Ecology

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Following the work in36, we construct an epidemiological model which tracks the disease dynamics and population of two species of hosts following the introduction of a pathogen. The native host (hereafter simply referred to as “type 1”) is vulnerable to the disease, but due to being well adapted to the native habitat has high fecundity when uninfected. The invasive host (hereafter referred to as “type 2”), has coevolved defenses to the pathogen that increase both its tolerance of and resistance to the disease, but is not inherently as well-adapted to the habitat in the absence of infection (i.e., its intrinsic rate of growth in the new habitat is lower than that of the native).Our initial conditions correspond to a population of uninfected type 1 hosts with a small number of both uninfected and infected type 2 hosts, representing an invasion by a novel competitor carrying a novel pathogen into the type 1 population. We consider a vector-borne pathogen, and make the simplifying assumption that there is an already abundant competent vector species in the habitat. (For this initial formulation, we considered a scenario of mosquito-borne infections in birds, such as avian malaria37 or West Nile virus38, to motivate concrete choices.)The model couples two biological dynamics: the daily vector-borne spread of the disease among hosts, and a yearly host breeding cycle. We simulate in discrete time-steps that represent days using an SIR model taking into account the interactions between the disease, the two species of host, and the vectors. The model also includes a passive death rate for hosts of vectors, which increases for hosts while infected. While the vectors are assumed to breed daily, the hosts reproduce as part of an assumed annual breeding season, every (t_c) time-steps (typically equal to 365). These dynamics were informed by considering an annually breeding bird population in a tropical environment, however, they are not meant to reflect the realism of any one biological system. They are chosen here merely to allow a clean interpretation of modeled scenarios. Future models should explore the impact of greater variety in the dynamics of possible vector and host reproductive patterns.Epidemiological modelThe model tracks eight variables corresponding to combinations of host species and vectors with their infection status. Hosts may be of type 1 or 2, and are either susceptible to the disease ((S_1, S_2)), currently infected ((I_1, I_2)), or recovered ((R_1, R_2)). We assume that recovery is complete and recovered individuals suffer no residual effects from their infection aside from a lifelong immunity to becoming reinfected. (We later set the recovery rate for host type 1 to 0, so (R_1 = 0) at all times, but leave it defined for the sake of generality.) For simplicity, we model using only one stage of infection in which individuals are both infectious and symptomatic. The model also tracks the status of the vector population, which may either be susceptible ((S_v)) or infected ((I_v)). We assume that vectors do not recover from the disease, but also suffer no negative effects from being infected, acting only as carriers.For convenience of notation, we denote the total number of hosts$$begin{aligned} H = S_1 + I_1 + R_1 + S_2 + I_2 + R_2 end{aligned}$$and the relative frequencies of infection within their respective population$$begin{aligned} F_1 = frac{I_1}{H}, F_2 = frac{I_2}{H},F_v = frac{I_v}{S_v+I_v} end{aligned}$$which allows some equations to be written more compactly. Table 1 shows a summary of these variables.Table 1 Variables.Full size tableThe model also has several constant parameters that affect the dynamics. (beta _j) determines the probability that hosts of type j become infected when bitten by a single infected vector. We typically set (beta _1 > beta _2), making type 2 hosts less likely to become infected.Likewise, (delta _j) determines the probability that a vector becomes infected when biting an infected host of type j.(b_j) determines the bite rate for vectors on host type j. We assume that each vector bites the same number of hosts per day, so each vector’s probability of becoming infected depends only on the frequency of infection among hosts, while each host will be bitten more if there are more vectors.