Philippa Kaur

Lehtonen12 presents three simple models with the same broad structure: a single mutant individual with divergent mating behaviour arises in a population of ‘residents’ that all play the same strategy, and the success of that mutant is then followed (Figs. 1, 2). Specifically, Lehtonen investigates the fitness benefits of increased mating for mutant males in comparison to mutant females. Two important parameters can be varied: (i) the degree of anisogamy (defined here as the ratio of sperm number to egg number), which captures how divergent males and females are in the size (and thus number) of gametes they produce, and (ii) the efficiency of fertilisation, which determines how easily gametes can find and fuse with each other. If fertilisation is highly efficient, then gametes of the less numerous type will achieve nearly full fertilisation; on the other hand, inefficient fertilisation can result in gametes of both sexes going unfertilised.Fig. 2: Structure of the three models of Lehtonen12, showing differences in mating behaviour between resident males (green), resident females (blue) and mutant males and females (both yellow).For illustration, we suppose that females produce four eggs each and males produce eight sperm (the anisogamy ratio in nature is typically much higher). In Model 1, resident individuals spawn monogamously in a ‘nest’ (black outline), whereas mutant males and females can bring additional partners to their nest to spawn in a group. In Model 2, resident individuals divide their gametes equally among m spawning groups, each consisting of m individuals of each sex (shown here with m = 2). Mutant males and females instead divide their gametes among a larger or smaller number of groups, mmutant (shown here with mmutant = 4). In Model 3, there is a further sex asymmetry in addition to anisogamy: Fertilisation takes place inside the female’s body. Resident individuals mate with m partners (shown here with m = 2), whereas mutant males and females mate with a larger or smaller number of partners, mmutant (shown here with mmutant = 4).Full size imageIn the first two models, fertilisation is external and no assumptions are made about pre-existing differences between the sexes apart from the number of gametes they produce. In other words, males and females are identical except that males produce sperm in greater numbers than females produce eggs. In Model 1, resident individuals are assumed to mate monogamously, whereas a mutant can monopolise multiple partners of the opposite sex (Fig. 2). Importantly, both male and female mutants can bring additional partners back to their ‘nest’ to spawn in a group. When fertilisation is highly efficient, females can fertilise all of their eggs by bringing back a single male, and there is simply no benefit (in this model) of seeking further partners (Fig. 1A). In contrast, anisogamy means that males always produce at least some gametes in excess, and thus can benefit from seeking additional mates. When fertilisation is inefficient, however, both sexes benefit from increasing the concentration of opposite-sex gametes at their ‘nest’ (Fig. 1B). This latter benefit is sex-symmetric, whereas the former continues to apply only to males. As a consequence, the Bateman gradients are always steeper for males than for females (Fig. 1A, B), confirming Bateman’s argument.Model 2 similarly assumes external fertilisation, but in this case the resident males and females meet in groups consisting of m individuals of each sex (Fig. 2). Fertilisation occurs via group spawning. It is assumed that each resident individual divides its gametes evenly across M groups, whereas mutant individuals can instead spread their gametes over a larger or smaller number of groups (note that the author assumes that M = m, but this assumption could be relaxed without undermining the core argument). Spreading gametes out across a larger number of spawning groups does not increase the concentration of opposite-sex gametes they encounter (Fig. 2). However, a mutant that spreads its gametes more widely reduces the density of its own gametes across those groups in which it spawns. This in turn results in there being more opposite-sex gametes for each gamete of the mutant’s sex in those groups. For example, in Fig. 2, mutant males spawn in twice as many groups as resident males and thereby halve the density of their own sperm in each group. The resulting egg-to-sperm ratio of (frac{4}{6}=frac{2}{3}) is more favourable than the ratio of (frac{4}{8}=frac{1}{2}) that the resident males experience. Mutant females can similarly increase local sperm-to-egg ratios by spreading their eggs over more groups. However, in contrast to males, this only leads to fitness benefit if fertilisation is inefficient, and even then the benefit to females is very modest (scarcely perceptible in Fig. 1D). Gamete spreading reduces wasteful competition among the mutants’ own gametes for fertilisation. Such ‘local’ gamete competition, like gamete competition more generally, is stronger among sperm than among eggs because sperm are more numerous under anisogamy13,14. Consequently, as in Model 1, Bateman gradients are always steeper in males (Fig. 1C, D). Recall that the results of the above models emerge in the absence of any assumptions beyond the sex difference in the number of gametes produced.The third and final model allows for a further pre-existing difference between the sexes in addition to anisogamy: internal fertilisation, which is common and widespread in animals (Fig. 2)15. Each female is assumed to mate with m males, while each male divides his gametes evenly among m females. As in the previous two models, males benefit more than females from additional matings under most conditions. However, in the particular case where fertilisation is highly inefficient and the ratio of sperm to eggs is not too large, the pattern can theoretically reverse, such that female Bateman gradients exceed their male counterparts (Fig. 1F). The reason is that the effects of gamete concentration are asymmetric under internal fertilisation: Multiple mating by a female increases the local concentration of sperm its eggs experience, whereas a male’s multiple mating does not increase the concentration of eggs around its sperm (Fig. 2). Under conditions of severe sperm limitation—due to both weak anisogamy and highly inefficient fertilisation—this can lead to females benefitting more from additional matings than males (Fig. 1F). Although intriguing, it is unclear whether this finding has any empirical relevance, as sperm limitation is probably rarely severe in internal fertilisers. Under more realistic conditions of moderate to high fertilisation rates, sex differences in the degree of local gamete competition once again become decisive, and male Bateman gradients exceed their female counterparts (Fig. 1E). More

Model descriptionThe system dynamics model divided an urban dog population into the following subpopulations: (i) free-roaming dogs (both owned and unowned free-roaming, i.e. unrestricted dogs found on streets), (ii) shelter dogs (unowned restricted dogs living in shelters), and (iii) owned dogs (owned home-dwelling restricted dogs) (Fig. 1). The subpopulations change in size by individuals flowing between the different subpopulations or from flows extrinsically modelled (i.e. flows from subpopulations not included in the systems model; the acquisition of dogs from breeders and friends to the owned dog population, and the immigration/emigration of dogs from other neighbourhoods).Ordinary differential equations were used to describe the dog population dynamics. The models were written in R version 3.6.128, and numerically solved using the Runge–Kutta fourth order integration scheme with a 0.01 step sizes using the package “deSolve”29,30. For the baseline model, Eqs. (1–3) were used to describe the rates of change of dog subpopulations in the absence of management.Baseline free-roaming dog population (S):$$frac{dS}{dt}={r}_{s}times Stimes left(1-frac{S}{{K}_{s}}right)+alpha times O-delta times S$$
