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ModelsConsider an IPD game with misperception such as implementation errors and observation errors22,23,31. Due to the misperception, the parameter in the real game changes from (omega _1=[T_1,R_1,P_1,S_1]) to (omega _2=[T_2,R_2,P_2,S_2]), and only player X notices the change. Thus, player Y’s cognition of the parameter is (omega _1), while player X’s cognition of the parameter is (omega _2). In each round, player X chooses a strategy from its strategy set (Omega _X={{mathbf {p}}=[p_{cc},p_{cd},p_{dc},p_{dd}]^T|p_{xy} in [0,1],xyin {cc,cd,dc,dd}}), e.g., (p_{xy}) is player X’s probability for cooperating with given previous outcome (xyin {cc,cd,dc,dd}). Similar to (Omega _X), player Y’s strategy set is (Omega _Y={{mathbf {q}}=[q_{cc},q_{dc},q_{cd},q_{dd}]^T|q_{xy} in [0,1],xyin {cc,dc,cd,dd}}). According to Press and Dyson7, this game can be characterized by a Markov chain with a state transition matrix (M=[M_{jk}]_{4times 4}) (see “Notations” for details). Denote ({mathbf {v}}=[v_{cc},v_{cd},v_{dc},v_{dd}]^T) as a probability vector such that ({mathbf {v}}^T M={mathbf {v}}^T) and (v_{cc}+v_{cd}+v_{dc}+v_{dd}=1). Let ({mathbf {S}}^{omega _i}_{X}=[R_i,S_i,T_i,P_i]^T), and ({mathbf {S}}^{omega _i}_{Y}=[R_i,T_i,S_i,P_i]^T,) (iin {1,2}). The expected utility functions of players are as follows:$$begin{aligned} begin{aligned} u_X^{omega _i}({mathbf {p}},{mathbf {q}})={mathbf {v}} cdot {mathbf {S}}^{omega _i}_{X}, u_Y^{omega _i}({mathbf {p}},{mathbf {q}})={mathbf {v}} cdot {mathbf {S}}^{omega _i}_{Y},iin {1,2}. end{aligned} end{aligned}$$Denote (G_1 = {{mathbf {P}}, {varvec{Omega }}, {mathbf {u}}, omega _1}), and (G_2={{mathbf {P}},{varvec{Omega }},{mathbf {u}},omega _2}), where ({mathbf {P}}={X,Y}), ({varvec{Omega }}=Omega _Xtimes Omega _Y), and ({mathbf {u}}={u_X^{omega _i},u_Y^{omega _i}}, iin {1,2}). Thus, the actual utilities of players are obtained through (G_2), and in the view of player Y, they are playing game (G_1). In the view of player X, they are playing game (G_2) but player X knows that player Y’s cognition is (G_1). (G_1) and (G_2) are shown in Table 2.Table 2 Utility matrices in IPD games with misperception.Full size tableLet ({mathbf {p}}_0=[1,1,0,0]^T). For (iin {1,2}), ({mathbf {p}}=alpha {mathbf {S}}^{omega _i}_{X} +beta {mathbf {S}}^{omega _i}_Y +gamma {mathbf {1}}+{mathbf {p}}_0), where (alpha ,beta ,gamma in {mathbb {R}}), is called a ZD strategy7 of player X in (G_i) since the strategy makes the two players’ expected utilities subjected to a linear relation:$$begin{aligned} alpha u_X^{omega _i}({mathbf {p}},{mathbf {q}})+beta u_Y^{omega _i}({mathbf {p}},{mathbf {q}})+gamma =0, end{aligned}$$for any player Y’s strategy ({mathbf {q}}). All available ZD strategies for player X in G can be expressed as (Xi (omega _i)={{mathbf {p}}in Omega _X|{mathbf {p}}=alpha {mathbf {S}}^{omega _i}_{X} +beta {mathbf {S}}^{omega _i}_Y +gamma {mathbf {1}}+{mathbf {p}}_0,alpha ,beta ,gamma in {mathbb {R}} }.) Also, the three special ZD strategies are denoted as:

(1)

equalizer strategy7,12: ({mathbf {p}}=beta {mathbf {S}}^{omega _i}_{Y}+gamma {mathbf {1}}+{mathbf {p}}_0);

(2)

extortion strategy7,13: ({mathbf {p}}=phi [({mathbf {S}}^{omega _i}_X-P_i{mathbf {1}})-chi ({mathbf {S}}^{omega _i}_Y-P_i{mathbf {1}})]+{mathbf {p}}_0,chi geqslant 1);

(3)

generous strategy14,15: ({mathbf {p}}=phi [({mathbf {S}}^{omega _i}_X-R_i{mathbf {1}})-chi ({mathbf {S}}^{omega _i}_Y-R_i{mathbf {1}})] +{mathbf {p}}_0,chi geqslant 1).

Based on the past experience, player Y knows that player X prefers ZD strategies, which has been widely considered in many IPD games7,9. To avoid that player Y notices the change, which may result in potential decrease of player X’s utility21 or collapse of the model28, player X keeps choosing ZD strategies according to (G_1), such that the strategy sequence matches player Y’s anticipation. To sum up, in our formulation,

the real game is (G_2);

player Y thinks that they are playing game (G_1), and player X thinks that they are playing game (G_2);

player X knows that player Y’s cognition is (G_1);

player Y believes that player X chooses ZD strategies;

player X tends to choose a ZD strategy according to (G_1) to avoid player Y’s suspicion of misperception.

