Non-pharmaceutical interventions, vaccination, and the SARS-CoV-2 delta variant in England: a mathematical modelling study.

BACKGROUND: England's COVID-19 roadmap out of lockdown policy set out the timeline and conditions for the stepwise lifting of non-pharmaceutical interventions (NPIs) as vaccination roll-out continued, with step one starting on March 8, 2021. In this study, we assess the roadmap, the impact of the delta (B.1.617.2) variant of SARS-CoV-2, and potential future epidemic trajectories. METHODS: This mathematical modelling study was done to assess the UK Government's four-step process to easing lockdown restrictions in England, UK. We extended a previously described model of SARS-CoV-2 transmission to incorporate vaccination and multi-strain dynamics to explicitly capture the emergence of the delta variant. We calibrated the model to English surveillance data, including hospital admissions, hospital occupancy, seroprevalence data, and population-level PCR testing data using a Bayesian evidence synthesis framework, then modelled the potential trajectory of the epidemic for a range of different schedules for relaxing NPIs. We estimated the resulting number of daily infections and hospital admissions, and daily and cumulative deaths. Three scenarios spanning a range of optimistic to pessimistic vaccine effectiveness, waning natural immunity, and cross-protection from previous infections were investigated. We also considered three levels of mixing after the lifting of restrictions. FINDINGS: The roadmap policy was successful in offsetting the increased transmission resulting from lifting NPIs starting on March 8, 2021, with increasing population immunity through vaccination. However, because of the emergence of the delta variant, with an estimated transmission advantage of 76% (95% credible interval [95% CrI] 69-83) over alpha, fully lifting NPIs on June 21, 2021, as originally planned might have led to 3900 (95% CrI 1500-5700) peak daily hospital admissions under our central parameter scenario. Delaying until July 19, 2021, reduced peak hospital admissions by three fold to 1400 (95% CrI 700-1700) per day. There was substantial uncertainty in the epidemic trajectory, with particular sensitivity to the transmissibility of delta, level of mixing, and estimates of vaccine effectiveness. INTERPRETATION: Our findings show that the risk of a large wave of COVID-19 hospital admissions resulting from lifting NPIs can be substantially mitigated if the timing of NPI relaxation is carefully balanced against vaccination coverage. However, with the delta variant, it might not be possible to fully lift NPIs without a third wave of hospital admissions and deaths, even if vaccination coverage is high. Variants of concern, their transmissibility, vaccine uptake, and vaccine effectiveness must be carefully monitored as countries relax pandemic control measures. FUNDING: National Institute for Health Research, UK Medical Research Council, Wellcome Trust, and UK Foreign, Commonwealth and Development Office.

Emergent Shapes of Trait-Based Competition Functions from Resource-Based Models: A Gaussian Is Not Normal in Plant Communities.

AbstractIn community ecology, it is widely assumed that organisms with similar traits compete more intensely with one another for resources. This assumption is often encoded into theory and empirical tests via a unimodal competition function, which predicts that per capita competitive effect declines with separation in traits. Yet it remains unknown how well this function represents the true effect of traits on competitive outcomes, especially for long-lived plant communities, where lifetime fitness is difficult to estimate. Here, we evaluate the shape of competition functions embedded in two resource-based (RB) models, wherein plants compete for shared, essential resources. In the first RB model individuals compete for two essential nutrients, and in the second they compete for light in a size-based successional setting. We compared the shapes of the competition functions that emerged from interactions within these RB models to the unimodal function and others shapes commonly applied. In few instances did the trait-based competition function emerging from the RB model even vaguely resemble any of the shapes previously used. The mismatch between these two approaches suggests that theory derived using fixed competition functions based on trait separation may not apply well to plant systems, where individuals compete for shared resources. The more promising path will be to model depletion of resources by populations in relation to their traits, with its consequences for fitness landscapes and competitive exclusion.

How functional traits influence plant growth and shade tolerance across the life cycle.

