Ecology

Study site and demographic dataThe study was carried out in Volcanoes National Park, the Rwandan part of the Virunga massif, which is further shared with Uganda and the Democratic Republic of the Congo. We focused on habituated mountain gorilla groups monitored by the Dian Fossey Gorilla Fund’s Karisoke Research Center, often referred to as the Karisoke subpopulation. Since 1967, groups in this subpopulation have been followed on a near daily basis. Through the mid-2000s, the Karisoke groups generally numbered three but over the last decade, group fission events and new group formations resulted in an average of ten groups in the region (see42,43). During daily observations, detailed demographic data are recorded, such as group composition, birthdate and death date, group transfers (for further details see Strier et al.50). The data used for this study covers demographic data from 1967 to 2018 and includes 396 recognized individuals.Epidemiological dataWe obtained published data on four variables that control the disease dynamics of COVID-19 in humans, namely (a) the basic reproductive number (R0)34,35, (b) the infection fatality rate (IFR) based on estimates from China and Italy24,25,36,37, (c) the probability of developing immunity and (d) the duration of immunity37,38,39,41.Stochastic projection modelWe used the stochastic projection model proposed by Colchero et al.51, that models population dynamics for both sexes on fully age-dependent demographic rates. The model incorporates the yearly variance–covariance between demographic rates, while it accounts for infanticide as a function of the number of silverbacks (mature males > 12 years old) in the population51. Because of this relationship between infanticide and number of silverbacks, this source of mortality changes in time and cannot be assumed to be part of the infant mortality rate. To explore the extinction probability for the Karisoke subpopulation as a function of different diseases, we gathered information from the model on the proportion of individuals that died for each disease and the frequency of outbreaks (i.e., how often outbreaks occurred).Demographic-epidemiological projection model for COVID-19We constructed a predictive population model that combines the species’ baseline demographic rates with a model based on the susceptible-infected-recovered-susceptible (SIRS) framework. As the baseline demographic rates, we used the age-specific mortality and fecundity estimated by Colchero et al.51 for mountain gorillas (Karisoke subpopulation). We defined four epidemiological stages, namely (a) susceptible, (b) infected, (c) immune and (d) dead, each of which we further divided into a fully age-specific structure (Fig. 1). Based on recent research on COVID-19 on humans, we assumed that the dynamics of the model allowed for the recovered individuals to be divided into either susceptible or immune37,38,39,41. Furthermore, we incorporated the potential age-specific infection fatality rate (IFR) based on current estimates from medical and epidemiological research24,25,36,37, adjusted to the lifespan of the gorillas by means of the logistic function$$qleft(xright)=frac{{q}_{M}}{1+{text{exp}}left[-0.2left(x-25right)right]},$$
(1)
where qM is the maximum infected mortality probability. Similarly, we modeled the probability of developing immunity as a function of the strength of the disease, which, based on recent research, we measured as mirroring Eq. (1) as$$mleft(xright)=frac{{M}_{I}}{1+{text{exp}}left[-0.2left(x-25right)right]},$$
(2)
where MI is the maximum immunity probability (Fig. 2B).To explore the potential impact of COVID-19 on the growth rate of the Karisoke mountain gorilla subpopulation, we varied four of the critical epidemiological variables, namely (a) the basic reproductive number, R0, from 0.5 to 6 (which helps to simulate factors such as increased group density, which may increase the likelihood of transmission), (b) the maximum infected mortality probability, qM = (0.3, 0.6) (Fig. 2A), (c) the immunity duration, TI to 1, 3, 6, and 12 months, and (d) the maximum immunity probability, MI, from 0.2 to 0.8 (Fig. 2B). As time units we used year fractions in half months (i.e., t1 − t0 = 0.5/12), which allowed us to simplify the model, based on current information on the average time of serial interval and incubation period in humans21. This implementation assumes that susceptible individuals could become infected at the beginning of the time interval, while infected individuals in time interval t would either recover (immune or susceptible) or die in t + 1.The deterministic structure of the model implies that the number of individuals in each sex, age and epidemiological stage was given by the possible contribution from the other stages 1/2 month before. This is, the number of susceptible individuals of age x at time t is given by the difference equation$$begin{aligned} n_{s,x,t} & = p_{x – 1} left{ {n_{s,x – 1,t – 1} + n_{i,x – 1,t – 1} left[ {1 – qleft( {x – 1} right)} right]left[ {1 – mleft( {x – 1} right)} right]} right} \ & quad + n_{{m,x – T_{i} ,t – T_{i} }} prodlimits_{{j = x – T_{i} :j > 0}}^{x – 1} {p_{j} – n_{i,x,t} } , \ end{aligned}$$where the ns,x,t is the number of susceptible individuals of age x at time t, and subscripts i and m refer to infected and immune individuals, respectively. For simplicity of notation, we do not include a subscript for sex, although the model does distinguish between sexes. The probability px is the age-specific survival probability. Functions q(x) and m(x) are as in Eqs. (1) and (2). Similarly, the number of immune individuals at time t and age x are$${n}_{m,x,t}={n}_{i,x-1,t-1}left[1-qleft(x-1right)right]mleft(xright)+sum_{{j:0le jle {T}_{i}wedge x-j >0}}{p}_{x-j}{n}_{i,x-j,t-j}.