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Scanning electron microscopy and energy spectrum analysisThe SEM images show the morphological structures of DA and Al-DA before and after adsorption (Fig. 1). DA and Al-DA have disk-like microstructures29 with sur-faces containing both large and small pores, that is, DA and Al-DA have unique multi-level pore structures. The main component of DA and Al-DA is silica, which has a large specific surface area, good thermal stability, and is a natural green material for use as a water treatment agent with a porous structure31. The micrographs show that before adsorption, the DA surface is smooth with a distinct pore structure, whereas modification with aluminium hydroxide makes DA coarse and loose because of the formation of amorphous aluminium hydroxide colloids32. After adsorption, the surface pore structure is covered over for DA and completely covered over for Al-DA, which indicates that F− reacts with Al3+ to form nanoscale precipitates22. The results of the EDS analysis (Fig. 2) show that the content of elemental Al increased from 3.96 to 12.74% after DA was modified with aluminium hydroxide, indicating that Al adhered effectively to the modified DA surface. After adsorption, the content of elemental Al decreased from 3.96 to 1.36% for DA and from 12.74 to 2.03% for Al-DA, which fully confirmed that fluorine preferentially combined with Al to form aluminium precipitates during adsorption, thereby decreasing the Al content.Figure 1SEM images of DA and Al-DA before and after adsorption. (A) Before DA adsorption. (B) After DA adsorption. (C) Before Al-DA adsorption. (D) After Al-DA adsorption.Full size imageFigure 2EDS graphs of DA and Al-DA before and after adsorption. (A) Before DA adsorption. (B) After DA adsorption. (C) Before Al-DA adsorption. (D) After Al-DA adsorption.Full size imageXRD analysisThe surface mineral composition and crystallinity of the materials before and after adsorption were analyzed by XRD (Fig. 3). In the DA and Al-DA patterns, the wide diffraction peaks at approximately 22.0°, 26.0°, and 50.0° mainly correspond to amorphous SiO2, and the diffraction peak at approximately 35° mainly corresponds to amorphous Al2O3, indicating that the material is polycrystalline29. It has been re-ported that amorphous materials may be good adsorbents because of a large specific surface area and numerous active sites33. Many Al(OH)3 peaks and NaCl peaks appear in the XRD pattern of Al-DA, indicating the successful modification of DA by aluminium hydroxide. After adsorption, Na3AlF6 peaks appear in the DA pattern, and Na3AlF6 and AlF3 peaks appear in the Al-DA pattern, whereas the characteristic peaks of NaCl are absent in the Al-DA pattern, which indicates the participation of NaCl in the adsorption process. It has been demonstrated that in the presence of excess sodium fluoride in the reaction solution, the generated aluminium fluoride combines with sodium fluoride to form a NaAlF4 intermediate, which is subsequently converted to cryolite complexes by further adsorption of sodium fluoride34. This result confirms the XRD mapping results.Figure 3XRD patterns of DA and Al-DA before and after adsorption.Full size imageInfrared analysisFigure 4 shows the FTIR spectra of DA and Al-DA before and after adsorption: peaks at 3418, 1635, 1096, 791, and 538 cm−1 appear in the spectrum of DA spectrum before adsorption, and peaks at 3630, 3449, 1637, 1094, 913, 793, and 538 cm−1, appear in the Al-DA spectrum before adsorption. The strong and broad band centered at 3418 cm−1 is due to the stretching vibration of the adsorbed water hydroxyl group (O–H) and the surface hydroxyl group, the vibrational peak at approximately 1635 cm−1 is probably from bound water or the surface hydroxyl group; the peaks at 1096 cm−1 and 538 cm−1 correspond to siloxane groups (Si–O–Si–) and an Al–O absorption band, respectively; and the strong oscillations at 791 cm−1 may be attributed to inorganic Al salts35,36,37. The original absorption peak in the DA spectrum is shifted in the spectrum of DA modified with aluminium hydroxide, confirming the successful modification of DA. The shift of the band at 3418 cm−1 in the DA spectrum to a higher frequency at 3623 cm−1 in the DA spectrum after fluoride absorption is caused by fluoride bonding and has been previously reported38. Another noticeable change in the spectra of DA and Al-DA before and after adsorption is the increase or decrease in the intensity of bending vibrations of specific peaks because the highly electronegative fluoride may have an inductive effect on the respective groups that leads to a blueshift, and