Ecology

Here we provide an overview of the key elements of our framework including describing the contact function that links economic activities to contacts, the SIRD (Susceptible-Infectious-Recovered-Dead) model, the dynamic economic model governing choices, and calibration. The core of our approach is a dynamic optimization model of individual behavior coupled with an SIRD model of infectious disease spread. Additional details are found in the SI.Contact functionWe model daily contacts as a function of economic activities (labor supply, measured in hours, and consumption demand, measured in dollars) creating a detailed mapping between contacts and economic activities. For example, all else equal, if a susceptible individual reduces their labor supply from 8 to 4 h, they reduce their daily contacts at work from 7.5 to 3.75. Epidemiological data is central to calibrating this mapping between epidemiology and economic behavior. Intuitively, the calibration involves calculating the mean number of disease-transmitting contacts occurring at the start of the epidemic and linking it to the number of dollars spent on consumption and hours of labor supplied before the recession begins.We use an SIRD transmission framework to simulate SARS-CoV-2 transmission for a population of 331 million interacting agents. This is supported by several studies (e.g.,77,78) that identify infectiousness prior to symptom onset. We consider three health types m ∈ {S, I, R} for individuals, corresponding to epidemiological compartments of susceptible (S), infectious (I), and recovered (R). Individuals of health type m engage in various economic activities ({A}_{i}^{m}), with i denoting the activities modeled. One of the ({A}_{i}^{m}) is assumed to represent unavoidable other non-economic activities, such as sleeping and commuting, which occur during the hours of the day not used for economic activities (see SI 2.3.1). Disease dynamics are driven by contacts between susceptible and infectious types, where the number of susceptible-infectious contacts per person is given by the following linear equation:$${{{{{{{{mathscr{C}}}}}}}}}^{SI}({{{{{{{bf{A}}}}}}}})=mathop{sum}limits_{i}{rho }_{i}{A}_{i}^{S}{A}_{i}^{I}$$
(1)
while similar in several respects to prior epi-econ models15,16,74, a methodological contribution is that ρi converts hours worked and dollars spent into contacts. For example, ρc has units of contacts per squared dollar spent at consumption activities, while ρl has units of contacts per squared hour worked.We also consider robustness to different functional forms in Fig. 6F, G as a reduced-form way to consider multiple consumption and labor activities with heterogeneous contact rates. Formally:$${{{{{{{{mathscr{C}}}}}}}}}^{SI}({{{{{{{bf{A}}}}}}}})=mathop{sum}limits_{i}{rho }_{i}{({A}_{i}^{S}{A}_{i}^{I})}^{alpha },$$
(2)
where α  > 1 (convex) corresponds to a contact function where higher-contact activities are easiest to reduce or individuals with more contacts are easier to isolate. α  More

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Trait modelsOur analysis included 491,001 unique trait measurements across 18 traits, encompassing 13,189 tree species from 2313 genera, reflecting ~21% of all known tree species33 (Fig. 1). Traits were measured at 8683 locations across the globe and 373 distinct eco-regions (Supplementary Tables 1, 2), with georeferenced measurements capturing 15% of known tree species in Eurasia, 13% in South America, 9% in Oceania, and 6% in North America and Africa33. The raw data covered 22% of all trait-by-species combinations (Fig. 1b, Supplementary Fig. 2), nearly identical to other large-scale trait analyses across the entire plant kingdom5,17,30. Yet there was considerable variation in coverage across traits, with traits such as specific leaf area and leaf nitrogen measured on more than 60% of all species, versus traits such as crown diameter and conduit diameter, which captured fewer than 5% of species (Fig. 1b, Supplementary Fig. 2). Across all species, 423 had more than 10 unique traits measured, and two species (Picea abies and Pinus sylvestris) had measurements for all 18 traits. In general, there was highly consistent coverage across taxonomic orders and traits (Supplementary Fig. 1), with gymnosperms being slightly overrepresented (comprising 3.1 ± 6.8% of measurements in the database versus ~1% of all known tree species34,35, Fig. 1a), in part reflecting the wider geographic range of many gymnosperms relative to angiosperms36.To explore relationships in functional traits at the individual level, we used random-forest machine-learning models to estimate missing trait values for each individual tree as a function of its environment and phylogenetic history. We also conducted a second set of analyses where trait expression was estimated using phylogenetic information only, which allowed us to include additional non-georeferenced data (Fig. 1), while also quantifying the relative contribution of environmental information on trait expression (Supplementary Fig. 6). Following standard approaches5,15,29,30, all traits were log-transformed and standardized to allow for