(gamma _j) determines the proportion of infected hosts of type j that recover from the disease each day. We typically set (gamma _1 = 0 < gamma _2), meaning infected hosts of type 1 do not recover, while infected type 2 recover after an average of (1/gamma _2) days.(mu _{j-}) determines the daily death rate for uninfected hosts of type j and (mu _{j+}) determines the death rate for infected host of type j. We typically set (mu _{1-} = mu _{2-}< mu _{2+} < mu _{1+}), meaning uninfected hosts have the same death rate regardless of type, infected type 2 have a higher death rate than uninfected hosts, and infected type 1 have the highest. (Both susceptible and recovered hosts are considered to be uninfected.) Table 2 shows a summary of parameters related to the SIR dynamics.Equation 1 shows continuous ordinary differential equations approximating the dynamics. Note that the actual model instantiates these in discrete time-steps using the forward Euler method with (h = 1).$$ begin{aligned}&frac{dS_1}{dt} = - S_1 beta _1 b_1 I_v /H - S_1 mu _{1-} \&frac{dI_1}{dt} = S_1 beta _1 b_1 I_v /H - gamma _1 I_1 - I_1 mu _{1+} \&frac{dR_1}{dt} = I_1 gamma _1 - R_1 mu _{1-} \&frac{dS_2}{dt} = -S_2 beta _2 b_2 I_v /H - S_2 mu _{2-} \&frac{dI_2}{dt} = S_2 beta _2 b_2 I_v /H - I_2 gamma _2 - I_2 mu _{2+} \&frac{dR_2}{dt} = I_2 gamma _2 - R_2 mu _{2-}\&frac{dS_v}{dt} = alpha _v H -S_v delta _1 b_1 F_1 -S_v delta _2 b_2 F_2 -S_v mu _v\&frac{dI_v}{dt} = S_v delta _1 b_1 F_1 + S_v delta _2 b_2 F_2 - I_v mu _v\ end{aligned} $$ (1) Table 2 Parameters for SIR dynamics.Full size tableFollowing a standard SIR model, susceptible hosts can become infected, and infected hosts become recovered, but each equation also contains a negative term corresponding to deaths. Thus, the total population of hosts is strictly decreasing in this time-frame. We assume that the vectors breed on a much shorter timescale than hosts, so we include a term for their births here, while host births are implemented by a yearly breeding event. We assume no vertical disease transmission, so all new vectors begin in the susceptible category. We assume that the daily birthrate for each vector increases with access to hosts, and decreases with competition among other vectors for hosts and breeding sites, so we set it equal to (frac{alpha _v H}{S_v + I_v}), where (alpha _v) is a constant scaling factor. Since the birthrate for each vector contains the total number of vectors in its denominator, the total number of vector births in the population will simply be (alpha _v H).A population with a larger number of hosts will be able to sustain a larger number of vectors. For a population with a constant number of hosts, the equilibrium vector population will be proportional to the number hosts: aH where (a = frac{alpha _v}{mu _v}) is the equilibrium vector density (number of vectors per host). For instance if (a = 2), then in equilibrium there will be twice as many vectors as hosts. Given a fixed number of hosts, the population of vectors will asymptotically approach the equilibrium value. In practice the total number of hosts is constantly changing, so the population of vectors will chase after this moving equilibrium, though for our standard parameters (alpha _v) and (mu _v) are sufficiently large such that this will occur on a short timescale, and the population of vectors remains close to the current equilibrium value.Breeding eventTable 3 shows a summary of parameters related to the breeding event. Every (t_c) days (typically 365), a breeding event occurs according to the following process.Table 3 Parameters for breeding event.Full size tableLet$$begin{aligned}&Delta S_1 = t_c alpha _{1-}(S_1+R_1)+t_calpha _{1+} I_1 \&Delta S_2 = t_c alpha _{2-}(S_2+R_2)+t_calpha _{2+} I_2 \ end{aligned}$$be the number of new host offspring of each type born this generation. In order to maintain consistency of temporal units among the parameters, each birthrate parameter is multiplied by (t_c). Let H be the current total number of hosts. Let$$begin{aligned} c = {left{ begin{array}{ll} 0 &{} hbox {if } H ge kappa \ 1 &{} hbox {if } H + Delta S_1 + Delta S_2 le kappa \ frac{kappa -H}{Delta S_1 + Delta S_2} &{} hbox {otherwise} \ end{array}right. } end{aligned}$$be the proportion of offspring that survive to adulthood. (None, if the population is already above carrying capacity. All, if the difference between the reproducing population size and the carrying capacity exceeds the new births. If the population is approaching carrying capacity, juvenile mortality scales proportionally so that