Philippa Kaur

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

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

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

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Direct habitat lossAccording to the global projections of urban expansion under five SSPs17 (Supplementary Note 3 and Supplementary Fig. 1), 36–74 million hectares (Mha) of land areas will be urbanized by 2100, representing a 54–111% increase compared with the baseline year of 2015. Among these, 11–33 Mha natural habitats (Supplementary Table 1) will become urban areas by 2100. Across SSP scenarios, the patterns of change in losses of total habitat, forest, shrubland, and grassland are consistent with the global projections of urban expansion (Fig. 1). In terms of urban encroachment on wetlands, wetland will undergo the largest loss under scenario SSP4 than under other scenarios. However, if the sustainable pathway of scenario SSP1 is properly implemented, this will enable us to conserve the global wetland. The greatest loss of other habitat will occur under scenario SSP3, but the minimal loss of other habitat will occur under scenario SSP1. Under the five different SSP scenarios, the United States, Nigeria, Australia, Germany, and the UK are consistently predicted to have greater habitat loss due to urban expansion (Supplementary Table 2).Fig. 1: Future direct habitat loss due to urban expansion under SSP scenarios.a The habitat loss by 2100 for each habitat type. Bars indicate the mean habitat loss area (five scenarios) for each habitat type. Error bars represent mean values ± 1 SEM for the loss of each habitat type under five scenarios, n = 5 scenarios. Points represent data in five scenarios. b The losses in total area, forest, shrubland, grassland, wetland, and other land.Full size imageThere are obvious disparities in the hot spots and cold spots of habitat loss under the five SSP scenarios (Fig. 2 and Supplementary Figs. 2–6). Potential hot spots of habitat loss are concentrated in regions such as the northeastern, southern, and western coasts of the United States, the Gulf of Guinea coastal areas, Sub-Saharan Africa, and the Persian Gulf coastal areas. Under scenario SSP5, parts of central and western Europe will also become hot spots. However, under other scenarios, the cold spots will be particularly concentrated in eastern and southern Europe. East Asia and South Asia, which are represented by China, India, and Japan, are dominated by cold spots (Supplementary Figs. 2–6), because these regions may experience a decline in urban land demand from 2050 to 2100 (for examples in China, see Supplementary Figs. 7–11), although they are currently the most populous regions in the world.Fig. 2: Future hot spots and cold spots of habitat loss due to urban expansion under SSP scenarios by 2100.Figures for the United States (a), Europe (b), Africa (c), and China (d) are presented separately. The Gi_Bin identifies statistically significant hot spots and cold spots. Statistical significance was based on the p-value and z-score (two-sided), and no adjustments were made for multiple comparisons.Full size imageOur scenario projections show that the largest natural habitat loss is expected to occur in the temperate broadleaf and mixed forests biome (except for scenario SSP3). In addition, many biomes will experience proportionate loss of natural habitat. These biomes include the tropical and subtropical coniferous forests biome, the temperate coniferous forests biome, the flooded grasslands and savannas biome, the Mediterranean forests, woodlands, and scrub biome, and the mangroves biome (Supplementary Table 3). Although the rate of future habitat loss is small at the global scale, it can be large in some areas. For example, the habitat in the temperate broadleaf and mixed forests may decrease by 1.4% under scenario SSP5. At the ecoregion scale, about 9% of 867 terrestrial ecoregions will lose more than 1% of habitat due to urban expansion (Supplementary Fig. 12). In the future, four ecoregions—the Atlantic coastal pine barrens, the coastal forests of the northeastern United States, and the Puerto Rican moist and dry forests—will experience more than 20% of habitat loss.Urban expansion threatens biodiversity prioritization schemesTo reflect the potential impact of urban expansion on protected areas (Supplementary Note 4), the analyses presented here were based on the assumption that urban expansion within protected areas is not strictly restricted and can even occur in the currently gazetted protected areas (Supplementary Note 5, Supplementary Figs. 13 and 14). In 2015, urban areas with a total area of 30,594 km2 were distributed in 28,152 protected areas, accounting for 12.6% of global protected areas (Supplementary Figs. 15 and 16). Moreover, 38% of the urban land-use changes within protected areas were due to the conversion of natural habitats into urban land between 1992 and 2015. If urban expansion continues without strict restrictions, 13.2–19.8% of the protected areas will be affected by urban land by 2100, and urban land will occur in 29,563–44,400 protected areas with a total urban land area of up to 46,705–89,901 km2 across the five SSP scenarios (the lowest and highest proportions of urban land in each protected area by 2100 under SSP3 and SSP5 scenarios are presented in Supplementary Figs. 17 and 18).We also found that 0.90% of all terrestrial biodiversity hotspots (Supplementary Note 6), which are the world’s most