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Tagging deployments and study subjectsTable 1 contains an overview of the fields in the metadata file (JWS_metadata.xlsx) providing extensive background details on each of the 79 tag deployments and 63 study subjects. The data in this file give essential contextual information needed to understand the methodological, environmental, and demographic factors surrounding the deployments, which are critical for further examination and hypothesis testing of the sensor data. These metadata fall into several specific categories, but are not limited to, (i) information on the deployed electronic devices (platform, model, Platform Transmitter Terminal identifications), (ii) sharks (unique identifying numbers, sex, length), (iii) capture event (date, location, duration, methodology, interaction type), and (iv) the reporting period (duration, linear surface travel distance).Table 1 Metadata descriptions of the sharks, tagging operations, and deployments for all tags included in the database.Full size tableFigure 1 illustrates a typical C. carcharias tagging operation. This involves a contracted commercial fishing vessel with purpose-built gears to capture sharks (Fig. 1a) and a research crew to handle animals, monitor health (Fig. 1b) and attach electronic tags (Fig. 1c). More details on the tagging program and its methodologies are provided elsewhere14,19,20. Figure. 2 provides summaries of the deployment schedule, geographic locations, devices, and capture operations. Of note, 39.7% (25/64) of all tagging operations involved collaborations with commercial fishery operators (Fig. 2f–h), whose engagement was temporarily impacted (Fig. 2a) during the scientific review process when the population was under consideration for US Endangered Species Act listing. Figure 3 displays the demographic focus on small juvenile C. carcharias, with modest deployment durations and travel distances.Fig. 1Depiction of a typical research operation for capturing and tagging juvenile White Sharks in the Southern California Bight. (a) Aquarium research vessel (RV Lucile) with crew approaching a contracted purse seine vessel containing a captured juvenile white shark. (b) Research crew on the RV Lucile leading the shark into a sling, where it is subsequently transferred to the vessel’s deck for tagging. (c) Successfully applied PAT and acoustic tags each positioned lateral of the dorsal fin, anchored via leaders, and affixed with titanium darts (yellow arrows). All images taken by Steve McNicholas (Great White Shark 3D) for the Monterey Bay Aquarium and used with permission.Full size imageFig. 2Metadata summaries of the field program that deployed biologging tags on juvenile white sharks in the southern California Current. (a) Deployment schedule for 72 electronic tags released on 64 White Sharks from 2001–2020 (b) Tagging activity peaked in the late summer months when the population is most locally abundant. Field operations decreased from 2011–2013 when the population was being considered for listing under the U.S. Endangered Species Act (ESA). (c) Deployments focused on opportunities in the Southern California Bight coastline and included deployments in the nursery area of Bahía Sebastian Vizcaíno, Mexico and releases after exhibition at the Monterey Bay Aquarium. (d) Researchers released a variety of pop-up archival transmitting (PAT, 58 sharks), acoustic (21 sharks), and smart position and temperature (SPOT, 20 sharks) tags. This manuscript only reports the geolocation, temperature and depth data from the PAT and SPOT platforms. (e) Half (35 of 64, 54.7%) of all sharks received multiple tags, primarily to compare their relative performance. (f) Most tags (38 of 64, 60.3%) were deployed during focused scientific research operations. (g) The remainder were joint operations resulting from opportunistic bycatch in commercial fisheries using various gears and (h) Targeting various species. “Jab” gear refers to research operations that uses pole extensions to apply tags to sharks without capturing and handling.Full size imageFig. 3Demographic and deployment summaries from the juvenile white shark tagging program. (a) Total body length (TL) histogram indicates that most individuals tagged were either neonates ( More