the population will hit carrying capacity but not exceed it.)Then$$begin{aligned}&S_1 + c Delta S_1 rightarrow S_1 \&S_2 + c Delta S_2 rightarrow S_2 \ end{aligned}$$We assume there is no vertical disease transmission, so all new hosts begin in the susceptible category. We assume that the host population is iteroparous, such that the new offspring and the existing adult population both carry over to the next generation. If the new population would exceed the carrying capacity, we assume the limited space or supplies reduces the number of successful offspring so that the population exactly reaches the carry capacity by reduction in juvenile survival rather than population-wide competition that could also reduce the adult population.The carrying capacity is therefore what drives the interspecific host competition. Because births of both species are summed and then normalized by the total number of births, the higher the birthrate of one host, the larger a fraction of the available space it will capture during the breeding event. Similarly, the lower the death-rate of a host, the less space it frees up for the next breeding event. Even if one host species would be able to sustain a stable population on its own, the presence of a more fit competitor can lead to the extinction of the less fit type by driving its effective birth rate down.Immune-reproductive trade-offs and boundary conditionsWe assume that host type 1 is evolutionarily stable in the absence of the disease; an uninfected monoculture population below the carrying capacity will have at least as many births as deaths each cycle. In a continuous version of this model where births and deaths happened simultaneously, this might be defined by (alpha _{1-} ge mu _{1-}) . However in our model, the population spends many days decreasing due to deaths before the next breeding event occurs. The population exponentially decays throughout the cycle, and then jumps up during the breeding event. The number of new host births is proportional to the number of hosts at the start of the breeding event, which will be the lowest value of any other time during the cycle. Thus, the birth rate needs to be high enough that the surviving hosts can compensate despite their diminished numbers. Taking this into account, we get the condition$$begin{aligned}&alpha _{1-} ge frac{1-(1- mu _{1-})^{t_c}}{(1-mu _{1-})^{t_c}} \ end{aligned}$$Which is a higher bound on (alpha _{1-}) than the simpler one above, but will be close to it if (mu _{1-}) and (t_c) are small.To implement the scenario in which type 2 has increased resistance and tolerance to the disease at the expense of overall fecundity, we implement the following boundary conditions:$$begin{aligned}&beta _1 > beta _2 \&0 = gamma _1< gamma _2 \&mu _{1-} = mu _{2-}< mu _{2+} < mu _{1+} \&alpha _{1-} > alpha _{2-} > alpha _{2+} > alpha _{1+} end{aligned}$$Type 2 hosts are less likely to contract the disease, and are able to recover from it, while type 1 lack the immunological strength to eradicate it completely. Additionally, while both types of host are weakened by the disease, type 2 suffer fewer negative effects. However, this stronger immune response comes at the cost of reducing their birth rate when compared to healthy type 1 hosts.Due to the heterogeneous population, there is ambiguity in defining (R_0) for the disease. The two types of host have different transmission rates and durations of infection, and will therefore be responsible for different amounts of disease spread. To resolve this, we define several related values. Let (R_0^j) be the (R_0) of the disease in a homogeneous population of type j hosts: the average number of hosts infected (indirectly, through vectors) from a single infected host in a population consisting entirely of type j hosts.$$begin{aligned}&R_0^1 = frac{delta _1 beta _1 a b_1^2}{mu _v mu _{1+}} \&R_0^2 = frac{delta _2 beta _2 a b_2^2}{mu _v (mu _{2+}+gamma _2)} end{aligned}$$We simplify the equation for (R_0^1) since (gamma _1 = 0). We define w to be the frequency of host type 1: (w := (S_1 + I_1)/H). Then (R_0) for the vectors is$$begin{aligned} R_0^v = R_0^1 w + R_0^2 (1-w) end{aligned}$$which will also be the effective (R_0) of the disease for the hosts in the mixed population.For simplicity of results, we restrict to the case where type 1 is more infectious overall than type 2, in particular (R_0^1 > R_0^2). This allows us to avoid edge cases in simulation outcomes which are beyond the scope of this paper. We intend to lift this restriction and study these outcomes in future work.NoteAlthough usual epidemiological model formulations can rely on the value 1 as the boundary condition for (R_0) to determine the epidemic potential of an outbreak, in this case we are calculating effective (R_0) in a dynamic host population, such that the decrease in disease spread due to saturation from recovered hosts and already infected hosts increases the actual thresholds. More accurate criteria require a technical and somewhat cumbersome analysis, which we leave for a future paper. More