$$We incorporated this mechanistic structure into a stochastic model, where all contributions from time t to t + 1 were drawn from binomial or Poisson distributions. For instance, the total new number of infected individuals, Ni,t, was obtained as a random draw from a Poisson distribution with expected value$$Eleft[{N}_{i,t}right]={text{min}}left[{{R}_{0}N}_{i,t-1},{N}_{t}right],$$where Nt is the total number of individuals in the study subpopulation. We then distributed randomly these individuals into different available ages and sex corresponding to the term ni,x,t, in the susceptible equation above. The number of newborns, Bx,t, at each age for which there were available females at time t was drawn from a binomial distribution with expected value$$Eleft[{B}_{x,t}right]=left({n}_{s,x,t}+{n}_{m,x,t}right){f}_{x}$$where fx is the age-specific average female fecundity rate and ns,x,t and nm,x,t refers to the number of susceptible and immune females, respectively, of age x at time t. The sex of each newborn was then determined by means of a Bernoulli draw with probability given by the proportion of males in the population. Thus, if the draw produced 1 for that individual, it became a male, and if 0 a female.For each scenario, we ran stochastic simulations for 2000 iterations for 10 years and recorded the average number of individuals at each age–sex and epidemiological state at every month. We then ran long-term stochastic simulations for four scenarios with R0 = 3 and maximum immunity probability MI = 0.2. For these, we recorded also the number of subpopulations that went extinct at each month. More

We assembled a unique dataset of range-wide observations of Yucca available from iNaturalist. These provided the bases for determining presence and absence of flowers for our two focal species, and while flowering Yucca are likely to be more photographed, we still had sufficient absences for these common and iconic species to use in downstream models. These models were effective at predicting flowering phenology of the two focal species with generally high accuracy during the normal flowering season. Unlike other frameworks for predicting phenology, our approach is not to estimate an onset, median or termination timing of a phenophase. Rather, our goal was to determine whether climate and daylength covariates provide a basis for predicting the probability of open flowers during normal and anomalous bloom periods. This approach is enabled by having dense reporting of presence-absence data generated by growing community science resources.Model fitting revealed that probability of flowering is determined by complex interactions between climate and daylength, suggesting the critical importance of climate context. This importance for arid-adapted Yucca is in line with other studies of phenology of desert plants, from Saguaro in the desert Southwest of North America9 to lilies in arid environments in Africa25. Yet, we were surprised that flowering of Yucca does not necessarily always rely on increased precipitation. We expected precipitation would be a critical limiting factor in desert environments, and for Mojave yucca in particular, precipitation is a strong driver positively influencing the odds of flowering during spring and summer. However, for both species, flowering odds are also relatively high during cold and drier conditions earlier in the season (Fig. 3). These results may relate to precipitation falling as snow rather than rain during late winter—another avenue for further exploration in follow up studies.Joshua trees and Mojave yucca have different growth forms and are of vastly different sizes at maturity, and therefore, may be expected to react differently to climatic drivers. However, our findings indicate that the same interacting climate variables drive flowering phenology for both species, and the overall shape of their seasonal phenology curves are similar (Fig. 2). The main differences in our models are likely attributed to adapted differences in overall bloom timing; in particular, Y. schidigera generally blooms later in the year than Y. brevifolia (Fig. 2). For example, Y. brevifolia only blooms under highest daylength conditions if it is unusually cold and wet, while Y. schidigera flowering odds can often exceed 50% under warm and wet conditions when daylength is long (Fig. 