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Renewal processes represent development under variable conditionsThe consequence of a drastic environmental change can be demonstrated by introducing a shift in development time during the process. For demonstration, we consider a scenario where a group of individuals enter into a favourable environment reducing development time from (40pm 5) time units to (20pm 5).We show, in Fig. 1, that our dynamic pseudo-stage-structured MPM yields a gradual stage completion with an average development time of approximately (30pm 5) steps (solid dark lines) when conditions shift at ({tau }=20) (each step corresponds to 1 time unit). The target Erlang-distributed development trajectories without the shift are shown as dashed gray lines. The snapshots of the population structure, represented by the development indicator q, taken at each time step, show that half of the development is complete at the time of the switch and the switch accelerates the accumulation of q (Fig. S1).Figure 1Response to change in development time. The number of developing individuals is simulated by using the cumulative development process and compared to (a) the age-dependent development process, (b) an ODE representation, (c) an LCT representation, and (d) a DDE representation. Solid dark lines show the cumulative development and thick blue lines show the alternative models. Dashed gray lines mark the two target trajectories before and after the shift in development time (marked with red crosses).Full size imageIn age-dependent development, a sharp transition, instead of a gradual one, is observed at the (20^{th}) step (Fig. 1a). The switch results in the majority of individuals reaching target development age immediately at the time of switch. Previous work, reported in Erguler et al.59 and Erguler et al.55, aimed at modelling population dynamics under variable conditions, based on this dynamic age-dependent framework. Our results suggest that cumulative development might improve the fit to the data, prediction accuracy, and applicable geospatial range of these models.We see in Fig. 1b that the canonical ODE framework represents an exponentially distributed development time and a shift in rate at (t=20). The LCT extension to the framework helps to incorporate time dependence and represent the long and short development time distributions (Fig. 1c). The resulting model accommodates change in the rate parameter (gamma ) (Eq. 8), e.g doubling of (gamma ) changes development time from (40pm 5) to (20pm 2.5). However, to accommodate the required shift, the model needs to be transformed from a 66-dimensional system to an 18-dimensional one, which is beyond the scope of this work. We argue that in cases where development time distribution is fixed a priori (excluded from model calibration), the LCT framework provides a significant advantage over canonical ODEs. Although the framework has been used in the field of infectious disease epidemiology64,65, it has recently been applied to the modelling of vector population dynamics30.The DDE framework also yields a gradual development trajectory with an intermediate duration (Fig. 1d). However, the distribution tends towards the longer development trajectory compared to the one achieved with cumulative development. The canonical DDE framework assumes a homogenous cohort, where all individuals react in the same way to variations in development rate. The assumption gives rise to sharp stage transitions within a single generation if all individuals are introduced at the same time. As a potential workaround, it has been proposed to generate a plausible population history, through variable entry times, until the required (or observed) developmental variation builds up31,32. Variation in development rates then acts upon the population and results in the modification of the existing age-structure. It is worthwhile to mention that a recent extension to the DDE framework to accommodate trait variation in population dynamics34 might also accommodate changing development rates within a single stage; however, it has not yet been employed at this scale.Cumulative development is in agreement with the widely known degree-day (DD) framework, where development time is predicted by the heat accumulating in organisms46. Although the rate of accumulation in response to environmental conditions varies considerably, the DD framework implies that the combination of two different rates yields an average development time (also seen with cumulative development in Fig. 1). Experimental evaluation of this will be the topic of future research.It is worth mentioning that our dynamically structured renewal process-based MPM follows the assumption of random population heterogeneity9,11; namely, at the individual level, the future behaviour of an organism is not affected by its historical behaviour. However, trait variation within a population is prevalent in many species, and is known to impact population dynamics and species interactions34,66,67. Future development of our framework will consider improving upon this limitation.Environmental variation transformed into development timesSeveral non-linear relationships have been proposed to represent the temperature dependence of insect development68. A common feature is the presence of low and high temperature thresholds beyond which development is prohibitively slow. Often, there exists an optimum between the thresholds where the process is most efficient. A typical relationship between temperature and development rate, reported in Briere et al.50, is seen in Fig. 2a. Mean development time, given by the reciprocal of rate in Fig. 2b, exhibits the two thresholds and the optimum.Figure 2Development under environmental variation. In (a), development rate (Eq. 9) is shown with (alpha =1.5times 10^{-5}), (T_L=0^oC), and (T_H=50^oC). In (b), mean development time is shown together with the probability densities of three temperature regimes ((rho _L), (rho _M), and (rho _H)). In (c), the number of individuals completing development at each step are shown with respect to the three temperature regimes. Solid lines indicate the median, shaded areas indicate the (90%) range of 1000 simulations, and thick lines indicate simulations with the expected values of each regime.Full size imageTo investigate how temperature variation is transformed into cumulative development time, we assumed three variation regimes at relatively low, medium, and high temperatures ((rho _L), (rho _M), and (rho _H), respectively). Densities of the corresponding Gaussian probability distributions are plotted in Fig. 2b. Accordingly, each variation is transformed by a slightly different region of the rate function (Eq. 9). Eventually, the three development time distributions emerge as shown in Fig. 2c.We found that the output of (rho _H) is skewed towards longer durations compared to what we would otherwise obtain if we simulated the process under constant conditions with the mean of (rho _H). The impact of variation in the middle range, (rho _M), is similar to that of (rho _H), but less pronounced. Conversely, the output of (rho _L) is skewed towards shorter durations. Our results suggest that, when development is already highly efficient, variation in temperature causes frequent encounters of longer (but not shorter) development durations, eventually extending the overall duration of the process. In the low efficiency range, development takes long to complete, but frequent encounters of relatively short durations—especially as the process approaches its optimum duration—triggers completion earlier than in the case of no variation.Overall, our model predictions are in agreement with the rate summation effect, which states that the different outcomes obtained under constant and varying temperatures is due to the non-linear relationship between temperature and development rate (the Kaufmann effect)16. Furthermore, acceleration of development in insects subjected to varying high temperatures, its retardation at varying low temperatures, and low variability of development time in the linear range of the rate curve have been widely discussed69. Several groups have reported evidence in support of this effect, which is also in agreement with our results. For instance, Vangansbeke et al. (2015) reported for three insect species, Phytoseiulus persimilis, Neoseiulus californicus, and Tetranychus urticae, that varying temperatures with a lower mean yields faster development compared to the yield at mean constant temperatures70. However, observations of this phenomenon might result in different responses for different species at similar temperatures due to the difference in rate curves. Identification of the optimum temperature range may facilitate comparison. For instance, Carrington et al. (2013) assumed (26^oC) as optimum based on the high dengue incidence in Thailand, and showed that large variations around (26^oC) increases development time for the dengue vector, Aedes aegypti71. Wu et al. (2015) demonstrated that development is faster at around (26^oC) compared to (23^oC) for the fly, Megaselia scalaris, and found that varying temperatures at around (23^oC) accelerates the process47. Finally, in a modelling study employing DDs, Chen et al. (2013) reported that larger diurnal temperature ranges relate to additional DD accumulation and faster development in grape berry moth, Paralobesia viteana72. Under the realistic non-optimum field conditions, where these simulations had been performed, a decrease in development time is expected in response to varying temperatures according to our results.We note that the variation in development times is due to temperature since we ignore intrinsic stochasticity to demonstrate the impact of (rho ) in isolation. The deterministic setup removes the upper limit in the number of distinct pseudo-stage indicators: a different q emerges from each k, and a different k emerges from each (rho ). Since the number of pseudo-stages quickly exhausts the computational resources, we set the precision of q to the nearest 100(^{th}) decimal point, effectively capping the number of pseudo-stages at 100 (see Accuracy of the pseudo-stage approximation). As shown in Fig. S2, the approximation has a negligible impact on accuracy.Environmental dependency extracted from life tables under constant conditionsHaving discussed the importance of environmental variability in development, in this section, we employ a well-established experimental method to unravel the relationship between temperature and development time in a common mosquito species. In contrast to invasive vectors, which effectively render new territories suitable for disease transmission, Culex species pose an imminent threat with their wide distribution and ornitophilic (Cx. pipiens biotype pipiens), mamophilic (Cx. pipiens biotype molestus), and intermixed (their hybrids) blood feeding behaviour. Here, we investigate the temperature dependencies of mortality and development of Cx. quinquefasciatus, the southern house mosquito, which is an important disease vector, widely distributed across the tropics and sub-tropics73,74.To infer the dependencies, we used a generic temperature-driven insect development model, described in Methods, and the life history observations performed at five constant temperatures (15, 20, 23, 27, and (30,^{circ })C) under laboratory conditions60,61. As a result of the inverse modelling procedure, detailed in Methods, we found that the generic model yields an overall match between the simulations and observations. In Fig. 3a, we present a comparison of observed and simulated maximum production and the stage-emergence times for pupae and adults. Here, we define the stage-emergence time as the time taken from the beginning of an experiment to the time when half of the maximum production of a stage (pupa or adult) is observed. In addition, in Fig. S3, we present the comparison of time trajectories separately for each temperature.Figure 3Inverse modelling of Cx. quinquefasciatus environmental dependency. The comparison of observed and simulated maximum pupa (P) and adult (A) production and the corresponding stage-emergence times is given in (a). Observations are represented with dots and simulations with box plots. The environmental dependency of larva and pupa development time (b) and mortality (c), derived by the posterior mode sample (Theta _q), is shown in (b,c). Solid lines represent the median and shaded areas represent the (90%) range.Full size imageWe found that the generic model faithfully replicates the observed development times of larvae and pupae. On the other hand, stage mortalities are predicted well at three temperatures, but are overestimated at 20 or (27,^{circ })C. The impact of temperature on mortality might be more complex than it is captured by the quartic equation (Eq. 11). Optimum survival seen at (27,^{circ })C suggests that the relationship might be non-symmetrical or multimodal. In addition, the observed variability in mortality suggests that the mismatch could also be due to experimental error or the intrinsic stochasticity of the biological processes.We extracted the functional forms of temperature dependence from the posterior samples, shown in Fig. 3b, c, and found that the data inform the model as expected within the temperature range of the experiments ((15{-}30,^{circ })C). Stage durations are