Plant species differ in many functional traits that drive differences in rates of photosynthesis, biomass allocation, and tissue turnover. However, it remains unclear how-and even if-such traits influence whole-plant growth, with the simple linear relationships predicted by existing theory often lacking empirical support. Here, we present a theoretical framework for understanding the effect of diverse functional traits on plant growth and shade tolerance by extending a widely used model, linking growth rate in seedlings with a single leaf trait, to explicitly include influences of size, light environment, and five prominent traits: seed mass, height at maturation, leaf mass per unit leaf area, leaf nitrogen per unit leaf area, and wood density. Based on biomass growth and allocation, this framework explains why the influence of traits on growth rate and shade tolerance often varies with plant size and why the impact of size on growth varies among traits. Specifically, we demonstrate why for height growth the influence of: (i) leaf mass per unit leaf area is strong in small plants but weakens with size; (ii) leaf nitrogen per unit leaf area does not change with size; (iii) wood density is present across sizes; (iv) height at maturation strengthens with size; and (v) seed mass decreases with size. Moreover, we show how traits moderate plant responses to light environment and also determine shade tolerance, supporting diverse empirical results.

Partitioning mortality into growth-dependent and growth-independent hazards across 203 tropical tree species.

Tree death drives population dynamics, nutrient cycling, and evolution within plant communities. Mortality variation across species is thought to be influenced by different factors relative to variation within species. The unified model provided here separates mortality rates into growth-dependent and growth-independent hazards. This model creates the opportunity to simultaneously estimate these hazards both across and within species. Moreover, it provides the ability to examine how species traits affect growth-dependent and growth-independent hazards. We derive this unified mortality model using cross-validated Bayesian methods coupled with mortality data collected over three census intervals for 203 tropical rainforest tree species at Barro Colorado Island (BCI), Panama. We found that growth-independent mortality tended to be higher in species with lower wood density, higher light requirements, and smaller maximum diameter at breast height (dbh). Mortality due to marginal carbon budget as measured by near-zero growth rate tended to be higher in species with lower wood density and higher light demand. The total mortality variation attributable to differences among species was large relative to variation explained by these traits, emphasizing that much remains to be understood. This additive hazards model strengthens our capacity to parse and understand individual-level mortality in highly diverse tropical forests and hence to predict its consequences.

Response to COVID-19 in South Korea and implications for lifting stringent interventions.

BACKGROUND: After experiencing a sharp growth in COVID-19 cases early in the pandemic, South Korea rapidly controlled transmission while implementing less stringent national social distancing measures than countries in Europe and the USA. This has led to substantial interest in their "test, trace, isolate" strategy. However, it is important to understand the epidemiological peculiarities of South Korea's outbreak and characterise their response before attempting to emulate these measures elsewhere. METHODS: We systematically extracted numbers of suspected cases tested, PCR-confirmed cases, deaths, isolated confirmed cases, and numbers of confirmed cases with an identified epidemiological link from publicly available data. We estimated the time-varying reproduction number, Rt, using an established Bayesian framework, and reviewed the package of interventions implemented by South Korea using our extracted data, plus published literature and government sources. RESULTS: We estimated that after the initial rapid growth in cases, Rt dropped below one in early April before increasing to a maximum of 1.94 (95%CrI, 1.64-2.27) in May following outbreaks in Seoul Metropolitan Region. By mid-June, Rt was back below one where it remained until the end of our study (July 13th). Despite less stringent "lockdown" measures, strong social distancing measures were implemented in high-incidence areas and studies measured a considerable national decrease in movement in late February. Testing the capacity was swiftly increased, and protocols were in place to isolate suspected and confirmed cases quickly; however, we could not estimate the delay to isolation using our data. Accounting for just 10% of cases, individual case-based contact tracing picked up a relatively minor proportion of total cases, with cluster investigations accounting for 66%. CONCLUSIONS: Whilst early adoption of testing and contact tracing is likely to be important for South Korea's successful outbreak control, other factors including regional implementation of strong social distancing measures likely also contributed. The high volume of testing and the low number of deaths suggest that South Korea experienced a small epidemic relative to other countries. Caution is needed in attempting to replicate the South Korean response in populations with larger more geographically widespread epidemics where finding, testing, and isolating cases that are linked to clusters may be more difficult.

Three keys to the radiation of angiosperms into freezing environments.

