Catch the wave: prairie dogs assess neighbours’ awareness using contagious displays

The jump–yip display of black-tailed prairie dogs (Cynomys ludovicianus) is contagious, spreading through a prairie dog town as ‘the wave’ through a stadium. Because contagious communication in primates serves to assess conspecific social awareness, we investigated whether instigators of jump–yip bouts adjusted their behaviour relative to the response of conspecifics recruited to display bouts. Increased responsiveness of neighbouring town members resulted in bout initiators devoting a significantly greater proportion of time to active foraging. Contagious jump–yips thus function to assess neighbours’ alertness, soliciting social information to assess effective conspecific group size in real time and reveal active probing of conspecific awareness consistent with theory of mind in these group-living rodents.     

Early and Late De Novo Tumors after Liver Transplantation in Adults: The Late Onset of Bladder Tumors in Men

Background

De novo tumors (DNT) after liver transplantation (LT) represent a growing concern.

Patients and Methods

We analyzed the incidence of DNT, type, time of onset, risk factors and mortality (as of 2010) in 494 adult patients transplanted in the last 26 years (1983–2009).

Results

DNT occurred in 41 (8.3%) of the patients. The Standardized Incidence Ratio (SIR) compared with the Italian population was 1.8. There was a higher incidence in males (SIR 2.0), an expected extremely high rate of Kaposi’s sarcoma (SIR 127.95) and unexpected higher rates of tumors of the bladder in males (SIR 3.3). The incidence of DNT was higher within the first two years of LT (SIR 2.7) for Kaposi’s sarcoma (SIR 393.3) and after 10 years (SIR 1.7) for bladder tumors (SIR 10.6). Multivariate analysis identified alcoholic cirrhosis (HR = 3.0, 95% CI = 1.2–7.8) and sclerosing cholangitis (HR = 3.5, 95% CI = 1.1–11.3) in the recipient as main risk factors for the occurrence of DNT.

Conclusions

Surveillance protocols for DNT must be specifically oriented to patients transplanted for alcoholic cirrhosis and sclerosing cholangitis. They should focus on early detection of Kaposi’s sarcomas, and more remarkably, on late development bladder tumors in men after LT.     

Coalescent inference for infectious disease: meta-analysis of hepatitis C

Genetic analysis of pathogen genomes is a powerful approach to investigating the population dynamics and epidemic history of infectious diseases. However, the theoretical underpinnings of the most widely used, coalescent methods have been questioned, casting doubt on their interpretation. The aim of this study is to develop robust population genetic inference for compartmental models in epidemiology. Using a general approach based on the theory of metapopulations, we derive coalescent models under susceptible–infectious (SI), susceptible–infectious–susceptible (SIS) and susceptible–infectious–recovered (SIR) dynamics. We show that exponential and logistic growth models are equivalent to SI and SIS models, respectively, when co-infection is negligible. Implementing SI, SIS and SIR models in BEAST, we conduct a meta-analysis of hepatitis C epidemics, and show that we can directly estimate the basic reproductive number (R₀) and prevalence under SIR dynamics. We find that differences in genetic diversity between epidemics can be explained by differences in underlying epidemiology (age of the epidemic and local population density) and viral subtype. Model comparison reveals SIR dynamics in three globally restricted epidemics, but most are better fit by the simpler SI dynamics. In summary, metapopulation models provide a general and practical framework for integrating epidemiology and population genetics for the purposes of joint inference.     

The Impact of the Species–Area Relationship on Estimates of Paleodiversity

Estimates of paleodiversity patterns through time have relied on datasets that lump taxonomic occurrences from geographic areas of varying size per interval of time. In essence, such estimates assume that the species–area effect, whereby more species are recorded from larger geographic areas, is negligible for fossil data. We tested this assumption by using the newly developed Miocene Mammal Mapping Project database of western North American fossil mammals and its associated analysis tools to empirically determine the geographic area that contributed to species diversity counts in successive temporal bins. The results indicate that a species–area effect markedly influences counts of fossil species, just as variable spatial sampling influences diversity counts on the modern landscape. Removing this bias suggests some traditionally recognized peaks in paleodiversity are just artifacts of the species–area effect while others stand out as meriting further attention. This discovery means that there is great potential for refining existing time-series estimates of paleodiversity, and for using species–area relationships to more reliably understand the magnitude and timing of such biotically important events as extinction, lineage diversification, and long-term trends in ecological structure.     