the formation of hydrogen bonds leads to a redshift and broadening of the spectral band. The shifts and changes of these peaks indicate the interaction of fluoride with the respective groups29. The new peak at approximately 1170 cm−1 in the spectra of DA and Al-DA with adsorbed fluoride may be due to the formation of Al-F bonds6. The IR spectra show that the formation of a new bonding electronic structure by surface complexation with F− is one of the main mechanisms for the adsorption of F−.Figure 4FTIR spectra of DA and Al-DA before and after adsorption.Full size imageZeta potential analysisThe zeta potential of the material surface plays a very key role in the adsorption process, which reflects the surface charge properties of the material under different pH conditions, and also reflects the surface properties of the material. To obtain the zero charge point of the material, we studied the potential change of the material under different pH values. The results are shown in Fig. 5. In the range of pH 3–11, the zeta potential of the two adsorbents decreased linearly with the increase in pH, and the pHzpc of DA and Al-DA were 9.84 and 10.61, respectively. When pH  More

Study siteOur study site is in an intensive agricultural landscape in NW Spain known as “Tierra de Campos”, which occupies part of three out of nine provinces of Castilla-y-León region (Palencia, Valladolid, and Zamora). This area is considered the main “hot-spot” of tularemia in Spain and Southern Europe16 and is characterized by higher-than-average vole abundances during outbreaks17.Iberian hare abundance indexYearly occurrence of vole outbreaks in NW Spain between 1996 and 2020 (i.e., 1997, 1998, 2007, 2008, 2014, 2019) were identified based on reports in the news (historical reconstruction18) and more recently (from 2009 onward) using common vole abundance indices obtained from live-trapping monitoring (i.e.4,19).To study the Iberian hare population trends we used regional hunting statistics available from the regional government (Junta de Castilla-y-León, CAZDATA Project, https://medioambiente.jcyl.es/web/es/caza-pesca/cazdata-banco-datos-actividad.html [Cited 2022 Sep 23]), which included hunting records as well as the number of hunting licences from 1974 to 2020. We used the number of hunted hares divided by the number of hunting licences each year as an abundance index for hares in “Tierra de Campos” (compiling data from the provinces of Palencia, Zamora and Valladolid). CAZDATA Project is an initiative proposed by the Hunting Federation of Castilla y León, which has the support of the regional government and, more importantly, the commitment of almost 60% of the hunting societies in the community to implement a system for monitoring hunting activity. Since this information is gathered by hunters for the benefit of the hunting activity, we are confidence on its reliability to carry out the present study.
Francisella tularensis prevalence in Iberian haresWe compiled data on F. tularensis prevalence in Iberian hares from 2007 to 2016 using previously published information from a passive surveillance program carried out by the “Regional Network of Epidemiological Surveillance” (Red de Vigilancia Epidemiológica de la Dirección General de Salud Pública) of Castilla-y-León region20. This provided us with information on hare tularemia prevalence (amount of positives/number of screened individual) each year within the three provinces from “Tierra de Campos”.Statistical analysesTo study Iberian hare population trends, we calculated an index of yearly hare population instantaneous growth rate (PGR) using the hunting bag data (hare abundance index) from 1996 to 2020. Hare PGR was calculated as follows:$$PGR= lnleft(frac{{AI}_{t}}{{AI}_{t+1}}right)$$where ln stands for natural logarithm, AIt is Iberian hare abundance index on year t. and AIt+1 is the Iberian hare abundance index on year t + 1. PGRs were estimated yearly from 1996 to 2019. This dependent variable was fitted to a Generalized Linear Mixed Model using the glmmTMB function (GLMMTMB, package glmmTMB21) and a gaussian family distribution and identity link function. The categorical variable vole outbreak year (i.e., with two levels: years with (1) or without vole outbreak (0), hereafter “Vole”) and “Province” (i.e., with three levels: Palencia, Valladolid and Zamora), and their interaction were used as explanatory variables. “Year” of sampling was included as a random factor (i.e., 1996–2019). Significance of the fixed effects in the models was calculated with Type II tests using the function Anova in the car package22. We previously checked the model for