well informed, and reflect the low variability seen in the data (the standard deviation is less than 1.5 days at all temperatures for both stages). Accordingly, pupae develop in less than 4 days, which is much shorter than the larva development time (between 10 and 20 days above (20,^{circ })C). The model predicts that the minimum temperature at which development occurs (from the larva stage) is (10.5,^{circ })C, which is close to (10.9,^{circ })C, reported in Grech et al.75.The observed variability in pupa and adult production suggests that survival is a highly stochastic process regardless of the controlled laboratory conditions. A deterministic model, such as the one used in this context, represents the mean of such processes but does not capture their variability. The simulated variability is a result of the uncertainty in parameter estimates. Model parameters contribute unequally to the output as a result of the model structure and the functional forms of temperature dependence, and the data inform certain parameters better than others76,77. For instance, daily mortality, shown in Fig. 3c, is more constrained for larva than pupa, which is likely due to the short duration of the pupa stage—changes in daily mortality have larger consequences as development time increases.We note that a well-informed model yields predictions in the form of verifiable hypotheses; however, these are not necessarily accurate predictions. Model accuracy is assessed when such hypotheses are experimentally tested as part of the cyclic process of model development78. Here, we demonstrated that our modelling framework can be used to derive biologically meaningful inferences and to help improve the understanding of the temperature dependence of Cx. quinquefasciatus.Greater information content of semi-field experimentsThe number of experiments required to test a range of conditions, including different combinations of multiple drivers, may quickly exhaust available resources. Moreover, variable conditions may have a previously unaccounted impact on development and mortality. In this section, we demonstrate that observations performed under variable conditions are valuable sources of information for our modelling framework, which is capable of representing the dynamics under such conditions.Cx. pipiens, the northern house mosquito, is a competent disease vector, widely distributed across the temperate countries in North America, Europe, Asia, and North and East Africa74,79. Unlike Cx. quinquefasciatus, Cx. pipiens biotype pipiens is known to enter a reproductive diapause phase, where adult females arrest oogenesis during harsh winter conditions80,81. When larvae are exposed to short photoperiods and low temperatures during development, they emerge as adults destined to diapause. Although Cx. pipiens biotype molestus has lost the ability to diapause, its immature stages have been reported to retain metabolic sensitivity to photoperiod82,83.To reveal the environmental dependence of the molestus biotype, we exposed its eggs to variable temperatures in semi-field conditions until adult emergence (or loss of cohort). The numbers of viable larvae, pupae, and adults observed in different experimental batches are given in Fig. S4. We employed the extended model with both temperature and photoperiod dependence (see Methods), and calibrated the model against seven of the semi-field experiments, performed in March, May, June, July, August, and September (Fig. S4(a), (b), (d), (f), (g), (i) and (j)).As a result, we found that the model replicates the patterns of abundance emerging in the observations, e.g. stage timing and maximum adult production, reasonably well in most of the experiments, regardless of the times during which they were performed (Figs. S5 and S6). Quantitative evaluation of the agreement reveals that the observed and simulated adult emergence times are less than a week apart (Table 1).Table 1 Comparison of observed and simulated adult emergence time and the total number of adults produced. Simulation output is given in terms of the median and (90%) range.Full size tableOn the other hand, we found that egg and larva mortalities, and also, pupa and adult production are highly variable in the observations (see Fig. S4(c), (f), and (g)). Spikes of larva mortality are seen in Spring and Autumn (especially in May, September, and October). Despite this variability, the difference between the predicted and observed adult production was around 11 or less, except in the case of the experiment E7, which unexpectedly yielded only one pupa and no adults.We obtain relatively large mismatches when predicting larva abundances, specifically where egg mortality is not predicted well (E5, E7, E8, E10, E11, E12). We hypothesise that the stress associated with rearing lab-grown specimens under variable conditions might elevate egg mortality, induce premature hatching, or affect the survival of the larvae produced. Since egg development starts inside gravid females, i.e. under the optimum conditions of the laboratory, the observable part of development subjected to variable conditions remains mainly the hatching behaviour. Consequently, we observed rapid and synchronous completion of the egg stage in all experiments (see Figs. S5 and S6). Being exposed to a narrow range of temperatures, relatively less information can be obtained on the environmental dependency of the egg stage. As a potential improvement, we recommend that future adaptations of the semi-field experiments consider using field-captured adult female mosquitoes as the source of eggs.In addition to egg mortality, we observed spikes of larva mortality in May (E3), July (E8), and in Autumn (E14, E15, and E16). A likely cause of such transient high mortality is brief temperature shifts towards the extremes. However, the rarity of such events prevents the inverse modelling procedure from adequately capturing their impacts on life processes. As a potential improvement, we recommend that the experiments are performed in overlapping time frames, increasing the likelihood of observing the impact of an extreme event at different times during development. We note that the early decline in larva abundance seen in Autumn could be a result of insufficient food supply due to the increased nutritional requirements. According to the proposed metabolic response to short photoperiods, larvae would require additional food to accumulate fat reserves in preparation for diapause, the state where adult females endure several months without feeding. This implies that development takes longer than it would at long photoperiods when subjected to similar temperature regimes.Using the extended model and the semi-field data, we identified the environmental dependencies shown in Fig. 4. The data informed about the temperature dependency of each life stage as well as the photoperiod dependency of larvae. As expected, the overall variability in the inferred dependencies is higher for Cx. pipiens compared to Cx. quinquefasciatus (Fig. 3). We found that the larva and pupa development times closely match the observations reported by Spanoudis et al.62 at long photoperiods (see Fig. S7). However, the development times reported in Kiarie-Makara et al.84 at short photoperiods and moderate temperatures do not suggest a significant impact of daylight, which could be due to the particular strain of Cx. pipiens used in these experiments. As expected, the temperature dependency of egg development was not well informed by the data in the current configuration of the model and the functional forms of environmental dependence.Figure 4Environmental dependency of Cx. pipiens development and mortality inferred from semi-field life table experiments. Solid lines represent the median and shaded areas represent the (90%) range.Full size imageWe found that the photoperiod dependency is significantly non-linear with an average threshold of 13.7 hours of daylight (Fig. 4c). Photoperiod-driven extension in development time (about 1.7 times more at 13:11 h L:D than at 15:9 h L:D) contributes to improving the accuracy of predictions at the end of the high season (Fig. S8). The critical photoperiod (CPP) agrees well with the ones identified for Cx. pipiens biotype pipiens85,86. For instance, Sanburg and Larsen reported that there is an exponential relationship between follicle sizes in adult females (signifying commitment to diapause) and the photoperiods they were exposed to during immature stages85. We inferred a similar (but reverse) gradient between photoperiod and the extension of larva development time from 15 to 12 hours of daylight (Fig. 4c).Risk assessment with annual development profilesWe extrapolated the development dynamics of Cx. pipiens over the calendar year by setting up a hypothetical experiment at the beginning of each week. We simulated the subsequent development dynamics and obtained the annual development profile as shown in Fig. 5. Accordingly, the immature stages begin development from late February and the first adults emerge in May (adults emerging late in May start developing in the experiments set up late in March). The profile is consistent with the regular Cx. pipiens high season in the region.Figure 5Annual development profile of Cx. pipiens in Petrovaradin, Serbia, in 2017. The outcome of each hypothetical semi-field experiment is plotted vertically along the y-axis at the date when the experiment is initiated. The maximum number of adults produced is given in blue, and the time it takes (from the date indicated on the x-axis) to produce half of the maximum is given in green. Solid lines represent the median and shaded areas represent the 90% range of model predictions. Outcomes of the semi-field experiments (dots) are plotted together with the model predictions. The time points marked with circles indicate the experiments used to calibrate the model. Estimated time of first adult emergence is given in the inset.Full size imageAs seen in Fig. 5, predicted adult emergence times agree well with the observations throughout the high season. However, there is a greater variation in the maximum number of adults than the times of emergence (extending to almost (40%) of the possible outcomes in early August). A greater variability (almost (80%) in August) is seen in the corresponding observations, which we transformed into the percentage of eggs emerging as adults (where available) to facilitate comparison. According to the model, variation in adult production is associated with the variation in both development times and mortality during immature stages. We recall that the uncertainty in the informed environmental dependencies is high around relatively less frequently encountered values—especially the lower and higher temperature extremes (Fig. 4). Specifically, egg development times cannot be identified precisely, but immediate hatching of the larvae is predicted between 20 and 25 °C. Consequently, we found that frequent exposure to temperatures outside the well-informed range have a significant impact on the variation in adult production (Fig. S9).We adopt the time of first adult emergence as a proxy of the first generation of adults in the season. According to our model, early adult emergence is a result of shorter development times and higher success rates, which indicates that the temperature conditions allow for an early first generation of adults. An early first generation greatly contributes to an early peak of adult abundance, which may increase the risk of vector-borne disease transmission in humans. For instance, an early peak of abundance may cause an early start of West Nile virus circulation and amplification in Culex pipiens and their avian hosts, which increases the likelihood of virus spillover to humans51,87. Anecdotal evidence shows that the anomalously hot April and May that occurred in 2018 in Serbia shifted the peak of Cx. pipiens abundance forward by more than one month (Petrić et al., unpublished). Similarly, 2018 was the year with the largest number of autochthonous West Nile virus infections throughout Europe (more than the total of the previous seven years together)88,89.In summary, our results showed that the semi-field experiments, when used in combination with our dynamic pseudo-stage-structured MPM, help to develop predictive models and inform over a wide range of environmental conditions. We developed a predictive model of Cx. pipiens biotype molestus development and gained insights into the specifics of temperature and photoperiod dependencies by reducing the need of extensive laboratory data. We used life history observations from 7 experiments performed under semi-field conditions and employed a generic model structure, largely uninformed on the specific environmental dependencies of the species. The cumulative development framework we introduced applies broadly to poikilotherms subjected to highly variable environmental conditions. Although the generic model structure helps to develop exploratory models and identify potential environmental dependencies, accuracy can be improved by customising the models for the known dependencies of particular species. With a straightforward extension of the development model to cover the complete life cycle (with egg laying and density dependence), it is possible to incorporate field observations of eggs or adult mosquitoes, and develop an environment-driven population dynamics model. More