Atrial Fibrillation as a Marker of Occult Cancer

Background

Recent studies suggest that cancer increases risk of atrial fibrillation. Whether atrial fibrillation is a marker for underlying occult cancer is unknown.

Methods

We conducted a cohort study (1980–2011) of all Danish patients with new-onset atrial fibrillation. To examine cancer risk, we computed absolute risk at 3 months and standardized incidence ratios (SIRs) by comparing observed cancer incidence among patients newly diagnosed with atrial fibrillation with that expected based on national cancer incidence during the period.

Results

Median follow-up time was 3.4 years among 269 742 atrial fibrillation patients. Within 3 months of follow-up, 6656 cancers occurred (absolute risk, 2.5%; 95% confidence intervals [CI], 2.4%–2.5%) versus 1302 expected, yielding a SIR of 5.11; 95% CI, 4.99–5.24. Associations were particularly strong for cancers of the lung, kidney, colon, ovary, and for non-Hodgkin''s lymphoma. The SIR within 3 months of follow-up was 7.02; 95% CI, 6.76–7.28 for metastatic and 3.53; 95% CI, 3.38–3.68 for localized cancer. Beyond 3 months of follow-up, overall cancer risk was modestly increased (SIR, 1.13; 95% CI, 1.12–1.15).

Conclusion

Patients with new-onset atrial fibrillation had a markedly increased relative risk of a cancer diagnosis within the next three months, however, corresponding absolute risk was small.     

Incidence of Cancer in ANCA-Associated Vasculitis: A Meta-Analysis of Observational Studies

ObjectiveThe purpose of this paper is to examine cancer incidence in patients with ANCA-associated vasculitis (AASV) derived from population-based cohort studies by means of meta-analysis.MethodsRelevant electronic databases were searched for studies characterizing the associated risk of overall malignancy in patients with AASV. Standardized incidence rates (SIRs) with 95% confidence intervals (CIs) were used to evaluate the strength of association. We tested for publication bias and heterogeneity and stratified for site-specific cancers.ResultsSix studies (n = 2,578) were eventually identified, of which six provided the SIR for overall malignancy, five reported the SIR for non-melanoma skin cancer (NMSC), four for leukemia, five for bladder cancer, three for lymphoma, three for liver cancer, four for lung cancer, three for kidney cancer, four for prostate cancer, four for colon cancer and four for breast cancer. Overall, the pooled SIR of cancer in AASV patients was 1.74 (95%CI = 1.37–2.21), with moderate heterogeneity among these studies (I² = 65.8%, P = 0.012). In sub-analyses for site-specific cancers, NMSC, leukemia and bladder cancer were more frequently observed in patients with AASV with SIR of 5.18 (95%CI = 3.47–7.73), 4.89 (95%CI = 2.93–8.16) and 3.84 (95%CI = 2.72–5.42) respectively. There was no significant increase in the risk of kidney cancer (SIR = 2.12, 95%CI = 0.66–6.85), prostate cancer (SIR = 1.45, 95%CI = 0.87–2.42), colon cancer (SIR = 1.26, 95%CI = 0.70–2.27), and breast cancer (SIR = 0.95, 95%CI = 0.50–1.79). Among these site-specific cancers, only NMSC showed moderate heterogeneity (I² = 55.8%, P = 0.06). No publication bias was found by using the Begg’s test and Egger''s test.ConclusionsThis meta-analysis shows that AASV patients treatment with cyclophosphamide (CYC) are at increased risk of late-occurring malignancies, particularly of the NMSC, leukemia and bladder cancer. However, there is no significant association between AASV and kidney cancer, prostate cancer, colon cancer and breast cancer. These findings emphasize monitoring and preventative management in AASV patients after cessation of CYC therapy is momentous.     

Determinants of Influenza Transmission in South East Asia: Insights from a Household Cohort Study in Vietnam