statistically robust comparisons. Environmental predictors included ten variables encompassing climate37,38,39,40, soil41, topographic42, and geological43 features. Phylogenetic history was incorporated via the first ten phylogenetic eigenvectors44,45 (see Methods). By including environmental information alongside phylogenetic information, this approach not only allowed us to impute species-level traits which have strong phylogenetic signals and weak environmental signals, as is traditionally done17,30 but also to robustly estimate traits which have a weak phylogenetic signal and are instead strongly sensitive to environmental conditions. Moreover, being a non-parametric approach, the random forest makes no a priori assumptions about how trait expression varies across phylogenetic groups or environments.Across all 18 traits, the best-fitting models explained 54 ± 14% of out-of-fit trait variation (VEcv, see Methods), ranging from 26% for stem diameter to 76% of the variation in leaf area (Supplementary Figs. 6, 7). This accuracy was quantified using buffered leave-one-out cross-validation to account for spatial and phylogenetic autocorrelation46, and thus serves as a conservative lower bound for species which are phylogenetically and environmentally distinct from the observations47. There was no significant relationship between out-of-fit cross-validation accuracy and sample size (R2 = 0.06, p = 0.33), highlighting the relatively broad taxonomic coverage for each trait (Fig. 1, Supplementary Fig. 1).Environmental variables and phylogenetic information had approximately equal explanatory power (relative importance of 0.51 vs 0.49 for environment vs. phylogeny), albeit with substantial variation across traits (Supplementary Fig. 9). The inclusion of environmental variables increased the explanatory power of the models by 35%, on average (Supplementary Fig. 6), with crown diameter, crown height, leaf density, and stem diameter exhibiting the largest relative increases (54%, 45%, 73%, and 26%, respectively), mirroring the fact that these traits have comparatively low phylogenetic signal relative to other traits (assessed via Pagel’s λ on the raw data, Fig. 4c). Seed dry mass was the only trait with a substantial increase in accuracy using the phylogeny-only model (25% improvement; Supplementary Fig. 6), reflecting the fact that seed dry mass had the strongest phylogenetic signal of all traits (Fig. 4c), and also because this trait has a substantial amount of additional non-georeferenced data that was included in the phylogeny-only models (Fig. 1b). Wood density was the only trait with nearly identical predictive power whether or not environmental information was included, whereas all other traits exhibited significantly reduced accuracy when environmental information was excluded (Supplementary Fig. 6).Relationships in tree trait expressionUsing the resulting trait models, we imputed missing trait values for every tree with at least one georeferenced trait measurement. For all traits except seed dry mass, we used the random-forest models accounting for environmental and phylogenetic information; for seed dry mass, we used the phylogeny-only model to estimate expression due to its substantially higher data availability and out-of-fit accuracy. For tree height, stem diameter, crown height, crown width, and root depth, we used quantile random forest48 to estimate the upper 90th percentile value for each species in its given location, thereby minimizing ontogenetic variation across a tree’s lifetime (see Methods). We used the resulting trait data to explore the dominant drivers of trait variation using species-weighted principal component analysis, accounting for an unequal number of observations across species.When considering all traits simultaneously, the first two axes of the resulting principal components (PC) capture 41% of the variation in overall trait expression (Fig. 2a; Supplementary Fig. 10; Supplementary Table 5). The first trait axis correlates most strongly with leaf thickness, specific leaf area, and leaf nitrogen (PC loadings of L = 0.77, 0.74, and 0.73, respectively). By capturing key aspects of the leaf-economic spectrum14, these traits reflect various physiological controls on leaf-level resource processing, tissue turnover and photosynthetic rates49. Thick leaves with low specific leaf area (SLA) can help minimize desiccation, frost damage, and nutrient limitation, but at the cost of reduced photosynthetic potential due to primary investment in structural resistance50. Accordingly, leaf nitrogen—a crucial component of Rubisco for photosynthesis51—trades off strongly with leaf thickness. This first axis thus captures the core distinction between “acquisitive” (fast) and “conservative” (slow) life-history strategies across the plant kingdom7,52, reflecting an organismal-level trade-off between the high photosynthetic potential in optimal conditions versus abiotic tolerance in suboptimal conditions. Nevertheless, leaf density—which is related to SLA and is a key feature of the leaf-economic spectrum—loads relatively weakly on this first trait axis compared to other leaf traits (L = −0.28 