In fact, player X can benefit from the misperception through the ZD strategy. For example, player X can adopt a generous strategy in (G_1) to not only promote player Y’s cooperation behavior, but also make player X’s utility higher than that of player Y, if the generous strategy is an extortion strategy in (G_2). A beneficial strategy for player X is able to maintain a linear relationship between players’ utilities or improve the supremum or the infimum of its utility in its own cognition. In the following, we aim to analyze player X’s implementation of a ZD strategy in IPD with misperception, and proofs are given in the Supplementary Information.Invariance of ZD strategyPlayer X’s ZD strategies may be kept in IPD games with misperception from implementation errors or observation errors. In particular, player X keeps choosing a ZD strategy ({mathbf {p}}) in (G_1) to avoid player Y’s suspicion about possible misperception. In the view of player X, it can also enforce players’ expected utilities subjected to a linear relationship if ({mathbf {p}}) is also a ZD strategy in (G_2). The following theorem provides a necessary and sufficient condition for the invariance of the linear relationship between players’ utilities.Theorem 1
Any ZD strategy ({mathbf {p}}) of player X in (G_1) is also a ZD strategy in (G_2) if and only if$$begin{aligned} frac{R_1-P_1}{2R_1-S_1-T_1}=frac{R_2-P_2}{2R_2-S_2-T_2}. end{aligned}$$
(1)

If (1) holds, player X can ignore the misperception and choose an arbitrary ZD strategy based on its opponent’s anticipation since it also leads to a linear relationship between players’ utilities, as shown in Fig. 1; otherwise, player X can not unscrupulously choose ZD strategies based on player Y’s cognition. There is a player X’s ZD strategy in player Y’s cognition which is not the ZD strategy in player X’s cognition. Further, because of the symmetry of (omega _1) and (omega _2), player X’s any available ZD strategy ({mathbf {p}}) in (G_2) is also a ZD strategy in (G_1) if and only if (1) holds. It indicates that (Xi (omega _1)=Xi (omega _2)) and player X can choose any ZD strategy based on its own cognition, which does not cause suspicion of the opponent since it is also consistent with player Y’s anticipation. Additionally, the slopes of linear relations between players’ utilities may be different, as also shown in Fig. 1, and player X can benefit from the misperception by choosing a ZD strategy to improve the corresponding slope.In fact, (1) covers the following two cases:

(1)

(2P_i=T_i+S_i), (iin {1,2}), is a sufficient condition of (1). Thus, when (2P_i=T_i+S_i), (iin {1,2}), player X’s any ZD strategy ({mathbf {p}}) in (G_1) is also a ZD strategy in (G_2). Actually, (2P_i=T_i+S_i), (iin {1,2}), means that the sum of players’ utilities when players mutual defect is equal to that when only one player chooses defective strategies.

(2)

(R_i+P_i=T_i+S_i), (iin {1,2}), is another sufficient condition of (1). Thus, when (R_i+P_i=T_i+S_i), (iin {1,2}), player X’s any ZD strategy ({mathbf {p}}) in (G_1) is also a ZD strategy in (G_2). Actually, (R_i+P_i=T_i+S_i), (iin {1,2}), means that the game has a balanced structure in utilities32. At this point, the relationship between cooperation rate and efficiency is monotonous, i.e., the higher the cooperation rate of both sides, the greater the efficiency (the sum of players’ utilities).

Furthermore, for the three special ZD strategies, player X can also maintain a linear relationship between players’ utilities in the IPD game with misperception.Figure 1Player X can also enforce a linear relationship between players’ utilities in its own cognition. Let (omega _1=[T,R_1,P_1,S]=[5,3,1,0]) and (omega _2=[T,R_2,P_2,S]=[5,frac{23}{7},frac{1}{7},0]), which satisfy (1). Consider that player X chooses two different ZD strategies in (a) and (b), respectively, and the red lines describe the relationships between players’ utilities in (G_1). We randomly generate 100 player Y’s strategies, and blue circles are ((u^{omega _2}_X,u^{omega _2}_Y)), correspondingly. Notice that blue circles are indeed on a cyan line in both (a) and (b).Full size imageEqualizer strategyBy choosing equalizer strategies according to player Y’s cognition, player X can unilaterally set player Y’s utilities, as shown in the following corollary.
Corollary 1
Player X’s any equalizer strategy ({mathbf {p}}) in (G_1) is also an equalizer strategy in (G_2) if and only if$$begin{aligned} frac{R_1-P_1}{R_2-P_2}=frac{R_1-T_1}{R_2-T_2}=frac{R_1-S_1}{R_2-S_2}. end{aligned}$$
(2)