3). Conversely, while Y. brevifolia has better odds of blooming in cold, dry conditions early in the year, even under wet conditions it can bloom with odds above 25%. In contrast, Y. schidigera is rarely in bloom in colder, wetter early season conditions.We also note the importance of including a polynomial term for daylength (Table 1), which always dramatically improved models (Table 1). The outcome, clearly visible in Fig. 3, is that responses of phenology are strongly non-linear across gradients. In sum, our work corroborates the importance of context dependence, finding that daylength, temperature, and precipitation interact in complex, nonlinear ways to influence flowering times.A key question we sought to answer in this work is whether we predict anomalous flowering events. Accelerating climate change means that species will experience conditions outside the range experienced for centuries. How species respond phenologically to these novel conditions is an area of active research26, but the focus has predominantly been on using yearly anomaly data, e.g. warmest years on record or via warming experiments27. Our efforts here are trying to predict a seasonal anomaly, where plants seasonally flowered outside of their presumed normal periods (e.g. in fall rather than spring). A key question of interest was whether the fall-winter bloom in 2018–2019 was itself triggered by anomalous climate conditions mirroring those of the usual bloom period.We examined this question by testing whether models, which were fit using data from years with a known normal blooming period, were able to predict presences and absences during the 2018–2019 fall-winter season. Our results show that we can predict absences with low error rates (4.7–6.7%, Table 2). However, these models had much higher rates for false positives (32.1–50.2%, Table 2). Our model predicts more anomalous blooming than actually observed. This suggests that, while Yucca might have been triggered to bloom by atypical cooler and wetter conditions, there are still factors not included in our models that limited the extent of anomalous blooming.It remains possible that co-evolution between Yucca and their obligate pollinator or florivore community28 may extend to how phenology is cued. It may also be that Yucca are responding not only to instantaneous climate conditions, such as mean photoperiod, but whether days are shortening or lengthening, and if so, it may be that the modeling approach used here is not sensitive enough to capture these types of more dynamic seasonal cues. Our work may also point to out-of-normal season blooming simply being more common and widespread than previously suspected, given broadly suitable climate conditions. A next step is to use growing community-science reporting of Yucca plants in flower to determine the rate of seasonally anomalous flowering from dense, range-wide community science observations enabled via resources such as iNaturalist.Finally, we note the value of examining predictive power of models using climate measurements over shorter and longer temporal windows. While these different climate accumulation windows are by nature highly autocorrelated, we found that data from the longer temporal window led to modest improvement of models based on AUC statistics. It is likely that the longer temporal window captures more information about GDD and overall water input in the environment. For example, a classic paper by Beatley5 that focused on shrub phenology in the Mojave showed fall and winter rains were precursor triggers of phenological events in spring. We also note congruence with the findings of Clair and Hoines13, who showed strong positive correlations with the 30-year averages of temperature and precipitation and fruit and seed mass in Joshua trees, although they focused on broader temporal scale questions. Connecting these longer timescale and broad spatial phenology studies, and aligning lags over different time-scales is a frontier area in phenology research. Finally, our findings should not necessarily be extrapolated more broadly for arid-adapted plants, and traits such as perenniality or woody versus herbaceous habit with associated differences in costs for growth and reproduction, may condition thresholds for needed accumulation of heat or water.We close by noting that phenology modeling is often treated as a one-off exercise where models are built, and results shared. We argue that the accelerating growth of new data resources and flexible modeling frameworks provide a means for models to iteratively improve. One key step towards this goal is faster annotation of phenology state. Here we hand-coded two key states in Yucca photographs1. These carefully vetted classifications can now provide the basis for more automated approaches for annotating photographs, e.g. via machine learning29. These new results can be fed into current models to test and improve model performance.Expanding data resources for modeling flower presence is one key step, but the development of improved phenology models that