Early flowering plants are thought to have been woody species restricted to warm habitats. This lineage has since radiated into almost every climate, with manifold growth forms. As angiosperms spread and climate changed, they evolved mechanisms to cope with episodic freezing. To explore the evolution of traits underpinning the ability to persist in freezing conditions, we assembled a large species-level database of growth habit (woody or herbaceous; 49,064 species), as well as leaf phenology (evergreen or deciduous), diameter of hydraulic conduits (that is, xylem vessels and tracheids) and climate occupancies (exposure to freezing). To model the evolution of species' traits and climate occupancies, we combined these data with an unparalleled dated molecular phylogeny (32,223 species) for land plants. Here we show that woody clades successfully moved into freezing-prone environments by either possessing transport networks of small safe conduits and/or shutting down hydraulic function by dropping leaves during freezing. Herbaceous species largely avoided freezing periods by senescing cheaply constructed aboveground tissue. Growth habit has long been considered labile, but we find that growth habit was less labile than climate occupancy. Additionally, freezing environments were largely filled by lineages that had already become herbs or, when remaining woody, already had small conduits (that is, the trait evolved before the climate occupancy). By contrast, most deciduous woody lineages had an evolutionary shift to seasonally shedding their leaves only after exposure to freezing (that is, the climate occupancy evolved before the trait). For angiosperms to inhabit novel cold environments they had to gain new structural and functional trait solutions; our results suggest that many of these solutions were probably acquired before their foray into the cold.

Model Adequacy and the Macroevolution of Angiosperm Functional Traits.

Making meaningful inferences from phylogenetic comparative data requires a meaningful model of trait evolution. It is thus important to determine whether the model is appropriate for the data and the question being addressed. One way to assess this is to ask whether the model provides a good statistical explanation for the variation in the data. To date, researchers have focused primarily on the explanatory power of a model relative to alternative models. Methods have been developed to assess the adequacy, or absolute explanatory power, of phylogenetic trait models, but these have been restricted to specific models or questions. Here we present a general statistical framework for assessing the adequacy of phylogenetic trait models. We use our approach to evaluate the statistical performance of commonly used trait models on 337 comparative data sets covering three key angiosperm functional traits. In general, the models we tested often provided poor statistical explanations for the evolution of these traits. This was true for many different groups and at many different scales. Whether such statistical inadequacy will qualitatively alter inferences drawn from comparative data sets will depend on the context. Regardless, assessing model adequacy can provide interesting biological insights-how and why a model fails to describe variation in a data set give us clues about what evolutionary processes may have driven trait evolution across time.

geiger v2.0: an expanded suite of methods for fitting macroevolutionary models to phylogenetic trees.

SUMMARY: Phylogenetic comparative methods are essential for addressing evolutionary hypotheses with interspecific data. The scale and scope of such data have increased dramatically in the past few years. Many existing approaches are either computationally infeasible or inappropriate for data of this size. To address both of these problems, we present geiger v2.0, a complete overhaul of the popular R package geiger. We have reimplemented existing methods with more efficient algorithms and have developed several new approaches for accomodating heterogeneous models and data types. AVAILABILITY AND IMPLEMENTATION: This R package is available on the CRAN repository http://cran.r-project.org/web/packages/geiger/. All source code is also available on github http://github.com/mwpennell/geiger-v2. geiger v2.0 depends on the ape package. CONTACT: mwpennell@gmail.com SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Conspecific density modulates the effect of predation on dispersal rates.

Dispersal decisions underlie the spatial dynamics of metacommunities. Prey individuals may disperse to reduce the risk of either predation or starvation, and both of these risks may depend on conspecific density. Surprisingly, there is little theory examining how dispersal rates should change in response to the combined effects of predation and changes in conspecific density. We develop such a model and show that, under certain conditions, predators may induce dispersal at low prey densities but not high prey densities. We then experimentally manipulate the density of the ciliate Paramecium aurelia and the perceived presence of its predator, the flatworm Stenostomum virginiamum, in a two-patch metacommunity to parameterise the model. Paramecium dispersed in response to Stenostomum at low densities, but they reduced their dispersal in response to predation risk at high predator densities. By applying our model to the empirical data, we show that this switch in dispersal strategy, linked to increases in prey density, occurred because predators increased the difficulty or risk of dispersal. Together, the model and experiment reveal that the effects of predators on dispersal are contingent on prey density. Previous studies have sometimes reported an increase in dispersal rate when predation risk is elevated, and other times a decrease in dispersal rate. Our demonstration of a switch point, with predation risk increasing dispersal at low prey densities but reducing dispersal above a threshold of prey density, may reconcile the diversity of prey dispersal behaviours reported in these previous investigations and observed in nature.