for axis 1, vs 0.20 for axis 2; Supplementary Table 5), highlighting important aspects of leaf structure that are not captured by this dominant trait axis53.Fig. 2: The dominant trait axes and relationships.Shown are the first two principal component axes capturing trait relationships across the 18 functional traits. a All tree species (n = 30,146 observations), b angiosperms only (n = 24,658), and c gymnosperms only (n = 5498). In a the three variables that load most strongly on each axis are shown in dark black lines, with the remaining variables shown in light grey. These same six variables are highlighted in b and c illustrating how the same relationships extend to angiosperms and gymnosperms (see Supplementary Figs. 10–12 for the full PCAs with all traits visible, and Supplementary Table 5 for the PC loadings).Full size imageThe second trait axis correlates most strongly with maximum tree height (PC loading of L = 0.77), crown height, (L = 0.75), and crown diameter (L = 0.88), highlighting the overarching importance of competition for light and canopy position in forests7 (Fig. 2a; Supplementary Fig. 10; Supplementary Table 5). Large trees and large crowns are critical for light access and for maximizing light interception down through the canopy54. Nevertheless, tall trees with deep crowns also experience greater susceptibility to disturbance and mechanical damage, primarily due to wind and weight25. Because of the massive carbon and nutrient costs required to create large woody structures55,56, larger trees are less viable in nutrient-limited or colder climates57, and in exposed areas with high winds or extreme weather events58. This second axis thus reflects a fundamental biotic/abiotic trade-off related to overall tree size, which is largely orthogonal to leaf-level nutrient-use and photosynthetic capacity.Despite substantial differences in wood and leaf structures between angiosperms and gymnosperms (e.g. vessels vs. tracheids), the two main relationships hold within, as well as across, angiosperms and gymnosperms (Fig. 2b, c; Supplementary Figs. 11, 12). Indeed, angiosperms and gymnosperms are subject to the same physical, mechanical, and chemical processes that determine the ability to withstand various biotic and abiotic pressures59.Collectively, these two primary trait axes capture two dominant ecological trade-offs that underpin tree survival in any given environment: (1) the ability to maximize leaf photosynthetic activity, at the cost of increased risk of leaf desiccation, and (2) the ability to compete for space and maximize light interception, at the cost of increased susceptibility to mechanical damage. By capturing two aspects of conservative-acquisitive life-history strategies, these two relationships closely mirror those seen when considering herbaceous species alongside woody species5,17. However, in line with our expectations, these two axes capture only ~40% of the variation in trait space, versus nearly ~75% of variation when considering only six traits across the entire plant kingdom5. Here, the first seven PC axes are needed to account for 75% of the variation across all 18 traits (Supplementary Table 5). Thus, while this analysis supports the universality of these two primary PC axes, it also demonstrates that the majority of trait variation in trees is unexplained by these two dimensions. As such, quantifying the full dimensionality of trait space by exploring multidimensional trait clusters is needed to better capture the wide breadth of tree form and function.Environmental predictors of trait relationshipsTo examine how environmental variation shapes trait expression across the globe, we next quantified the relationships between environmental conditions and the dominant trait axes. Using Shapley values60, we partitioned the relative influence of each environmental variable on the PC trait axes, controlling for all other variables in the model (see Methods).In line with previous analysis across the plant kingdom61, temperature variables were the strongest drivers of trait relationships (Fig. 3, Supplementary Figs. 17, 18), with annual temperature having the strongest influence both on leaf-economic traits (PC axis 1, Fig. 3c) and on tree-size traits (PC axis 2, Fig. 3d). Leaves face increased frost risk and reduced photosynthetic potential in colder conditions, such that ecological selection should favour thick leaves with low SLA over thin leaves with high SLA and high nutrient-use49. Trees in warm environments are more likely to experience strong biotic interactions, which should increase evolutionary and ecological selection pressures over time62,63, favouring tall species with large crowns that have high competitive ability and efficient light acquisition strategies. Annual temperature thus predominantly reflects the transition from gymnosperm- to angiosperm-dominated ecosystems, with this inflection point occurring at ~15 °C for both axes, demonstrating strong environmental convergence between the dominant axes of trait variation.Fig. 3: The relationship between environmental variables and trait axes.a, b The relative influence of the environmental