(1)
In the baseline model, the free-roaming dog population (Eq. 1) increases through the free-roaming dog intrinsic growth rate (rs), and the abandonment and roaming of dogs from the owned dog population (α) and decreases through adoption to the owned dog population (δ). The intrinsic growth rate is the sum of the effects of births, deaths, immigration, and emigration, which are not modelled separately. In this model, the growth rate of the free-roaming dog population is reduced depending on the population size in relation to the carrying capacity, through the logistic equation (rreal = rmax(1 − S/Ks))31. In the baseline simulation, the free-roaming dog population rises over time, until it stabilises at an equilibrium size.Baseline shelter dog population (H):$$frac{dH}{dt}=gamma times O-beta times H- {mu }_{h}times H$$
(2)
The shelter dog population (Eq. 2) increases through relinquishment of owned dogs (γ) and decreases through the adoption of shelter dogs to the owned dog population (β), and through the shelter dog death rate (µh). There is no carrying capacity for the shelter dog population as we assumed that more housing would be created as the population increases. This allowed calculation of the resources required to house shelter dogs.Baseline owned dog population (O),$$frac{dO}{dt}={r}_{o} times Otimes (1-frac{O}{{K}_{o}})+beta times H+delta times S-alpha times O-gamma times O$$
(3)
The owned dog population (Eq. 3) increases through the owned dog growth rate (ro), adoption of shelter dogs (β), and adoption of free-roaming dogs (δ); and decreases through abandonment/roaming (α) and relinquishment (γ) of owned dogs to the shelter dog population. The growth rate of the owned dog population (ro) combines the birth, death, and acquisition rates from sources other than the street or shelters (e.g. breeders, friends) and was modelled as density dependent by the limit to growth logistic formula (1 − O/Ko).Parameter estimatesDetailed descriptions of parameter estimates are provided in the supplementary information. The simulated environment was based on the city of Lviv, Ukraine. This city has an area of 182 km2 and a human population size of 717,803. Parameters were estimated from literature, where possible, and converted to monthly rates (Table 1). Initial sizes of the dog populations were estimated for the baseline simulation, based on our previous research in Lviv32. The carrying capacity depends on the availability of resources (i.e. food, shelter, water, and human attitudes and behaviour33) and is challenging to estimate. We assumed the initial free-roaming and owned dog populations were at carrying capacity. Initial population sizes for simulations including interventions were determined by the equilibrium population sizes from the baseline simulation (i.e. the stable population size, the points at which the populations were no longer increasing/decreasing).Table 1 Parameter description, parameter value, and minimum and maximum values used in the sensitivity analysis for the systems model.Full size tableEstimating the rate at which owned dogs are abandoned is difficult, as abandonment rates are often reported per dog-owning lifetime32,34 and owners are likely to under-report abandonment of dogs. Similarly, it is challenging to estimate the rate that owned dogs move from restricted to unrestricted (i.e. free-roaming). For simplicity, we modelled a combined abandonment/roaming rate (α) of 0.003 per month, estimated based on our previous research in Lviv and from literature34,35,36. We derive the owned dog relinquishment rate (γ) from New et al.37. We estimated shelter (β) and free-roaming adoption rates (δ) from shelter data in Lviv. We set the maximum intrinsic growth rate for the free-roaming dogs (rs) at 0.03 per month, similar to that reported in literature17,19,38. We assumed that demand for dogs was met quickly through a supply of dogs from births, breeders and friends and set a higher growth rate for the owned dog population (ro) at 0.07 per month.We assumed shelters operated with a “no-kill” policy (i.e. dogs were not killed in shelters as part of population management) and included a shelter dog death rate (µh) of 0.008 per month to incorporate deaths due to euthanasia for behavioural problems or health problems, or natural mortality. We modelled neutered free-roaming dog death rate (µn) explicitly for the CNR intervention at a minimum death rate of 0.02 per month38,39,40,41.InterventionsSix intervention scenarios were modelled (Table 2): sheltering; culling; CNR; responsible ownership; combined CNR and responsible ownership; and combined CNR and sheltering, representing interventions feasibly applied and often reported27. Table 2 outlines the equations describing each intervention. To simulate a sheltering intervention, a proportion of the free-roaming dog population was removed and added to the shelter dog population at sheltering rate (σ). In culling interventions, a proportion of the free-roaming dog population was removed through culling (χ).Table 2 Description of intervention parameters and coverages for simulations applied at continuous and annual periodicities.Full size tableFree-roaming dog population with sheltering intervention:$$frac{dS}{dt}={r}_{s}times Stimes left(1-frac{S}{{K}_{s}}right)+alpha times O-delta times S-sigma times S$$
(4)
Shelter dog population with sheltering intervention:$$frac{dH}{dt}=gamma times O-beta times H- {mu }_{h}times H+sigma times S$$
(5)
Free-roaming dog population with a culling intervention:$$frac{dS}{dt}={r}_{s}times Stimes left(1-frac{S}{{K}_{s}}right)+alpha times O-delta times S-chi times S$$
(6)
To simulate a CNR intervention, an additional subpopulation was added to the system (Eq. 7): (iv) the neutered free-roaming dog population (N; neutered, free-roaming). In this simulation, a proportion of the intact (I) free-roaming dog population was removed and added to the neutered free-roaming dog population. A neutering rate (φ) was added to the differential equations describing the intact free-roaming and the neutered free-roaming dog populations. Neutering was assumed to be lifelong (e.g. gonadectomy); a neutered free-roaming dog could not re-enter the intact free-roaming dog subpopulation. Neutered free-roaming dogs were removed from the population through the density dependent neutered dog death rate (µn); death rate increased when the population was closer to the carrying capacity. The death rate was a non-linear function of population size and carrying capacity modelled using a table lookup function (Fig. S1). Neutered free-roaming dogs were also removed through adoption to the owned dog population, and we assumed that adoption rates did not vary between neutered and intact free-roaming dogs.Neutered free-roaming dog population:$$frac{dN}{dt}=varphi times I-{mu }_{n}times N-delta times N$$
(7)
Intact free-roaming dog population with neutering intervention.$$frac{dI}{dt}={r}_{s}times Itimes left(1-frac{(I+N)}{{K}_{s}}right)+alpha times O-delta times I-varphi times I$$
(8)
To simulate a responsible ownership intervention, the baseline model was applied with decreased rate of abandonment/roaming (α) and increased rate of shelter adoption (β). To simulate combined CNR and responsible ownership, a proportion of the intact free-roaming dog population was removed through the neutering rate (φ), abandonments/roaming decreased (α) and shelter adoptions increased (β). In combined CNR and sheltering interventions, a proportion of the intact free-roaming dog population (I) was removed through neutering (φ) and added to the neutered free-roaming dog population (N), and a proportion was removed through sheltering (σ) and added to the shelter dog population (H).Intact free-roaming dog population with combined CNR and sheltering interventions:$$frac{dI}{dt}={r}_{s}times Stimes left(1-frac{(I+N)}{{K}_{s}}right)+alpha times O-delta times I-varphi times I- sigma times I$$
(9)