(2) is also a sufficient condition of (1). If (2) holds, player X can unilaterally set player Y’s utility by choosing any equalizer strategy in (G_1) even though they have different cognitions; otherwise, player X can not unscrupulously choose an equalizer strategy based on player Y’s cognition since it may not be an equalizer strategy in player X’s cognition.Extortion strategyBy choosing extortion strategies according to player Y’s cognition, player X can get an extortionate share, as shown in the following corollary.
Corollary 2
For player X’s extortion strategy ({mathbf {p}}) with extortion factor (chi >1) in (G_1), ({mathbf {p}}) is also an extortion strategy in (G_2) if (1) and the following inequality hold:$$begin{aligned} begin{aligned} (S_1-P_1)(R_2-P_2)-(R_1-P_1)(T_2-P_2)-chi ((T_1-P_1)(R_2-P_2)-(R_1-P_1)(T_2-P_2))1) in (G_1), ({mathbf {p}}) is also a generous strategy in (G_2) if (1) and the following inequality hold:$$begin{aligned} begin{aligned}(S_1-R_1)(R_2-P_2)-(R_1-P_1)(T_2-R_2)-chi ((T_1-R_1)(R_2-P_2)-(R_1-P_1)(T_2-R_2))b^1_i, iin {1,2}, end{aligned} end{aligned}$$
(5)
where (a^1_i) and (b^1_i,iin {1,2}) are parameters shown in “Notations”.
Actually, when player Y chooses the always cooperate (ALLC) strategy35, i.e., ({mathbf {q}}=[1,1,1,1]^T), player X gets the supremum of the expected utility in (G_1) and player X’s utility is improved in the IPD game with misperception.Figure 4Player X can use either equalizer strategies and extortion strategies to raise the supremum of its expected utility or generous strategies to raise the infimum of its expected utility. (a) and (b) consider that (omega _1=[T,R_1,P,S]) and (omega _2=[T,R_2,P,S]), where (R_1ne R_2); (c) considers that (omega _1=[T,R,P_1,S]) and (omega _2=[T,R,P_2,S]), where (P_1ne P_2). The red lines in (a), (b), and (c) describe utilities’ relationships when player X chooses an equalizer strategy, an extortion strategy, and a generous strategy in (G_1), respectively; The yellow area contains all possible relationships between players’ utilities in (G_2) if player X does not change its strategy. In (a) and (b), r is the supremum of player X’s utility in (G_1), and (r’) is lower than the supremum of player X’s utility in (G_2); In (c), l is the infimum of player X’s utility in (G_1), and (l’) is lower than the infimum of player X’s utility in (G_2).Full size imageExtortion strategyBy choosing extortion strategies according to player Y’s cognition, player X can also improve the supremum of its expected utility.
Corollary 5
For player X’s extortion strategy ({mathbf {p}}) with extortion factor (chi >1) in (G_1), the supremum of player X’s expected utility in (G_2) is larger than that in (G_1) if$$begin{aligned} begin{aligned}a^2_ichi ^2+b^2_ichi +c^2_i1), the infimum of player X’s expected utility in (G_2) is larger than that in (G_1) if$$begin{aligned} begin{aligned}a^3_ichi ^2+b^3_ichi +c^3_i More

Comparison of T
ag calculated from publicly available data and actual measurement dataThe calculated Tag (m2/kg-FM) in each year is summarized for each species in Supplemental Table 1:

The geometric means (GMs) of Tag values calculated using the collected samples ranged from 8.1 × 10−6 to 2.5 × 10−2 m2/kg-FM; the minimum was for western bracken fern in 2019 and the maximum was for koshiabura in 2018 at Kawamata, Fukushima.

The GMs of Tag values calculated using the publicly available data ranged from 1.6 × 10−5 to 1.2 × 10−2 m2/kg-FM and thus were similar to the actual measurement data. The minimum GM was for udo in 2019 and the maximum was for koshiabura in 2019. The geometric standard deviation (GSD) range was 1.5–4.5.