include more fitness-relevant responses is also important, such as number of flowers or fruits, potentially in relation to vegetative biomass. Individual yucca plants, for example, do not bloom annually even in favorable conditions, because vegetative growth must precede production of a heavy, high-cost inflorescence10. More sophisticated species-level models that link the full range of environmental conditions populations experience across their range with seasonal vegetative and reproductive biomass proxies are uncommon, mostly due to data limitations. Rather, studies typically focus on single, local areas or transect approaches across broad-scales30, with associated limitations for further prediction or forecasting.We argue that the ability to develop ecophysiological-guided, range-wide models are in reach, using the same community science photographs that so far have only been used to generate simple states such as open flower presence. Such models hold promise in helping to provide a basis for improved understanding of mechanisms underlying flowering, and better detection of anomalous blooming events and their consequences. For example, we don’t yet know if anomalous blooms produce fewer or greater flower numbers, as compared to normal periods. Do these blooms ultimately lead to the production of fruit and, if so, how much? Such next-step approaches are particularly critical and necessary, because as we experience more unusual weather phenomena and novel conditions, phenology prediction and understanding the consequences of phenological changes becomes even more challenging. As weather forecasting was improved by assimilating more data and building better process parameters, our hope is that similar methods with richer data types can improve the most difficult phenology prediction challenges. More

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Global statistical analysisOur first attempt to identify plausible effects of meteorological covariates on COVID-19 spread applied a comparative regression analysis. To this end, we focused on the exponential onset of the disease, as it is the epidemic phase that allows for a better comparison between countries or regions, without the confounding effect of intervention policies. We first determined, for each of the spatial units (either countries or NUTS (nomenclature of territorial units for statistics) 2 regions), the day in which 20 or more cumulative cases were officially reported. We then fitted the first-order polynomial function f(t) = x0 + rt for the next 20 days of log-transformed data, where t represents time (in days) and ({{x}_0}) is the value at initial condition t = 0. The r parameter can be understood as the exponential growth rate, and is then used to estimate the basic reproduction number (R0) using the estimated serial interval T for COVID-19 of 4.7 days53, such that R0 = 1 + rT (ref. 54). (We note that we are interested here in the relationship between the reproductive number and not in the actual inference of R0.) Once R0 was obtained for all our spatial units, we filtered our meteorological data to match the same fitting period (with a 10-day negative delay to account for an incubation and reporting lapse) for every spatial unit. To compute a single average of the meteorological variables per regional unit, we computed a weighted average on the basis of the population contribution of each grid cell to the total population of the region. We did so to have an aggregated value that would better represent the impact of these factors on the population transmission of COVID-19, as the same variation in weather in a high-density urban area is more likely to contribute to a change in population-level transmission than that of an unpopulated rural area. We then averaged the daily values of temperature and AH for each country and computed univariate linear models for each of these variables as predictors of R0. Given the somewhat arbitrary criteria to select the dates to estimate the R0 in each country, a sensitivity analysis was run to test the robustness of the regressions to changes in the related parameters. We tested 70 different combinations of two parameters: the total number of days used for the fit (18–27) and the threshold of cumulative COVID-19 cases used to select the initial day of the fit (15–45). We also calculated the weather averages by shifting the selected dates accordingly. Then, a linear model for each of the estimates was fitted for both T and AH. A summary of the distribution of parameter estimates (the regression slope coefficients and the R2 of the models) is shown in Extended Data Fig. 3.Bivariate time-series analysis with scale-dependent correlationsTo examine associations between cases and climate factors in more detail, SDC was performed on the daily time series of both COVID-19 incidence and a given meteorological variable. SDC is an optimal method for identifying dynamical couplings in short and noisy time series20,21. In general, Spearman correlations between incidence and a meteorological time series