Climate dataMonthly climate data (air temperature at 2 m and cloudiness) with a spatial resolution of 0.5° were obtained from the CRU Time Series 4.0.15 We extracted data from 1982 to 2018 to match the time series of satellite vegetation observations. The VPD was calculated as the difference between saturated water-vapour pressure and actual water-vapour pressure31. Temperature and vapour-pressure data used for the VPD calculation were obtained from CRU.Soil moisture dataThe daily root-zone soil moisture with a spatial resolution of 0.25° for the period 1980–2018 was obtained from the Global Land Evaporation Amsterdam Model (GLEAM v.3.3a)32. The dataset is based on radiation and air temperature from a reanalysis, a combination of gauge-based, reanalysis-based and satellite-based precipitation and satellite-based vegetation optical depth.Fire emission dataMonthly carbon emissions from biomass burning were obtained from the fourth-generation Global Fire Emission Database33. This dataset has a spatial resolution of 0.25° and provides global data on the burning area and emissions on three-hourly, daily and monthly timescales and estimates the contributions of different fire types. Emissions data can be obtained for different substances, such as carbon (C), dry matter (DM), carbon dioxide (CO2), carbon monoxide (CO) and methane (CH4).Satellite vegetation greenness dataThe satellite-based NDVI archived from the MODIS NDVI dataset with a spatial resolution of 0.5° and a temporal resolution of 16 days was used here to detect vegetation greenness changes. In addition, the solar-induced chlorophyll fluorescence product was used as a proxy of vegetation photosynthesis. We furthermore used the four-day clear-sky CSIF time series (2000–2019) with a spatial resolution of 0.05° × 0.05° from ref. 34 (https://osf.io/8xqy6/).GPP based on NIRvThe NIRv is a newly developed satellite vegetation index combining NDVI and near-infrared band reflectivity of vegetation and is recognized as a proxy of GPP35,36. We obtained the 0.05° NIRv_GPP from 1982 to 2018 from ref. 37. This product was produced by upscaling the relationships between NIRv and observed GPP to the global scale and was judged to perform well in capturing interannual trends of GPP37.Atmospheric CO2 dataIn situ observations of daily CO2 concentration at Point Barrow were obtained from the National Oceanic and Atmospheric Administration/Earth System Research Laboratory network. According to analyses of atmospheric transport and mixing processes, the CO2 signals detected at Barrow are suggested to be an integrated measure of carbon fluxes over both the high latitudes and the middle latitudes20.Ecosystem carbon fluxesSimulations of ecosystem carbon fluxes (GPP, TER and NEE) derived from process-based model simulations (TRENDY), empirical models based on flux tower observations (FLUXCOM) and atmospheric CO2 inversion models were jointly used for the investigation of net ecosystem carbon exchange over the northern middle and high latitudes.The TRENDY dataset is an ensemble of dynamic global vegetation model (DGVM) simulations that are forced by CRU–National Centers for Environmental Prediction historical climate and CO2 inputs38. The DGVMs use a bottom‐up approach to simulate terrestrial CO2 fluxes (for example, GPP, TER and NEE), and were extensively used to explore the mechanisms driving changes in carbon uptake and fluxes. The simulated GPP, TER and NEE from nine models of TRENDYv.8 (Supplementary Table 1) were used in this study. The S2 experiment, which considered the effect of both observed changes of CO2 and climate on ecosystem carbon fluxes, was selected for studying the changes of ecosystem carbon fluxes before and after the temperature shift.The FLUXCOM dataset is an upscaling product using empirical models forced by eddy-covariance data from 224 flux