Study origin and designThe MeadoWatch project (MW) is a project run collaboratively between the University of Washington (UW) and the United States National Park Service to monitor the phenology of alpine and subalpine wildflower species across large elevational gradients in Mount Rainier National Park (Fig. 2). MW was established in 2013 with the goal of understanding long-term effects of climate change on Mount Rainier National Park wildflower communities using community-science approaches. The first MW transect was established along Reflection Lakes, Skyline, and Paradise Glacier trail system in 2013 (9–11 plots). In 2015, MW expanded to include a second transect (15–17 plots) along the Glacier Basin trail (Fig. 1a). The MW transects span around 5 km each, over a 400 m altitudinal gradient (Reflection Lakes: 1490m–1889m a.s.l.; Glacier Basin: 1460m–1831m a.s.l.)Fig. 2Alpine meadows, plot extension, and target species. (a) Species-rich alpine meadow in Mount Rainier National Park (Mount Tahoma), showing many of the target species in the foreground. (b) MW volunteer coordinator Anna Wilson at a plot, indicating the arm span that defines the plot area (personal likeness used with confirmed consent). (c) Species composition and proportion of reports per species in each of the transects; species common to both trails are highlighted with striped shadowing. Photographs: A. John (a), L. Felker (b).Full size imagePlots are located along the side of each trail, marked with a colored survey marker. The area of each plot is defined by the arm-span of volunteers when they position themselves over the plot marker looking away from the trail (Fig. 2b). While less accurate than marking the corners of plots, this approach was used to avoid establishing permanent structures in wilderness areas within the National Park. The surveyed area in each plot is, on average, 1.25 m2. Each plot is also equipped with temperature sensors (HOBO Pendant Logger, Onset Computer Corp.) buried approximately 4 cm below the ground. Sensors are placed at the start of each fall season and removed at the beginning of each summer season for data downloading. The HOBO sensors provide an estimate for the date of snow disappearance and in-situ temperature at 3 hours intervals. Once plots are covered in snow, soil temperatures remain at 0 °C and show no diurnal variation, so that daily changes in temperatures above 1 °C can be used to determine the earliest date without snow cover20. We use these approaches to provide dates of snow appearance and disappearance, snow cover duration, and minimum soil temperatures for each year and plot. Occasionally, temperature data during the snow disappearing window were lost due to sensor failure or loss of sensors (which occurs because plots are not permanently marked and/or well-meaning visitors remove sensors). This, and the lack of temperature sensors in the first year of the project, resulted in approx. 20% of cases of missing data. In those cases, we used a data imputation method to estimate the missing values based on data from nearby plots and a parallel temperature data collection with 890 total observations. These estimates were highly reliable in filling the data gaps (see Appendix C in16 for further details).Focal speciesWe originally targeted 16 native wildflower species along each transect, which were chosen based on their abundance, ease of identification, and presence in the plot. Four of those target species were present on both transects. In 2016 we replaced one species with a different one (see further information below), making for a total of 17 species monitored (Fig. 2c). The focal species are: American bistort* (Polygonum bistortoides), avalanche lily (Erythronium montanum), bracted lousewort* (Pedicularis bracteosa), broadleaf arnica (Arnica latifolia), cascade aster (Aster ledophyllus; synonym Eucephalus ledophyllus), glacier lily (Erythronium grandiflorum), Gray’s lovage (Ligusticum grayi), magenta paintbrush (Castilleja parviflora), mountain daisy (Erigenon peregrinus; synonym Erigeron glacialis), northern microseris (Microseris alpestris; synonym Nothocalais alpestris), scarlet paintbrush (Castilleja miniata), sharptooth angelica (Angelica arguta), sitka valerian* (Valeriana sitchensis), subalpine lupine* (Lupinus arcticus; synonym Lupinus latifolius var. subalpinus), tall bluebell (Mertensia paniculata), Canby’s licorice-root (Ligusticum canbyi), and western anemone (Anemone occidentalis). Asterisks denote species monitored along both trails.Due to challenges in species identification, we dropped Canby’s licorice-root (Ligusticum canbyi) as a target species in 2016. Consequently, Ligusticum canbyi has limited replication in the database (Fig. 2c). While we included the phenological records of this species for the sake of completeness, we recommend focusing on the other 16 species, which are both better represented (in terms of data coverage) and are free of any potential misidentification issues.For additional information on the species, methods, identification cues, and image resources see: http://www.meadowatch.org, https://www.youtube.com/channel/UCGBFTKxf8FIWswMDxBavpuQ, and the appendices therein16.Data collection and volunteer trainingDuring the summer months, MW volunteers and scientists collect reproductive phenology data with a frequency between 3 and 9 trail reports per week. Each report records the presence or absence of 4 phenophases for each target species present in each of the plots. The phenophases are ‘budding’, ‘flowering’, ‘ripening fruit’, and ‘releasing seed’. Phenophases were defined as follows:BuddingThe beginning growth of the flower which has not yet opened. A plant is considered