Intervention length, periodicity, and coverageAll simulations were run for 70 years to allow populations to reach equilibrium. It is important to note that this is a theoretical model; running the simulations for 70 years allows us to compare the interventions, but does not accurately predict the size of the dog subpopulations over this long time period. Interventions were applied for two lengths of time: (i) the full 70-year duration of the simulation; and (ii) a five-year period followed by no further intervention, to simulate a single period of investment in population management. In each of these simulations, we modelled the interventions as (i) continuous (i.e. a constant rate of e.g. neutering) and (ii) annual (i.e. intervention applied once per year). Interventions were run at low, medium, and high coverages (Table 2). As the processes are not equivalent, we apply different percentages for the intervention coverage (culling/neutering/sheltering) and the percent increase/decrease in parameter rates for the responsible ownership intervention. Intervention coverage refers to the proportion of dogs that are culled/neutered/sheltered per year (i.e. 20%, 40% and 70% annually) and, for responsible ownership interventions, the decrease in abandonment/roaming rate and increase in the adoption rate of shelter dogs (30%, 60% and 90% increase/decrease from baseline values). To model a low (20%), medium (40%) and high (70%) proportion of free-roaming dogs caught, but where half of the dogs were sheltered and half were neutered-and-returned, combined CNR and sheltering interventions were simulated at half-coverage (e.g. intervention rate of 0.7 was simulated by 0.35 neutered and 0.35 sheltered). For continuous interventions, sheltering (σ), culling (χ), and CNR (φ) were applied continuously during the length of the intervention. For annual interventions, σ, χ, and φ were applied to the ordinary differential equations using a forcing function applied at 12-month intervals. In simulations that included responsible ownership interventions, the decrease in owned dog abandonment/roaming (α) and the increase in shelter adoption (β) was assumed instantaneous and continuous (i.e. rates did not change throughout the intervention).Model outputsThe primary outcome of interest was the impact of interventions on free-roaming dog population size. For interventions applied for the duration of the simulation, we calculated: (i) equilibrium population size for each population; (ii) percent decrease in free-roaming dog population; (iii) costs of intervention in terms of staff-time; and (iv) an overall welfare score. For interventions applied for a five-year period, we also calculated: (v) minimum free-roaming dog population size and percent reduction from initial population size; and (vi) the length of time between the end of the intervention and time-point at which the free-roaming dog population reached above 20,000 dogs (the assumed initial free-roaming dog population size of Lviv, based on our previous research32, see Supplementary Information for detail).The costs of population management interventions vary by country (e.g. staff salaries vary between countries) and by the method of application (e.g. method of culling, or resources provided in a shelter). To enable a comparison of the resources required for each intervention, the staff time (staff working-months) required to achieve the intervention coverage was calculated. While this does not incorporate the full costs of an intervention, as equipment (e.g. surgical equipment), advertising campaigns, travel costs for the animal care team, and facilities (e.g. clinic or shelter costs) are not included, it can be used as a proxy for intervention cost. Using data provided from VIER PFOTEN International, we estimated the average number of staff required to catch and neuter the free-roaming dog population and to house the shelter dog population in each intervention, using this data as a proxy for catching and sheltering/culling. The number of dogs that can be cared for per shelter staff varies by shelter. To account for this, we estimated two staff-to-dog ratios (low and high). Table 3 describes the staff requirements for the different interventions.Table 3 Staff required for interventions and the number of dogs processed per staff per day.Full size tableUsing the projected population sizes, the staff time required for each staff type (e.g. number of veterinarian-months of work required) was calculated for each intervention. Relative salaries for the different staff types were estimated (Table 3). The relative salaries were used to calculate the cost of the interventions by:[Staff time required × relative salary ] × €20,000.Where €20,000 was the estimated annual salary of a European veterinarian, allowing relative staff-time costs to be compared between the different interventions. Average annual costs were reported.To provide overall welfare scores for each of the interventions, we apply the estimated welfare scores on a one to five scale, for each of the dog subpopulations, as determined by Hogasen et al. (2013)22. This scale is based on the Five Freedoms (freedom from hunger and thirst; freedom from discomfort; freedom from pain, injury, or disease; freedom to express normal behaviour; freedom from fear and distress42,43) and was calculated using expert opinions from 60 veterinarians in Italy22. The scores were weighted by the participants’ self-reported knowledge of different dog subpopulations, which resulted in the following scores: 2.8 for shelter dogs (WH); 3.5 for owned dogs (WO); 3.1 for neutered free-roaming dogs (WN); and 2.3 for intact free-roaming dogs (WI)22.Using these estimated welfare scores, we calculated an average welfare score for the total dog population based on the model’s projected population sizes for each subpopulation (Eq. 10). For interventions running for the duration of the simulation, the welfare score was calculated at the time point (t) when the population reached an equilibrium size. For interventions running for five years, the welfare score was calculated at the end of the five-year intervention. The percentage change in welfare scores from the baseline simulation were reported.$$Welfare score= frac{{H}_{t}times {W}_{H}+{O}_{t}times {W}_{O}+{N}_{t}times {W}_{N}+{I}_{t}times {W}_{I}}{{H}_{t}+{O}_{t}+{N}_{t}+{I}_{t}}$$
(10)
Model validation and sensitivity analysisA global sensitivity analysis was conducted on all parameters described in the baseline simulation and all interventions applied continuously, at high coverage, for the full duration of the simulation. A Latin square design algorithm was used in package “FME”44 to sample the parameters within their range of values (Table 1). For the global sensitivity analysis on interventions, all parameter values were varied, apart from the parameters involved in the intervention (e.g. culling, neutering, abandonment/roaming rates). The effects of altering individual parameters (local sensitivity analysis) on the population equilibrium was also examined for the baseline simulation using the Latin square design algorithm to sample each parameter, individually, within their range of values. Sensitivity analyses were run for 100 simulations over 50 years solved with 0.01 step sizes. More