Annual GMs of Tag values calculated from publicly available data and actual measurement data are compared in Fig. 1. The values for individual years are represented by different points. The Tag values were distributed close to the 1:1 line, which suggested that Tag values calculated from the publicly available data generally agreed with those calculated from actual measurements. Hence, an obvious overestimation of Tag from the publicly available data described above was not observed in the present data. We confirmed that Tag calculated from the publicly available food monitoring data and the total deposition data from the airborne survey are reliable surrogates for actual measurement samples. We discuss Tag calculated from the publicly available data hereafter.Figure 1Comparison of annual geometric means of the aggregated transfer factor (Tag) calculated from publicly available data and actual measurement data. Circles, diamonds, and triangles indicate deciduous perennial spermatophytes, deciduous tree spermatophytes, and deciduous perennial pteridophytes, respectively. Values for individual years are represented by different points. Error bars indicate the geometric standard deviation in cases where more than three samples were available.Full size imageRelationship between soil deposition and radioactivity in edible wild plants from publicly available dataWe confirmed the relationship between deposition and concentration of 137Cs for the publicly available data for butterbur scape, fatsia sprout, and western bracken fern in a year (Fig. 2), as a representative deciduous perennial and tree spermatophyte, and deciduous perennial pteridophyte, respectively, in the year of the maximum number of detections. Butterbur scape, fatsia sprout, and western bracken fern showed positive significant, nonsignificant, and weak negative significant correlations, respectively (Spearman’s rank correlation, butterbur scape, p = 0.001, rs = 0.45; fatsia sprout, p = 0.85, rs = − 0.03; western bracken fern, p = 0.03, rs = − 0.21). Among 29 subdata with more than 20 detections for each species in a year, in addition to the data shown in Fig. 2, 13 showed statistically significant positive correlations (Butterbur scape in 2014 and 2016; bamboo shoot in 2012, and 2014 − 2019; fatsia sprout in 2013 and 2016; koshiabura in 2013; and ostrich fern in 2012), and western bracken fern in 2017 showed a significant negative correlation. These weak correlations may be affected by uncertainty in the deposition data. We used a representative deposition value for each municipality and the original deposition data grid was of low resolution (see the “Methods” section Radiocesium deposition data from airborne survey). Especially for the cases lacking a clear positive correlation, the degree of radiocesium absorption by edible wild plants was largely different even in the same deposition. Radiocesium uptake by plants in an environment is also affected by other factors (e.g., soil characteristics25,26). The edible wild plants targeted in the present study were not cultivated but were collected in a variety of environments, such as forests with high organic matter content in the soil and paddy field margins with poorly drained soil high in clay content, although we cannot precisely confirm the growth environment of each species included in the present study.Figure 2Correlation between deposition and concentration of 137Cs in three edible wild plants. Circles, diamonds, and triangles indicate butterbur scape, fatsia sprout, and western bracken fern, respectively. The three species are representative deciduous perennial and tree spermatophyte, and deciduous perennial pteridophyte, respectively, in the year of the maximum number of detections.Full size imageTemporal change in T
ag
The time-dependence of Tag for each species in the period 2012–2019 is shown in Fig. 3. The Tag values of deciduous perennial spermatophytes and pteridophytes showed a decreasing trend with time. Given that the bioavailability of 137Cs in the soil in the plant root zone decreased with time, as observed in previous studies27,28, we also observed a decrease in Tag. The Tag of deciduous trees did not show a decreasing trend with time.Figure 3Temporal change in the aggregated transfer factor (Tag) in the period 2012–2019. Circles, diamonds, and triangles indicate deciduous perennial spermatophytes, deciduous tree spermatophytes (including bamboo shoot), and deciduous perennial pteridophytes, respectively. Single exponential fitted lines are shown. Solid lines indicate statistically significant parameters (see Table 2).Full size imageAfter the Chernobyl nuclear accident, radiocesium concentrations in deciduous tree leaves decreased with time owing to the effect of direct deposition at an early stage and the following root uptake effect29, and the Tag of tree leaves decreased accordingly. In previous studies conducted in orchards after the Chernobyl and Fukushima accidents, radiocesium concentrations in deciduous tree leaves showed a decreasing trend30,31. The lack of a declining trend for woody edible wild plants Tag in the present study may be due to a smaller effect of direct deposition at the early stage resulting from interception by tall tree canopies in the vicinity. The height of trees with edible wild plants is usually at eye level. The samples collected soon after the accident were possibly affected by direct deposition, whereas in the latter study period, many of the data were from trees grown after the accident. If the effect of direct deposition was large, a declining trend in Tag might have been observed as observed in orchards. Thus, the absence of a declining trend in Tag indicates