budding if buds are present, but the stamen and pistils are not yet visible and available to pollinators.FloweringThe generally “showy” part of the plant that holds the reproductive parts (stamens and pistils). A plant is considered flowering when at least one flower is open, and the stamens and pistils are visible and available for pollination and reproduction.Ripening fruitThe fruit develops from the female part of the flower following successful pollination. In the target species, fruits can take many forms, from hard, fleshy capsules, juicy berries, to a feathery tuft on the end of a seed. A plant is in the ripening fruit stage when reproductive parts on at least one reproductive stalk are non-functional and the formation of the fruit part is clearly ongoing (visible), but seeds are not yet fully mature and not yet being dispersed.Releasing seedAfter the fruit ripens, seeds are released to be dispersed by gravity, wind, or animals. A plant is considered in the releasing seed stage if seeds are actively being released on at least one reproductive stalk (but there are still seeds present).A full description, including illustrations for each species’ phenophase and identification cues is available in http://www.meadowatch.org/volunteer-resources.html, as well as in Annex 1 – Supplementary Documentation. Multiple phenophases can be present simultaneously, depending on the species, and are noted independently. Additionally, volunteers are also asked to record the presence of snow (‘snow covered plot’, ‘partially covered plot’, or ‘snow-free plot’), and, since 2017, the presence of damage by herbivory (‘presence of browsed stems’) on each plot.In years not impacted by the SARS-Cov-2 pandemic MW volunteers attend an in-person 3-hour botanical and phenological training session taught by UW scientists at the beginning of each sampling season. Volunteers were also provided with detailed species-identification guides, including an extensive description of sampling methods and location of the plots. The trainings for the 2020 and 2021 seasons were held virtually via a series of online training videos. In these years, volunteers took a quiz on wildflower phenology, plant identification and data collection methods after viewing these videos and were required to ‘pass’ a certain threshold to volunteer (unlimited attempts were allowed). During these virtual trainings, volunteers were provided with digital copies of the species identification guides, with many returning volunteers using printed guides they had kept from previous years.At the end of their phenological hike, volunteers submit their data sheets either by depositing them in lockboxes located within the park, or by scanning and emailing them directly to mwatch@uw.edu. Data are then entered manually and stored in the UW repositories after being checked for consistency at the end of each sampling season.The parallel data collection by members of UW’s Hille Ris Lambers group (including PI, postdoctoral researchers, graduate students, and trained interns) acted as the following: (i) a quality-control, i.e., allowing us to compare the consistency in phenology assessments between volunteers and scientists, and (ii) a way to increase the temporal resolution and scale of the data, e.g., by reducing early season gaps and ‘weekend bias’17. This parallel expert sampling was carried out around once a week between 2013 and 2020, showing great consistency between the two groups. For detailed comparisons between volunteers and scientists’ assessments see the data validation section (as well as Appendix E in16).Processed dataIn addition to the raw phenological data, we also provide here parameters to construct the year, species, and plot-specific flowering phenology based on the timing of snow disappearance (as in16). Models describe unimodal probability distributions that were fitted with maximum likelihood models to binomial flowering data from each species, year, and plot. These curves have been used to estimate peak flowering dates and diversity and link them to reported visitor experiences16. Here, we provide the 3 parameters defining the unimodal curve of flowering probability per species i, plot j and year k: the duration of flowering (𝛿ijk), the maximum probability of flowering (𝜇ijk), and peak flowering (in DOY – ρijk); following the equations described in16 and https://github.com/ajijohn/MeadoWatch).The parameters of these probability distribution curves are ready-to-use values that can be broadly and easily used to estimate floral compositional change over past seasons due to changing environmental conditions—for example, to inform plant-pollinator interaction networks if combined with pollinator behavioral data (e.g.21). More

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NEWS
01 April 2022

Tropical forests have big climate benefits beyond carbon storage

Study finds that trees cool the planet by one-third of a degree through biophysical mechanisms such as humidifying the air.