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Testing H1 and H2 at community composition levelAs noted above, the simple fact that fungi grow more slowly than bacteria is the basis of the hypotheses that (H1) fungal communities should be more resistant than bacterial communities to drought stress, and (H2) that fungal communities should be less resilient than bacterial communities when the stress is relieved by rewetting18. In addition to growth rate, these two hypotheses may be related to differences in the form of growth between fungi and bacteria. For example, multicellular hyphal growth versus unicellular division or the greater thickness of fungal cell walls as compared to those of bacteria47,48. We tested H1 and H2 at the community composition level by blending the fungal and bacterial datasets generated from the same leaf, root, rhizosphere and soil samples collected from field-grown sorghum that had been either irrigated as a control, or subjected to preflowering drought followed by regular wetting beginning at flowering10,11.We followed the approach of Shade et al.17 to detect resistance and resilience, which had been developed for univariate variables, e.g., richness. For multivariate data, e.g., community composition, we modified it by calculating pairwise community dissimilarity for two groups: within-group (control-control pairs, drought-drought pairs, or rewetting-rewetting pairs), and between-group (control-drought pairs, or control-rewetting pairs). Ecological resistance to drought stress is detected by comparing compositional dissimilarity of between-group pairs (control-drought pairs) against within-group pairs (control-control pairs and drought-drought pairs) for each of the droughted weeks (weeks 3–8). Ecological resilience to rewetting is detected by assessing, from before to after rewetting, the change in the difference of compositional dissimilarity between within-group pairs and between-group pairs. Here, the point just before rewetting was week 8 and the points after rewetting were weeks 9–17. A t-test was used to assess the statistical significance of the differences in resistance or resilience between bacterial and fungal communities at each time point for each compartment.To account for the different resolutions of ITS and 16 S, we compared bacterial 16 S OTUs against both fungal ITS, species-level OTUs as well the fungal family level (Supplementary Fig. 1). The results of analyses using either fungal families or OTUs are consistent. Out of 36 comparisons (15 roots, 15 rhizospheres and 6 soils), different family and OTUs results were detected in four instances. In two of these, significances detected by OTUs were not detected by family (root, weeks 4 and 17) and, in the other two cases, significances detected by family were not detected by OTUs (rhizosphere, weeks 7 and 8). (Fig. 1). We report only results that are consistent at both the species and family levels (Fig. 1).In line with our first hypothesis, H1, we found that the resistance to drought stress for fungal mycobiomes was consistently stronger than that for bacterial microbiomes for weeks 5 in root, weeks 4–6 in rhizosphere, and weeks 4 and 6–8 in soil (Fig. 1, Supplementary Fig. 1 and Supplementary Table 2). In support of our second hypothesis, H2, when the stress of pre-flowering drought was relieved by rewetting, we found that the resilience of the bacterial communities was consistently higher than that for the fungi in weeks 9–16 in root, and weeks 11–17 in rhizosphere (Fig. 1, Supplementary Fig. 1 and Supplementary Table 2).Surprisingly, we found that resilience was stronger for fungal than bacterial communities in the first week (week 9) of rewetting in the rhizosphere (Fig. 1, Supplementary Fig. 1 and Supplementary Table 2). This high resilience of fungi may be associated with the quick growth of sorghum roots when rewetted. The rhizosphere zone around these newly formed roots may be quickly colonized by soil fungi, a community that was weakly affected by drought. This result suggests that re-assembly of the rhizosphere microbial community is more complex than previously expected.The finding that fungal community composition in the soil is not shaped by drought prevented us from further detecting resilience (Fig. 1). Note fungal community in early leaves was excluded from analysis due to the high proportion of non-fungal reads in sequencing11.Testing H1 and H2 at all-correlation levelNext, we moved from the comparison of whole communities to correlation among individual bacterial and fungal taxa to test the hypotheses about resistance, H1, and resilience, H2. As noted above, previous research provided the foundation for the stress gradient hypothesis, which predicts an increase in positive associations in stress32,33,34,35,36,37. Further, ecological modeling predicts that negative associations promote stability40. Concerning specific associations, studies of Arabidopsis and associated microbes reported that positive associations are favored within kingdoms, i.e., within bacteria or within fungi, while negative associations predominate between kingdoms38,39. Given these foundations, concerning H1, we expected an increase in the proportion of positive correlation by drought stress that would be strongest for B-B, followed by F-F, and lastly by B-F; for H2 we expected rewetting to cause a decrease in the proportion of positive correlation, again most strongly for B-B, followed by F-F, and lastly by B-F.Overall, at the all-correlation level, we found no consistent support for the differences postulated for bacterial and fungal responses in H1. For example, strong increases in the proportion of positive correlations under drought could be found in all microbial pairings for some compartments (B-B in leaf and root, F-F in rhizosphere and soil, and B-F in root and rhizosphere) (Fig. 2a, Supplementary Figs. 2, 3). Neither did we find consistent support for the differences ascribed to bacteria and fungi in H2 as the strongest decreases in the proportion of positive correlations during rewetting occurred at F-F in rhizosphere and soil, and B-B in leaf and root (Fig. 2b, Supplementary Figs. 2, 3).Fig. 2: Correlations of microbes in drought stress and drought relief.Estimates of combined correlations (row a) show an increase in positive correlations under drought stress across the four compartments (root, black; rhizosphere, blue; soil, red; leaf, green). Data points underlying the lines in the figure are provided in the alternative version in Supplementary Fig. 2. This result is in line with the stress gradient hypothesis which posits that stressful environments favor positive associations because competition will be less intense than in benign environments32,33,36,37. Note that positive trends in combined correlations can arise in two ways. First, from an increase of positive correlations (row b) that exceeds the rise in negative correlations (row c), e.g., Leaf bacterial-bacterial (Bac-Bac) correlations or rhizosphere fungal-fungal (Fun-Fun) correlations in the drought period (Negative correlations in row C values are multiplied by −1 to facilitate comparison). Second, from a decrease in negative correlations that exceeds a decrease in positive correlations, e.g., root bacterial-bacterial correlations or root bacterial-fungal (Bac-Fun) correlations in drought. Combined (a), positive (b) and negative (c) estimates of correlation (Spearman’s rho, ρ) are given for four compartments (root, rhizosphere, soil and leaf), and three types of correlations (Bacterium-Bacterium, Fungus-Fungus, Bacterium-Fungus). T-tests (two sided) were carried out for linear mixed effect modelling that incorporates link type and compartments as random factors. Detailed distribution densities of correlations are presented in Supplementary Fig. 3. Source data are provided as a Source Data file.Full size imageWe found support for the stress gradient hypothesis because drought increased the relative frequency of positive correlations among microbial taxa (Fig. 2a, Supplementary Figs. 2, 3). The increases were due, largely, to B-B correlations in leaf and F-F correlations in the rhizosphere during drought, when the relative frequency of positive correlations was increased (Fig. 2b, Supplementary Figs. 2, 3) and the frequencies of negative correlations were decreased or weakly increased (Fig. 2c, Supplementary Figs. 2, 3). Less obvious increases in the relative frequency of positive correlations (such as B-B in root, F-F in soil, and B-F in root and rhizosphere) occurred where drought reduced both positive and negative correlations, but the losses of negative correlations exceeded those of positive correlations (Fig. 2, Supplementary Figs. 2, 3).In support of the expectation that correlations would be more negative between taxonomic groups than within