towers, remote sensing data and climate data8,9,10. It provides estimates of global energy and carbon fluxes (http://www.fluxcom.org/). The empirical models were trained by three machine learning algorithms, including Random Forests, Artificial Neural Networks and Multivariate Adaptive Regression Spline, and thus provide a series of estimates of global carbon fluxes. We used the FLUXCOM carbon fluxes data driven by the European Centre for Medium-Range Weather Forecasts Reanalysis v.5 (ERA5) climate reanalysis from 1979 to 2018.The atmospheric CO2 inversion datasets provide estimates of NEE over land from long-term atmospheric CO2 measurements using atmospheric transport models. Three atmospheric CO2 inversion products were used here: monthly net biome production with a spatial resolution of 3.75° × 2.5° from the JENA CarboScope (version s76_vo2020) for the period 1976–2019, long-term global CO2 fluxes estimated by the NICAM-based Inverse Simulation for Monitoring CO2 (NISMON-CO2) between 1990 and 2019 and the Copernicus Atmosphere Monitoring Service12 (CAMS v.19r1) dataset between 1979 and 2019.Eddy-covariance CO2 observation dataThe eddy-covariance measurements of carbon fluxes from tower sites were obtained from the Integrated Carbon Observation System 2018 and the FLUXNET Network 2015. We selected 48 eddy-covariance CO2 observation sites with 10 yr continuous data (Supplementary Table 2) located north of 25° N and extracted temperature and NEE data from September to November to explore the change of ecosystem carbon exchange in autumn.NEE estimationThe monthly NEE was estimated as the difference between TER and GPP. The autumn (September to November) GPP and TER derived from TRENDY and FLUXCOM over the study region were obtained by aggregating GPP and TER from each grid cell weighted by the grid-cell area. The NEE derived from atmospheric CO2 inversions was directly used and compared against those from TRENDY and FLUXCOM. To compare the NEE before and after the temperature turning point, we divided the NEE time series into two periods: 1982–2003 and 2004–2018.Calculation of the AZCWe used observations of CO2 from Point Barrow to characterize the trends in the zero-crossing date of CO2 (downward in spring and upward in autumn). These trends roughly correspond to the beginning of net carbon uptake in spring and the beginning of net carbon release in autumn. According to the method of ref. 39, we obtained the detrended seasonal CO2 curve by separating the seasonal cycle from the long-term trend and short-term variations, fitting a function consisting of a quadratic polynomial for the long-term trend and four harmonics for the annual cycle to the daily data. The residuals from this function fit are then obtained. A 1.5-month and a 390-day full-width half-maximum-value averaging filter were used for the digital filtering of residuals to remove the short-term variations and the long-term trend, respectively. Then we got the zero-crossing dates when the detrended seasonal CO2 curve crosses the zero line from positive to negative and negative to positive, respectively.The autumn carbon release is calculated as the amount of CO2 released between the autumn zero-crossing date and the first week of September following ref. 21.Identification of turning point of temperatureWe used the piecewise linear regression method to determine the turning point of the mean autumn (September to November) temperature during 1982–2018 over the area north of 25° N. In addition, a moving t-test method was used to verify the turning-point identification. Then, the temporal trends of the mean autumn temperature before and after the turning point were calculated using the Mann–Kendall non-parametric trend test method, and the confidence intervals were determined using Sen’s slope statistics. According to the temperature trends before and after the turning point, we further identified the CAs as where the autumn temperature shows a decreasing trend after the turning point (2004) relative to that before the turning point, and WAs as regions outside the CAs. To maintain spatial integrity and continuity, we ignored the significance of the temperature trend when dividing the CAs and WAs.To verify that our analysis is not affected by the division of the time period and regions, we also identified the temperature turning point at each grid point using the piecewise linear regression method and then extracted those grid points with significant temperature change and significant NEE change (P  More