Freda Kreier

Freda Kreier

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Tropical forests create cloud cover that reflects sunlight and cools the air.Credit: Thomas Marent/Minden Pictures

Tropical forests have a crucial role in cooling Earth’s surface by extracting carbon dioxide from the air. But only two-thirds of their cooling power comes from their ability to suck in CO2 and store it, according to a study1. The other one-third comes from their ability to create clouds, humidify the air and release cooling chemicals.
How much can forests fight climate change?
This is a larger contribution than expected for these ‘biophysical effects’ says Bronson Griscom, a forest climate scientist at the non-profit environmental organization Conservation International, headquartered in Arlington, Virginia. “For a while now, we’ve assumed that carbon dioxide alone is telling us essentially all we need to know about forest–climate interactions,” he says. But this study confirms that tropical forests have other significant ways of plugging into the climate system, he says.The analysis, published in Frontiers in Forests and Global Change on 24 March1, could enable scientists to improve their climate models, while helping governments to devise better conservation and climate strategies.The findings underscore growing concerns about rampant deforestation across the tropics. Scientists warn that one-third of the world’s tropical forests have been mown down in the past few centuries, and another one-third has been degraded by logging and development. This, when combined with climate change, could transform vast swathes of forest into grasslands2.“This study gives us even more reasons why tropical deforestation is bad for the climate,” says Nancy Harris, forest-research director at the World Resources Institute in Washington DC.More than a carbon spongeForests are major players in the global carbon cycle because they soak up CO2 from the atmosphere as they grow. Tropical forests, in particular, store around one-quarter of all terrestrial carbon on the planet, making them “centrepieces for climate policy” in their home countries, Griscom says.
Tropical forests may be carbon sources, not sinks
“There’s clear evidence that the tropics are producing excellent climate benefits for the entire planet,” says Deborah Lawrence, an environmental scientist at the University of Virginia in Charlottesville and a co-author of the latest study. She and her colleagues analysed the cooling capacity of forests around the globe, in particular considering biophysical effects alongside carbon storage. Tropical forests, they found, can cool Earth by a whole 1 °C — and biophysical effects contribute significantly.Although scientists knew about these effects, they hadn’t understood to what extent the various factors counter global warming.Trees in the tropics provide shade, but they also act as giant humidifiers by pulling water from the ground and emitting it from their leaves, which helps to cool the surrounding area in a way similar to sweating, Griscom says.“If you go into a forest, it immediately is a considerably cooler environment,” he says.This transpiration, in turn, creates the right conditions for clouds, which like snow and ice in the Arctic, can reflect sunlight higher into the atmosphere and further cool the surroundings. Trees also release organic compounds — for example, pine-scented terpenes — that react with other chemicals in the atmosphere to sometimes create a net cooling effect.Locally coolTo quantify these effects, Lawrence and her colleagues compared how the various effects of forests around the world feed into the climate system, breaking down their contributions in bands of ten degrees of latitude. When they considered only the biophysical effects, the researchers found that the world’s forests collectively cool the surface of the planet by around 0.5 °C.
When will the Amazon hit a tipping point?
Tropical forests are responsible for most of that cooling. But this band of trees across Latin America, Central Africa and southeast Asia is under increasing pressure from climate change and deforestation. Both of these human-caused impacts can lead rainforests to dry out, says Christopher Boulton, a geographer at the University of Exeter, UK. Last month, he and his colleagues published a review2 of nearly 30 years’ worth of satellite images of the Amazon, the largest rainforest in the world. By measuring the biomass of the vegetation in the images, the team discovered that three-quarters of the Amazon is losing resilience — the ability to recover from an extreme weather event such as a drought.Threats to tropical rainforests are dangerous not only for the global climate, but also for communities that neighbour the forests, Lawrence says. She and her colleagues found that the cooling caused by biophysical effects was especially significant locally. Having a rainforest nearby can help to protect an area’s agriculture and cities from heatwaves, Lawrence says. “Every tenth of a degree matters in limiting extreme weather. And where you have forests, the extremes are minimized.”Governments across the tropics have struggled to conserve their forests despite more than two decades of global campaigns to halt deforestation, promote sustainable development and protect the climate. Lawrence says that her team’s findings make it clear that protecting forests is a matter of self-interest, and has immediate benefits for local communities.