assess whether there is a monotonic relation between the variables. SDC analysis was specifically developed to study transitory associations that are local in time at a specified temporal scale corresponding to the size of the time intervals considered (s). The two-way implementation (TW-SDC) is a bivariate method that computes non-parametric Spearman rank correlations between two time series, for different pairs of time intervals along these series. Different window sizes (s) can be used to examine increasingly finer temporal resolution. The results are sensitive to the value of this window size, s, with expected significant and highest correlation values at the scale of the transient coupling between variables. Correlation values decrease in magnitude as window size increases, and averages are computed over too long a time interval. Values can also decrease and become non-significant for small windows when correlations are spurious. Here, the method was applied for windows of different length (from s = 75 to 14 days) and, despite a weekly cycle showing up in some cases for small s, results removing this cycle were robust. We therefore did not remove this cycle.The results are typically displayed in a figure with the following subplots: (1) the two time series, to the left and top of the matrix of correlation values, respectively; (2) the matrix or grid of correlation values itself in the center, with significant correlations colored in blue when positive and in red when negative, with rows and columns corresponding to the temporal localization of the moving window along the time series on the left and top, respectively; (3) a time series at the bottom, below this grid, with the highest significant correlations for a given time (vertically, and therefore for the variable that acts as the driver, here the meteorological time series). To read the results, one starts at the diagonal and moves vertically down from it to identify a given lag for which significant correlations are found (the closest to the main diagonal). In some of the SDC figures, the time intervals with high local correlations are highlighted with boxes. These intervals alternate with other ones (left blank) for which no significant correlation is found. All colored areas correspond to significance levels of at least P  fs/fr, where fs is the sampling rate and fr the minimum frequency. Another strategy is that M be large enough that the M-lagged vector incorporates the temporal scale of the time series that is of interest. The larger the M, the more detailed the resulting decomposition of the signal. In particular, the most detailed decomposition is achieved when the embedding dimension is approximately equal to half of the total signal length. A compromise must be reached, however, as a large M implies increased computation, and too large a value may produce mixing of components. SSA is especially well suited for separating components corresponding to different frequencies in nonlinear systems. Here, we applied it to remove the weekly cycle.MSDC analysisMSDC provides a scan of the SDC analyses over a range of different scales (here, S from 5 to 100 days at 5-day intervals), by selecting the maximum correlation values (positive or negative) closer to the diagonal. The goal is to consider the evolution of transient correlations at all scales pooled together in a single analysis. The MSDC plot displays time on the x axis and scale (S) on the y axis, and positive and negative correlations either jointly or separately. The rationale behind MSDC is that correlations at very small scales can occur by chance because of coincident similar patterns, but that as one moves up to larger scales (by increasing S), the correlation patterns that are spurious tend to vanish, whereas those reflecting mechanistic links increase in strength. This increase in correlation values should occur up to the real scale of interaction, decreasing afterwards. By ‘real’, we mean here the temporal scale covering the extent of the interaction between the driver and the response process (in this case, the response of disease transmission to a given climate factor). Thus, continuity of the same sign correlations together with transitions to larger values are indicative of causal effects, whereas the rapid vanishing of small-scale significant correlations signals spurious ones.Process-based modelDescriptionThe dynamical model is a discrete stochastic model that incorporates seven different compartments: S, E, I, C, Q, R and D. The model structure is illustrated in Fig. 4. The transition probabilities of the stochastic model are based on the corresponding rates of the transitions between classes in the deterministic (mean-field) model (specified in Fig. 4b). These probabilities are defined as follows. P(e) = (1.0 − exp(−β dt)) is the probability of infection exposure of the susceptible class, where β = (1/N)(βII + βQQ) is the infection rate (of the deterministic model). P(i) = (1.0 − exp(−γ dt)) is the probability that an new exposed individual becomes infectious, where