biologically rich yet threatened terrestrial regions24, were urbanized in 2015. And this proportion (0.90%) is higher than that located in the rest of the Earth’s surface (0.51%) in 2015. By 2100, the new urban expansion will additionally occupy 1.5–1.8% of hotspot areas under the five SSP scenarios (Supplementary Table 4). Five biodiversity hotspots are projected to suffer the largest proportion of urban land conversion: the California Floristic Province (6–11%), Japan (6–8%), the North American Coastal Plain (4–8%), the Guinean Forests of West Africa (4–8%), and the Forests of East Australia (2–6%). In contrast, the East Melanesian Islands and the New Caledonia are almost unaffected by urban expansion. Biodiversity hotspots (e.g., the Guinean Forests of West Africa, the Coastal Forests of Eastern Africa, Eastern Afromontane, and the Polynesia-Micronesia) with few human disturbances in 2015 are projected to experience the highest percentage of future urban growth. Compared with the urban areas in 2015, by 2100, the urban areas in these four biodiversity hotspots will experience a disproportionate increase of 281–708, 294–535, 169–305, and 33–337%, respectively.The World Wildlife Fund (WWF) selected the ecoregions that are most crucial to the conservation of global biodiversity as Global 20025 (Supplementary Note 7). However, about 93% of the Global 200 ecoregions will be affected by future urban expansion. Although the proportion of urban land in each ecoregion will be less than 1% in 2100, the urban area located in these ecoregions will experience an increase of 74–160% from 2015 to 2100 across the five SSP scenarios (Supplementary Table 4). Four ecologically vulnerable ecoregions that have the highest urban growth rates are the Sudd-Sahelian Flooded Grasslands and Savannas, the East African Acacia Savannas, the Hawaii Moist Forest, and the Congolian Coastal Forests. By 2100, the urban areas in these four ecoregions will increase by 877–9955, 527–646, 18–902, and 500–1037%, respectively.The five SSP scenarios showed that the urban area is expected to increase by only 73–213 km2 in the Last of the Wild areas26 (see Supplementary Note 8 for descriptions about the Last of the Wild areas) by 2100 (Supplementary Table 4).Impacts of urban expansion on habitat fragmentationThe increasing exposures of natural habitat to urbanized land use may cause long-term changes in the function and structure of the natural habitat that is adjacent to urban areas13. To examine this proximity effect, we investigated the impact of future urban expansion on the nearest distance between urban areas and natural habitat (i.e., the distance from patch edges of urban areas to patch edges of the nearest natural habitats) under different SSP scenarios. Although the global urban area is expected to increase by 36–74 Mha by 2100, the impacts of future urban expansion on adjacent natural habitat are disproportionately large. Future urban expansion will make urban areas much closer to patch edges of 34–40 Mha natural habitat, which will inevitably threaten the natural habitat and increase the risk of biodiversity decline. The effects of urban expansion on adjacent patch edges of natural habitats are remarkably different across different scenarios. Specifically, the area of affected adjacent natural habitat is expected to be 38.45, 34.24, 40.31, 37.84, and 39.42 Mha under SSP1 to SSP5 scenarios by 2100, with the smallest effect under scenario SSP2, and the largest effect under scenario SSP3. Moreover, the scale of urban expansion does not correspond directly with the size of the impact. Several countries, including Mauritania, Algeria, Saudi Arabia, Western Sahara, and the United States, will have a large change in the distance from future urban areas to natural habitats due to urban expansion (Supplementary Table 5). Such effects also varied across different natural habitat types. The distance from the patch edges of urban areas to patch edges of (a) wetland, other land, and forest, (b) grassland, and (c) shrubland will generally be shortened by ~2000, ~1500 and ~900 m, respectively.In addition to the effect on the distance to the habitat edge, urban-caused habitat fragmentation is also reflected in reducing mean patch size (MPS)13, increasing mean edge index (edge density (ED), i.e., edge length on a per-unit area)27, and enlarging isolation (mean Euclidean nearest neighbor distance, ENN_MN)28 (Fig. 3). Taking the global ecoregions as the analysis unit, we found that within a 5 km buffer of urban areas, the median of MPS of natural habitats tends to show an overall decline trend, and the segmentation and subdivision of habitats become more obvious as future urban land expands. The median of MPS is the largest under scenario SSP1, followed by SSP4, SPP2, and SSP3 with some fluctuations in between, and the smallest MPS is found with the most fragmented landscape under scenario SSP5. A smaller patch size indicates that the inner parts of the habitat are subject to higher risk of being influenced by external disturbance. Future urban expansion also tends to cause an increase in the ED of natural habitat, which is often linked with smaller patches or more irregular shapes, and therefore poses a threat to biodiversity that influences many ecological processes (e.g., the spread of dispersal and predation)13,27,28. Scenario SSP1 shows the best performance in maintaining a low habitat ED and a high level of biodiversity conservation. However, under scenario SSP5, ED will experience a rapid