taxonomic groups, we found that the relative frequency of positive correlations was generally lower for B-F than B-B and F-F correlations (Fig. 2, Supplementary Figs. 2, 3). Moreover, as ecological modeling has indicated that negative associations should promote stability of communities40, we hypothesize that B-F correlations would be more stable than B-B and F-F networks in response to drought stress. However, we found no support for this hypothesis, as B-F correlations (for example in root) did not always show the least response to drought stress (Fig. 2, Supplementary Figs. 2, 3).Testing H1 and H2 at species co-occurrence levelFor our final test of H1 (resistance) and H2 (resilience) we focused on co-occurrence networks based on significant, positive correlations. These networks have been reported to be destabilized for bacteria but not for fungi in mesocosms subject to drought stress19, and shown to be disrupted for bacteria in natural vegetation studied over gradients of increasing aridity41,42. Using these results as guides, for H1 we expected that drought stress should disrupt co-occurrence networks most strongly for B-B, followed by F-F, and lastly by B-F. For H2 we expected that relief of stress by rewetting should strengthen microbial co-occurrence networks most strongly for B-B, followed by F-F, and lastly by B-F.For this test we constructed microbial co-occurrence networks using significant positive pairwise correlations between microbial taxa, B-B, F-F and B-F, and compared the network complexity between fully irrigated control and drought, and between control and rewetting following drought. In general, we found no consistent support for the difference between bacteria and fungi inherent in H1. Rhizosphere was the one compartment where B-B vertices dropped and F-F vertices rose in response to drought, as expected, but this result was offset in root and soil, where vertices dropped in all networks, B-B, F-F and B-F (Figs. 3, 4; Supplementary Figs. 4, 5). Analysis by co-occurrence networks highlighted the differences between plant compartments. In root drought strongly disrupted networks of B-B, B-F and F-F, but in the other three compartments, network disruption was weaker, and networks were even enhanced by drought for F-F in rhizosphere and B-B in leaf (Figs. 3, 4).Fig. 3: Networks of significant positive cross-taxonomic group correlations (bacteria and fungi).a Fungal operational taxonomic units (OTUs) (blue) and bacterial OTUs (black) are graphed as nodes. Significant positive Spearman correlations are graphed as edges (ρ  > 0.6, false discovery rate adjusted P  More

Population genetic data collection from primary data sourcesFigure 4 describes the overall data collection workflow for the four datasets that comprise CaliPopGen. We first identified literature potentially containing population genetic data for California by querying the Web of Science Core Collection (https://webofknowledge.com/) for relevant literature from 1900 to 2020 with the terms: topic = (California*) AND topic = (genetic* OR genomic*) AND topic = (species OR taxa* OR population*). We included only empirical peer-reviewed literature and excluded unreviewed preprints. In using these search terms, our goal was to broadly identify genetic papers focused on California with population or species-level analyses, while avoiding purely phylogenetic studies or those focused on agricultural or model species. This resulted in 4,942 unique records.Fig. 4Flow chart of the data collection process that generated the CaliPopGen databases.Full size imageWe next screened titles and abstracts to retain articles that: (1) provided data on populations of species which are self-sustaining without anthropogenic involvement; (2) included at least some eukaryote species; (3) included population(s) sampled within California; (4) mentioned measures of genetic diversity or differentiation; and (5) were not reviews (thus restricting our search to only primary literature). We retained 1869 studies after this first pass of literature screening (see Technical Validation for estimate of inter- and intra-screener bias).Our second, more in-depth screening pass involved reading the full text of these 1869 studies. We had two goals. First, we confirmed that retained papers fully met all five of our inclusion criteria (the first screen was very liberal with respect to these criteria, and many papers failed to meet at least one criterion after close reading). Second, we eliminated papers where the data were not presented in a way that allowed us to extract population-level information. For example, many of the more systematics-focused studies pooled samples from large, somewhat ill-defined regions (“Sierra Nevada” or “Southern California”); if such regions were larger than 50 km in a linear dimension, we deemed them unusable for making geographically-informative inferences. Other studies presented summaries of population data, often in the form of phylogenetic networks or trees, but did not include information on actual population genetic parameters and therefore were not relevant to our database. We retained 528 publications after this second pass.From this set of papers, we extracted species, locality, and genetic data for each California population or sampling locality described in each study (Fig. 3A). This included Latin binomial/trinomial, English common name, population identifiers, and geographic coordinates of sampling sites. We also noted population/sampling localities that were interpreted as comprised of interspecific hybrids, and listed both parental species. We collected population genetic diversity and differentiation statistics for each unique genetic marker for each population/sampling locality; as a result, a sampling locality may have multiple entry rows, one for each locus or marker type. Parameters extracted for each population/marker combination include sample size, genetic marker type, gene targets, number of loci, years of sampling, and reported values for effective population size (Ne), expected (HE) and observed (HO,) heterozygosity, nucleotide diversity (π, pi), alleles-per-locus (APL), allelic richness (AR), percent polymorphic loci (PPL), haplotype diversity (HDIV), inbreeding coefficient (e.g. FIS, FIT, GIS), and pairwise population genetic comparison parameters (FST, GST, DST, Nei’s D, Jost’s D, or phi). We note that while there are technical differences between allelic richness and alleles-per-locus, source literature often used the terms interchangeably, and we include the parameters and their values as named in the source. We define marker type as the general category of genetic marker used (e.g., “microsatellite” or “nuclear”), while gene targets are the specific locus/loci (e.g., “COI”). We present these data in two separate datasets, one containing all population-level genetic summary statistics (Dataset 121, see Fig. 3C and detailed description in Table 1) and a second for estimates of pairwise genetic differentiation (Dataset 221, see Fig. 3D and detailed description in Table 2).Table 1 Description of the population genetic data in Dataset 121.Full size tableTable 2 Description of the pairwise genetic distance data in Dataset 221.Full size tableAll genetic data were extracted directly from the source literature. However, we also updated or added to the metadata for these population genetic values in several ways. We included kingdom, phylum, and a lower-level taxonomic grouping for each species (usually class), and updated scientific and common names based on the currently accepted taxonomy of the Global Biodiversity Information Facility22. When geographic coordinates were not provided for a sampling locality, as was frequently the case in the older literature, we used Google Maps (https://www.google.com/maps) to georeference localities based on either in-text descriptions or embedded figure maps guided by permanent landmarks like a bend in a river or administrative boundaries. Because this can only yield approximate coordinates, we recorded