variables on the two dominant PC axes. The ten variables are sorted by overall variable importance in the models (see Methods). Yellow points are observations which have high values of that environmental variable; blue values are the lowest. Points to the right of zero indicate a positive influence on the PC axis; points to the left indicate a negative influence (see also Supplementary Figs. 17, 18). c–h The relationships between environmental variables and PC axis values for the three variables in a with the strongest influence. Values above zero show a positive influence on PC axis values; values less than zero indicate a negative influence.Full size imageBeyond annual temperature, each trait axis demonstrated different relationships with climate, soil, and topographic variables (Fig. 3a, b, Supplementary Figs. 17, 18). Percent sand content had the second-highest influence on the first trait axis (Fig. 3e), supporting patterns seen across the entire plant kingdom17. Sand content is a strong proxy for soil moisture and soil-available nutrients such as phosphorous, and is therefore closely tied to leaf photosynthetic rates64. In contrast to previous work, however, we find that soil characteristics have correspondingly little effect on the second axis of trait variation (Fig. 3b; Supplementary Fig. 18). Instead, precipitation was the second strongest driver of tree height and crown size (Fig. 3f), with large trees with large crowns becoming consistently more frequent with increasing precipitation. These results highlight that, despite the primary importance of temperature, the main climate stressors to trees (e.g. xylem cavitation and embolism, fire regimes, and leaf desiccation) typically arise via interactions between temperature, soil nutrients, and water availability.For both axes, elevation was the third strongest driver of trait values (Fig. 3g, h), highlighting a critical component of tree functional biogeography that extends beyond climate and soil. Yet the effects of elevation on trait expression differed somewhat across the two axes. For the first axis related to leaf-economic traits, there is little influence at low elevations, followed by a sharp transition at ~2000 m towards gymnosperm-dominated species with thick leaves, low SLA, and low leaf N. For the second trait axis related to tree size, elevation instead has a strong positive influence on tree height and crown size at low elevations, which becomes increasingly less influential past ~500 m. Such results partly reflect the transition from angiosperm to gymnosperm-dominated stands at higher elevations (blue vs. red points, Fig. 3g, h), and potentially the role of environmentally mediated intraspecific variation in traits such as tree height65,66.These results demonstrate close alignment of the dominant trait PC axes across biogeographic regions. Despite the orthogonality of these axes in trait species, environmental conditions place similar constraints on both trait axes, particularly at the environmental extremes (e.g. warm, moist, low elevation vs. cold, dry, high elevation), leading to convergence of the dominant trait axes across environmental gradients.Trait clusters at the global scaleTo better explore the multidimensional nature of trait relationships that are not fully covered by the dominant two axes, we subsequently identified groups of traits that form tightly coupled clusters and which reflect distinct aspects of tree form and function.Our results show that these 18 traits can be grouped into eight trait clusters, each of which reflects a unique aspect of morphology, physiology, or ecology (Fig. 4a, Supplementary Fig. 23). The largest trait cluster (Fig. 4a, pink cluster) demonstrates wood/leaf integration of moisture regulation and photosynthetic activity via the inclusion of leaf area, stem conduit diameter, stomatal conductance, and leaf Vcmax (the maximum rate of carboxylation). Distinct from this cluster are the three traits loading most strongly on PC axis 1 (SLA, leaf thickness and leaf N; Fig. 4a, yellow), highlighting complementary aspects of the leaf-economic spectrum indicative of acquisitive vs. conservative resource use15. The role of leaf K and P in leaf nutrient economies are well established7,67, and yet these traits form a distinct cluster from the other leaf-economic traits (Fig. 4a, light blue) due to their relatively high correlation with tree height and crown size, particularly for leaf K, which loads almost equally on both trait axes (Fig. 4b, Supplementary Table 5).Fig. 4: Trait correlations and functional clusters.a Trait clusters with high average intra-group correlation. The upper triangle gives the species-weighted correlations incorporating intraspecific variation. The lower triangle gives the corresponding correlations among phylogenetic independent contrasts, which adjusts for pseudo-replication due to the non-independence of closely related species. The size of the circle denotes the relative strength of the correlation, with solid circles denoting positive correlations and open circles denoting negative correlations (see Supplementary Fig. 19 for the numeric values). b PC loadings for