overdispersion and distribution fitting using function simulateResiduals (package DHARMa23, simulations = 999). The variable PGR expresses the change between year t and t + 1. We included AI at t as a covariate in the model, in order to take into account density-dependence in hare PGR (the extent to which the abundance changes in between year t and t + 1 depends on the abundance during year t). For this to make biological sense, we rescaled the covariable AI so that it has mean equal to zero. Thus, the effect of the other predictor variables in the model (i.e., “Vole” and “Province”) was interpreted as the effect that these variables have on PGR when the abundance value is at 0. Thus, the effect of “Vole” and “Province” on PGR will be obtained by the mean value of abundance.We assessed the effect of vole outbreak years on the Iberian hare’s population PGR by running a multiple Pearson correlation (function ggscatter) between PGR and AI, considering both, PGR for all the years of the study period (i.e., 1996–2019) and only those years where vole outbreaks were detected (i.e., 1997, 1998, 2007, 2008, 2014, 2019).Finally, we tested for difference in the prevalence of F. tularensis on Iberian hare’s during years with or without vole outbreaks using a GLMMTMB21 with a binomial family distribution and a logit link function, where prevalence of F. tularensis in hares was the dependent variable, and “Vole” outbreak years and “Province” (i.e. Palencia, Valladolid and Zamora) were the responses variables. In this case, the variable “Vole” outbreak years included three levels (i.e. 0 = no vole outbreak, 1 = vole outbreak year, 2 = one year after vole outbreak), to assess if F. tularensis prevalence in hare also persist one year after a vole outbreak. “Year” of sampling was included as a random factor (i.e., 2007–2016). Due to the limited sample size, we did not include the interaction between “Vole” and “Province” to not overfit the model. We also previously checked the model for overdispersion and distribution fitting using function simulateResiduals (package DHARMa23, simulations = 999). All analysis were carried out using the R statistical computing environment24. More

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Random forest: feature importance and interactivityOur random forests produced highly accurate predictions of local stability when trained on model output from the full dataset (e.g., AUC = 0.998 across all 5 parameters, see Fig. 2A) and all tested subsets. Running random forests on the full results set with all five parameters as predictors indicated both demographic and trophic rates were important to understanding resultant model stability. Moreover, results reveal that whether in multi-stage (red line; Fig. 2A) or single stage herbivory (e.g., ({a}_{2}) = 0, ({a}_{F}) ≥ 0; blue line Fig. 2A), parameters’ contribution to predictive power is related to their interactivity with other parameters (blue line; Fig. 2A). Note, a similar analysis with ({a}_{2})  > 0 and ({a}_{F}) = 0 is not possible because this type of herbivory is always stable.This interactivity was apparent in our attempts to understand how our specific parameters affected the behavior of our model in Eq. (1) via studying their effects as features in driving random forest predictions. Initial investigations into individual feature effects revealed that the effect of any single feature (parameter) on trophic dynamics could change substantially based on the values of our other features (parameters). Specifically, the average marginal effects (e.g., PD plots; Fig. S3) on simulation dynamics belied a high degree of variability in feature effects throughout the simulation data (e.g., ICE plots; Fig. S3).Breaking down results into further subsets of set specific attack rates with varying demographic rates revealed that this variability in feature effects was largely based on the changes in feature importance and effect over different allocations of herbivory on ontogenetic stages. This breakdown affected the relationship between importance and interactivity (Fig. 2A) such that it was inconsistent but still visible in aggregate across our simulation parameters (Fig. 2B,C). Figure 2D–F depict how different allocations and intensity of herbivory across plant ontogeny change the influence of each demographic parameter in driving model stability.Given how the influence of plant demographic rates over model behavior changed across trophic allocation (Fig. 2D–F), we first focused in depth analysis on variable demographic rates across static allocations of herbivore attack rates. By limiting the number of varying