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DatasetsWe use the Amazon basin (http://worldmap.harvard.edu/data/geonode:amapoly_ivb, accessed 28 January 2021) as our region of study. To determine the grid cells that are contained within Brazil for a subset of analysis, we use the ‘maps’ package in R (v.3.3.0; https://CRAN.R-project.org/package=maps). This is also used in the plotting of country outlines. The main dataset used to determine forest health is from VODCA33, of which we use the Ku-band product. These data are available at 0.25° × 0.25° at a monthly resolution from January 1988 to December 2016. We also use NOAA AVHRR NDVI34. For precipitation data, we use the CHIRPS dataset40 downloaded from Google Earth Engine at a monthly resolution. Finally, to determine land cover types, we used the IGBP MODIS land cover dataset MCD12C1 (ref. 37). All these datasets are at a higher spatial resolution than the VODCA dataset and thus we downscale them to match the lower resolution. Our SST data comes from HadISST49, where we define a North Atlantic region (15–70° W, 5–25° N), for which we take the spatial mean. The mean monthly cycle is then removed to produce anomalies.For the vegetation datasets that we measure the resilience indicators on (below), we use STL decomposition (seasonal and trend decomposition using Loess)51 using the stl() function in R. This splits time series in each grid cell into an overall trend, a repeating annual cycle (by using the ‘periodic’ option for the seasonal window) and a residual component. We use the residual component in our resilience analysis. The first 3 yr of data had large jumps in VOD which were seen when testing other regions of the world as well as in the Amazon region. Hence, we restrict our analysis to the period January 1991 to December 2016.To test the robustness of the detrending, we also vary the size of the trend window in the stl() function. The results from these alternatively detrended time series are shown in Supplementary Fig. 4. The results are also robust to varying the window used to calculate the seasonal component rather than using ‘periodic’; at the strictest plausible value of 13, we still see the same increases in AR(1) (Supplementary Fig. 5).For the AMO index shown in Supplementary Fig. 13, data come from the Kaplan SST dataset and can be downloaded from https://psl.noaa.gov/data/timeseries/AMO/.Grid cell selectionWe use the IGBP MODIS land cover dataset at the resolution described above to determine which grid cells to use in our analysis. The dataset is available at an annual resolution from 2001 to 2018 (but we only use the time series up to 2016 to match the time span of our VOD and NDVI datasets). To focus on changes in forest resilience, we use grid cells where the evergreen BL fraction is ≥80% in 2001. Grid cells are treated as human land-use area if the built-up, croplands or vegetation mosaics fraction is >0%. We remove grid cells that have human land use in them from our forest analysis, regardless of if there is ≥80% BL fraction in the grid cell.We measure the minimum distance between forested Amazon basin grid cells and human land-use grid cells in 2016 (believing this to be the most cautious and least biased way to measure distance) using the latitude and longitude of each grid point and computing the great-circle distance. We use human land-use grid cells over a larger area than the basin, so that we can determine the closest distance to human land use, regardless of whether this human land use lies within the basin. We also measure the minimum distance from human land use or roads in Brazil, where we have reliable data on state and federal roads (https://datacatalog.worldbank.org/dataset/brazil-road-network-federal-and-state-highways). As in the main text, we reiterate that these minimum distances can be viewed as the maximum distance from human land use as our data will not include roads for the full Amazon basin, or non-federal or non-state roads in Brazil that will have human activity associated with them.To ensure that the pattern of changes in resilience is not a consequence of more settlements being in the southeast of the region, combined with the gradient of rainfall from northwest to southeast typical of the rainforest, we measure the correlation between MAP and the distances from the urban grid cells, which is very weak (Spearman’s ρ = 0.109, P  More