each trait and each of the first two principal component axes, illustrating which functional trait clusters align most strongly with the dominant axes of trait variation (see Supplementary Table 5 for the full set of PC loadings). c The species-level phylogenetic signal of each trait (Pagel’s λ), calculated using only the raw trait values.Full size imageTree height and crown size form their own distinct cluster (Fig. 4a, dark green), further supporting the inference that these traits reflect key aspects of tree form and function independent of the leaf-economic spectrum. Yet leaf area, despite being part of the cluster reflecting moisture regulation and photosynthetic activity, loads almost equally on PC axes 1 and 2 (Fig. 4b, Supplementary Table 5), highlighting that it serves as an intermediary between the two key aspects of tree size and leaf economics. It is a critical driver of moisture regulation and photosynthetic capacity, while also playing an important role in the light acquisition, leaf-turnover time, and competitive ability54,68.There are two additional two-trait clusters, both of which load relatively poorly on the two primary PC axes: (1) stem diameter and bark thickness (Fig. 4, dark blue), and (2) wood and leaf density (Fig. 4, light green). Bark thickness increases with tree size not only as a result of bark accumulation as trees age, but also due to the functional/metabolic needs of the plant69,70. From an ecological perspective, thick bark can be critical for defense against fire and pest damage (mainly a thick outer bark region), for storage and photosynthate transportation needs (mainly a thick inner bark region)71,72. Yet such relationships are strongly ecosystem-dependent, with tree size emerging as the dominant driver at the global scale70. In contrast, wood density and leaf density are strongly linked to slow/fast life-history strategies, where denser plant parts reduce growth rate and water transport6,15 but protect against pest damage, desiccation, and mechanical breakage6,50,56. As such, leaf density captures fundamentally unique aspects of leaf form and function relative to other leaf traits such as SLA53 (Fig. 4b, Supplementary Table 5), and our results support the inference that these translate into fundamentally different ecological strategies73. Collectively, these two-trait clusters each demonstrate unique and complementary mechanisms that insulate trees against various disturbances and extreme weather events, but at the cost of reduced growth, competitive ability, and productivity under optimal conditions (see Supplementary Notes).Lastly, two traits each comprise their own unique cluster: root depth and seed dry mass (Fig. 4a, purple and orange, respectively). Root growth is subject to a range of belowground processes (e.g. root herbivory, depth to bedrock), and our results confirm previous work demonstrating a clear disconnect between aboveground and belowground traits23,74,75. Root depth accordingly has a relatively weak phylogenetic signal (λ = 0.44, Fig. 4c) but a strong environmental signal (Supplementary Figs. 6, 9), reflecting distinct belowground constraints on trait expression23. In contrast, seed dry mass exhibits the strongest phylogenetic signal (λ = 0.98, Fig. 4c) and weakest environmental signal of any trait (Supplementary Figs. 6, 9), and it accordingly was the only trait where the phylogeny-only model performed substantially better (Supplementary Fig. 6). In line with previous work, seed dry mass has moderate correlations with various other traits underpinning leaf economics and tree size5,28 (e.g. ρ = 0.28, −0.22, and 0.22 for tree height, leaf K, and leaf density, using the raw data), yet it exhibits relatively weak correlation with most other traits, placing it in a distinct functional cluster. Reproductive traits are subject to unique evolutionary pressures26, indicative of different seed dispersal vectors (wind, water, animals) and various ecological stressors that uniquely affect seed viability and germination26. The emergence of root depth and seed dry mass as solo functional clusters thus supports the previous inference that belowground traits74 and reproductive traits26 reflect distinct aspects of tree form and function not fully captured by leaf or wood trait spectrums. More

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Model structureWe used the PoPS (Pest or Pathogen Spread) Forecasting System11 version 2.0.0 to simulate the spread of SLF and calibrated the model (Fig. 6) using Approximate Bayesian Computation (ABC) with sequential Markov chain and a multivariate normal perturbation kernel18,19. We simulated the reproduction and dispersal of SLF groups (at the grid cell level) rather than individuals, as exact measures of SLF populations are not the goal of surveys conducted by USDA and state departments of agriculture. Reproduction was simulated as a Poisson process with mean β that is modified by local conditions. For example, if we have 5 SLF groups in a cell, a β value of 2.2, and a temperature coefficient of 0.7, our modified β value becomes 1.54 and we draw five numbers from a Poisson distribution with a λ value of 