Dietary innovations spurred the diversification of ruminants during the Caenozoic.

Global climate shifts and ecological flexibility are two major factors that may affect rates of speciation and extinction across clades. Here, we connect past climate to changes in diet and diversification dynamics of ruminant mammals. Using novel versions of Multi-State Speciation and Extinction models, we explore the most likely scenarios for evolutionary transitions among diets in this clade and ask whether ruminant lineages with different feeding styles (browsing, grazing and mixed feeding) underwent differential rates of diversification concomitant with global temperature change. The best model of trait change had transitions from browsers to grazers via mixed feeding, with appreciable rates of transition to and from grazing and mixed feeding. Diversification rates in mixed-feeder and grazer lineages tracked the palaeotemperature curve, exhibiting higher rates during the Miocene thermal maxima. The origination of facultative mixed diet and grazing states may have triggered two adaptive radiations--one during the Oligocene-Miocene transition and the other during Middle-to-Late Miocene. Our estimate of mixed diets for basal lineages of both bovids and cervids is congruent with fossil evidence, while the reconstruction of browser ancestors for some impoverished clades--Giraffidae and Tragulidae--is not. Our results offer model-based neontological support to previous palaeontological findings and fossil-based hypothesis highlighting the importance of dietary innovations--especially mixed feeding--in the success of ruminants during the Neogene.

Epidemiological drivers of transmissibility and severity of SARS-CoV-2 in England.

As the SARS-CoV-2 pandemic progressed, distinct variants emerged and dominated in England. These variants, Wildtype, Alpha, Delta, and Omicron were characterized by variations in transmissibility and severity. We used a robust mathematical model and Bayesian inference framework to analyse epidemiological surveillance data from England. We quantified the impact of non-pharmaceutical interventions (NPIs), therapeutics, and vaccination on virus transmission and severity. Each successive variant had a higher intrinsic transmissibility. Omicron (BA.1) had the highest basic reproduction number at 8.3 (95% credible interval (CrI) 7.7-8.8). Varying levels of NPIs were crucial in controlling virus transmission until population immunity accumulated. Immune escape properties of Omicron decreased effective levels of immunity in the population by a third. Furthermore, in contrast to previous studies, we found Alpha had the highest basic infection fatality ratio (2.9%, 95% CrI 2.7-3.2), followed by Delta (2.2%, 95% CrI 2.0-2.4), Wildtype (1.2%, 95% CrI 1.1-1.2), and Omicron (0.7%, 95% CrI 0.6-0.8). Our findings highlight the importance of continued surveillance. Long-term strategies for monitoring and maintaining effective immunity against SARS-CoV-2 are critical to inform the role of NPIs to effectively manage future variants with potentially higher intrinsic transmissibility and severe outcomes.

Quantifying the effect of delaying the second COVID-19 vaccine dose in England: a mathematical modelling study.