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Site selectionOur study focused on the mixed-conifer zone of the Sierra Nevada which is dominated by Ponderosa pine (Pinus ponderosa), Jeffrey pine (Pinus jeffreyi), Incense cedar (Calocedrus decurrens), White fir (Abies concolor) and California black oak (Quercus kelloggii). Common shrubs include Deer brush (Caenothus integerrimus), Mountain whitethorn (Caenothus cordulatus), Greenleaf manzanita (Arctostaphylos patula) and Prostrate ceanothus (Caenothus prostrates). Study sites in the Eldorado National Forest near Placerville, CA (38°45′N 120°20′W), were in and near the area burned during the King Fire (Fig. 2).We sampled sites in the mixed-conifer zone between 4000–6000 ft in three burn categories: unburned, low-to-moderate severity and high severity. We selected sites that occurred in similar pre-burn habitat (moderate to dense conifer forest) based on remotely-sensed vegetation class data from the California Wildlife Habitat Relationships program (CWHR)16. No site experienced wildfire or controlled burns in the preceding century23. Burn categories were based on remote sensing relative differenced Normalized Burn Ratio (RdNBR) canopy cover calibrated for the Sierra Nevada24. We validated these burn categories as meaningful and discrete with remote sensing (immediately post fire) and field data (3 years post-fire). Monitoring Trends in Burn Severity (MTBS) maps classify burn severity with Landsat reflectance imagery of pre-fire and post-fire conditions at 30-m resolution25. MTBS assigns pixels a value based on burn severity: 0 = outside the burn boundary; 1 = unburned-low severity within the fire perimeter; 2 = low severity; 3 = moderate severity; 4 = high severity). At each site, we determined the mean MTBS value of pixels in the small-mammal trapping grid (90 × 90 m) and a 225 m buffer (the largest home range diameter for small mammals we captured)26 extended on all sides. Immediately after the fire, the three burn categories differed significantly in tree cover and remote sensing scores of burn severity25 and are still different in tree surveys three years later.We sampled 27 sites, each 4 ha in size. To minimize site-specific influences, we paired sites across treatments to account for elevation, slope, pre-burn vegetation characteristics, pre-burn forest management, ownership, and soil type. Each burn category received nine sites. We blocked sites across burn severities (one site in each burn category per block). Site locations were chosen for accessibility, but all sites were at least 50 m from access roads and at least 200 m apart (sites were >1 km apart on average). We also excluded areas that experienced or were scheduled to experience salvage logging post fire. Occasionally, field conditions at a site location did not align with remotely sensed data classifications, a site was not large enough for homogeneous sampling plots or was dominated by slopes >30 degrees. In these cases, sites were moved to nearby locations that satisfied the site selection criteria.Sampling designIn this study we report the body size, abundance and biomass density of plants and free-living animals using a variety of methods in three different fire severities. Each site consisted of a 200 m × 200 m plot (4 ha) around which sampling methods were organized (Fig. 3). We collected data for organisms with 19 different sampling methods that were scaled to the abundance and body size of targeted organisms. Some methods were not performed at all sites, and some methods were pooled across sites (within treatments) due to low sampling success. Below, we explain each sampling method and detail any variation in its application across sites. To minimize seasonal effects, we sampled all sites in a block at the same time, over 4–5 continuous days, between late June and early September 2017. Weather was consistently hot and dry during this period with no pronounced variation. All animal survey procedures were approved by UC Davis IACUC (protocol number CA-17-451736) and carried out under CDFW permit #SC-3638.Species inclusionTo evaluate the effects of wildfire-burn severity on community structure we assembled a list of organisms and life stages encountered during our sampling of the Eldorado National Forest. Every animal in our list was broken into ontogenetic life stages. Plants were broken into constituent parts (e.g. leaves, roots, seeds) rather than stages. Every organism in our lists had at least one life stage observed by this study in the Eldorado National Forest. Not all life stages in the list were directly observed, many were inferred. These life stages were suspected to occur in the habitat but were not observed (or quantified) because (1) it was impractical (e.g. mycorrhizae), (2) our sampling methods did not capture them (e.g. larval insects in plant tissues) or (3) they could not be identified to species (e.g. arthropod eggs). Stages (not species) were excluded when they did not occur in the terrestrial habitat (e.g. aquatic larvae). Stages (or parts) were lumped when they could not be distinguished in terms of their resources or consumers (e.g. parasitoid wasp eggs, larvae and pupae). Unobserved stages were omitted from a burn category community if they were feeding (e.g. not eggs) but did not have any resources. All life stages, observed or not, received a body size estimate.This approach has several benefits. First, it fills life-cycle gaps without artificially inflating species richness (e.g. having a node labelled “bird eggs”). Second, unobserved life stages may not be major biomass contributors, but they do make important contributions to food-web structure and population dynamics. Including life stages without abundance information is useful because it allows their inclusion in analyses of network structure, informs consumer-resource body-size ratios and allows comparisons to other food datasets organized around body size, but lacking abundance estimates.A comprehensive food web required the inclusion of non-living nodes like detritus which is an important resource for many consumers. Fire creates strong spatial structure in woody detritus, so we collected mass-density information on it and partitioned detritus into types (e.g., woody vs. leaf) and size classes. We did not collect mass-density information on carcasses but treated them similarly by partitioning them into logarithmic size classes to reflect their availability to different consumers (e.g., tick carcasses vs. deer carcasses). We have also included the biotic products honeydew and dung due to their importance to certain consumer groups in the system. We have not done so here but future efforts may wish to include nutrients as resources for plants to capture gradients and competition. Finally, analyses may wish to augment our lists by explicitly including fire as a consumer/herbivore as opposed to an external force shaping treatment effects.Below we describe the methods used to quantify the richness, abundance, and biomass density of these organisms in each of our burn categories. Unless noted, sampling effort did not vary with burn category.Species resolutionMost entries in the species list represent ontogenetic stages or constituent parts. With the exception of a few nodes (i.e. algae, moss, lichen, mycorrhizae, saprophytic bacteria, saprophytic fungi and nematodes) this ecological resolution is consistent throughout the list. Taxonomic information was assigned using the Global Biodiversity Information Facility database27, but taxonomic resolution varies. Vertebrates are identified at the species level. Invertebrates, while distinguished as morphospecies, were not identified below the family level in many cases. Despite not always being identified to the lowest taxonomic category, entries represent life stages of distinct species or groups, and are accompanied by all the taxonomic information we could provide at that level of resolution.Biomass density estimationEach species observed in our sampling methods received a biomass density estimate. Biomass density was estimated as the product of mean individual body mass and density. We estimated body-mass either by weighing individuals directly, or conservatively estimating their mass volumetrically. For the latter, we measured the length (tip of abdomen to tip of head), width (max width of body excluding appendages) and depth (max depth of body excluding appendages) of individual organisms and converted into an approximate volumetric shape (e.g. ellipsoid, cylinder, hemisphere, etc.)28,29. Mass was estimated by multiplying this volume by a tissue density of 1.1 g/mL30,31,32. Body sizes for stages that were not directly observed were inferred from published records and databases. Density estimates were derived from the sampling methods discussed below and varied with burn category. Mean and standard errors were derived from the nine replicate sites within each treatment, unless otherwise stated. Due to the brief sampling window at each site, these estimates should be regarded as point estimates rather than integrated over time.Plant samplingVegetation transectsTo estimate density and biomass of trees, shrubs, and ground cover, we conducted vegetation transects at each site. Transects were located within each 200 m × 200 m plot but were offset from other sampling methods by 10 m to avoid trampling. Transect direction was chosen at random and two transects were run in parallel. Each transect was 50 m in length but width (and distance between transects and sampling area) varied with sampling method as detailed below.Ground coverTo estimate plant ground cover, we surveyed 1 m2 quadrats at 5 m intervals on each 50 m transect. Summed, this gave a pooled ground cover sample area of 20 m2 at each site. Within each quadrat we estimated the percent cover and average height of grasses, forbs, woody litter, soft-loose and soft-rooted litter, shrubs, and trees. We identified small trees, shrubs and dominant forbs (i.e., forbs with the greatest cover at a site) to species. We then used cover area and height to estimate a volume for each species or group. Volumes were later multiplied by taxon-specific measurements of mass-to-volume ratios derived from vegetation box quadrats to obtain biomass estimates for each ground cover species or group.Canopy coverTo estimate canopy cover, above each of the 20 ground cover sampling locations, we identified each tree species overhead and estimated its absolute canopy cover. This gave a pooled canopy cover sample area of 20 m2 at each site. Canopy cover estimates were incorporated into arthropod biomass density estimates from fogging.TreesTo estimate tree density, we identified and measured all trees that exceeded 15 cm diameter-at-breast-height (DBH) within a 15 m wide band extending the length of each 50 m vegetation transect. Small trees (DBH 1 cm. We estimated shrub volume (length × width × height) and biomass density by combining volume and density estimates with taxon-specific measurements of mass-to-volume ratios derived from vegetation box quadrats. We estimated above ground biomass for small trees using species-specific DBH-to-biomass conversions33.