that the effect of direct deposition was relatively small.As an additional possibility for the absence of a declining trend in tree Tag, the continuous supply of bioavailable radiocesium from the organic layer on the forest floor may affect the temporal change in Tag. Compared with the managed conditions in orchards of previous studies30,31, an organic layer develops on the soil surface in a forest and, therefore, reabsorption of radiocesium from the organic layer via the roots may be more active. Imamura et al.17 also observed a similar trend to that in the present study, namely that radiocesium concentrations in leaves of the canopies of the deciduous tree konara oak (Quercus serrata) did not show a temporal change from 2011 to 2015 in two Fukushima forests. These authors’ results included the effect of direct deposition on the tree bodies at an early stage of the accident, although the emergence of leaves was after the deposition. Nevertheless, a clear decreasing trend in the radiocesium concentration was not observed, which implies that a deciduous tree actively absorbs radiocesium via the roots in Fukushima forests, and a sufficient amount of radiocesium is absorbed to conceal a decline at an early stage owing to the effect of direct deposition.Single exponential fitted lines for each species are shown in Fig. 3. The estimated parameters and the Teff (year) calculated with Eq. (2) in “Methods” section are presented in Table 2. The Teff for Tag values that showed a decreasing trend was approximately 2 years, except for bamboo shoot. Tagami and Uchida10 reported that the Teff of the slow loss component for three edible wild plants of deciduous perennial spermatophytes was 970–3830 days. The 137Cs decline in pteridophytes, and deciduous shrub and herbaceous species on the floor of European forests was reported to be 1.2–8 years for Teff excluding the rapid loss component after the Chernobyl nuclear accident32. The present results are thus within the range of previous studies.Table 2 Estimated parameters and standard errors for correlations of Tag (m2/kg-FM) in the period 2012–2019 with time (day) calculated using Eq. (3) and effective half-lives [Teff, (year)] calculated using Eq. (2) for 11 parts of 10 edible wild plant species. A0 is estimated initial Tag, and λ (/day) is the 137Cs loss rate in edible parts of the plants.Full size tableFor bamboo shoot, applying a single exponential function, a relatively long Teff of 8.3 years was estimated. The Tag decreased between 2012 and 2014, and thereafter no notable change was observed. This observation may reflect the effect of rapid and a slow loss components. Indeed, we applied a two-component exponential function for bamboo shoot, and observed Teff of 0.7 years and − 7.8 years for the rapid and slow loss components, respectively. For edible wild tree species, statistically significant single exponential fitted lines were not observed, which reflected the absence of change in Tag with time, as discussed above in this section.The Tag varied for all species, varying by 1–3 orders of magnitude within a year that included more than two detections (Fig. 3, Supplemental Table 1). As demonstrated in previous studies5, the present study also showed substantial variation in Tag values, which may be for several reasons. Recently, Tagami et al.12 calculated Tag using the radiocesium concentration in edible wild plants measured by local municipalities from higher-resolution publicly available data (accurate to district level) for giant butterbur, bamboo shoot, fatsia sprout, and koshiabura. The municipalities in these authors’ study are located within the present study area. These authors’ results differed in being one or two orders of magnitude smaller than the present results. The lower resolution of the present deposition data may be one of the causes of the greater Tag variation. The other source of variation is the site dependency of radiocesium absorption by edible wild plants from the soil as described above. Clarification of factors that contribute to the variation in Tag other than 137Cs deposition, and its trends consistent with species, is necessary, which will decrease uncertainty and lead to more accurate estimation of Tag of 137Cs with wild plants.Summary of T
ag for estimation of long-term ingestion dose to the publicTo estimate long-term potential ingestion dose to the public, Tag with small temporal variability excluding high values at the early stage after the accident is required. However, for the edible wild plant species in the present study, no Tag information in an equilibrium condition from before the Fukushima accident is available. Therefore, average values of Tag for the period after the decrease in Tag has weakened and a certain number of samples is available would be appropriate. The Teff for Tag showing a decreasing trend was approximately 2 years except for bamboo shoot, which has not shown any temporal variation since 2014. The Tag for the other species, udo, uwabamisou, momijigasa, fatsia sprout, koshiabura and Japanese royal fern, has not shown temporal variation throughout 2012–2019 (see the “Results and discussion” section Temporal change in Tag). Therefore, Tag values since 2014 are applicable for estimation of long-term potential ingestion dose to the public. The GMs and GSDs of the Tag values for 2014–2019 for each species are shown in Table 3 listed in order of decreasing GM.Table 3 Aggregated transfer factor (m2/kg-FM) calculated from publicly available data for 2014–2019 for 11 parts of 10 edible wild plant species.Full size tableSignificant differences in Tag were observed among the species (one-way ANOVA with Tukey’s post hoc test, p  More

