral pneumonia in China. Person-to-person transmission has been demonstrated, but, to our knowledge, the spreading of novel coronavirus takes place due to an asymptomatic carrier. Most models are not considering testing and underlying network topology that shows the spreading pattern. By failing to integrate testing into the epidemiological model, models missed a vital opportunity to better understand the role of asymptomatic infection in transmission. In this work, we propose a model considering testing as well as asymptomatic infection considering underlying network topology. We extract the transmission parameters from the data set of COVID-19 of India and apply those parameters in our proposed model. The simulation results support our theoretical derivations, which show the impact of testing and asymptomatic carrier in infection spreading.

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Research on telomeres in the fields of ecology and evolution has been rapidly expanding over the last two decades. This has resulted in the formulation of a multitude of, often name-given, hypotheses related to the associations between telomeres and life-history traits or fitness-facilitating processes (and the mechanisms underlying them). However, the differences (or similarities) between the various hypotheses, which can originate from different research fields, are often not obvious. Our aim here is therefore to give an overview of the hypotheses that are of interest in ecology and evolution and to provide two frameworks that help discriminate among them. We group the hypotheses (i) based on their association with different research questions, and (ii) using a hierarchical approach that builds on the assumptions they make, such as about causality of telomere length/shortening and/or the proposed functional consequences of telomere shortening on organism performance. Both our frameworks show that there exist parallel lines of thoughts in different research fields. Moreover, they also clearly illustrate that there are in many cases competing hypotheses within clusters, and that some of these even have contradictory assumptions and/or predictions. We also touch upon two topics in telomere research that would benefit from further conceptualization. This review should help researchers, both those familiar with and those new to the subject, to identify future avenues of research.

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Using negative oxygen ion (NOI) observations, with an hourly resolution, the automatic weather station (AWS), and a comparative analysis of three well-known scenic locations, namely, Zoige Wetland Nature Reserve (ZWNR), Sichuan Panda Nature Habitat (PNH), and Hangzhou West Lake (HWL) Scenic Area was performed and the dynamic mechanisms of typical wetlands in response to a NOI surge were investigated. The findings are as follows. ① At HWL, NOI concentration was higher than in the metropolitan center. The influence of meteorological conditions on NOI in the ZWNR wetland and PNH in southwest China was more significant than that in Hangzhou in the eastern densely populated metropolitan areas. ② Sensitive contribution parameters of microphysical meteorological conditions are given, including the atmospheric condensation rates (fc) and supersaturation (S), as well as the height and amount of low cloud (H0 and M). A parametric model of exponential attenuation driven by the size of water vapor (fog droplets) is given for diagnosing the NOI concentration change in natural wetlands. At the critical threshold of S > 4%, the NOI rapidly increases to the maximum value. ③ Based on parametric principle of the wet aerodynamics of natural wetlands, the NOI meteorological condition index of the quasi-linear relationship with real-time NOI observation is established. The geographical distribution band of the high concentration of NOI in China is given, which meeting with the typical famous wetlands and giant panda habitat NOI characteristics in China. It provides the application prospects for NOI diagnosis and prediction.

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Fire disturbance has increased in some tundra ecosystems due to anthropogenic climate change, with important ramifications for terrestrial carbon cycling. Assessment of the potential impact of fire-regime change on tundra carbon stocks requires long-term perspectives because tundra fires have been rare historically. Here we integrated the process-based Dynamic Organic Soil version of the Terrestrial Ecosystem Model with paleo-fire records to evaluate the responses of tundra carbon stocks to changes in fire return interval (FRI). Paleorecords reveal that mean FRIs of tundra ecosystems in Alaska ranged from centennial to millennial timescales (200-6000 years) during the late Quaternary, but projected FRIs by 2100 decrease to a few hundred years to several decades (70-660 years). Our simulations indicate threshold effects of changing FRIs on tundra carbon stocks. Shortening FRI from 5000 to 1000 years results in minimal carbon release (<5%) from Alaskan tundra ecosystems. Rapid carbon stock loss occurs when FRI declines below 800 years trigger sustained mobilization of ancient carbon stocks from permafrost soils. However, substantial spatial heterogeneity in the resilience/sensitivity of tundra carbon stocks to FRI change exists, largely attributable to vegetation types. We identified the carbon stocks in shrub tundra as the most vulnerable to decreasing FRI because shrub tundra stores a large share of carbon in combustible biomass and organic soils. Moreover, our results suggest that ecosystems characterized by large carbon stocks and relatively long FRIs (e.g. Brooks Foothills) may transition towards hotspots of permafrost carbon emission as a response to crossing FRI thresholds in the coming decades. These findings combined imply that fire disturbance may play an increasingly important role in future carbon balance of tundra ecosystems, but the net outcome may be strongly modulated by vegetation composition.