Understory plants
To estimate the volume and cover of understory vegetation we used three-dimensional box quadrats. These box quadrats consisted of a canvas-walled rectangular box with the floor panel removed, that was placed over the understory to be surveyed. The canvas walls prevent arthropods from escaping as they were also used in arthropod sampling. Each box quadrat measured 1 m × 0.5 m × 0.5 m, covering a ground area of 0.25 m2. At each site, we placed box quadrats at three locations representative of the dominant vegetation. This gave a pooled sample area of 0.75 m2 at each site. To generate a volume estimate, within each box we estimated the percent cover and maximum height of each plant species. Leaf litter was treated separately but also quantified. Then, using a Velcroed flap as access (designed to prevent bugs from escaping), we collected and weighed all the above ground plant biomass, separated by species and type (litter, branches, leaves, etc.). A subsample of material (up to 1 kg) from each plant species and type was retained and returned to the station to extract the associated arthropods via Berlese funnels (detailed below).
For each plant species measured in the vegetation box samples, we estimated a mass-to-volume ratio. We estimated the biomass of understory plants by combining our mass-to-volume ratios with volume estimates from ground cover transects. For taxa present in ground cover transects but not vegetation boxes, or with fewer than three measurements of mass-to-volume ratio, we pooled measurements from higher taxonomic levels. For example, if there was only one measurement of species A, but two measurements for a congener, species B, we used measurements for both species A and B to represent the mass-to-volume ratio of each. In this way, we estimated mean mass-to-volume ratios for every species-type encountered in the shrub and cover transects.
Coarse woody debrisTo estimate the mass density of woody detritus we quantified it according to the method detailed in Waddell (2002). Specifically, we used the center of the vegetation transect as a line-intercept for woody detritus. Woody debris was recorded if its longitudinal axis intersected the transect line, its diameter at the point of intersection was ≧ 12.5 cm; it was ≧ 1 m long and it was not decayed to the point of disintegration. For each piece of woody detritus, we measured the diameter at both ends, the length, and the stage of decay. Length was measured only for the portion exceeding 12.5 cm in diameter. We estimated the volume (m3) for each piece of debris:$$V{m}^{3}=left.frac{(pi /8)({D}_{s}^{2}+{D}_{L}^{2})l}{10,000}right)$$
(4)
({D}_{S}^{2}) is small diameter (cm), ({D}_{L}^{2}) is the large diameter (cm) and l is the length (m)34. We converted this estimate to a volume-density (m3 ha−1) estimate:$${m}^{3}h{a}^{-1}=left(frac{pi }{2;{L}_{t}}right)left(frac{V{m}^{3}}{{l}_{i}}right)f$$
(5)
Lt is the combined transect length (100 m), lt is the length of the individual piece, f is a conversion for area (10,000 m3 ha−1)34. Finally, we converted this is a dry-weight biomass density (kg ha−1):$$kg;h{a}^{-1}=({m}^{3}h{a}^{-1})left(frac{1000,kg}{{m}^{3}}right)SpGast D$$
(6)
SpG is a specific gravity estimate and D is the correction for the state of decay34. Specific gravity can be a species-specific estimate. Woody debris is difficult to identify to species so we applied a single specific gravity estimate to all debris weighted by the relative abundance of tree species in our surveys. We used a weighted specific gravity of 0.382, estimated by multiplying the mean specific gravity of Pinaceae (0.372) by their relative abundance (0.947) and adding that to the specific gravity of Quercus (0.566) multiplied by their relative abundance (0.053). We applied the weighted means to the decay corrections in Waddell (2002).Species of uncertain identificationSome plant identifications were difficult, particularly at burned sites, where some individuals were identified to genus or family. To assign species identities to individuals classified a higher taxonomic rank at a focal site, we first randomly selected a proxy site from the nine unburned sites. This proxy approach is possible because the composition of burned and unburned sites was similar before the fire. Proxy sites were randomly selected from among all the unburned sites because the spatial grouping didn’t lend itself to maintaining distinctions between blocks. Using the species abundance distribution of the focal plant taxon at the proxy site, we randomly assigned (with replacement) plant species identities to unidentified individual plants at the focal site. We repeated this random sampling 999 times, then estimated the resulting mean species abundance and bootstrapped standard errors at the treatment level.Invertebrate samplingGiven the diversity of invertebrates in the ecosystem, and the biases associated with each invertebrate sampling method, we employed several methods to quantitatively survey the entire community.Arthropods on understory plantsTo estimate the density of arthropods on understory plants we collected them along with plant material in the box quadrats. Up to 1 kg of plant material of each species was bagged inside box quadrats and transported to the field station for processing. Insects were extracted from the plant material in Berlese funnels that were hung in the shade at ambient temperatures and powered with 60 W frosted-incandescent bulbs. All plant samples were processed in funnels for 72 hours, after which they were checked twice a day (collecting jars changed). After no additional arthropods had been collected for 24 hours samples were removed. Arthropods were placed in ethanol for later identification. After identification, arthropod densities were estimated as the product of the arthropod-to-volume ratio for each plant and the total volume of each plant estimated from transects. We collected 4543 individual arthropods from 170 morphospecies associated with plant material from box quadrats, processed in Berlese funnels.Soil-dwelling arthropodsTo estimate the density of soil-dwelling arthropods we collected soil cores. Alongside each box, we collected four cores, each 10 cm in diameter. Two shallow cores were sunk to a depth of 5 cm, giving a combined (6 replicates total) sample area of 0.0471 m2 at each site. Shallow cores, which targeted small arthropods (e.g. collembola, diplura, acari), were collected and transported back to the field station for processing in Berlese funnels. Soil samples were processed in Berlese funnels in the same manner as plant material. Two deep cores were sunk to a depth of 15 cm, giving a combined (6 replicates total) sample area of 0.0471 m2 at each site. Deep cores targeted large invertebrates (e.g. lumbricidae, myriapoda) and were processed by hand in the field. Any large invertebrates encountered were placed in ethanol for later identification. After identification, densities were estimated as the quotient of counts and area sampled. We collected 690 individual arthropods from 57 morphospecies from soil cores.Arthropods on hard substrateTo estimate the density of arthropods like wasps and spiders on tree trunks, rock and logs we visually surveyed these hard substrates. In three locations at each site, we surveyed all hard substrates within a cylinder 5 m in diameter and 2 m in height. The total sample area at each site was 58.9 m2. All invertebrates larger than 2 cm in length were collected and fixed in ethanol for later identification. After identification, hard substrate densities were estimated as the quotient of counts and sample area. Hard substrate surveys yielded 616 individual arthropods from 74 morphospecies.Understory arthropodsTo estimate the arthropod densities associated with understory shrubs at each site we supplemented box quadrats with sweep net surveys. We used nets with a 38 cm diameter opening (Bioquip) to sweep the same 5 m diameter area as the hard substrate surveys. Three replicates at each site gave a total sample area of 58.9 m2. Net sweeps were performed at a constant pace of 2 arcs per meter. All invertebrates collected were fixed in ethanol for later identification. After identification, arthropod densities were estimated as the quotient of counts and sample area. Sweep net surveys yielded 706 individual arthropods from 168 morphospecies.Canopy arthropodsTo survey arboreal arthropods, we used a thermal fogger to loft insecticidal fog into the tree canopy. While this method can sample a large area, we were hampered by permit and accessibility issues at some sites. As a result, we sampled a representative subset of 12 sites (6 unburned, 3 high severity, and 3 low-to-moderate severity) with canopy fogging. Chemical fogging remains the most widely used method for sampling canopy arthropods35,36,37. It is notoriously difficult to assess canopy arthropods with any other method35. We used an IGEBA TF-35 Thermal Fogger to disperse a pyrethrum-based insecticide (EverGreen Crop Protection EC 60-6) into the forest canopy. During each fog we dispersed 4 L of solution (a 7% concentration of insecticide in a water-based carrier-dispersant) in 10 minutes over two representative trees and one live shrub at each site. Live trees were sampled at unburned sites, dead trees were sampled at high severity sites, and one dead and one live tree were sampled at low-to-moderate severity sites. Fogging was done under low-wind conditions allowing the thermal fogger and temperature gradients to lift the fog into the canopy. White 2.25 m2 tarps were placed beneath the fogged area to collect insects. The number of tarps used varied with the size and shape of the canopy. After an optimal elapsed drop-time of 120 minutes37, arthropods were collected from tarps and placed in ethanol for later identification. To estimate site-level arthropod abundance using canopy fogging, we estimated the density per square meter of tarp for each morphospecies and habitat type (living tree, dead tree, or shrub), then multiplied these densities by the total area covered by each habitat type. The area covered by each fogged habitat type was obtained from canopy cover transects (trees) and shrub transects (shrubs). Mean and standard errors for density estimates were estimated using the 3 (or 6) sites per treatment. Canopy fogging yielded 16,353 individual arthropods from 489 morphospecies.Strong-flying insectsTo estimate the diversity and relative abundance of strong-flying arthropods, we utilized blacklight traps (Miniature Downdraft Blacklight (UV) Trap Model 912). We supplemented our sampling with blacklight traps, because strong flying arthropods (e.g. vespid wasps) may not be adequately sampled by fogging or sweep netting. Black lights were deployed at sites prior to dusk on the third night of bat acoustic surveys (see below). Each site received one trap and black lights were not deployed on rainy or windy nights. Samples were collected the following morning. To preserve their integrity for later identification, lepidoptera samples were removed and frozen, other flying insects were fixed in ethanol. Black light traps collected 5,508 individuals from 279 morphospecies.Black light samples were only used to estimate densities for those species not regularly captured with other methods. Two hundred fifteen morphospecies were only found in black light samples. Black light traps, which can sample large areas, are an efficient means of generating diversity estimates for nocturnal flying insects. However, black light traps generate activity densities rather than absolute densities, over sample areas that vary within and between nights. To convert counts to density estimates for morphospecies collected only in black lights we paired them with an analogous species (based on taxonomy and body size). These density analogues were captured at the same site in both black lights and at least