estimated accuracy as the radius of our best estimate of possible error in kilometers. If coordinates were provided in degree/minute/seconds, we used Google Maps to translate them to decimal degrees. In cases where coordinates were not provided and locality descriptions were too vague to determine coordinates with less than 50 km estimated coordinate error, we did not attempt to extract coordinates but still provide the genetic data. All coordinates are provided in the web Mercator projection (EPSG:3857). We excluded studies that reported genetic parameter values only for samples aggregated regionally (“Southern California” or “Sierra Nevada”). If marker type was not explicitly included, we classified marker type based on the gene targets reported, if provided.Life history trait data collectionTo increase the utility of CaliPopGen, we also assembled data on life history traits for all animal (Dataset 321) and plant (Dataset 421) species contained in Datasets 121 and 221. We assembled trait data that have previously been shown to correlate with genetic diversity, including those related to reproduction, life cycle, and body size, as well as conservation status (e.g.23,24,25,26,). Life history data were compiled by first referencing large online repositories, often specific to taxonomic groups, like the TRY plant trait database27, and the Royal Botanic Gardens Kew Seed Information Database28. If trait data for species of interest were unavailable from these compilations, we conducted keyword literature searches for each combination of species and life history trait, and extracted data from the primary literature. When data were not available for the subspecies or species for which we had genetic data, we report values for the next closest taxonomic level, up to and including family, as available in the literature.For both animals and plants, we defined habitat types as marine, freshwater, diadromous, amphibious, or terrestrial. Marine species include those that are found in brackish or wetland-marine habitats, as well as bird species that primarily reside in marine habitats. Freshwater species include those that are found in wetland-freshwater habitats, as well as species that primarily reside in freshwater. The diadromous category includes fish species that are catadromous or anadromous. We considered species to be amphibious if they have an obligatory aquatic stage in their life cycle, but also spend a significant portion of their life cycle on land. Terrestrial species were defined as those that spend most of their life cycle on land and are not aquatic for any portion of their life cycle. In a few cases (e.g., waterbirds that are both freshwater and marine, semi-aquatic reptiles), a species could reasonably be placed in more than one category, and we did our best to identify the primary life history category for such taxa. If the taxonomic identity of an entry was hybrid between species or subspecies, this was noted in the speciesID column and no life history data were reported.The CaliPopGen Animal Life History Traits Dataset 321 (description of dataset in Table 3) includes habitat type, lifespan, fecundity, lifetime reproductive success, age at sexual maturity, number of breeding events per year, mode of reproduction, adult length and mass, California native status, listing status under the US Endangered Species Act (ESA), listing status under the California Endangered Species Act (CESA), and status as a California Species of Special Concern (SSC). For some traits, value ranges were recorded–for example, minimum to maximum lifespan. In other cases, we recorded single values and, when available, a definition of this single value, (for example, minimum, average, or maximum lifespan). We report either the range of the age of sexual maturity (minimum to maximum), or a single value, depending on the available literature. For sexually dimorphic species, we report female adult length and weight when available, because female body size often correlates with fecundity. Across animal taxonomic groups, different measures of body size and length measurements are often used, reflecting community consensus on how to measure size. Given this variation, we report the type of length measurement, if available, as Standard Length (SL), Fork Length (FL), Total Length (TL), Snout-to-Vent Length (SVL), Straight-Line Carapace (SLC), or Wingspan (WS).Table 3 Description of the animal life-history data in Dataset 321.Full size tableThe CaliPopGen Plant Life History Traits Dataset 421 (description of dataset in Table 4) includes habitat type, lifespan, life cycle, adult height, self-compatibility, monoecious or dioecious, mode of reproduction, pollination and seed dispersal modes, mass per seed, California native status, NatureServe29 element ranks (global and state ranks, see Table 5 for definitions), listing status under the Federal Endangered Species Act (ESA), and listing status under the California Endangered Species Act (CESA). In contrast to most animal species, plant lifespan was typically reported as a single value. We define life cycles as the following: Annual: completes full life cycle in one year; Biennial: completes full life cycle in two years; Perennial: completes full life cycle in more than two years; Perennial-Evergreen: perennial and retains functional leaves throughout the year; Perennial-Deciduous: perennial and loses all leaves synchronously for part of the year. Some species are variable (for example, have annual and biennial individuals), and in those cases we attempted to characterize the most common modality.Table 4 Description of the plant life-history data in Dataset 421.Full size tableTable 5 Description of the Conservation status (Heritage Rank) from California Natural Diversity Database29.Full size tableBecause of the paucity of data available for chromists and fungi, we did not extract life history trait data for the relatively few species in these taxonomic groups.Data visualization and summaryWe used the R-package raster (v3.1–5) to visualize the spatial extent of the data in CaliPopGen in Fig. 3. Panel (A) shows a summary plot of all unique populations of both the Population Genetic Diversity in Dataset 121 and the Pairwise Population Differentiation in Dataset 221. Panel (B) shows the total number of unique populations in each California terrestrial ecoregion. Panel (C) depicts all data entries of Population Genetic Diversity Dataset 121, summed for each 20×20 km grid cell. Panel (D) shows the density of pairwise straight lines drawn between pairs of localities in the Pairwise Population Differentiation Dataset 221, depicted as the total number of lines per 20×20 km grid cell. The number of populations and species of both Datasets 121 & 221 are summarized for each marine and terrestrial ecoregion in Table 6.Table 6 Summary of total numbers of populations and species per California ecoregion, separately for population genetic and pairwise datasets.Full size table More