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The aim of this study was to investigate the effects of heat on the validity of end-test power (EP) derived from a 3-min all-out test (3MT), which is considered as an alternative method for determining the conventional critical power. Twelve male cyclists were required to perform incremental exercise tests (IET) and 3MTs in both high temperature (HT; 35 °C) and thermoneutral temperature (NT; 22 °C) environments. Maximal oxygen uptake (VO2max), and first and second ventilatory thresholds (VT1 and VT2, respectively) against the power output (wVO2max, wVT1, and wVT2) were measured during IETs. EP was recorded during the 3MTs. A significant correlation was observed between wVT2 and EP under NT (r = 0.674, p < 0.05) and under HT (r = 0.672, p < 0.05). However, wVO2max, wVT1, wVT2, and EP were significantly higher in NT than in HT (p < 0.05). In conclusion, although the physiological stress induced by HT might impair exercise performance, the EP derived from 3MT can validly estimate wVT2 under HT conditions.

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Although absolute jump heights should be considered an important factor in judging the performance requirements of volleyball players, limited data is available on age-appropriate categories. The purpose of this study is to determine the differences in specific anthropometric characteristics and jumping performance variables in under-19 female volleyball players in relation to playing position and performance level. The sample of subjects consisted of 354 players who prepared for the U19 Women's Volleyball European Championship 2020 (17.4 ± 0.8 years, 1.81 ± 0.07 m, 67.5 ± 7.1 kg). Playing positions analyzed were setters (n = 55), opposites (n = 37), middle blockers (n = 82), outside hitters (n = 137), and liberos (n = 43). The results showed player position differences in every performance level group in variables of body height, spike, and block jump. Observed differences are a consequence of highly specific tasks of different positions in the composition of the team. Players of different performance levels are significantly different, with athletes of higher-ranked teams achieving better results. The acquired data could be useful for the selection and profiling of young volleyball players.

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Predicting the outbreak risks and/or the inflection (turning or tipping) points of COVID-19 can be rather challenging. Here, it is addressed by modeling and simulation approaches guided by classic ecological theories and by treating the COVID-19 pandemic as a metapopulation dynamics problem. Three classic ecological theories are harnessed, including TPL (Taylor's power-law) and Ma's population aggregation critical density (PACD) for spatiotemporal aggregation/stability scaling, approximating virus metapopulation dynamics with Hubbell's neutral theory, and Ma's diversity-time relationship adapted for the infection-time relationship. Fisher-Information for detecting critical transitions and tipping points are also attempted. It is discovered that: (i) TPL aggregation/stability scaling parameter (b > 2), being significantly higher than the b-values of most macrobial and microbial species including SARS, may interpret the chaotic pandemic of COVID-19. (ii) The infection aggregation critical threshold (M 0) adapted from PACD varies with time (outbreak-stage), space (region) and public-health interventions. Exceeding M 0, local contagions may become aggregated and connected regionally, leading to epidemic/pandemic. (iii) The ratio of fundamental dispersal to contagion numbers can gauge the relative importance between local contagions vs. regional migrations in spreading infections. (iv) The inflection (turning) points, pair of maximal infection number and corresponding time, are successfully predicted in more than 80% of Chinese provinces and 68 countries worldwide, with a precision >80% generally.

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Ionizing radiation creates free radicals, the effect of which is enhanced by the presence of oxygen; a low oxygen level produces radioprotective effects for insects compared with irradiation in ambient air. Modified (controlled) atmosphere packaging is used for maintaining quality and shelf-life extension; therefore, treatment efficacy may be affected, and there is a need to determine the critical O2 levels that may cause radioprotective effects. Late third-instar Bactrocera dorsalis (Hendel) larvae were irradiated in bags filled with ambient or low-oxygen air (0%, 2%, 4%, 6%, 8% O2) and were exposed to radiation doses of 8 to 64 Gy with intervals of 8 Gy. Efficacy was measured by the prevention of adult emergence. Dose-response data on mortality (failure of adult emergence) were analyzed via two-way ANOVA (analysis of variance), ANCOVA (analysis of covariance), and probit regression. The difference in radiotolerance was only significant in 0% O2 atmospheres through two-way ANOVA; therefore, the 95% confidence limits (CLs) of lethal dose ratios at LD99 were used to determine significant differences between treatments at different O2 levels. The differences in radiotolerance were significant in 0% and 2% O2 but insignificant in 4%, 6%, and 8% O2 environments when compared with radiation in ambient air. The critical threshold of radioprotective effects for late third-instar B. dorsalis larvae is an O2 level of ≥4% and <6%, but a maximum radiation dose of 14 Gy can compensate for this effect during phytosanitary irradiation treatment.