doi: https://doi.org/10.1038/d41586-022-00934-6

ReferencesLawrence, D., Coe, M., Walker, W., Verchot, L. & Vandecar, K. Front. For. Glob. Change https://doi.org/10.3389/ffgc.2022.756115 (2022).Article 

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Boulton, C. A., Lenton, T. M. & Boers, N. Nature Clim. Change 12, 271–278 (2022).Article 

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Ebola datasetThe 2018–2020 DRC EVD outbreak lasted over 24 months and spread over 3 distinct spatial and temporal waves. Between the emergency declaration of the EVD outbreak in northern DRC on August 1, 2018 and the outbreak’s official end on June 25, 2020, the DRC Ministry of Health has reported a total of 3481 cases (including confirmed and probable), 1162 recoveries, and 2299 deaths16 in the provinces of Northern Kivu, Southern Kivu, and Ituri. The dataset considered here is a large subset of the entire EVD database compiled by the University of Kinshasa School of Public Health, which comprises 3117 total case records (confirmed and probable) recorded between May 3, 2018, and September 12, 2019. The data included partially de-identified but still detailed patient information, such as each person’s location, date of symptom onset and hospitalization, as well as discharge due to recovery or death. These individual records came from the Ebola treatment centers in 24 different health zones, spread out among the three DRC provinces of Northern Kivu, Southern Kivu, and Ituri.Of the 24 health zones, 77.1% of all cases were from only 6: Beni, Butembo, Katwa, Kalunguta, Mabalako, and Mandima. Only 9.7% of cases were under the age of 18. There is also a slightly larger proportion of females contracting the disease, comprising 57.0% of the cases. Approximately 5% of the cases were health care workers. About one-third of the EVD fatalities were not identified until patient’s death and thus not effectively isolated from the time of infection. Although over 170,000 contacts of confirmed and probable Ebola cases had been monitored across all affected health zones for 21 days after their last known exposure by the end of the epidemic, some of the contact tracing was incomplete due to insecurity that prevented public health response teams from entering some communities. The overall case density map is presented in panel (A) of Fig. 1 with the animated version of the map presented in the online appendix in Fig. A.1. Notice that the high-density areas, particularly Butembo, Katwa, and Beni, are all spatially small health zones corresponding to cities or towns with larger populations.Figure 1DRC Ebola dataset. (A) The spatial distribution of 3481 EVD cases across the northern DRC health zones during Ebola 2018–2020 outbreak. (B) The flowchart of personal records available up to September 12, 2019 available for the current analysis. The total number of available individual disease records was 3080. Map created using open software R17 with geospatial data obtained from18.Full size imageFigure 2Daily incidence and removal rates. Daily incidence (grey bars) and removal counts (red dots) during DRC Ebola 2018–2020 outbreak between August 15, 2018 and September 12, 2020 along with their respective trendlines (loess smoothers). The blue trendline above the plot represents daily effective reproduction number (mathcal{R}_t) defined as the ratio of daily number of new infections to new removals. The vertical lines indicate cut-off dates for data collection in each wave as listed in Table 1.Full size imageTable 1 Observed cases by EVD wave.Full size tableCase alerts and definitionsSince early August, 2018, the DRC Ministry of Health has been collaborating with several international partners to support and enhance EVD response activities through its emergency operations center in Goma. To the extent possible given regional security considerations19, the response teams were deployed to interview patients and their suspected contacts using a standardized case investigation form classifying cases as suspected, probable, or confirmed. A suspected case (whether surviving or not) was defined as one with the acute onset of fever (over 100(^{circ })F) and at least three Ebola-compatible clinical signs or symptoms (headache, vomiting, anorexia, diarrhea, lethargy, stomach pain, muscle or joint aches, difficulty swallowing or breathing, hiccups, unexplained bleeding, or any sudden, unexplained death) in a North Kivu, South Kivu, or Ituri resident or any person who had traveled to these provinces during this period and reported the signs or symptoms defined above. A patient who met the suspected case definition and died but from whom no specimens were available