one other method with explicit absolute densities. We estimated the mean relative abundance ratios of these species in black lights across all sites in which they co-occurred. We then multiplied the density of the ecological analog by these abundance ratios to estimate densities of all species that were collected only in the black light traps.Larval biomass densityTo estimate the density of larval Formicidae, lepidoptera and coleoptera, we partitioned them according to the relative abundance of their adults present in the same treatments. Larvae for many hemimetabolous invertebrates can be difficult to identify without molecular methods. When larvae could not be identified to species, they were binned into categories of Formicidae, lepidoptera and coleoptera. We then collected body size information and density estimates for these stages. Larval densities were then partitioned according to the relative abundance of adults within each treatment. Adults were eligible to receive larvae if (1) they belonged to the same taxonomic rank as the larvae, (2) they did not already have any observed larval stages, (3) there were available resources for their larvae in the treatment.Vertebrate samplingSmall mammalsTo estimate the density of mammals less than 2.5 kg we used live traps uniformly distributed over a 90 m × 90 m grid38. We placed 100 traps 10 m apart, alternating between large (7.5 cm × 9 cm × 23 cm) and extra-large Sherman traps (10 cm × 11.5 cm × 38 cm)39. Traps were baited (a mix of oats, peanut butter, bird seed and molasses) and covered with natural materials for insulation. Traps were locked open and pre-baited for three days and then operated for three consecutive nights. Traps were closed during the day due to high daytime temperatures and lack of shade, particularly in the high severity burn areas. Traps were re-opened in the late afternoon. Captured mammals were identified to species (or individuals during recaptures), weighed, measured and fit with ear tags for future identification, then released. In 7,906 trap nights (adjusted for trap failures), we had 988 captures of 11 species of small mammals.Live-trapping and marking of small mammals allowed us to estimate their abundance using spatial capture-recapture (SCR) models40. These models use individual detections in combination with detection locations (here, location of a given live trap within the grid) to estimate density while accounting for imperfect detection and variation in detection due to variability in individual exposure to the trapping grid. When data are collected across several trapping grids, as in the present study, the joint modeling of all data allows estimation of grid-level covariate effects on density41. We used this framework to analyze data from all 27 plots jointly and allowed for density to vary according to burn category of a site (unburned, low-to-moderate severity or high severity), so that, for example, all unburned sites had the same density of a given species. If a species was never caught in a burn category, we fixed its density (and consequently, its biomass) to 0 for all sites in that burn category.Because trapping data for most species was too sparse to fit species-specific models, we grouped ecologically similar species and built models that shared parameters among grouped species. In this manner, we analyzed the joint data of mice and chipmunks: Brush mouse (Peromyscus boylii), Deer mouse (Peromyscus maniculatus), Pinyon mouse (Peromyscus truei) and Western harvest mouse (Reithrodontomys megalotis), Yellow-pine chipmunks (Tamias amoenus), Long-eared chipmunks (Tamias quadrimaculatus) and Shadow chipmunks (Tamias senex).In the mouse model, Brush mouse and Pinyon mouse densities were assumed to have the same response to burn category (but not the same densities), whereas Deer mice were allowed a different response to burn category. This choice was made based on capture frequencies of species in the different burn categories. Pinyon mice and Western harvest mice had a fixed density of 0 in low-to-moderate and high severity burn sites. All species shared the same detection parameters.Even combined, the chipmunk data captures were too sparse to estimate species specific densities. We therefore treated all chipmunks like a single species to estimate overall chipmunk density, then calculated species specific densities by multiplying overall density with the proportion of individuals of a given species in the data. For example, if species A made up 50% of all individuals in the data, we would calculate density for species A by multiplying overall chipmunk density by 0.5. This model entails the assumption that the effect of burn category on density was the same for all chipmunks, which seems reasonable based on capture frequencies.We built species-specific SCR models for California ground squirrels (Otospermophilus beecheyi) and Dusky-footed woodrats (Neotoma fuscipes); for the latter we fixed density to 0 in high severity sites. Northern flying squirrels were only caught 3 times at unburned sites, so we set its density to 0 in low-to-moderate and high severity sites, and used a published density estimate from a Sierra Nevada site42 for unburned sites. Because individuals of Trowbridge’s shrew (Sorex trowbridgii) were never recaptured and had high rates of trap mortality, we estimated their abundance using non-spatial removal models43 for unburned and moderately burned sites and set their abundance to 0 at high severity sites. We transformed abundance to density by dividing it by the 8100 m2 area (90 × 90 m) of the live trapping grid.We fit SCR models in R using the package “secr” ver. 3.1.344, and removal models using the package RMark ver. 2.2.445.BirdsTo estimate the diversity and density of birds, we conducted point count surveys46. Each site had two point-count stations, spaced at least 200 m apart, that were surveyed on the same day. Counts were conducted at each site on three different days per season. To mitigate migration effects all counts were conducted between mid-June and mid-July. Bird surveys did not take place when it was raining, extremely cold (20 kmh). Wind speeds were obtained with handheld anemometers. Point counts began 15 minutes after sunrise and were completed by 10:00 AM, corresponding to when passerine birds are most active. Each survey consisted of one ten-minute count, split into two five-minute periods. Each individual bird was recorded only once over the entire count. Trained observers identified all birds to species by sight or sound and estimated the number of individuals of each species within 100 m of the sampling point. This gave us a sample area of 15,708 m2 at each site. Birds that flew through or were detected outside of the survey area or survey time were documented but not included in richness or density estimates. During 162 point-surveys we observed 1,039 birds from 52 species (107 individuals could not be identified).The repeated point counts allowed us to estimate bird abundance and density using N-mixture models47. These models use repeated counts of individuals to estimate abundance within a sampling unit (in this case, the 100 m radius point count) while accounting for imperfect detection. Because abundance estimates refer to a set area, these can be converted to densities. Because data for some bird species were sparse, we fit data of all species jointly in a community model48. In community models, each species has its own set of parameters, but species-specific parameters are modeled as coming from a common underlying distribution that is shared by the community of species (essentially, a species-level random effect). This constitutes a form of information sharing, which improves parameter estimates for data-sparse species. In our community N-mixture model, we allowed for species-specific detection probabilities, as well as species-specific effects of burn category on abundance. We further included a fixed (across species) effect of the amount of wind during a given survey on detection, as wind can impair auditory detection of birds. We implemented the community N-mixture model in a Bayesian framework using the program JAGS ver. 4.2.049 accessed through R with the package jagsUI ver. 1.5.050. JAGS fits models using Markov chain Monte Carlo (MCMC) algorithms; we ran 100,000 MCMC iterations and discarded the first 50,000 as burn-in. We checked for chain convergence using the Gelman-Rubin statistic51; all parameters had a value 2.5 kg we used camera traps. At each site, we deployed two Reconyx HC600 Hyperfire cameras, which have a no-glow infrared flash, preventing disturbance to wildlife and detection by humans. To reduce false triggers, we set cameras in shaded locations and cleared vegetation in front. Cameras were deployed along landscape features that suggested animal movement: game trails, forest openings, abandoned dirt roads, etc. Cameras were set at least 50 m apart and strapped to trees 40 cm above the ground and 1–2 m away from the edge of a trail or opening. Cameras were operated for 24 hours a day, with 3 consecutive pictures per trigger and no time lapse between triggers. All 54 camera traps were installed by early-July and retrieved in mid-September. Cameras were checked after four to six weeks for SD card and battery replacement. All pictures were reviewed manually for species identification; identified pictures of animals were organized into camera and species-specific folders for post-processing in the R computing environment ver. 3.4.352 using the package camtrapR ver. 0.99.553. Even though some bird and small mammal species were occasionally photographed by camera traps, we excluded their photo-records from further analysis. After adjusting for malfunction, cameras operated for 4,238 trapping nights over which they assembled 12,243 independent records (detections that were at least one hour apart if of the same species at the same camera) comprising 10 species of mammals >2.5 kg.Because camera-trap images do not allow identification or counting of individuals for analysis with SCR or N-mixture models, we used the Royle-Nichols (RN) occupancy modeling framework54 to estimate abundance of medium/large mammal species. Occupancy models55 use repeated species detection/non-detection data from a collection of sampling locations to estimate species occurrence probability while accounting for imperfect detection. The RN model makes use of the fact that the probability of detecting a species at a site increases with the abundance of that species at that site, allowing estimation of site-level abundance from species level detection/non-detection data. We used the R package camtrapR53 to convert raw camera trap data for each species into a binary (detected = 1, not detected = 0) location-by-occasion format. Because of their proximity, we considered both cameras at a given plot to constitute a single sampling location. We defined an occasion as 10 consecutive days of sampling. To account for malfunctioning of some cameras, we calculated effort as the number of days per occasion that each pair of cameras was functional.Because data for some species were sparse, we jointly analyzed data for all species in a community RN model (see Birds for a description of community models); we allowed for species-specific detection probabilities as well as species-specific effects of burn category on species abundance and included a fixed effect (across species) of effort on detection. The RN model returns sampling location level estimates of abundance, but in contrast to bird and reptile surveys, which were explicitly linked to a specific sampled area, the area sampled by a camera trap is not easily defined. Mammals recorded in the relatively small detection zone of a camera use much larger areas. We calculated densities of large mammals by dividing the abundance estimates from the RN model by the average home