Erebia pronoe exhibits highly structured and strongly differentiated mitochondrial lineages, which are consistent with the distribution of previously described morphotaxa and analyses of Dincă et al.10 These genetic lineages are also reflected to varying degrees in the nuclear markers. The observed mito-nuclear discordances can be explained by different evolutionary rates of genetic markers, the effects of Wolbachia infections, and introgression. These aspects are discussed in more detail in the following sections on the phylogeographic history of this species complex.Mito-nuclear discordance and the systematic status of Erebia melas
Based on genital morphology and nuclear markers, E. melas represents a distinct group to E. pronoe. The common area of origin of both species was probably located in the eastern Alps, which is supported by a RASP analysis based on the nuclear markers. However, E. melas acts as an ingroup of E. pronoe based on the mitochondrial markers, and a RASP analysis indicates a common origin for both taxa in the Carpathian region. Since most Erebia species in Europe have at least parts of their distribution in the Alps21 and are adapted to Alpine environments and habitats22,23, we consider an eastern Alpine origin of the ancestor of E. pronoe and E. melas more likely. This hypothesis subsumes the assumption that the genetic proximity on the mitochondrial level was probably caused by hybridisation and introgression events, which could have occurred as a result of several eastward advances of E. pronoe to the Balkan Peninsula (see below). This seems plausible, because the ability and tendency of E. pronoe to hybridise with other Erebia species have been demonstrated repeatedly12,24,25.The existence of Wolbachia strain 2 in both species, and its distribution from the Pyrenees (in E. pronoe) to the Balkan Peninsula (in E. melas) also speaks for a common origin of both species. Thus, Wolbachia strain 2 might represent the ancient strain present in the common ancestor of this species group, surviving today at the geographic margins (i.e. Pyrenees, western Alps, Balkan Peninsula), but which at some time was replaced in the centre of the butterfly’s range (i.e. the eastern and central Alps) by strain 1. The link between co-occurrence in a common area and prevalence of one Wolbachia strain was also recently demonstrated in other Erebia species26 and might facilitate mitochondrial introgression27.Intraspecific differentiation and glacial refugia of Erebia pronoe
The Pyrenean region is inhabited by one of the oldest and most differentiated intraspecific lineages of E. pronoe. The high genetic diversity in the Pyrenees speaks for large effective population sizes throughout time, enabled by mostly altitudinal shifts in response to climatic cycles, and a lack of major genetic bottlenecks. Compared to the Pyrenean group, the genetic diversity of the western Alpine populations, also well differentiated from all other groups, is lower. This lower diversity was probably the result of repeated cold stage retreat to a geographically more restricted refugium at the foot of the south-western Alps, a well-known refugial area for numerous species28.We cannot say conclusively whether the populations in the Pyrenean region or in the western Alps differentiated first, due to the contradictory genetical markers. The higher evolutionary rate of the mitochondrial markers, the allopatric distribution, and the hybridisation with diverse Erebia species may have led to a greater differentiation of the Pyrenees and/or a loss of the genetic link between the western Alps and the Pyrenees. Since a link between the western Alps and the Pyrenees is still well reflected in the nuclear data set and by the shared Wolbachia strain 2, we consider the most likely scenario to be an early Pleistocene or even Pliocene expansion from the western Alps to the Pyrenees, with subsequent isolation and differentiation. Thus, the Pyrenees-western Alps populations might first have separated as one group from an eastern Alps group s.l., as suggested by nuclear information, and not in two independent events, as suggested by mitochondrial genes.Simultaneously to the split between western Alps and Pyrenees, a separation of the eastern Alpine group s.l. into a southern Alpine subgroup and an eastern Alpine subgroup should have occurred. The southern Alpine subgroup displays a high genetic diversity in their nuclear markers, but a significantly lower diversity in the mtDNA. This might be explained by the existence of a cold-stage refugial area in the southern Alps or their margin, supporting the constant survival of large populations, but also a reshaping of the mtDNA patterns through introgression from the eastern Alpine subgroup during secondary contact when both subgroups expanded into formerly glaciated east-central Alpine areas. The isolated occurrence of Wolbachia strain 1 and mitochondrial haplotypes H29 and H30 (shared with the eastern Alps subgroup) in the southern Alps further support the hypothesis of gene flow from the eastern Alpine region into the southern Alpine populations and vice versa.The eastern Alpine subgroup probably survived glacial periods in a large, cohesive refugium at the eastern edge of the Alps, as has been demonstrated for numerous other species28. This area is also seen as a potential centre of origin of the entire taxon. From there, a recent (most likely postglacial) dispersal must have taken place, which should be responsible at least partly for the star-like pattern of this group in both mitochondrial and nuclear haplotype networks. However, further dispersal events out of the eastern Alps during previous interglacials and maybe even going back to the Pliocene have to be postulated to explain the entire range dynamics in E. pronoe.Apparently, multiple advances out of the eastern Alps into the Balkan mountain systems have taken place from several independent glacial refugia in the region, as indicated by the different mtDNA lineages in Slovenia, western Balkan mountains, and eastern Balkan mountains. A separation between the eastern and western Balkans, and hence also separate glacial refugia in both areas, was frequently observed for mountain taxa28,31. This pattern may have resulted from a succession of independent dispersal events from the eastern Alps throughout the younger Pleistocene, with subsequent regional extinction events and/or independent dispersal events across the Carpathians, as has been demonstrated for numerous other species29.A similar pattern of two independent colonisation events also applies to the Carpathians. Thus, the highly isolated populations in the south-eastern Carpathians must go back to an older expansion out of the eastern Alps. This probably took place during one of the last interglacial phases. The route most likely followed the Carpathian arc, but only a few populations survived at their south-eastern edge. This underlines the phylogeographic independence of this part of the Romanian Carpathians, which is also supported by studies on numerous other mountain species30,31,32. On the other hand, the Tatra mountains, as the northernmost part of the Carpathians, were colonised very recently, most likely postglacially, out of the eastern Alpine area. The strong and rather recent link between these two areas is also supported by phylogeographic studies on many taxa30,33,34.Because of the slower evolutionary rate of nuclear DNA and the resulting incomplete lineage sorting, nuclear markers can contribute little to the reconstruction of these presumably recent events. In line with that, the Valais lineage also has little nuclear differentiation but is clearly distinguished from the western and eastern Alpine lineages by the exclusive mtDNA haplotype H17 and Wolbachia strain 3. The presence of a single, highly differentiated mtDNA haplotype and an exclusive Wolbachia strain indicates a selective sweep. This lineage most likely represents a chronological relict of an interglacial expansion of the eastern Alpine subgroup to the western-central Alps surviving since then in this area, finding glacial refugia in nearby unglaciated areas and becoming infested by a Wolbachia strain not present in any other E. pronoe lineage, hence accelerating its differentiation.Another selective sweep was probably the cause of the mito-nuclear unconformity in the southern Alps lineage. The occurrence of the mtDNA haplotypes H29 and H30 and the Wolbachia strain 1 indicate mitochondrial hybridisation between the eastern and southern Alpine lineages during an expansive interglacial phase. As a result, Wolbachia infection probably occurred, which might have impoverished the mitochondrial diversity of the southern Alps lineage.Consequences for subspecific differentiation in Erebia pronoe
In general, the support given by our data for the so-far described subspecies decreases from west to east. Erebia pronoe glottis Fruhstorfer, 1920, distributed in the Pyrenees, represents the best-supported subspecies. Fixed mitochondrial amino acid changes emphasize the distinctness of this taxon, which might be well advanced in the process of speciation; we cannot even exclude the possibility that it has already reached full species rank. The genetic separation of the western Alps from the Valais, geographically separated along the main Alpine ridge, justifies the recognition of the taxa E. pronoe vergy (Ochsenheimer, 1807) and E. pronoe psathura Fruhstorfer, 1920, respectively, and is supported by both marker sets as well as by the existence of two different Wolbachia strains. The eastern Alpine subgroup resembles the nominotypical E. pronoe pronoe. The existence of at least one lineage in the southern Alpine area is supported by both marker sets. A finer separation based on the mitochondrial markers is not possible, because of recent introgression events affecting east Alpine haplotypes, as also indicated by the existence of Wolbachia strain 1. This population group could be assigned to the taxon E. pronoe gardeina Schawerda, 1924, or to E. pronoe tarcenta Fruhstorfer, 1920, considering their ranges. Nevertheless, a final decision requires further regional studies. Erebia pronoe fruhstorferi Warren, 1933 was accepted to be widely distributed in the Balkan mountain systems. However, our data suggest independent lineages in the western and eastern Balkan mountain systems of which only the eastern populations can be assigned to this taxon. The lineage of the Slovenian Alps is primarily based on mitochondrial markers and morphological characteristics7. The existence of an independent lineage for the highly isolated populations in the southern Carpathians, justifies the subspecies status of E. pronoe regalis Hormuzachi, 1937. Both marker sets display a differentiation, which was more pronounced in the nuclear than in the mitochondrial DNA. More