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Overview of the study areaBased on the actual cultivation of peanuts, the Huang-Huai-Hai region is selected as the study area (Fig. 1). The main body of the study area is the Huang-Huai-Hai Plain (North China Plain), which is a typical alluvial plain resulting from extensive sediment deposition carried by the Yellow River, the Huaihe River and the Haihe River and their tributaries, and the hills in central and southern Shandong Peninsula adjacent to it. Administrative zones include 5 provinces, 2 cities, 53 cities and 376 counties (districts). In China, The Huang-Huai-Hai region is an important production and processing centre for agricultural products, with a total land area of 4.10 × 105 square kilometers and cultivated fields of 2.15 × 107 hm2, accounting for 4.3% and 16.3% of the total amount of the country, respectively. It belongs to temperate continental monsoon climate with distinct seasons, accumulated temperature of 3600–4800 degrees above 10 °C, frost-free period of 170–200 days and annual precipitation of 500–950 mm27. The Huang-huai-hai region is the largest peanut growing area, accounting for more than 50% of the country’s peanut production and area28.Figure 1Location of the study areas. The figure was made in the ArcGIS 10.2 platform (https://www.esri.com/en-us/home).Full size imageData sourcesThe data used in the study mainly include meteorological data, geographic information data and crop data. The meteorological data comes from China Meteorological Information Center (http://data.cma.cn), including the daily maximum temperature (℃), daily minimum temperature (℃), daily average temperature (℃), daily precipitation (mm) and daily average wind speed (M/s) observed by 186 ground observation meteorological stations in the Huang-Huai-Hai region from 1960 to 2019 (Fig. 1). Geographic information data include elevation DEM data (resolution of 1 km × 1 km) and land use data in the study area, which are from the resource and environmental science and data center of Chinese Academy of Sciences (http://www.resdc.cn). Crop data, including peanut sowing area and yield data, are derived from the statistical yearbooks of provinces and cities in the study area and China Agricultural Technology Network (http://www.cast.net.cn).Data processingMeteorological data processingAnusplin software is a tool to interpolate multivariate data based on ordinary thin disks and local thin disk spline functions, enabling the introduction of covariates for simultaneous spatial interpolation of multiple surfaces, suitable for meteorological data time series29. First, the Anusplin software is used to spatially interpolate the meteorological data and suitability data of the peanut growing season (April to September) from 1960 to 2019 based on the elevation data with a resolution of 1 km × 1 km. The Inverse Distance Weight (IDW) interpolation can make the meteorological data after Anusplin interpolation maintain consistency with the original data, and is able to improve the interpolation accuracy. Finally, the meteorological and suitability data set with a resolution of 1 km × 1 km is obtained. ArcGIS and MATLAB software were used to count the median of regional meteorological factors in agricultural fields of different cities (counties), and the meteorological factors and suitability of different periods of peanut growth season in each city (county) were obtained.Yield data processingMany factors affect crop yield formation, which can be generally divided into three main categories: meteorological conditions, agronomic and technological measures, and stochastic factors. Agricultural technical measures reflect the development level of social production in a certain historical period and become time technology trend output, which is referred to as trend output for short, and meteorological production reflects short period yield components that are affected by meteorological elements. Stochastic factors account for a small proportion and are often ignored in actual calculations30. The specific calculation is as follows:$$Y={Y}_{t}+{Y}_{w}$$
(1)

where Y is the actual yield (single production) of the crop, Yt is the trend yield, and Yw is the meteorological yield.In this paper, a straight-line sliding average method is used to simulate the trend yield. The straight-line sliding average method is a very commonly used method to model yield, and it considers the change in the time series of yield within a certain stage as a linear function, showing a straight line, as the stage continuously slides, the straight line continuously changes the position, and the backward slip reflects the continuous change in the evolution trend of the yield history31. The regression models in each stage are obtained in turn, and the mean value of each linear sliding regression simulation value at each time point is taken as its trend yield value. The linear trend equation at some stage is:$${Y}_{i}left(tright)={a}_{i}+{b}_{i}t$$
(2)
where i = n-k + 1, is the number of equations; k is the sliding step; n is the number of sample sequences; t is the time serial number. Yi(t) is the function value of each equation at point t. there are q function values at point t. the number of q is related to n and k. Calculate the average value of each function value at each point:$$overline{{Y }_{i}(t)}=frac{1}{q}sum_{j=1}^{q}{Y}_{i}left(tright)$$
(3)
Connecting the (overline{{Y }_{i}(t)}) value of each point can represent the historical evolution trend of production. Its characteristics depend on the value of k. Only when k is large enough, the trend yield can eliminate the influence of short cycle fluctuation. After comparison and considering the length of yield series, k is taken as 5 in this paper.After the trend yield is obtained, the meteorological yield is calculated using Eq. (1), then the relative meteorological production is$${Y}_{r}=frac{{Y}_{w}}{{Y}_{t}}$$
(4)
The relative meteorological yield shows that the relative variability of yield fluctuation deviating from the trend, that is, the amplitude of yield fluctuation, is not affected by time and space, and is comparable. However, when the value is negative, it indicates that the meteorological conditions are unfavorable to the overall crop production, and the crop yield reduction, that is, the yield reduction rate32.Characteristics of spatial and temporal distribution of climatic resources in the Huang-Huai-Hai regionCollect meteorological resource data from 1960 to 2019. Taking 1960–1989 as the first three decades of the study and 1990–2019 as the last three decades, the climatic resource changes of peanut growth in the Huang-Huai-Hai region are analyzed by interpolation of heat resources (average temperature), water resources (precipitation) and light resources (sunshine hours) in the study area in two periods combined with topographic factors.Establishment of suitability modelAccording to the definition of phenological time and growth period of peanut planting practice in the Huang-Huai-Hai region, the growth season of peanut is divided into three growth periods and five growth stages (Table 1). Temperature, precipitation and sunshine hours are the necessary meteorological factors to determine the normal development of peanut. Therefore, combined with climatic resources in the study area, temperature, precipitation and sunshine suitability model was introduced to quantitatively analyze the suitability of peanut planting.Table 1 Division of peanut growth periods.Full size tableTemperature suitability modelTemperature is a very important factor in the growth period of peanut, and the change of temperature in different growth periods will have a great influence on the yield and quality of peanut. As a warm-loving crop, accumulated temperature plays a decisive role in the budding condition and nutrient growth stage of peanut. Temperature determines the quality of fruit and the final yield of peanut. Beta function33 is used to calculate temperature suitability, which is universal for crop-temperature relationship. The specific calculation is as follows:$${F}_{i}left(tright)=frac{(t-{t}_{1}){({t}_{h}-t)}^{B}}{({t}_{0}-{t}_{1}){({t}_{h}-{t}_{0})}^{B}}$$
(5)
where the value of B is shown in$$B=frac{{t}_{h}-{t}_{0}}{{t}_{0}-{t}_{1}}$$
(6)
where Fi(t) is the temperature suitability of a certain growth period; t is the daily average temperature of peanut at a certain development stage; t1, th and t0 are the lower limit temperature, upper limit temperature and appropriate temperature required for each growth period of peanut. Refer to the corresponding index system and combined with the peanut production practice in Huang-Huai-Hai region34,35,36, determine the three base point temperature of peanut in each growth period, as shown in the Table 2.Table 2 Three fundamental points temperature and crop coefficient of peanut at each growth stage in the study area.Full size tablePrecipitation suitability modelPeanut has a long growth period, which is nearly half a year. Insufficient or excessive water during the growth period has a great impact on the growth and development, pod yield and quality of peanut. Combined with the actual situation of Huang-Huai-Hai region and peanut precipitation / water demand index, the water suitability function is determined and calculated as follows:$${text{F}}_{{text{i}}} left( {text{r}} right) = left{ {begin{array}{*{20}l} {frac{{text{r}}}{{0.9{text{ET}}_{{text{c}}} }}} hfill & {r < 0.9E{text{T}}_{{text{c}}} } hfill \ 1 hfill & {0.9E{text{T}}_{{text{c}}} le r le 1.2E{text{T}}_{{text{c}}} } hfill \ {frac{{1.2{text{ET}}_{{text{c}}} }}{{text{r}}}} hfill & {r > 1.2E{text{T}}_{{text{c}}} } hfill \ end{array} } right.$$