γ denotes the incubation rate. P(r) = (1.0 − exp(−Λ dt)) is the recovery probability, where λ0(1 − exp(λ1t)) is the (deterministic) recovery rate. P(p) = (1.0 − exp(−α dt)) is the protection probability, where α = α0exp(α1t). P(d) = (1.0 − exp(−K dt)) is the mortality probability, with K = k0exp(k1t). P(re) = (1.0 − exp(−τ dt)) is the release probability from confinement, where τ = τ0exp(τ1t). Finally, P(q) = (1.0 − exp(−δ  dt)) is the detection probability, where δ is the quarantine rate (for example, at which infected individuals are isolated from the rest of the population).In the model, both infected non-detected and infected detected individuals can infect susceptible ones. In the model incorporating temperature in the transmission rate, the respective values of βI and βQ are calculated as follows:$${beta }_{I}(t)={beta }_{I},T_{mathrm{inv}}(t);quad {beta }_{Q}(t)={beta }_{Q},T_{mathrm{inv}}(t)$$where (T_{mathrm{inv}}=fleft(frac{1-T(t)}{bar{T}}right)), with (bar{T}) corresponding to the overall mean of the temperature time series and f(·) to a Savitzky–Golay filter, used to smooth the temperature series with a window size of 50 data points and a polynomial order of 3. When the infection rate is constant, we simply omit the temperature term. For further comparison, in a third model, β is specified with a sinusoidal function of period equal to 12 months and an estimated phase.The number of individuals transitioning from compartment i to j at time t are determined by means of binomial distributions P(Xi,P(y)), where Xi corresponds to one of the compartments S, E, I, Q, R, D, C, and P(y) to the respective transition probability defined above. Thus,

e(t) = P(S(t), P(e)), new exposed individuals at time t

p(t) = P(S(t), P(p)), protected individuals at time t

i(t) = P(E(t), P(i)), new infected not detected individuals at time t

q(t) = P(I(t), P(q)), new infected and detected individuals at time t

r(t) = P(Q(t), P(r)), total recovered individuals at time t

d(t) = P(Q(t), P(d)), total dead individuals at time t

re(t) = P(C(t), P(re)), individuals released from confinement at time t

Then, the final dynamics are given by the following equations:$$S(t)=S(t-{rm{d}}t)-e(t)-p(t)+re(t)$$$$E(t)=E(t-{rm{d}}t)+e(t)-i(t)$$$$I(t)=I(t-{rm{d}}t)+i(t)-q(t)$$$$Q(t)=Q(t-{rm{d}}t)+q(t)-r(t)-d(t)$$$$R(t)=R(t-{rm{d}}t)+r(t)$$$$D(t)=D(t-{rm{d}}t)+d(t)$$$$C(t)=C(t-{rm{d}}t)+p(t)-re(t)$$CalibrationThe model was implemented using Python and calibrated by means of the least squares algorithm of the scipy library. The error function minimized with this algorithm was obtained from the normalized residuals on the basis of total cases (Q + R + D) and deaths (D).To search parameter space, we ran 100 calibrations starting from different initial choices of parameter combinations. The tolerance for termination in the change of the cost function was set to 1 × 10−10. Tolerance for termination by the norm of the gradient was also set to 1 × 10−10, and the tolerance for termination by the change of the independent variables was set to 1 × 10−10. The solver was the lsmr method (which is suitable for problems with sparse and large Jacobian matrices) with a differential step of 1 × 10−5. With this configuration, each fitting run usually converged after ~500 iterations.ValidationTo compare the model including an effect of T in the transmission rate to those without it, we calculated the chi-square, Akaike information criterion (AIC) and Bayesian information criterion (BIC) indices for the residuals obtained from the optimization process. The resulting values are shown in Supplementary Table 1.Our choice of T to modulate the infection rate (β) instead of AH underlies the fact that the temporal dynamics of both factors roughly follow the same shape, with the advantage that T shows less oscillatory behavior than AH. This fact adds stability to the model when the inverse relationship is used in the calculation of β (Supplementary Information). This selection is further reinforced by the results from the SDC analyses, which yielded larger correlations for temperature, even when penalizing for the larger autocorrelation structure.Our choice to modulate β using T instead of AH follows from the fact that the temporal dynamics of both climate variables present roughly the same shape, with the advantage that T exhibits weaker oscillations. This less fluctuating pattern provides stability to the model fitting when the inverse relationship is used in the calculation of β (Supplementary Information). Additionally, the transient correlations obtained with SDC yielded higher values for T than for AH (even when accounting for concurrent levels of autoregression in the two variables). More