BACKGROUND: The UK was the first country to start national COVID-19 vaccination programmes, initially administering doses 3 weeks apart. However, early evidence of high vaccine effectiveness after the first dose and the emergence of the SARS-CoV-2 alpha variant prompted the UK to extend the interval between doses to 12 weeks. In this study, we aimed to quantify the effect of delaying the second vaccine dose in England. METHODS: We used a previously described model of SARS-CoV-2 transmission, calibrated to COVID-19 surveillance data from England, including hospital admissions, hospital occupancy, seroprevalence data, and population-level PCR testing data, using a Bayesian evidence-synthesis framework. We modelled and compared the epidemic trajectory in the counterfactual scenario in which vaccine doses were administered 3 weeks apart against the real reported vaccine roll-out schedule of 12 weeks. We estimated and compared the resulting numbers of daily infections, hospital admissions, and deaths. In sensitivity analyses, we investigated scenarios spanning a range of vaccine effectiveness and waning assumptions. FINDINGS: In the period from Dec 8, 2020, to Sept 13, 2021, the number of individuals who received a first vaccine dose was higher under the 12-week strategy than the 3-week strategy. For this period, we estimated that delaying the interval between the first and second COVID-19 vaccine doses from 3 to 12 weeks averted a median (calculated as the median of the posterior sample) of 58 000 COVID-19 hospital admissions (291 000 cumulative hospitalisations [95% credible interval 275 000-319 000] under the 3-week strategy vs 233 000 [229 000-238 000] under the 12-week strategy) and 10 100 deaths (64 800 deaths [60 200-68 900] vs 54 700 [52 800-55 600]). Similarly, we estimated that the 3-week strategy would have resulted in more infections compared with the 12-week strategy. Across all sensitivity analyses the 3-week strategy resulted in a greater number of hospital admissions. In results by age group, the 12-week strategy led to more hospitalisations and deaths in older people in spring 2021, but fewer following the emergence of the delta variant during summer 2021. INTERPRETATION: England's delayed-second-dose vaccination strategy was informed by early real-world data on vaccine effectiveness in the context of limited vaccine supplies in a growing epidemic. Our study shows that rapidly providing partial (single-dose) vaccine-induced protection to a larger proportion of the population was successful in reducing the burden of COVID-19 hospitalisations and deaths overall. FUNDING: UK National Institute for Health Research; UK Medical Research Council; Community Jameel; Wellcome Trust; UK Foreign, Commonwealth and Development Office; Australian National Health and Medical Research Council; and EU.

Quantitative traits and diversification.

Quantitative traits have long been hypothesized to affect speciation and extinction rates. For example, smaller body size or increased specialization may be associated with increased rates of diversification. Here, I present a phylogenetic likelihood-based method (quantitative state speciation and extinction [QuaSSE]) that can be used to test such hypotheses using extant character distributions. This approach assumes that diversification follows a birth-death process where speciation and extinction rates may vary with one or more traits that evolve under a diffusion model. Speciation and extinction rates may be arbitrary functions of the character state, allowing much flexibility in testing models of trait-dependent diversification. I test the approach using simulated phylogenies and show that a known relationship between speciation and a quantitative character could be recovered in up to 80% of the cases on large trees (500 species). Consistent with other approaches, detecting shifts in diversification due to differences in extinction rates was harder than when due to differences in speciation rates. Finally, I demonstrate the application of QuaSSE to investigate the correlation between body size and diversification in primates, concluding that clade-specific differences in diversification may be more important than size-dependent diversification in shaping the patterns of diversity within this group.

Leveraging community mortality indicators to infer COVID-19 mortality and transmission dynamics in Damascus, Syria.

The COVID-19 pandemic has resulted in substantial mortality worldwide. However, to date, countries in the Middle East and Africa have reported considerably lower mortality rates than in Europe and the Americas. Motivated by reports of an overwhelmed health system, we estimate the likely under-ascertainment of COVID-19 mortality in Damascus, Syria. Using all-cause mortality data, we fit a mathematical model of COVID-19 transmission to reported mortality, estimating that 1.25% of COVID-19 deaths (sensitivity range 1.00% - 3.00%) have been reported as of 2 September 2020. By 2 September, we estimate that 4,380 (95% CI: 3,250 - 5,550) COVID-19 deaths in Damascus may have been missed, with 39.0% (95% CI: 32.5% - 45.0%) of the population in Damascus estimated to have been infected. Accounting for under-ascertainment corroborates reports of exceeded hospital bed capacity and is validated by community-uploaded obituary notifications, which confirm extensive unreported mortality in Damascus.

Key epidemiological drivers and impact of interventions in the 2020 SARS-CoV-2 epidemic in England.