To guide control policies, it is important that the determinants of influenza transmission are fully characterized. Such assessment is complex because the risk of influenza infection is multifaceted and depends both on immunity acquired naturally or via vaccination and on the individual level of exposure to influenza in the community or in the household. Here, we analyse a large household cohort study conducted in 2007–2010 in Vietnam using innovative statistical methods to ascertain in an integrative framework the relative contribution of variables that influence the transmission of seasonal (H1N1, H3N2, B) and pandemic H1N1pdm09 influenza. Influenza infection was diagnosed by haemagglutination-inhibition (HI) antibody assay of paired serum samples. We used a Bayesian data augmentation Markov chain Monte Carlo strategy based on digraphs to reconstruct unobserved chains of transmission in households and estimate transmission parameters. The probability of transmission from an infected individual to another household member was 8% (95% CI, 6%, 10%) on average, and varied with pre-season titers, age and household size. Within households of size 3, the probability of transmission from an infected member to a child with low pre-season HI antibody titers was 27% (95% CI 21%–35%). High pre-season HI titers were protective against infection, with a reduction in the hazard of infection of 59% (95% CI, 44%–71%) and 87% (95% CI, 70%–96%) for intermediate (1∶20–1∶40) and high (≥1∶80) HI titers, respectively. Even after correcting for pre-season HI titers, adults had half the infection risk of children. Twenty six percent (95% CI: 21%, 30%) of infections may be attributed to household transmission. Our results highlight the importance of integrated analysis by influenza sub-type, age and pre-season HI titers in order to infer influenza transmission risks in and outside of the household.     

Evaluating an icon of population persistence: the Devil's Hole pupfish

The Devil''s Hole pupfish Cyprinodon diabolis has iconic status among conservation biologists because it is one of the World''s most vulnerable species. Furthermore, C. diabolis is the most widely cited example of a persistent, small, isolated vertebrate population; a chronic exception to the rule that small populations do not persist long in isolation. It is widely asserted that this species has persisted in small numbers (less than 400 adults) for 10 000–20 000 years, but this assertion has never been evaluated. Here, we analyse the time series of count data for this species, and we estimate time to coalescence from microsatellite data to evaluate this hypothesis. We conclude that mean time to extinction is approximately 360–2900 years (median 410–1800), with less than a 2.1% probability of persisting 10 000 years. Median times to coalescence varied from 217 to 2530 years, but all five approximations had wide credible intervals. Our analyses suggest that Devil''s Hole pupfish colonized this pool well after the Pleistocene Lakes receded, probably within the last few hundred to few thousand years; this could have occurred through human intervention.     

Comparison of deterministic and stochastic SIS and SIR models in discrete time

The dynamics of deterministic and stochastic discrete-time epidemic models are analyzed and compared. The discrete-time stochastic models are Markov chains, approximations to the continuous-time models. Models of SIS and SIR type with constant population size and general force of infection are analyzed, then a more general SIS model with variable population size is analyzed. In the deterministic models, the value of the basic reproductive number R0 determines persistence or extinction of the disease. If R0 < 1, the disease is eliminated, whereas if R0 > 1, the disease persists in the population. Since all stochastic models considered in this paper have finite state spaces with at least one absorbing state, ultimate disease extinction is certain regardless of the value of R0. However, in some cases, the time until disease extinction may be very long. In these cases, if the probability distribution is conditioned on non-extinction, then when R0 > 1, there exists a quasi-stationary probability distribution whose mean agrees with deterministic endemic equilibrium. The expected duration of the epidemic is investigated numerically.     

Direct evidence for an acylated thiol as an intermediate in papain- and ficin-catalysed hydrolyses

1. Methyl thionohippurate was prepared and shown to be a specific substrate for both papain and ficin. 2. The ultraviolet-absorption properties of the acyl-enzyme intermediate for both papain and ficin with methyl thionohippurate was that expected of an acyl-thiol. The possibility that other functional groups present in papain or ficin might be the site of acylation has been excluded. 3. The change in extinction at the absorption maximum with time was as expected for the acyl-enzyme on the basis of the known Michaelis–Menten parameters for methyl thionohippurate. 4. The variation of extinction with initial substrate concentration for both papain and ficin was that expected from the Michaelis–Menten parameters. 5. The extinction of the absorption maximum of the thionohippuryl-enzyme intermediate was suppressed by the addition of methyl hippurate to the extent predicted from the Michaelis–Menten parameters. 6. The decay of the extinction for the acyl-enzyme was arrested by adjusting the pH of the solution to 2·5. 7. These experiments provide compelling evidence that the acylation by substrate of both papain and ficin takes place through a thiol residue.     