Study sites and samplingThe study was conducted in Garhwal region (Western Himalaya) from 2016 to 2017 at eight Rhododendron arboreum rich areas in four hill districts (Chamoli, Tehri, Pauri and Rudraprayag). Voucher specimen of Rhododendron arboreum collected and have been deposited in the Herbarium, Botany department, HNB Garhwal University (specimen no. GUH 8510)6. Identification of R. arboreum has been done through A Field Guide book authored by Rai et al.7. Since it is a wild species and flowers have been collected for our research and field study under the permission from competent authority of State Forest Department, Govt. of Uttarakhand. According to IUCN’s Red List Categories and Criteria, globally Rhododendron arboreum comes under Least Concern (LC) category8. These sites are situated between 30°08′47″ to 30°24′06″ N latitude and 78°25′05″ to 79°12′39″ E longitude with altitudes from 1820 m asl in Nandasain and 2270 m asl in Jadipani (Table 1; Fig. 1). All sites were well stocked (mean stand density ≥ 500 tree/ha) with Rhododendron arboreum trees mixed with Quercus leucotrichophora. We referred these resource rich sites as R. arboreum habitats (Table 1). Stratified random sampling method (i.e. stand density and CBH class’s strata) were carried out these eight sites. Total sampled area 0.2 ha in each site; two sample plots (size of each plot is 0.1 ha or 31.62 × 31.62 m) nested within 0.2 ha in each site were laid out for trees enumeration. Sample size (number of R. arboreum tree) for a total population in each site were 166 in Phadkhal; 110 in Khirsu; 104 in Khadpatiya; 166 in Ghimtoli; 80 in Jadipani; 74 in Ranichauri; 74 in Nandasain and 96 in Nauti. Out of the standing trees in sample plots, flower bearing trees were 96 in Phadkhal; 90 in Khirsu; 102 in Khadpatiya; 126 in Ghimtoli; 64 in Jadipani; 58 in Ranichauri; 68 in Nandasain and 82 in Nauti, and without flower or smaller trees were 70 in Phadkhal; 20 in Khirsu; 02 in Khadpatiya; 40 in Ghimtoli; 16 in Jadipani; 16 in Ranichauri; 06 in Nandasain and 14 in Nauti. The individuals of all tree species in each plot were recorded along with their CBH (circumference at breast height, 1.3 m above from the ground). Individuals were categorized as mature trees (≥ 31 cm CBH), saplings (11–30 cm CBH) and seedlings (≤ 10 cm CBH)9. Further all the tree individuals have been grouped into 8 CBH classes: (A) 5–15 cm, (B) 16–25 cm, (C) 26–35 cm, (D) 36–45 cm, (E) 46–55 cm, (F) 56–65 cm, (G) 66–75 cm, (H) 76–85 cm. Recorded data were used for the analysis of density10.Table 1 Physical characteristics of study sites in four districts of Garhwal region.Full size tableFigure 1Locations of Rhododendron arboreum study sites in Garhwal region (ARC GIS software 10.5 version was used for map preparation. The map was created by Mr. Raman Patel, Research scholar, Dept. of Geology, HNB Garhwal University, Srinagar, Uttarakhand, India).Full size imageFlower yield estimationFlower yield (kg/tree) was estimated during full bloom (flowering season/harvest season February–April 2017). In each sample plot, numbers of flower bearing trees varied from 29–63 trees/0.1 ha. At each site of 0.2 ha sample plot, total 40 trees, 05 flower bearing trees in each of the 08 CBH classes were marked for estimation of flower yield. The number of main branches, the number of sub- branches/offshoots per main branches (i.e. average per five randomly selected main branches per tree), and the amount of flower per sub-branches/offshoot (i.e. the average per five offshoots from the low, middle and upper canopy of each tree) were counted form marked individuals. This way flower yield/tree was calculated9,11,12.The flowers from all CBH classes in each site were mixed and weighted in 5 lots of 1 kg each. The number of flowers in each lot was then counted and the mean value (400.0 ± 9.56) was considered as a standard for conversion into kilograms. Based on this conversion flower yield kg/tree was obtained. Flower yield data were pooled and mean yield (kg/tree) for each CBH class (A–H) calculated. For each site, flower yield in kg/0.2 ha was obtained by multiplying flower yield/tree by the density of flower bearing trees/0.2 ha. The total yield kg/ha for each site was calculated as total yield = (yield/ha) × density of flower bear trees/ha9,11,12.Extraction/harvesting and marketing trendsFlower extraction and collection were totally dependent on market availability and accessibility of site; one of the selected sites (Ranichauri) was easily accessible, while Phadkhal, Khirsu and Jadipani were moderately accessible. Khadpatiya, Ghimtoli, Nandasain and Nauti sites were far-flung from market (Table 1). The highest extraction was recorded between second week of February and first week of April. During this period, data was obtained for three consecutive days at each site.Questionnaire based survey was carried out in selective forest fringe villages. Across the sites, total sixteen villages were selected for questionnaire survey, three villages each in Jadipani, Ranichauri, Nandasain and Nauti sites, while one village each in Phadkhal, Khirsu, Khadpatiya and Ghimtoli. In each village 15 families were randomly chosen for semi-structured questionnaire survey.Considering the market availability for trading of the R. arboreum flower products, Nandasain and Nauti sites are located nearest to local market whereas Khadpatiya and Ghimtoli sites are farthest