Spatial and temporal distribution of ecological vulnerabilityBased on the SPCA model, the temporal and spatial distribution of ecological vulnerability in Shennongjia is obtained, as shown in Fig. 3. From 1996 to 2018, the area of micro vulnerability areas continued to increase and occupied a dominant position. Moreover, their distribution pattern tended to be gradually integrated, indicating that the structure and function of the ecosystem in most areas of Shennongjia were relatively complete, and in a healthy and stable state. However, the ecological environment of the severely vulnerable areas in the northeast, south and southwest of Shennongjia is in a trend of continuous deterioration, and the risk of extreme vulnerability is gradually emerging. From the spatial distribution of ecological vulnerability in 2018, it can be seen that the extremely vulnerable areas have increased significantly, and exhibit a dense and continuous distribution trend in some areas, accompanied by the development of rapid urbanization and highway traffic construction. There are also high-risk ecological vulnerable zones and the extremely vulnerability areas.Figure 3Spatial and temporal distribution of ecological vulnerability in Shennongjia. Spatial and temporal distribution of ecological vulnerability for (a) 1996, (b) 2007, (c) 2018 in Shennongjia, China.Full size imageIt can be seen from the area proportion of different levels of vulnerable areas (Fig. 4) that the area proportion of micro and extremely vulnerable areas increased significantly. Specifically, the area proportion of micro vulnerable areas increased from 59.98% in 1996 to 71.02% in 2018, while the area proportion of extremely vulnerable areas increased from 1.23% in 1996 to 7.32% in 2018. This shows that the ecological vulnerability of Shennongjia exhibits a significant two-level differentiation trend.Figure 4Proportion of the area of vulnerable districts at all levels in Shennongjia.Full size imageDynamic change of ecological vulnerabilityDuring the study period, the areas with a positive fitting slope account for more than 90% of the total area of the study area, which indicates that the overall vulnerability of Shennongjia presents a downward trend. According to the natural discontinuity point method, the dynamic change results of ecological vulnerability in Shennongjia are divided into five levels (Fig. 5), in order to discern the spatial angle more intuitively and clearly. It can be seen that the ecological vulnerability of most regions exhibits a decreasing trend, while the ecological vulnerability of certain regions increases.Figure 5Dynamic changes of ecological vulnerability in Shennongjia. Changes in the ecological vulnerability of Shennongjia in different periods: (a) 1996–2007, (b) 2007–2018, (c) 1996–2018.Full size imageFrom 1996 to 2007, whether the spatial distribution trend of ecological vulnerability increased or decreased is not obvious. However, from 2007 to 2018, the areas with significantly increased ecological vulnerability were concentrated in Yangri and Songbai in the northeast and near the Hongping airport in Shennongjia in the midwest. During this same time period, in the areas around the main urban areas and along the roads that were seriously disturbed by human activities, ecological vulnerability also exhibited a decreasing trend.Change trend of comprehensive ecological vulnerability indexAnnual change of the comprehensive ecological vulnerability indexThe results of the comprehensive ecological vulnerability index of 1996, 2007, and 2018 are 2.77, 2.71, and 2.51, respectively. From the annual change of the ecological vulnerability index in Shennongjia (Fig. 6), it can be seen that the ecological vulnerability of Shennongjia showed a downward trend from 1996 to 2018, and the stability and health of the ecosystem were improved overall.Figure 6Annual change of the comprehensive ecological vulnerability index. CEVI, comprehensive ecological vulnerability index.Full size imageAmong them, the decline of ecological vulnerability is relatively small from 1996 to 2007, which may be ascribed to the preliminary implementation of restrictive policies, such as banning logging and returning farmland to forest, which reduced ecological exposure factors, such as illegal logging and deforestation. From 2007 to 2018, the comprehensive index of ecological vulnerability in Shennongjia decreased significantly, which is mainly due to the designation of national nature reserves and the implementation of various ecological protection projects36. While reducing the exposed ecological disturbance, it simultaneously markedly improved the adaptability of the ecosystem, and further reduced the overall ecological vulnerability of the region.Changes of the comprehensive ecological vulnerability Index in different townsAccording to the comprehensive index of ecological vulnerability of eight towns in the Shennongjia (Table 5, Fig. 7), the ecological vulnerability difference of each town is obvious. In 2018, the comprehensive index of ecological vulnerability of each town is lower than that in 1996 and 2007. The results show that the average value of CEVI is, from high to low, Yangri, Xiaguping, Songbai, Xinhua, Jiuhu, Hongping, Muyu, and Songluo. The maximum value of the CEVI appeared in Yangri in 1996, and the minimum value occurred in Songluo in 2018.Table 5 Comprehensive ecological vulnerability index of towns.Full size tableFigure 7Radar chart of the comprehensive ecological vulnerability index of towns.Full size imageDriving factors of spatial and temporal evolution of ecological vulnerabilityThe formation and evolution of ecological vulnerability in Shennongjia constitutes a dynamic process, which is the result of interactions of human and natural factors. Based on the principle of SPCA of ecological vulnerability, the transformed principal components are extracted, and the rotated factor load matrix is obtained to reflect the different effects of various factors on the evaluation results. Each principal component possesses a different ability to explain the original index factors, but it has similar rules in the first four principal components (Table 6). The cumulative contribution rate of the first four principal components in the three groups of data reached more than 80%, which can reflect the information of most factors, and thus it has good representativeness.Table 6 Principal component loading and score.Full size tableAmong the first principal component and the third principal component, the contribution of land-use type index (C9) is higher; in the second principal component, the contribution of population density (C1) is higher; among the fourth principal components, the contribution of vegetation coverage (C13) is higher. Moreover, the contribution of other factors in different years and main components is dissimilar.The influence of land-use type