increase in the second half of the 21st century. Meanwhile, the ENN_MN will increase substantially in the future, suggesting that areas with the same habitat type will become increasingly isolated, irregular, dispersed, or unevenly distributed due to the barrier of urban land. This will affect the speed of dispersal and patch recolonization. Scenario SSP1 is also most conducive to maintaining the proximity of natural habitats with the same habitat type. Other scenarios show relatively similar performance.Fig. 3: Future urban expansion effects on habitat fragmentation under SSP scenarios.a Mean patch size (MPS), b edge density (ED), c mean Euclidean nearest-neighbor distance (ENN_MN).Full size imageImpacts of urban expansion on terrestrial biodiversityWe focus on biodiversity in three common vertebrate taxa (i.e., amphibians, mammals, and birds) in our analyses. Future land system conversion to urban land will cause an average of 34% loss in the overall relative species richness. Land conversion from dense forest, mosaic grassland and open forest, mosaic grassland, and bare and natural grassland to urban land will cause the highest overall relative biodiversity loss (48%, 95% confidence interval (CI): 34–59% on a 1 km grid). These land systems with a high risk of biodiversity loss are concentrated in the United States, Europe, and Sub-Saharan Africa (Supplementary Fig. 19). Overall, the negative effect of future urban expansion on the total abundance of species will be more pronounced than that on species richness. Urban land changes will result in an average of 52% overall loss in relative total abundance of species. In particular, the losses of dense forest, natural grassland, and mosaic grassland, due to conversion to urban land, will lead to a high risk of species loss (62%, 95% CI: 38–76%).In terms of the number of species (i.e., all amphibians, mammals, and birds), future urban expansion will cause an average loss of 7–9 species and a loss of up to ~197 species per 10 km grid cell by 2100 across the five SSP scenarios (Fig. 4 and Supplementary Fig. 20). Species loss is most likely to be concentrated in Sub-Saharan Africa (particularly the Gulf of Guinea coast), the United States, and Europe. In addition, southeastern Brazil, India, and the eastern coast of Australia are also relatively high-risk areas. However, the specific effects of urban expansion vary substantially across different SSP scenarios. For instance, under scenario SSP5, urban expansion will pose a fatal threat to the global species richness in areas with urban development potential (species richness loss will occur in ~740 Mha land areas), whereas under the divided pathway (SSP4) and regional rivalry pathway (SSP3) scenarios, urban expansion will threaten the richest biodiversity hotspots, such as Sub-Saharan Africa and Latin America (Supplementary Fig. 20).Fig. 4: Potential biodiversity loss due to future urban expansion under SSP scenarios.The biodiversity loss in terms of the number of terrestrial vertebrate species (amphibians, mammals, and birds) lost per 10 km grid cell in the North America (a), Europe (b), the Gulf of Guinea coast (c), and East Asia (d).Full size imageWe also found a loss of up to 12 species of threatened amphibians, mammals, and birds (including vulnerable, endangered, or critically endangered categories defined in the IUCN Red List), and a loss of up to 40 species of small-ranged amphibians, mammals, and birds (small-ranged species are species with a geographic range size smaller than the median range size for that taxon)29 due to future urban expansion by 2100. There are a few scattered areas that will be hotspots for the loss of threatened species, such as West Africa, East Africa, northern India, and the eastern coast of Australia (Supplementary Fig. 21). The loss of small-ranged species will concentrate in fewer areas (Supplementary Fig. 22). We have identified 30 conservation priority ecoregions with high risks of habitat loss and small-ranged species loss due to future urban expansion (Supplementary Table 6). These conservation priority ecoregions are all found in Latin America and Sub-Saharan Africa (Supplementary Fig. 23). However, some hotspots outside of these conservation priority regions, such as tropical Southeast Asia, the west coast of the United States, and northern New Zealand, will also be affected (Supplementary Fig. 23).The top 5% 10 km grid cells with the highest loss in species richness (28–38 species potentially being lost) scatter across adjacent urban areas. However, only 6.4–8.6% of these regions are covered by the current global network of protected areas. These areas are often overlooked, and thus receive relatively low conservation spending. Ecoregions in Sub-Saharan African, Central and South America, Southeast Asia, and Australia will be responsible for the top 43% of average species loss across the SSP scenarios (Fig. 5). Kenya, Swaziland, Brunei, Zambia, Republic of Congo, and Zimbabwe will face the largest potential species richness loss (approximately > 29 species lost per 10 km grid cell) under all five SSP scenarios (Supplementary Fig. 24 and Supplementary Table 7).Fig. 5: Average potential biodiversity loss per 10 km grid cell in ecoregions due to future urban expansion under SSP scenarios.The mean potential biodiversity loss represents the average number of terrestrial vertebrate species (amphibians, mammals, and birds) lost per 10 km grid cell.Full size image More

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