ranges of the recorded species. We fit the community RN model in a Bayesian framework as described for birds, running 30,000 MCMC iterations and discarding the first 15,000 as burn-in. All chains converged, according to the Gelman-Rubin statistic.To obtain estimates for home range size and individual mass of large mammals, we searched the scientific literature for studies conducted in similar habitat (temperate coniferous forests) and for home ranges, during the summer and fall seasons. When no information from a similar habitat was available, we used studies from forested areas. When no information for target species was available, we used information from congeners. When multiple studies were available, we calculated the mean across studies, weighted by sample size if provided. Similarly, when studies provided information separately for males and females, we calculated a weighted mean. For some large mammal species, we only found information on annual home ranges, and to approximate a summer/fall home range, we multiplied these annual ranges by 0.67.BatsTo survey bat community composition and abundance, we conducted acoustic sampling at each site. We placed a Wildlife Acoustics Songmeter SM4BAT FS echolocation detector at each site for a minimum of three consecutive nights. The detectors were set to record from sunset to sunrise when bats are most active. We attached microphones to t-posts placed in open areas, elevating them 2.5 meters from the ground to minimize signal attenuation from nearby vegetation and canopy. Bat calls were analyzed using SonoBat software to assess likely species for each file. These identifications were vetted by an experienced bat researcher, Ted Weller (USDA Forest Service). One site (B3U1) was not sampled with bat detectors, whereas two sites had one and two additional nights sampled, respectively. During 81 recorder nights, acoustic recorders captured 17,484 calls, of which 7348 were identified to 17 species.Similar to camera traps, bat calls recorded by acoustic recorders do not allow counting or identifying individuals. Therefore, we built a community RN model to estimate abundance for bats. The model structure was identical to that described for medium/large mammals, except that it did not include any covariate on detection probability. Analogous to our medium/large mammal analysis, we used literature information on average home range size to convert bat abundance to bat density. We ran the bat model for 150,000 iterations and discarded the first 75,000 iterations as burn-in. All chains converged according to the Gelman-Rubin statistic.ReptilesTo estimate community composition and density of reptiles, we conducted timed searches within the 90 m × 90 m small mammal trapping grids at each site. This gave us a sample area of 8100 m2 at each site. Reptile surveys were conducted either prior to small mammal trapping or two weeks post to minimize impacts from sampling disturbance. Reptile surveys were conducted between 8:00 am and 10:00 am by teams of two to four, for a total of one person-hour. We performed reptile surveys three times at each site, with at least one week between surveys. During searches, all refugia (i.e., rocks, logs) within the plot were carefully overturned and then replaced. In addition to reptile species, we documented time of day and weather, as well as cover type and cover length if applicable. Our reptile surveys yielded 145 records of two snake species and four lizard species. Two additional snake species were observed incidentally during other sampling methods.Repeated counts of reptiles allowed us to use N-mixture models47 to estimate abundance and density. However, reptile data were extremely sparse and contained few species, precluding the use of a full community model as fit for birds. Instead, we structured reptile data into three groups: snakes (Western terrestrial garter snake (Thamnophis elegans) and Yellow-bellied racer (Coluber constrictor)), Alligator lizards (Elgaria coerulea and E. multicarinata) and Western fence lizards (Sceloporus occidentalis). We then combined data from all groups in a single N-mixture model, allowing for group-specific abundances. Due to sparse data, we only estimated an effect of burn category on abundance for fence lizards. Abundance for other species groups was assumed to be constant across burn categories in the model. To obtain species and burn category specific estimates of abundance, we combined model estimates of abundance with raw counts of individuals. For the two snakes, we calculated species level abundance by burn category by multiplying overall model-estimated snake abundance with the proportion of individuals made up by each species in each burn category. Because some Elgaria sp. observations could not be identified to species level, we did not attempt to calculate species specific abundances (but we note that the majority of observations was of E. coerula). We calculated species/group density by dividing abundance by the size of the sampling unit, in this case, a 90 × 90 m square. We fit the N-mixture model in R using the package unmarked ver. 0.12.256.Species identificationVertebrates were identified in the field or from photographs. Invertebrate specimens were collected and fixed in the field for identification in the lab where they were split into morphospecies using published keys57,58 and consultation with experts at the UC Davis Bohart Museum. Morphospecies were not always identified to lower taxonomic levels but were distinguished from similar species by coarse morphological characters. Prior to density estimation some morphospecies were aggregated based on taxonomy, body size, sample methodology, co-occurrence patterns and the difficulty in distinguishing members of the group. The rationales behind aggregations are documented in the raw invertebrate sampling data.Body size estimationFood webs are commonly organized around body size59,60,61,62,63 and we include length and mass estimates for all life stages in our data set. We assume mean body size does not change substantially across burn severities and use a single estimate for all life stages regardless of treatment. When possible, we measured 10 individuals for each morphospecies and life stage (for invertebrates and small mammals only, as individuals from other taxonomic groups were not handled). Body mass for small mammals was measured directly with a Pesola scale. Body length estimates for invertebrates were derived from the longest measurement. Volumetric estimates were derived by applying the measured length, height and width to the three-dimensional shape that most closely approximates that of the organism (e.g. ellipsoid, rectangular prism, cylinder, hemisphere, cone). We estimated biomass by multiplying these volumetric estimates by a tissue density of 1.1 g/mL30.Body sizes for organismal life stages observed but not captured (e.g. adult birds and large mammals) were estimated from the literature. Life stages for many organisms were not directly observed (e.g. lepidoptera eggs) but are almost certainly present. For these stages we again used the literature to estimate the body sizes. For example, we used a data set of egg sizes from 6,700 insect species to inform estimates for the species in our study64. The species list indicates the estimation method and literature source used to estimate the body size of each individual life stage is included in the species list.LinksEcological networks can be broken into two types: Undirected and directed. Undirected networks include bipartite networks (e.g. plant-pollinator, host-parasite) and social-networks. In undirected networks, interactions (links) and their participants (nodes) are observed at the same time. Links are not inferred in undirected ecological networks (unless false-negatives due to sampling error are taken into account) because they are directly observed (e.g. tick removed from a lizard). Undirected links can be weighted (interaction strength) by counting observations.Directed networks include food webs. Most food web links are inferred because it is not feasible to evaluate all possible consumer-resource interactions in a system through direct observation. The number of possible consumer-resource interactions in a food web is equivalent to the number of nodes squared. There were 3,084 nodes in the Eldorado National Forest, resulting in 9,511,056 potential consumer-resource interactions. In the scope of an ecological study, it is rarely feasible to directly observe most feeding links for most species15, much less an entire web, though molecular methods are bringing this closer to possibility for some guilds (e.g. large mammalian herbivores)65. While often detailed for birds and mammals, published accounts of direct observations of diets are often general (e.g. “Species A eats organic matter”) or entirely lacking for other groups. Restricting link assignments only to those that are directly observed will not create an accurate or unbiased food web.To assign resources to consumers we supplemented our own field observations with published diet records, expert opinion and rule-based filters. In the absence of direct observation, rule-based filters are an important tool for sorting through the huge number of potential feeding interactions. Filters varied with the species and ontogenetic stages to which they were applied but consisted of two main types: Encounter and compatibility. Encounter filters determine the potential for consumers to interact with resources. Encounter filters are based on habitat co-occurrence, forging strategy and diel activity patterns. Applied to links that have passed through encounter filters, compatibility filters determine the outcome of a potential encounter. Compatibility filters are based on consumer diet information, consumer diet breadth, resource palatability, and consumer-resource body size ratios. For inclusion in the food web, a link must pass through both filters.Link assignmentAll species were considered potential resources. For feasibility and reproducibility, species were broken into groups of encounter filters. First, we separated plants, fungi and detritus from other metazoans.Fig. 2Sampling sites map and King Fire perimeter. We sampled 27 sites total in the Eldorado National Forest, California, three years after the King Fire, nine in each burn category: Unburned, moderate severity, and high severity. Features not indicated in legend are typical of topological maps.Full size imageFig. 3Representative map of sampling design. We employed 19 different methods to estimate the richness and biomass density of organisms in the Eldorado National Forest, California, three years after the King Fire. Methods were conducted entirely within or centered within the 200 × 200 m site perimeter. Methods were paired in space and time when useful (e.g. black lights and acoustic bat surveys), and separated when necessary to avoid interference (e.g. small mammal trapping grid and vegetation transects). All methods at a site were conducted over 4–5 consecutive days.Full size imageThe first encounter filter was a loose group consisting of primary producers, non-living resources (e.g. detritus, carcasses), and saprophytes. In this first filter, primary producers were broken into parts (e.g. root, seed, leaves, etc). With few exceptions (i.e. moss, lichens, algae) primary producers in this filter group were evaluated as families or species. Saprophytes were evaluated as spores or adults. These groups served as the encounter filter for primary consumers and fungivores.Next, we partitioned all other metazoans into smaller encounter filters based on phylogeny, behavior, activity, habitat and palatability. A species’ life stage can be a member of multiple resource groups. These groups served as the encounter filter for most predatory or omnivorous organism stages. These encounter filters included:

Flying invertebrates

Nocturnal flying invertebrates

Diurnal flying invertebrates

Non-flying invertebrates

Ground-dwelling invertebrates

Ground-dwelling invertebrates excluding spider eggs

Soft-bodied ground dwelling invertebrates

Invertebrates on plants

Invertebrates on plants excluding spider eggs

Soft-bodied invertebrates on plants

Invertebrates on trees

Reptiles

Birds

Small mammals

Large mammals

Encounter filter exposure was tailored to consumer type. For consistency, consumers were broken into phylogenetic and ontogenetic guilds (e.g. lepidoptera larvae). For example, web-building spiders were exposed to flying insects, but not small-mammals encounter filters. Compatibility filters are specific to species and stage. For example, while both are exposed to the flying-insects encounter filter, adult and juvenile web-building spiders will have different compatibility filters because they have different consumer-resource body size ratios. Phylogenetic and ontogenetic consumer guilds are detailed below, but the decisions for each of the 178,655 links assignments in the food web can be found in and reproduced with the R code accompanying this manuscriptSpidersAs common, generalist insectivores, spiders are important consumers in the network66. To assign them resource links, spiders were broken into three ontogenetic stages: adult, egg, juvenile. Spiders were then separated into 17 consumer guilds by Family. The 87 spider species that could not be identified at the family level were assumed to be web-building spiders. To assign feeding interactions, we applied one or more invertebrate resource group filters (see above) to the members (species and stages) of each spider guild. Next, each link passed through a consumer-resource body size filter before being included in the network. For example, web-building spiders were assigned to capture flying insects and consume insects larger than 20% of their own body-length (as mesh size sets a lower limit of prey size) and less than 200% of their own body length67. Because of the generality of their filter-feeding hunting strategy, web-building spiders accounted for nearly half (32,663) of interactions with spiders as consumers. Additionally, when it was reported in the literature, adult members of a guild were assigned to consume nectar.Herbivorous beetlesTo assign consumer links to non-predatory beetles, their larval and adult stages were separated into Family-level feeding guilds. When information was available, links were evaluated at the species-stage level rather than the Family level. Resource links containing primary producers and non-living resources (detritus, carcasses, dung, etc) were assessed based on direct observation, published reports and expert opinions. When feeding on living plants, beetles were assigned to specific tissue types (e.g. flower, leaves, roots). For example, Cerambycidae_sp_2 was assigned to feed on the stems of Arctostaphylos patula as well as stems of plants from the family Rhamnaceae. This assigned 10,289 consumer links to herbivorous beetles.Larval lepidopteraCaterpillars were the most speciose herbivore group in the network. Larval lepidoptera vary greatly in host plant range and the quantity of information on their feeding habitats and were not lumped into guilds whenever possible. Microlepidoptera were not identified below the order level and were assumed to feed like Gelechiidae caterpillars (many species of which have been documented in Eldorado National Forest). We assigned links to caterpillars with resource filters of host plants and parts based on published diet records, palatability, expert opinion and observed co-occurrence between potential hosts and adults. This assigned 2,434 consumer links to caterpillars.Adult lepidopteraAdult lepidoptera feed primarily or exclusively on nectar from flowering plants. The host ranges for most adult lepidoptera are not well described. To assign nectar links, adult lepidoptera were grouped into families and passed through resource filters based on published records, co-occurrence, and expert opinion. Non-feeding adult moths were removed from link consideration. These filters assigned 5,854 nectar links to adult lepidoptera.Adult hymenoptera as herbivoresMost species of hymenoptera are parasitoids as larvae and free-living as adults (eusocial hymenoptera are a notable exception). Many adult parasitic wasps supplement their protein intake with nectar and pollen. The plant host ranges for solitary adult wasps are not well known. We applied nectar and pollen resource filters to adult hymenoptera based on published records, co-occurrence and expert opinion. These filters assigned 4,880 links to adult hymenoptera.Predatory beetlesPredatory and scavenging beetles are important consumers in terrestrial ecosystems. At the family level, the diets of predatory beetles are well-described relative to other arthropods. We grouped predatory and scavenging beetles into family guilds. We applied resource filters to predatory and scavenging beetles based on published records and expert opinion, habitat overlap, foraging strategy, palatability, and body size. These filters assigned 10,320 resource links to predatory beetles.FliesFlies in the Eldorado National Forest are a speciose group with diverse consumer strategies: herbivores, predators, scavengers, detritivores, parasitoids, and micropredators. Because of their trophic diversity each dipteran family was treated as its own guild, even then there were often large ontogenetic diet shifts across stages within a guild. We applied resource filters to dipterans based on published records and expert opinion of their diet. These filters were based on habitat overlap, palatability, and for predatory stages consumer-resource body size ratios. These filters assigned 9,541 resource links to flies.Hymenopteran parasitoidsParasitoid wasps are a diverse group that can have strong, even regulatory, effects on their host populations. We applied resource filters to hymenopteran parasitoid larvae in a three-step process. First, we used published records and expert opinion to establish their host range and host specificity. Next, we looked for the subset of potential hosts that co-occured with adult parasitoids across the most sites. Finally, we retained the subset of those host species whose adult body sizes were equivalent to or slightly larger than adult parasitoids. These filters assigned 4,695 host links to parasitoid wasps.Other hymenopteraThe remaining hymenoptera were composed of wood wasps and gall wasps, as well as bees, predatory wasps and ants. Host plant links were assigned to wood wasps and gall wasps in the same way as larval lepidoptera. Nectar links were assigned to bees in the same way as adult lepidoptera. Prey links were assigned to solitary and eusocial wasps in the same way as insectivorous gleaning birds. Ants were treated as generalist omnivores whose links were assigned links in a manner similar to all of the above.HemipteraHemiptera were the most abundant consumer group in the Eldorado National Forest. Hemiptera use their proboscis to feed on fluids, either as herbivores or predators. To accommodate this variation in consumer strategies resource filters were assigned to individual hemiptera species based on phylogeny. Host plants were assigned to herbivores based on field observations, published records and expert opinion. Plant fluids (with the exception of sap from soft woods) were not included in the node list, so herbivores were assigned feeding links based on the plant tissues that they pierced (i.e. stem or leaves). Predatory hemiptera were assigned insects on plants passed through consumer-resource body size filters. When more specific dietary information was available resource filters were further refined. These filters assigned 3,177 links to the hemipteraCollembolaFrom soil to canopy, springtails were widely distributed across Eldorado National Forest habitats and are important resources for arthropod secondary consumers. Collembola are herbivores, detritivores and fungivores. Little diet information is available for collembola, which were assigned resource filters based on habitat and phylogeny (order). Habitat was determined by collection method, and resource availability was determined by habitat. These, phylogenetic-habitat-resource filters assigned 140 links to the collembola.Bark licePsocoptera were common on plants in the Eldorado National Forest, feeding on algae, lichen, moss, fungi and detritus. They exhibit little variation in diet and were assigned resource filters as a group at the Order level. This small set of resource filters assigned 120 links to the psocoptera.ThripsThysanoptera were common and abundant consumers in the Eldorado National Forest, whose diets can range from herbivory to facultative predation and predation. To accommodate this variation in consumer strategy, resource filters were assigned to individual thysanoptera species based on phylogeny. Host plants for herbivores were based on field observations, supplemented with published records and expert opinion. Thysanoptera predators were assigned soft-bodied insects on plants passed through consumer-resource body size ratio filters. These resource filters assigned 924 links to thysanoptera.BatsBats are important consumers of arthropods. Arthropod encounter filters were determined by bat foraging strategies reported in the literature. Juvenile bats were treated separately. Aerial hawking bats capture nocturnal flying insects. Gleaning bats capture insects on plants. Pallid bats (Antrozous pallidus) which fly close to the ground, capture arthropods on the ground and understory plants. These arthropod filters then passed through consumer-resource body size ratio filters, which assigned 4,621 links to adult bats.BirdsBirds were the most speciose vertebrate group in the Eldorado National Forest. This diversity is reflected in their diets. Bird resource filters were based on published records and expert opinion. Herbivorous birds that were reported to feed on a type of plant tissue were assumed to feed on all tissues of that type, unless the literature indicated resource specialization. For example, if a bird was reported to feed on a fruit, it was assumed to feed on all fruit in the system. Resource links for predatory and omnivorous birds were passed through consumer-resource body size ratio filters. These filters assigned 56,584 links to birds as consumers.Small mammalsMammals 2.5 kg were comparatively uncommon but important consumers in the Eldorado National Forest. Large mammal resource filters were based on published records and expert opinion. Herbivorous large mammals that were reported to feed on a type of plant tissue were assumed to feed on all tissues of that type, unless the literature indicated resource specialization. Resource links for omnivorous and predatory large mammals were passed through consumer-resource body size ratio filters. These filters assigned 840 links to large mammals as consumers.Juvenile mammalsJuvenile mammals were considered unweaned. Nursing mammals were included in the species list because they are more vulnerable than adults and are potential resources to different consumers as a result. Unweaned mammals “feed” on their mothers, who are considered their only resource link. Nursing filters assigned 38 links to juvenile mammals.ReptilesWhile not diverse or common, reptiles on the mountain slopes of Eldorado National Forest are potentially important consumers for many groups. Reptile resource filters were assigned based on published records and expert opinion. All resource links were passed through consumer-resource body size ratio filters. These filters assigned 1,487 links to reptiles.MitesMites are ubiquitous and important consumers in many habitats but are often overlooked because of their small size and taxonomic difficulty. Mites were treated as consumer groups based on taxonomy. Resources for predatory mites were based on habitat and passed through consumer-resource body size ratios filters. Resource filters assigned 2,971 links to mites.Miscellaneous arthropodsA few arthropods not discussed above were not speciose enough to be dealt with separately here. These remaining miscellaneous arthropods were treated as groups at various taxonomic levels. Encounter and compatability filters for these groups were based on published records. Encounter filters for predatory (centipedes, odonates, pseudoscorpions, solfugids, mantids, opiliones, neuroptera, embioptera, pauropoda, eusocial wasps) and omnivorous (dermaptera) groups were based on habitat and passed through consumer-resource body size filters. Encounter filters were assigned by habitat for detritivores, herbivores and fungivores (archeognatha and isopods). These filters assigned 3,157 links to miscellaneous arthropods as consumers. More