1.54. β and dispersal parameters were calibrated to fit the observed patterns of spread. For this application of PoPS, we replaced the long-distance kernel (α2) with a network dispersal kernel based on railroads, along which SLF and tree of heaven are commonly observed7. For each SLF group dispersing, if a railroad is in the grid cell with SLF, we used a Bernoulli distribution with mean of γ (probability of natural dispersal) to determine if an SLF group dispersed via the natural Cauchy kernel with scale (α) or along the rail network. This network dispersal kernel accounts for dispersal along railways if SLF is present in a cell containing a rail line. The network dispersal kernel added three new parameters to the PoPS model: a network file that contained the nodes and edges, minimum distance that each railcar travels, and the maximum distance that each railcar travels. Unlike typical network models, which simulate transport simply between nodes, our approach allows for SLF to disembark a railcar at any point along an edge, more closely mimicking their actual behavior. This network therefore captures the main pathway of SLF long-distance dispersal, i.e., along railways.Fig. 6: Model structure for spotted lanternfly (SLF, Lycorma delicatula).Unused modules in the PoPS model are gray in the equation. a The number of pests that disperse from a single host under optimal environmental conditions (β) is modified by the number of currently infested hosts (I) and environmental conditions in a location (i) at a particular time (t); environmental conditions include seasonality (X) and temperature (T) (see supplementary Fig. 3 for details on temperature). Dispersal is a function of gamma (γ), which is the probability of short-distance dispersal (alpha-1, α1) or long-distance via the rail network (N (dmin, dmax)). For the natural-distance Cauchy kernel, the direction is selected using 0-359 with 0 representing North. For the network kernel, the direction along the rail is selected randomly, and then travel continues in that direction until the drawn distance is reached. Once SLF has landed in a new location, its establishment depends on environmental conditions (X, T) and the availability of suitable hosts (number of susceptible hosts [S] divided by total number of potential hosts [N]). b We used a custom host map for tree of heaven (Ailanthus altissima) to determine the locations of susceptible hosts. The number of newly infested hosts (ψ) is predicted for each cell across the contiguous US.Full size imageSpotted lanternfly model calibrationWe used 2015–2019 data (over 300,000 total observations including both positive and negative surveys) provided by the USDA APHIS and the state Departments of Agriculture of Pennsylvania, New Jersey, Delaware, Maryland, Virginia, and West Virginia to calibrate model parameters (β, α1, γ, dmin, dmax). The calibration process starts by drawing a set of parameters from a uniform distribution. Simulated results for each model run are then compared to observed data within the year they were collected, and accuracy, precision, recall, and specificity are calculated for the simulation period. If each of these statistics is above 65% the parameter set is kept. This process repeats until 10,000 parameter sets are kept; then, the next generation of the ABC process begins: the mean of each accuracy statistic becomes the new accuracy threshold, and parameters are drawn from a multivariate normal distribution based on the means and covariance matrix of the first 10,000 kept parameters. This process repeats for a total of seven generations. Compared to the 2020 and 2021 observation data (over 100,000 total observations including both positive and negative surveys), the model performed well, with an accuracy of 84.4%, precision of 79.7%, recall of 91.55%, and specificity of 77.6%. In contrast, a model run using PoPS’ previous long-distance kernel (α2) instead of the network dispersal kernel had an accuracy of 76.5%, precision of 68.1%, recall of 92.68%, and specificity of 57.2%.We applied the calibrated parameters and their uncertainties (Fig. 7) to forecast the future spread of SLF, using the status of the infestation as of January 1, 2020 as a starting point and data for temperature and the distribution of SLF’s presumed primary host (tree of heaven, Ailanthus altissima) for the contiguous US at a spatial resolution of 5 km.Fig. 7: Parameter distributions.a Reproductive rate (β), b natural dispersal distance (α1), c percent natural dispersal (γ), d minimum distance (dmin), e maximum distance (dmax).Full size imageWeather dataOverwinter survival of SLF egg masses, and therefore spread, is sensitive to temperature (see ref. 2). To run a spread model in PoPS, all raw temperature values are first converted to indices ranging 0–1 to describe their impact on a species’ ability to survive and reproduce. We converted daily Daymet20 temperature into a monthly coefficient ranging 0–1 (Supplementary Fig. 1) and then rescaled from 1 to 5 km by averaging 1-km pixel values. We used weather data 1980–2019 and randomly drew from those historical data to simulate future weather conditions in our