features, we use multivariate analysis to develop a fuller understanding of dynamics in subsections of the data which functioned as a scaffolding for further investigation. Specifically, we took a hierarchical approach, first developing an understanding of single-stage herbivory as a basis to study single-stage dominant herbivory (Fig. 3), which then leads us to a better overall understanding of our system’s dynamics across all trophic rates.Figure 3Interactive feature effects on model behavior. Across different herbivory allocations, partial dependence (PD) plots (A,C,E) show interactive effects between maturation rates on categorical simulation stability. Threshold plots (B,D,F) extend this analysis to include gradations of seed production rates. (A,B) Herbivory allocation ({a}_{F}) = 1.0 and ({a}_{2}) = 0.0. (A) Partial dependence plot shows probability of stability across all values of ({r}_{F}). (B) Threshold plot shows the location of the threshold between stable and unstable dynamics in {({g}_{12}),({g}_{2F})} parameter space as a function of seed production levels (({r}_{F})). (C,D) Herbivory allocation ({a}_{F}) = 0.2 and ({a}_{2}) = 1.0. (C) Partial dependence plot shows probability of stability across all values of ({r}_{F}). (D) Threshold plot shows the location of the threshold between stable and unstable dynamics in {({g}_{12}), ({g}_{2F})} parameter space as a function of seed production levels (({r}_{F})). (E,F) Herbivory allocation ({a}_{F}) = 1.0 and ({a}_{2}) = 0.2. (E) Partial dependence plot shows probability of stability across all values of ({r}_{F}). (F) Threshold plot shows the location of the threshold between stable and unstable dynamics in {({g}_{12}), ({g}_{2F})} parameter space as a function of seed production levels (({r}_{F})).Full size imageSingle stage consumptionIn the case of the seedling-only herbivore (({S}_{2}); via ({a}_{2})  > 0 and ({a}_{F}) = 0), all simulations produced stable trophic dynamics. This occurs because density loss in the seedling stage means more juveniles never reach maturity and reproduce themselves19. This essentially reduces the effective reproduction rate, limits the reproductive plant density, and decreases resources available to the herbivore (similar to lowering intrinsic reproduction in the classic Lotka–Volterra model). In fact, seedling herbivory only induced oscillations at higher handling times, a common effect of high handling time (results not shown).On the other hand, concentrating consumption on the fecund stage ((F)) can induce both stable and oscillating trajectories (Fig. S4). Consumption of (F) does not induce the same regulation of reproductive potential that stabilizes under seedling-only consumption, and so is vulnerable to boom/bust populations cycles. We chose the two most consistently important (Fig. 2B) and interactive (Fig. 2C and Fig. S5) parameters, ({g}_{12}) and ({g}_{2F}), in order to search for dominant effects on model behavior and their interactions. These parameters functioned as focal axes for our two-dimensional PD plots36. These PD plots depict the estimates of marginal effect of each parameter on random forest predictions, which in this case is categorical stability (Fig. 3A). We can see that stability estimates are increased by lowering either or both per-capita germination and/or maturation rates (({g}_{12}) and ({g}_{2F})). Demographically, reduced maturation rates shift the ratio of plant population density across its ontogeny, creating a larger juvenile population shielded from consumer pressure. Trophically, this restricts resources for the herbivore, thereby limiting losses in plant density due to herbivory (({theta }_{F})) relative to the overall plant density.This mechanism is so influential in determining trophic dynamics, its effect on stability is statistically detectable pre-simulation via equilibrium values. Losses in plant density due to herbivory are labeled under brackets in Eq. (1) as ({theta }_{F}) and ({theta }_{2}), which we can represent as ({theta }_{F}^{*}) and ({theta }_{2}^{*}) at equilibria. Relative to overall plant density we can define a ratio for plants of consumptive losses to total density (L:D ratio) such that:$$mathrm{L}:mathrm{D ratio}=({theta }_{F}^{*}+ {theta }_{2}^{*})/({S}_{1}^{*} +{S}_{2}^{*}+{F}^{*}).$$
(2)
When applied as a predictor variable on the same adult-herbivory subsection presented in Fig. 3A via a simple linear regression, we can see that L:D ratio alone explains ~ 45% of the variance of the maximum eigenvalue in simple linear models (F-statistic: 4578 on 1 and 5598 DF, p-value:  More

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