(7)
where Fi(r) is the water suitability of a certain growth period; r is the accumulated precipitation of peanut in a certain development period; ETc is the water demand of peanut in each growth period.$${mathrm{ET}}_{mathrm{c}}={mathrm{K}}_{mathrm{c}}cdot {mathrm{ET}}_{0}$$
(8)
where Kc is the peanut crop coefficient (Table 2) and ET0 is the crop reference evapotranspiration, which is calculated by the Penman Monteith method recommended by the international food and Agriculture Organization (FAO).Sunshine suitability modelSunshine hours are an important condition for photosynthesis. The “light compensation point” and “light saturation point” of peanut are relatively high, and more sunshine hours are required for photosynthesis. Under certain conditions of water, temperature and carbon dioxide, photosynthesis increases or decreases with the increase or decrease of light. Relevant studies show that when the sunshine hours reach more than 55% of the available sunshine hours, the crops reach the appropriate state to reflect the light37. The following formula is used to calculate the sunshine suitability of peanut in each growth period.$${mathrm{F}}_{mathrm{i}}left(mathrm{s}right)=left{begin{array}{l}frac{mathrm{S}}{{mathrm{S}}_{0}} quad S{mathrm{S}}_{0}end{array}right.$$
(9)
where Fi(s) is the sunshine suitability of peanut in a certain development period, S is the actual sunshine hours in a certain growth period, S0 is 55% of the sunshine hours (L0), and the calculation method of L0 refers to the following formula.$${mathrm{L}}_{0}=frac{2mathrm{t}}{15}$$
(10)
$$mathrm{sin}frac{mathrm{t}}{2}=sqrt{frac{mathrm{sin}(45^circ -frac{mathrm{varnothing }-updelta -upgamma }{2})times mathrm{sin}(45^circ +frac{mathrm{varnothing }-updelta -upgamma }{2})}{mathrm{cosvarnothing }times mathrm{cosdelta }}}$$
(11)
where Φ is the geographic latitude, δ is the declination, γ is the astronomical refraction, t is the angle.Comprehensive suitability modelPeanut has different needs for meteorological elements such as temperature, sunshine and precipitation in different growth periods. In order to analyze the impact of meteorological factors in different growth periods on yield, correlation analysis was conducted between the suitability of temperature, precipitation and sunshine in each growth period and the relative meteorological yield of peanut, and the correlation coefficient of each growth period divided by the sum of the correlation coefficients of the whole growth period was used as the weight coefficient of the suitability of temperature, precipitation and sunshine in each growth period (Table 3). The climatic suitability of each single element in peanut growing season is calculated by using formulas (12) and (13):Table 3 The weight coefficients of climatic suitability at each growth stage.Full size table$$left{begin{array}{c}{mathrm{b}}_{mathrm{ti}}=frac{{mathrm{a}}_{mathrm{ti}}}{sum_{mathrm{i}=1}^{mathrm{n}}{mathrm{a}}_{mathrm{ti}}}\ {mathrm{b}}_{mathrm{ri}}=frac{{mathrm{a}}_{mathrm{ri}}}{{sum }_{mathrm{i}=1}^{mathrm{n}}{mathrm{a}}_{mathrm{ri}}}\ {mathrm{b}}_{mathrm{si}}=frac{{mathrm{a}}_{mathrm{si}}}{{sum }_{mathrm{i}=1}^{mathrm{n}}{mathrm{a}}_{mathrm{si}}}end{array}right.$$
(12)
$$left{begin{array}{c}F(t)={sum }_{mathrm{i}=1}^{mathrm{n}}left[{mathrm{b}}_{mathrm{ti}}{mathrm{F}}_{mathrm{i}}(mathrm{t})right]\ F(r)={sum }_{mathrm{i}=1}^{mathrm{n}}left[{mathrm{b}}_{mathrm{ri}}{mathrm{F}}_{mathrm{i}}(mathrm{r})right]\ F(s)={sum }_{mathrm{i}=1}^{mathrm{n}}left[{mathrm{b}}_{mathrm{si}}{mathrm{F}}_{mathrm{i}}(mathrm{s})right]end{array}right.$$
(13)
where bti, bri and bsi are the weight coefficients of temperature, precipitation and sunshine suitability in the i growth period respectively, ati, ari and asi are the correlation coefficients between temperature, precipitation and sunshine suitability and meteorological impact index of peanut yield in the i growth period respectively, and F(t), F(r) and F(s) are the temperature, precipitation and sunshine suitability in peanut growth season respectively.Then, the geometric average method is used to obtain the comprehensive suitability of peanut growth season, as shown in formula (14).$$F(S)=sqrt[3]{F(t)times F(r)times F(s)}$$
(14)
Verification of climatic zoning resultsDrought and flood disaster indexOn the basis of previous studies, in view of the different water demand of peanut in different development stages, this paper adds the water demand of peanut in different development stages as an important index to calculate, and constructs a standardized precipitation crop water demand index (SPRI) that can comprehensively characterize the drought and flood situation of peanut, so as to judge and analyze the occurrence of drought and flood disasters of peanut.Step 1: calculate the difference D between precipitation and crop water demand at each development stage$${D}_{i}={P}_{i}-{ET}_{ci}$$
(15)
where Pi is the precipitation in the i development period (mm), and ETci is the crop water demand in the i development period (mm).Step 2: normalize the data sequence.Since there are negative values in the original sequence, it is necessary to normalize the data when calculating the standardized precipitation crop water demand index. The normalized value is the SPRI value. The normalization method and drought and flood classification are consistent with SPEI index38,39,40.Chilling injury indexBased on the results of previous studies41, the abnormal percentage of caloric index was selected as the index of low-temperature chilling injury of peanut to judge and analyze the occurrence of chilling injury in different growth stages. The specific calculation process and formula are as follows:Step 1: calculate the caloric index of different development stages.Combined with the growth and development characteristics of peanut and considering the appropriate temperature, lower limit temperature and upper limit temperature at different growth stages of peanut, the caloric index can reflect the response of crops to environmental heat conditions. The average value of daily heat index is taken as the heat index of growth stage to reflect the influence of heat conditions in different growth stages on crop growth and development. Refer to formulas (5) and (6) to calculate the heat index Fi(t) at different development stages.Step 2: calculate the percentage of heat index anomaly$${I}_{ci}=frac{{F}_{i}(t)-overline{{F }_{i}(t)}}{overline{{F }_{i}(t)}}times 100%$$
(16)
where Ici is the Chilling injury index of stage i, Fi(t) is the heat index of stage i, and (overline{{F }_{i}(t)}) is the average value of the heat index of stage i over the years.Heat injury indexBased on the results of previous studies42, taking the average temperature of 26 °C, 30 °C and 28 °C and the daily maximum temperature of 35 °C, 35 °C and 37 °C as the critical temperature index to identify the heat damage of peanut in three growth stages, if this condition is met and lasts for more than 3 days, it will be recorded as a high temperature event.Disaster frequencyDisaster frequency (Pi) is defined as the ratio of the number of years of disaster at a certain station to the total number of years in the study period43, which is calculated by formula (17).$${P}_{i}=frac{n}{N}times 100%$$
(17)
where n is the number of years of disaster events to some extent at a certain growth period at a certain station, and N is the total number of years. More