was considered a probable case. A confirmed Ebola case was defined as a suspected case with at least one positive test for Ebola virus using reverse transcription polymerase chain reaction (RT-PCR)20 testing. Patients with suspected Ebola were isolated and transported to an Ebola treatment center for confirmatory testing and treatment2.Onset and removalIn our analysis of the DRC dataset, we focused on dates of symptom onset and removal, with removal defined as either a death/recovery at home or transfer to an Ebola treatment center (ETC). It was assumed that, once in the treatment center, the probability of further infection spread by an isolated individual was very small due to the strict safety protocols—and later due also to vaccination of healthcare personnel and family members who were in contact with the suspected Ebola case. As summarized in panel (B) of Fig. 1, we were able to access 3117 out of 3481 individual records of confirmed and probable Ebola cases. Of these 3117 records, 37 were missing both the onset and recovery dates and were removed from further analysis. In about 30% of the remaining records, either their dates of onset or removal were missing. A detailed flow diagram summarizing the amount of missing data and data processing leading to the final dataset is presented in panel (B) of Fig. 1. The distribution of the original and the partially imputed records across the three waves of infection is provided for further reference in Table 1.Spatial and temporal patternsThroughout the pandemic, the incidence rates exhibited strong spatial and temporal patterns that can be summarized as three distinct waves of infections with approximate boundaries marked by vertical lines in Fig. 1. The distribution of weekly reported cases across the most affected health zones listed in Table 1 is provided in the bar plot and in the corresponding animation in the appendix (see Figure A.1). As seen from the bar chart and the animated plot, the epidemic was initially driven largely by infections in the health zones of Beni, Mandima and Mabalako. After several months, the incidence of new cases in these zones subsided, but the epidemic moved south to the health zones of Katwa and Butembo, where the majority of new infections was registered between weeks 22 to 45 of the epidemic (see Panel (A) in Figure A.1 in the online Appendix). In the final spatial shift, around week 49, the epidemic returned to the health zones of Beni, Mandima, and Mabalako, where it was mostly extinguished around week 60 (September 2019). Isolated Ebola incidences occurred sporadically across northern DRC until end of the outbreak was officially declared in June 2020.The empirical patterns of incidence and removal for EVD cases are summarized in Fig. 2 with the bar and the dot plots representing the daily numbers of new infections and removals, respectively. As seen from the plot, these daily counts closely follow a three-wave temporal pattern in Table 1. This is further evident from the black and red trendlines representing the loess smoothers (see21). The daily ratio of new cases and removals may be interpreted as a crude estimate of the effective reproduction number (mathcal{R}_t) defined more formally in (2) in Model for Data Analysis below. In particular, the blue trendline for (mathcal{R}_t) indicates that towards the end of the observed time period, the number of removals outpaced the number of new infections ((mathcal{R}_t 0) and (r_t = 0) where (beta > 0) is the rate of infection, (gamma > 0) is the rate of recovery and (rho > 0) is the initial amount of infection. In particular, the model implies the existence of the basic reproduction number (mathcal{R}_0) (R-naught), which determines the average speed of disease spread11 and is given by the formula$$mathcal{R}_0=beta /gamma .$$If (mathcal{R}_0 > 1), the proportion of infected initially rises and then subsides, with the final proposition of surviving susceptibles given by (s_infty = 1 – tau > 0) where (tau) is know as the epidemic’s final size. In typical statistical analysis, an estimate of (mathcal{R}_0) is obtained by separately estimating the parameters (beta) and (gamma). Another important quantity related to (1) is the effective reproduction number, which is typically defined as$$begin{aligned} mathcal{R}_t= mathcal{R}_0 s_t. end{aligned}$$
(2)