Coupled model experiments for detecting vegetation-climate feedbackWe quantified changes of near-surface (2-m) air temperature (Ta) in response to the observed NH greening for all active growing seasons during 1982–2014 using IPSL-CM. We defined the three growing seasons (spring, summer, and autumn) across the entire NH domain as periods of March-April-May (MAM), June-July-August (JJA), and September-October-November (SON), respectively. For each season, a pair of transient numerical experiments was performed by modifying LAI: a dynamic vegetation experiment (SCE) forced by annually and seasonally varying LAI from satellite observations36, and three seasonal control experiments (({{{{{{rm{LAI}}}}}}}_{{{{{{rm{CTL}}}}}}}^{{{{{{rm{MAM}}}}}}}), ({{{{{{rm{LAI}}}}}}}_{{{{{{rm{CTL}}}}}}}^{{{{{{rm{JJA}}}}}}}), and ({{{{{{rm{LAI}}}}}}}_{{{{{{rm{CTL}}}}}}}^{{{{{{rm{SON}}}}}}}) for MAM, JJA, and SON, respectively) forced by annually varying LAI for all seasons, except in the season of interest when the LAI was fixed to the climatological conditions observed during 1982–2014 (Fig. S1). For all experiments, other boundary conditions, including sea surface temperature (SST), sea ice fraction (SIC), and atmospheric CO2 concentrations, were kept consistent (Methods). Therefore, differences between SCE and the control experiments characterized the effects of the observed LAI changes on Ta (hereafter denoted as ΔTa), both intra- and inter-seasonally. Multimember paired ensembles were generated for each coupled model experiment by performing 30 repeated runs but with different initial conditions (see Methods).The capacity of the IPSL-CM GCM for simulating the seasonal variations and spatial patterns of Ta was assessed by comparing the SCE simulation results with the observation-based Ta data (Methods). Throughout most of the growing season (May to October), the SCE simulation well reproduced the increasing trend and interannual variability of the NH land mean Ta observed during 1982–2014 (Fig. S2). Observational data showed that the strongest NH warming occurred in early spring (March and April) and late autumn (November). However, the SCE simulation failed to capture the exceptionally strong warming during the transitional seasons, leading to the underestimation of the annual mean warming trend (SCE: 0.237 ± 0.024 °C decade−1; observed: 0.362 ± 0.048 °C decade−1). This underestimation stemmed from a negative bias in the increase of downwelling shortwave radiation, possibly due to an absence of short-lived forcing and bias in the cloud systems37. Overall, the SCE reproduced the geographical patterns of seasonal warming reasonably well (Fig. S3), which strengthened our confidence in the model projections. Notably, it successfully captured the observed amplified warming over pan-arctic and semi-arid regions, as well as the few cases of regional cooling, such as that over northwestern North America during MAM (Fig. S3).Intra-seasonal temperature responses to NH LAI changesFor the period from 1982 to 2014, satellite-retrieved LAI showed statistically significant increasing trends (p  0.1), strong and significant JJA cooling (−0.044 ± 0.008 °C decade−1, p  0.1) (intra-seasonal feedbacks shown in Fig. 1b). The LAI-induced JJA Ta trend was equivalent to cooling of −0.15 ± 0.03 °C in JJA over the study period, offsetting the overall SCE-simulated near-surface air warming over this period by ~12.5%. This strong JJA cooling was further supported by a significant negative correlation (r = −0.64, p  0.1) or SON (r = 0.07, p  > 0.1) (Fig. S4a, c), during which the LAI-induced changes accounted for only 1.3% (MAM) and −3.2% (SON) of the concurrent greenhouse warming. We also verified the robustness of our results by performing equilibrium experiments with an independent model, the NCAR Community Atmosphere Model coupled with Community Land Model (CAM-CLM, Methods). Indeed, this model generated a similarly strong LAI-induced cooling in JJA (−0.18 °C, p  0.1) and SON (−0.05 °C, p  > 0.1) (Fig. S5).Fig. 1: Intra- and inter-seasonal temperature responses to leaf area index (LAI) changes.a Monthly trends (shadings) of Northern Hemisphere (NH) mean LAI during 1982–2014 used as input to the seasonal simulations. The dashed curve and transparent bars indicate trends of monthly LAI and seasonally aggregated LAI values, respectively. b Linear trends of Ta driven by LAI changes within the same season (intra-seasonal) and other growing seasons (inter-seasonal). Error bars in a, b indicate uncertainty ranges [1 – standard deviation (SD)]. c Monthly trends of LAI-induced air temperature changes (ΔTa), with red and blue shadings representing positive and negative trends, respectively. The bottom panel shows the overall ΔTa trends induced by LAI changes in all growing seasons, calculated as the sum of ΔTa trends from the three seasonal runs shown separately in the above panels. ***p  More