Dark extinction: the problem of unknown historical extinctions

The extinction of species before they are discovered and named (dark extinction, DE) is widely inferred as a significant part of species loss in the ‘pre-taxonomic’ period (approx. 1500–1800 CE) and, to some extent, in the ‘taxonomic period’ (approx. 1800–present) as well. The discovery of oceanic islands and other pristine habitats by European navigators and the consequent introduction of destructive mammals, such as rats and goats, started a process of anthropogenic extinction. Much ecosystem change happened before systematic scientific recording, so has led to DE. Statistical methods are available to robustly estimate DE in the ‘taxonomic period’. For the ‘pre-taxonomic period’, simple extrapolation can be used. The application of these techniques to world birds, for example, suggests that approximately 56 DEs occurred in the ‘taxonomic period’ (1800–present) and approximately 180 in the ‘pre-taxonomic period’ (1500–1800). Targeting collection activities in extinction hotspots, to make sure organisms are represented in collections before their extinction, is one way of reducing the number of extinct species without a physical record (providing that collection efforts do not themselves contribute to species extinction).     

Inferring Influenza Infection Attack Rate from Seroprevalence Data

Seroprevalence survey is the most practical method for accurately estimating infection attack rate (IAR) in an epidemic such as influenza. These studies typically entail selecting an arbitrary titer threshold for seropositivity (e.g. microneutralization [MN] 1∶40) and assuming the probability of seropositivity given infection (infection-seropositivity probability, ISP) is 100% or similar to that among clinical cases. We hypothesize that such conventions are not necessarily robust because different thresholds may result in different IAR estimates and serologic responses of clinical cases may not be representative. To illustrate our hypothesis, we used an age-structured transmission model to fully characterize the transmission dynamics and seroprevalence rises of 2009 influenza pandemic A/H1N1 (pdmH1N1) during its first wave in Hong Kong. We estimated that while 99% of pdmH1N1 infections became MN_1∶20 seropositive, only 72%, 62%, 58% and 34% of infections among age 3–12, 13–19, 20–29, 30–59 became MN_1∶40 seropositive, which was much lower than the 90%–100% observed among clinical cases. The fitted model was consistent with prevailing consensus on pdmH1N1 transmission characteristics (e.g. initial reproductive number of 1.28 and mean generation time of 2.4 days which were within the consensus range), hence our ISP estimates were consistent with the transmission dynamics and temporal buildup of population-level immunity. IAR estimates in influenza seroprevalence studies are sensitive to seropositivity thresholds and ISP adjustments which in current practice are mostly chosen based on conventions instead of systematic criteria. Our results thus highlighted the need for reexamining conventional practice to develop standards for analyzing influenza serologic data (e.g. real-time assessment of bias in ISP adjustments by evaluating the consistency of IAR across multiple thresholds and with mixture models), especially in the context of pandemics when robustness and comparability of IAR estimates are most needed for informing situational awareness and risk assessment. The same principles are broadly applicable for seroprevalence studies of other infectious disease outbreaks.     

The Butterflies of Barro Colorado Island,Panama: Local Extinction since the 1930s

Few data are available about the regional or local extinction of tropical butterfly species. When confirmed, local extinction was often due to the loss of host-plant species. We used published lists and recent monitoring programs to evaluate changes in butterfly composition on Barro Colorado Island (BCI, Panama) between an old (1923–1943) and a recent (1993–2013) period. Although 601 butterfly species have been recorded from BCI during the 1923–2013 period, we estimate that 390 species are currently breeding on the island, including 34 cryptic species, currently only known by their DNA Barcode Index Number. Twenty-three butterfly species that were considered abundant during the old period could not be collected during the recent period, despite a much higher sampling effort in recent times. We consider these species locally extinct from BCI and they conservatively represent 6% of the estimated local pool of resident species. Extinct species represent distant phylogenetic branches and several families. The butterfly traits most likely to influence the probability of extinction were host growth form, wing size and host specificity, independently of the phylogenetic relationships among butterfly species. On BCI, most likely candidates for extinction were small hesperiids feeding on herbs (35% of extinct species). However, contrary to our working hypothesis, extinction of these species on BCI cannot be attributed to loss of host plants. In most cases these host plants remain extant, but they probably subsist at lower or more fragmented densities. Coupled with low dispersal power, this reduced availability of host plants has probably caused the local extinction of some butterfly species. Many more bird than butterfly species have been lost from BCI recently, confirming that small preserves may be far more effective at conserving invertebrates than vertebrates and, therefore, should not necessarily be neglected from a conservation viewpoint.     

Incidence of Second Malignancies for Prostate Cancer

Introduction

There is a need to assess risk of second primary cancers in prostate cancer (PCa) patients, especially since PCa treatment may be associated with increased risk of second primary tumours.