We fitted a model of SARS-CoV-2 transmission in care homes and the community to regional surveillance data for England. Compared with other approaches, our model provides a synthesis of multiple surveillance data streams into a single coherent modeling framework, allowing transmission and severity to be disentangled from features of the surveillance system. Of the control measures implemented, only national lockdown brought the reproduction number (Rt eff) below 1 consistently; if introduced 1 week earlier, it could have reduced deaths in the first wave from an estimated 48,600 to 25,600 [95% credible interval (CrI): 15,900 to 38,400]. The infection fatality ratio decreased from 1.00% (95% CrI: 0.85 to 1.21%) to 0.79% (95% CrI: 0.63 to 0.99%), suggesting improved clinical care. The infection fatality ratio was higher in the elderly residing in care homes (23.3%, 95% CrI: 14.7 to 35.2%) than those residing in the community (7.9%, 95% CrI: 5.9 to 10.3%). On 2 December 2020, England was still far from herd immunity, with regional cumulative infection incidence between 7.6% (95% CrI: 5.4 to 10.2%) and 22.3% (95% CrI: 19.4 to 25.4%) of the population. Therefore, any vaccination campaign will need to achieve high coverage and a high degree of protection in vaccinated individuals to allow nonpharmaceutical interventions to be lifted without a resurgence of transmission.

Naomi: a new modelling tool for estimating HIV epidemic indicators at the district level in sub-Saharan Africa.

INTRODUCTION: HIV planning requires granular estimates for the number of people living with HIV (PLHIV), antiretroviral treatment (ART) coverage and unmet need, and new HIV infections by district, or equivalent subnational administrative level. We developed a Bayesian small-area estimation model, called Naomi, to estimate these quantities stratified by subnational administrative units, sex, and five-year age groups. METHODS: Small-area regressions for HIV prevalence, ART coverage and HIV incidence were jointly calibrated using subnational household survey data on all three indicators, routine antenatal service delivery data on HIV prevalence and ART coverage among pregnant women, and service delivery data on the number of PLHIV receiving ART. Incidence was modelled by district-level HIV prevalence and ART coverage. Model outputs of counts and rates for each indicator were aggregated to multiple geographic and demographic stratifications of interest. The model was estimated in an empirical Bayes framework, furnishing probabilistic uncertainty ranges for all output indicators. Example results were presented using data from Malawi during 2016-2018. RESULTS: Adult HIV prevalence in September 2018 ranged from 3.2% to 17.1% across Malawi's districts and was higher in southern districts and in metropolitan areas. ART coverage was more homogenous, ranging from 75% to 82%. The largest number of PLHIV was among ages 35 to 39 for both women and men, while the most untreated PLHIV were among ages 25 to 29 for women and 30 to 34 for men. Relative uncertainty was larger for the untreated PLHIV than the number on ART or total PLHIV. Among clients receiving ART at facilities in Lilongwe city, an estimated 71% (95% CI, 61% to 79%) resided in Lilongwe city, 20% (14% to 27%) in Lilongwe district outside the metropolis, and 9% (6% to 12%) in neighbouring Dowa district. Thirty-eight percent (26% to 50%) of Lilongwe rural residents and 39% (27% to 50%) of Dowa residents received treatment at facilities in Lilongwe city. CONCLUSIONS: The Naomi model synthesizes multiple subnational data sources to furnish estimates of key indicators for HIV programme planning, resource allocation, and target setting. Further model development to meet evolving HIV policy priorities and programme need should be accompanied by continued strengthening and understanding of routine health system data.

Reduction in mobility and COVID-19 transmission.

In response to the COVID-19 pandemic, countries have sought to control SARS-CoV-2 transmission by restricting population movement through social distancing interventions, thus reducing the number of contacts. Mobility data represent an important proxy measure of social distancing, and here, we characterise the relationship between transmission and mobility for 52 countries around the world. Transmission significantly decreased with the initial reduction in mobility in 73% of the countries analysed, but we found evidence of decoupling of transmission and mobility following the relaxation of strict control measures for 80% of countries. For the majority of countries, mobility explained a substantial proportion of the variation in transmissibility (median adjusted R-squared: 48%, interquartile range - IQR - across countries [27-77%]). Where a change in the relationship occurred, predictive ability decreased after the relaxation; from a median adjusted R-squared of 74% (IQR across countries [49-91%]) pre-relaxation, to a median adjusted R-squared of 30% (IQR across countries [12-48%]) post-relaxation. In countries with a clear relationship between mobility and transmission both before and after strict control measures were relaxed, mobility was associated with lower transmission rates after control measures were relaxed indicating that the beneficial effects of ongoing social distancing behaviours were substantial.