on ecological vulnerabilityWhether due to natural or human factors, the original properties of the ecosystem are altered by changing the surface cover. Therefore, land-use type is an important factor affecting regional ecological vulnerability. The difference of surface cover leads to the difference of ecological community, and then produces varied ecological environmental benefits. Forest land is the most important land-use type in the study area, and the ecological vulnerability of the distribution area is mainly micro degree and light. However, consider the important ecological value of the forest ecosystem, attention should be given to its vulnerability. The ecological vulnerability of the construction land is mainly severe and extreme, which is largely due to the expansion of construction land, which destroys the original ecological structure and ecological community. Furthermore, a large number of manmade patches replace natural patches in the construction land, and biodiversity decreases, leading to the decline of the stability of ecological structures and the increase of vulnerability.The influence of population density on ecological vulnerabilityPopulation density is one of the most direct exposure factors in the vulnerability of ecological environments. Population density is generally higher than that in high area, and it is also a region with a developed economy and high urbanization. In these areas, human activities are frequent, which usually impart a negative disturbance to the natural environment, including the rapid expansion of cultivated land and construction land area, as well as high discharge of production and domestic wastewater waste, which has caused great pressure on the ecological environment, leading to a significant increase in ecological vulnerability.The influence of vegetation cover on ecological vulnerabilityFrom 1996 to 2018, the vegetation coverage of the Shennongjia exhibited an overall upward trend, which is of positive significance to the reduction of the vulnerability of the ecosystem. Vegetation, as the main body of the land ecosystem, maintains the balance of ecological environment through interactions with climate, landform, and soil37. Extant literature shows that the change of vegetation coverage is an major factor of regional ecological environment change, and has a clear indication function for the change of regional ecological environment38. The spatial distribution trend of ecological vulnerability in the Shennongjia is markedly similar to that of vegetation coverage. The ecological vulnerability of regions with higher vegetation coverage is lower, exhibiting a significant negative correlation. In the Shennongjia, the change of vegetation coverage is also obviously influenced by human factors.Contribution of landscape pattern index to ecological vulnerabilityThe spatial distribution of each index in Shennongjia have been obtained from previous studies47. From the unary linear regression analysis, in the years of 1996, 2007 and 2018, the NP, LPI, AI, DIVISION and SHDI are all significantly correlated with the ecological vulnerability index (Fig. 8).Figure 8Scatter plot of linear regression of landscape pattern index and ecological vulnerability index. EVI, ecological vulnerability index.Full size imageIn the case of different independent variable combinations in 1996, 2007 and 2018, the multiple regression relationship between the independent variable and the dependent variable of each group is significantly correlated, and the multiple linear regression equation of the full model is obtained as follows:$$1996{:};;{text{ Y}} = 6.443 + 0.014{text{X}}_{1} + 0.006{text{X}}_{2} – 0.038{text{X}}_{3} – 0.066{text{X}}_{4} + 0.058{text{X}}_{5}$$$$2007{:};;{text{ Y}} = 4.497 + 0.016{text{X}}_{1} + 0.007{text{X}}_{2} + 0.793{text{X}}_{3} – 0.047{text{X}}_{4} – 0.305{text{X}}_{5}$$$$2018{:};;{text{ Y}} = – 1.980 + 0.037{text{X}}_{1} + 0.006{text{X}}_{2} + 0.703{text{X}}_{3} + 0.019{text{X}}_{4} – 0.123{text{X}}_{5}$$The contribution rate of landscape pattern index to ecological vulnerability in different years of 1996, 2007, and 2018 is shown in Table 7. The contribution of AI and NP to ecological vulnerability in 1996 was high; the contribution of NP and AI to ecological vulnerability was higher in 2007; and the NP in 2018 had the highest contribution to ecological vulnerability, reaching 95.77%.Table 7 Contribution of the landscape pattern index to the ecological vulnerability index.Full size tableBased on the analysis results from 1996 to 2018, the contribution of NP and AI to ecological vulnerability is relatively high. The main reason for this is that the forest coverage rate of Shennongjia is as high as 91%. Specifically, with the forest as the landscape matrix, the NP is small and the connectivity between patches is high, showing a trend of aggregation. The degree of landscape fragmentation is relatively low and decreases annually, and ecological vulnerability decreases with the decrease of the degree of landscape fragmentation, Therefore, the impact of NP and AI on ecological vulnerability is highly significant.The AI and ecological vulnerability index always exhibit a significant negative correlation in the study period. In the 1996 research results, the contribution of AI to ecological vulnerability is the most obvious. Combined with the spatial distribution of ecological vulnerability, it can be seen that most of the severe and extremely vulnerable areas are distributed in areas with low AI. Most of them are the distribution areas of artificial patches, such as rural living areas, airports, tourism centers, etc., which are obviously disturbed by human activities, resulting in low connectivity among various landscape types, which greatly reduces the aggregation degree of landscape and increases regional vulnerability.There is also a significant positive correlation between the NP and the ecological vulnerability index. This is especially the case in 2018, when the contribution of the NP to ecological vulnerability is as high as 95.77%, which is mainly attributable to the urbanization construction of Songbai town in Shennongjia. Combined with the land-use structure map, it can be seen that the number of construction land patches in the northeast region increased sharply. In this process, the renewal of patches aggravates the degree of landscape fragmentation and plays a key role in the aggravation of regional vulnerability risk.Although the impact of LPI, SHDI and DIVISION on ecological vulnerability always exists, the contribution is not very significant. Among them, SHDI contributed 10.38% in 2007, which was more sensitive to the unbalanced distribution of each patch type. In areas with high SHDI, landscape heterogeneity is high, the ecological pattern is unstable, and ecological vulnerability increases. More

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