from local market. As far as the access to resources is concerned, four sites represent open and easy access to resource and four sites represent open and moderate access of resource (Table 1). During questionnaire survey, villagers were asked about the number of persons involved in resource collection (hereafter referred as collectors), age of collectors, timing of collection (early morning and late evening) etc. Ten individuals in each group (adults and children) were randomly interviewed on their harvest load to generate data on the average collection per individual, the number of days spent in flower collection, and the total income generated through this activity.Squash/juice making factories are generally located nearby urban centers; local NGOs and small entrepreneurs are engaged in this work. These peoples purchase flower from the collectors or middleman for preparation of value product (squash). Collectors of each families (varied from n = 15 in Nanadasain to n = 31 in Jadipani) and buyers (n = 5 each site) were contacted to obtain information on the benefits accrued. The income values are given in Indian rupees (USD 1 = Rs. 68.00, 2017 exchange rates). Projections of potential (probable/-could generate) income (with flower processed into juice or squash) were made. The involvement of rural inhabitants as flowers collectors and the income that subsequently accrued (within a 10 km radius of fringe area) was also analyzed for sixteen villages across the sites. One adult member from each household was contacted in a village to collect information on involvement of flower collection/extraction.Juice/squash preparation methods and value-added productsThe collected flowers are graded for their size and healthiness and the stamens are separated from petals by laborers in the juice processing unit. Petals are cleaned washed with tap water and grinded into small pieces. The petal mass is retained in the water and then boiled for one hour. The slurry (aqueous solution) obtained in this process is left at room temperature for cooling and when it get cold, filtered through linen cloth. The filtrate solution is the pure juice of the flower. For the preparation of squash from the pure juice, about 2 kg of sugar is boiled in one liter of water. Further one liter of pure juice and a small quantity of citric acid (10 g/2 kg sugar) are added to this solution. The mixture is boiled again for 30 min and then left to cool at room temperature13. The obtained solution known as squash is then filtered through linen cloth and stored into containers and bottles for marketing. For long term storage and good test and aroma small amount of sodium benzoate and vanilla or kawra is also mixed in the squash.Cost–benefit analysis of value- added productsThe cost–benefit analysis of value added products prepared from the R. arboreum flowers was calculated in Rs./day which includes labour charges of workers involved in flower collection and materials/items required for preparation of different value added products viz: sugar, preservatives, essence, plastic containers/bottles, packaging materials etc. Labour charge was calculated on the basis of existing daily wages as per market rates. The monetary output was calculated as per the current market rates of the products (Table 2). The cost- benefit analysis of the squash product prepared from the flowers was calculated as Rs./day which includes: (i) Man days incumbent for the flowers extraction from the forest and for the preparation of squash product, (ii) Essential items such as sugar, preservatives etc. and their monetary equivalents, (iii) The total quantity of squash product and their monetary equivalents.Table 2 Market cost in rupees (Rs.) of essential commodity in the preparation of R. arboreum juice/squash in Garhwal region.Full size tableStatistical analysisData failed to meet the assumption of normality (Shapiro–Wilk test) as well as homogeneity (Levene statistic); therefore, a non-parametric test (i.e. Independent–Samples Kruskal–Wallis test) was applied for one-way ANOVA. However, to find the interaction of site and cbh on flower production (yield), the same data set was subjected to two-way analysis using univariate analysis. To find if (?) flower yield depends on tree diameter or not, data of actual cbh and flower yield per tree were used to determine a correlation (Pearson Correlation Coefficient) between them. In case of correlation found significant then regression equation was developed to predict flower production based on tree diameter. All analysis were performed using IBM-SPSS 16.0 version14.Ethics approval and consent to participateAll necessary approval, free prior informed consent, permit, and certification were secured. This was done to adhere to the ethical standards of human participation in scientific research. This study was approved by Research and Consultancy Cell (Ethics Committee) of HNB Garhwal University, Srinagar Garhwal, Uttarakhand, India. All the methods were performed in accordance with the relevant guidelines and regulations. More