Methods

We calculated standardized incidence ratios (SIRs) for second primary tumours comparing men diagnosed with PCa between 1980 and 2010 in the Canton of Zurich, Switzerland (n = 20,559), and the general male population in the Canton.

Results

A total of 1,718 men developed a second primary tumour after PCa diagnosis, with lung and colon cancer being the most common (15 and 13% respectively). The SIR for overall second primary cancer was 1.11 (95%CI: 1.06–1.17). Site-specific SIRs varied from 1.19 (1.05–1.34) to 2.89 (2.62–4.77) for lung and thyroid cancer, respectively. When stratified by treatment, the highest SIR was observed for thyroid cancer (3.57 (1.30–7.76)) when undergoing surgery, whereas liver cancer was common when treated with radiotherapy (3.21 (1.54–5.90)) and kidney bladder was most prevalent for those on hormonal treatment (3.15 (1.93–4.87)). Stratification by time since PCa diagnosis showed a lower risk of cancer for men with PCa compared to the general population for the first four years, but then a steep increase in risk was observed.

Conclusion

In the Canton of Zurich, there was an increased risk of second primary cancers among men with PCa compared to the general population. Increased diagnostic activity after PCa diagnosis may partly explain increased risks within the first years of diagnosis, but time-stratified analyses indicated that increased risks remained and even increased over time.     

Eutherians experienced elevated evolutionary rates in the immediate aftermath of the Cretaceous–Palaeogene mass extinction

The effect of the Cretaceous–Palaeogene (K–Pg) mass extinction on the evolution of many groups, including placental mammals, has been hotly debated. The fossil record suggests a sudden adaptive radiation of placentals immediately after the event, but several recent quantitative analyses have reconstructed no significant increase in either clade origination rates or rates of character evolution in the Palaeocene. Here we use stochastic methods to date a recent phylogenetic analysis of Cretaceous and Palaeocene mammals and show that Placentalia likely originated in the Late Cretaceous, but that most intraordinal diversification occurred during the earliest Palaeocene. This analysis reconstructs fewer than 10 placental mammal lineages crossing the K–Pg boundary. Moreover, we show that rates of morphological evolution in the 5 Myr interval immediately after the K–Pg mass extinction are three times higher than background rates during the Cretaceous. These results suggest that the K–Pg mass extinction had a marked impact on placental mammal diversification, supporting the view that an evolutionary radiation occurred as placental lineages invaded new ecological niches during the Early Palaeocene.     

A dynamic global equilibrium in carnivoran diversification over 20 million years

The ecological and evolutionary processes leading to present-day biological diversity can be inferred by reconstructing the phylogeny of living organisms, and then modelling potential processes that could have produced this genealogy. A more direct approach is to estimate past processes from the fossil record. The Carnivora (Mammalia) has both substantial extant species richness and a rich fossil record. We compiled species-level data for over 10 000 fossil occurrences of nearly 1400 carnivoran species. Using this compilation, we estimated extinction, speciation and net diversification for carnivorans through the Neogene (22–2 Ma), while simultaneously modelling sampling probability. Our analyses show that caniforms (dogs, bears and relatives) have higher speciation and extinction rates than feliforms (cats, hyenas and relatives), but lower rates of net diversification. We also find that despite continual species turnover, net carnivoran diversification through the Neogene is surprisingly stable, suggesting a saturated adaptive zone, despite restructuring of the physical environment. This result is strikingly different from analyses of carnivoran diversification estimated from extant species alone. Two intervals show elevated diversification rates (13–12 Ma and 4–3 Ma), although the precise causal factors behind the two peaks in carnivoran diversification remain open questions.     

The Risk of Cancer among Taiwanese Female Registered Nurses: A Nationwide Retrospective Study

Background

To evaluate the risk of cancer among Taiwanese female registered nurses (RNs) using a nationwide population-based dataset.

Methods

We recruited female RNs without antecedent cancer from the Taiwan National Health Insurance Research database during 2000–2010. Standardized incidence ratios (SIRs) of cancer were calculated. We also compared rates of Papanicolaou (Pap) smear use between the RNs and the general population matched by age and sex.