Although equation (1) is typically considered in the context of an average behavior of a large population, for our purposes we interpret it as defining the individual histories of infection and recovery, according to the idea of the dynamic survival analysis (DSA) discussed recently in10 and24 and also briefly summarized in the Appendix. With the DSA approach, we interpret equation (1) as the so-called stochastic master equation25 describing the change in probability of a randomly selected individual being at time t either susceptible, infected, or removed. These respective probabilities are represented by the scaled proportions (s_t/(1+rho )), (iota _t/(1+rho )), and (r_t/(1+rho )) and evolve according to (1). As outlined in10, the DSA-based interpretation of the classical SIR equations has a number of advantages that make it particularly convenient for analyzing epidemic data consisting of individual histories of infection onsets and removals, which is exactly the type of data available in the DRC Ebola dataset. The fact that the model is individual-based implies also that we can vary the parameters (theta =(beta ,gamma ,rho )) to account for individual covariates and changes in the parameter values over time, as different waves of infection sweep through the population. Finally, for the purpose of our analysis, it is also important to note that the DSA model does not require any knowledge of the size of the susceptible population subjected to the epidemic pressure. For the DRC dataset, that assumption would be difficult to justify due to spatial and temporal heterogeneity of the epidemic and the frequent movements of local populations driven by political conflicts and insecurity. Another element complicating the determination of the size of susceptible population was the ring vaccination campaign that has been conducted since 2019 wherever possible in the northern DRC during periods of relative stability, despite local mistrust and supply issues. This campaign ultimately resulted in over 250,000 vaccinations.Note that, because (s_0 = 1), the values of (mathcal{R}_0) and (mathcal{R}_t) coincide for (t = 0). Moreover, (s_t = exp left( -mathcal{R}_0 int _0^t r_u mathrm {d}u right)) is a decreasing function of time and therefore, so is (mathcal{R}_t). However, in practice, this implication is problematic. Rewriting (mathcal{R}_t = – {dot{s}}_t/ {dot{r}}_t) suggests that a crude but sensible way to estimate (mathcal{R}_t) empirically is to take the ratio of daily number of new infections to new removals. The empirical (mathcal{R}_t) thus estimated will not be necessarily monotonically decreasing. In the light of possibly changing parameters and the effective population size, we have adopted this approach to estimating the daily effective reproduction number (mathcal{R}_t) in Fig. 2.Parameter estimationWe assume that, for each of the three waves of the epidemic, we have a separate and independent set of parameters (theta) and that, in each wave, we observe (n_T) histories (records) of infection. The i-th individual history may be represented either by the times of disease onset and removal ((t_i,T_i)) or by (t_i) or (T_i) times alone ((t_i,circ )) or ((circ ,T_i)) ((circ) denoting missing value). We assume that among the available (n_T) histories we have n complete records ((t_i,T_i)), (n_1) incomplete ones ((t_i,circ )) and (n_2) incomplete ones ((circ ,T_i )). The wave-specific DSA likelihood function for n complete data records is (see Appendix)$$begin{aligned} begin{aligned} {mathcal {L}}_C(theta vert t_1ldots ,t_n,T_1,ldots ,T_n,T)=(s_T-1)^{-n}prod _{i=1}^n {dot{s}}_{t_i}gamma ^{w_i}e^{-gamma (T_i wedge T -t_i)} end{aligned} end{aligned}$$
(3)
where T is the available time horizon and (w_i) is the binary variable indicating whether (T_i) is right-censored (that is, (T_iwedge T =T)) in which case (w_i = 0) and otherwise (w_i = 1). For the remaining (n_1+n_2) records that are partially incomplete, the wave-specific DSA likelihood function is$$begin{aligned} begin{aligned} {mathcal {L}}_I(theta vert t_1ldots ,t_{n_1},T_1,ldots ,T_{n_2},T)= (s_T-1)^{-(n_1+n_2)} gamma ^{n_2}prod _{i=1}^{n_1} {dot{s}}_{t_i} prod _{i=1}^{n_2} (rho e^{-gamma T_i }-iota _{T_i}) end{aligned} end{aligned}$$
(4)
where we assume that (T_i1). Given the wave-specific time horizons (T’s), the set of parameters for each epidemic wave was estimated independently using 2 independent chains of 3000 iterations, with a burn-in period of 1000 iterations. The chains’ convergence assessed using Rubin’s R statistic28. The analysis resulted in approximate samples from the posterior distribution of (theta) for each of the three waves of the epidemic (see e.g., Fig. 4).Ethics statement on human subjects and methodsThe research was conducted in accordance with the relevant guidelines and regulations of the US law and OSU Institutional Review Board. The research activities involving human subjects discussed in the paper meet the US federal exemption criteria under 45 CFR 46 and 21 CFR 56. More