simulations, to account for uncertainty in future weather conditions.Tree of heaven distribution mappingSLF is known to feed on >70 species of mainly woody plants7, but tree of heaven is commonly viewed as necessary, or at least highly important, for SLF spread. Young nymphs are host generalists, but older nymphs and adults strongly prefer tree of heaven (in Korea21; in Pennsylvania, US22), and experiments in captivity23 and in situ9 have shown that adult survivorship is higher on the tree of heaven and grapevine than other host plants, likely due to the presence and proportion of sugar compounds important for SLF survival23. Secondary compounds found in tree of heaven also make adult SLF more unpalatable to avian predators24, and researchers have hypothesized that these protective compounds may be passed on to eggs21. For these reasons, tree of heaven is widely considered the primary host for SLF and linked to SLF spread1,25.We, therefore, used tree of heaven as the host in our spread forecast. We estimated the geographic range of tree of heaven using the Maximum Entropy (MaxEnt) model26,27. We chose to use niche modeling because tree of heaven has been in the US for over 200 years and is well past the early stage of invasion at which niche models perform poorly; instead, tree of heaven is well into the intermediate to equilibrium stage of invasion, when niche models perform well28. We obtained 19,282 presences for tree of heaven in the US from BIEN29,30 and EDDmaps31 and selected the most important variables from an initial MaxEnt model of all 19 WorldClim bioclimatic variables32. Our final climate variables were mean annual temperature, precipitation of the coldest quarter, and precipitation of the driest quarter. Given that tree of heaven is non-native and invasive in the US, prefers open and disturbed habitat, and is commonly found along roadsides and in urban landscapes33, we also included distance to major roads and railroads as an additional variable in our model, to account for the presence of disturbed habitat as well as approximate urbanization and anthropogenic degradation. For each 1-km cell in the extent, we calculated distance to the nearest road and nearest railroad using the US Census Bureau’s TIGER data set of primary roads and railroads34. We used our final MaxEnt model to generate the probability of the presence of tree of heaven for each 1-km cell, then reset all cells with a probability ≤0.2 to a value of 0 to minimize overprediction of the tree of heaven locations (because cells ≤0.2 contained less than 1% of the presences used to build the model). We rescaled the remaining probability values 0–1. We used 10% of the tree of heaven presence data to validate the model, which performed well: 95% of the validation data set locations had a probability of presence greater than 65%. We then rescaled the 1-km MaxEnt output to 5 km using the mean value of our 1-km cells, in order to reduce computational time.Forecasting spotted lanternflyWe used the Daymet temperature data and distribution of tree of heaven to simulate SLF spread with PoPS, assuming no further efforts to contain or eradicate either tree of heaven or SLF. We ran the spread simulation 10,000 times from 2020 to 2050 for the contiguous US. After running all 10,000 iterations, we created a probability of occurrence for each cell for each year by dividing the number of simulations in which a cell was simulated as being infested in that year by 10,000 (the total number of simulations). This gave us a probability of occurrence per year. We downscaled our probability of occurrence per year from 5 km to 1 km and set the probability to 0 in 1-km pixels with no tree of heaven occurrence.Data for mapping and comparisonWe compared our probability of occurrence map in 2050 to the SLF suitability map created by Wakie et al.1 using niche modeling to see how well the two modeling approaches would agree if SLF were allowed to spread unmanaged (Fig. 5). Wakie et al.1 categorized pixels below 8.359% as unsuitable, between 8.359% and 26.89% as low risk, between 26.89% and 51.99% as medium risk, and above 51.99% as high risk. To facilitate comparison, we used this same schema to categorize pixels as low, medium, or high probability of spread.We converted the yearly raster probability maps to county-level probabilities in order to examine the yearly risk to crops in counties. We performed this conversion using two methods: (1) the highest probability of occurrence in the county (Supplementary Movie 2) and (2) the mean probability of occurrence in the county (Fig. 1 and Supplementary Movie 1). The first method provides a simple, non-statistical estimate of the probability of SLF presence by assigning the county the value of the highest cell-level probability; the second accounts for all of the probabilities of the cells in the county and typically results in a higher county-level probability. We used USDA county-level production data10 for grapes, almonds, apples, walnuts, cherries, hops, peaches, plums, and apricots to determine the amount of production at risk each year (Fig. 2).Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More