Results

A total of 2,077 cancers developed among 184,809 female RNs, with a follow-up of 1,371,910 person-years (median follow-up of 7.86 years), leading to an increased SIR of 1.10 [95% confidence interval (CI) 1.05–1.15]. RNs aged between 40–59 years also had a significantly increased SIR (1.14, 95% CI 1.08–1.21). For specific cancer types, RNs had an increased SIR for breast (1.28, 95% CI 1.19–1.37), thyroid (1.26, 95% CI 1.10–1.43), lung and mediastinum (1.36, 95% CI 1.13–1.62), and uterine cancers (1.23, 95% CI 1.01–1.49). A decreased SIR was found for cervix (0.48, 95% CI 0.37–0.61) and liver and biliary tract cancers (0.68, 95% CI 0.50–0.90). Pap smear use averaged 5.80 times per person among female RNs aged 35 years or older and 5.50 times per person in the age-matched control group (p = 0.009).

Conclusion

This study found that overall cancer risk was higher among female RNs than general population. For individual cancers, the risks of breast, lung, thyroid and uterine cancer were higher and the risks of cervix and liver cancer were lower than general population. The lower risk of cervical cancer might be partially explained by the increased use of Pap smears in the RNs group. Further large, unbiased population-based prospective studies are needed to investigate the association between nurses and cancer risk and identify the risk factors of cancer in nurses.     

The Probability of Extinction of Infectious Salmon Anemia Virus in One and Two Patches

Single-type and multitype branching processes have been used to study the dynamics of a variety of stochastic birth–death type phenomena in biology and physics. Their use in epidemiology goes back to Whittle’s study of a susceptible–infected–recovered (SIR) model in the 1950s. In the case of an SIR model, the presence of only one infectious class allows for the use of single-type branching processes. Multitype branching processes allow for multiple infectious classes and have latterly been used to study metapopulation models of disease. In this article, we develop a continuous time Markov chain (CTMC) model of infectious salmon anemia virus in two patches, two CTMC models in one patch and companion multitype branching process (MTBP) models. The CTMC models are related to deterministic models which inform the choice of parameters. The probability of extinction is computed for the CTMC via numerical methods and approximated by the MTBP in the supercritical regime. The stochastic models are treated as toy models, and the parameter choices are made to highlight regions of the parameter space where CTMC and MTBP agree or disagree, without regard to biological significance. Partial extinction events are defined and their relevance discussed. A case is made for calculating the probability of such events, noting that MTBPs are not suitable for making these calculations.     

A Rational Approach to Estimating the Surgical Demand Elasticity Needed to Guide Manpower Reallocation during Contagious Outbreaks

Background

Emerging infectious diseases continue to pose serious threats to global public health. So far, however, few published study has addressed the need for manpower reallocation needed in hospitals when such a serious contagious outbreak occurs.

Aim

To quantify the demand elasticity of the major surgery types in order to guide future manpower reallocation during contagious outbreaks.

Materials and Methods

Based on a nationwide research database in Taiwan, we extracted the monthly volumes of major surgery types for the period 1998–2003, which covered the SARS period, in order to carry out a time series analysis. The demand elasticity of each surgery type was then estimated by autoregressive integrated moving average (ARIMA) analysis.

Results

During the study period, the surgical volumes of most selected surgery types either increased or remained steady. We categorized these surgery types into low-, moderate- and high-elastic groups according to their demand elasticity. Appendectomy, ‘open reduction of fracture with internal fixation’ and ‘free skin graft’ were in the low demand elasticity group. Transurethral prostatectomy and extracorporeal shockwave lithotripsy (ESWL) were in the high demand elasticity group. The manpower of the departments carrying out the surgeries with low demand elasticity should be maintained during outbreaks. In contrast, departments in charge of surgeries mainly with high demand elasticity, like urology departments, may be in a position to have part of their staff reallocated.

Conclusions

Taking advantage of the demand variation during the SARS period in 2003, we adopted the concept of demand elasticity and used a time series approach to figure out an effective index of demand elasticity for various types of surgery that could be used as a rational reference to carry out manpower reallocation during contagious outbreak situations.     

Understanding evolutionary and ecological dynamics using a continuum limit

Continuum limits in the form of stochastic differential equations are typically used in theoretical population genetics to account for genetic drift or more generally, inherent randomness of the model. In evolutionary game theory and theoretical ecology, however, this method is used less frequently to study demographic stochasticity. Here, we review the use of continuum limits in ecology and evolution. Starting with an individual‐based model, we derive a large population size limit, a (stochastic) differential equation which is called continuum limit. By example of the Wright–Fisher diffusion, we outline how to compute the stationary distribution, the fixation probability of a certain type, and the mean extinction time using the continuum limit. In the context of the logistic growth equation, we approximate the quasi‐stationary distribution in a finite population.