Ecology

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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Water ecological security evaluation results of Yellow River BasinIndex weight analysisThis study selects the index weights in 2009, 2014, and 2019 for comparative analysis. As shown in Table 3, in terms of space, in the pressure layer, indicator A6 (Water area) has the most prominent weight, and indicator A3 (Natural population growth rate) has the most negligible weight; in the state layer, indicator B6 (Proportion of wetland area to total area) has the most prominent weight, and B1 (COD emissions per 10,000 yuan GDP) has the most negligible weight; in the response layer, indicator C3 (Green area rate of built-up area) has the most prominent weight, and indicator C2 (Centralized treatment rate of urban domestic sewage) has the most negligible weight. In summary, water area, wetland area, and built-up green space are the key indicators affecting the water ecology of the Yellow River Basin, including natural factors and economic and social factors.Table 3 Water ecological security index weight.Full size tableIn terms of time, indicators A6 and B6 have equal weights in three years and have always been in an important position. The weight of indicator C1 (the rate of stable compliance of wastewater discharge by industrial enterprises) has fallen for three consecutive years, from 0.38 to 0.09. It shows that after years of environmental management in various cities, the rate of compliance with wastewater discharge standards of industrial enterprises has been continuously increasing. It plays a positive role in the construction of water ecological security. The weight of indicator C3 has increased significantly in three years, from 0.31 in 2009 to 0.90 in 2019, indicating that with the continuous development of urbanization, the built-up area has become larger and larger, which has a massive impact on water ecological security. Therefore, the green area in the built-up area is vital, which is the key to ensuring the urban ecological environment. It is also a critical factor in maintaining the water ecological security.Trend analysis of water ecological securityThis study is based on Eq. (4) to calculate the WESI of the nine provinces in the past ten years, as shown in Fig. 3. From the perspective of the changes in WESI from 2009 to 2019, the overall trend is slowly increasing. Compared with 2009, WESI increased by 5.96% in 2019, but the average annual growth rate was only 0.59%. The sharp rise stage was in 2009–2012, with an average annual growth rate of 1.84%. Since 2009, there has been no inferior V water in the main stream of the Yellow River, and the water quality has been improving year by year. During this period, the nine provinces implemented the Yellow River Basin Flood Control Plan under the guidance of The State Council. The plan calls for strengthening infrastructure construction in the Yellow River Basin and conducting work such as river improvement and soil and water conservation. Therefore, we will promote the restoration of water ecology in the river basin and improve the safety of water ecology. From 2012 to 2019, WESI showed a trend of ups and downs. This is because the provinces have gradually shifted their development focus to the economy after achieving significant results in restoring water ecology in the river basin. The rapid economic development has brought more significant pressure to environmental governance and hindered water ecological safety improvement.Figure 3Trend map of water ecological security index (WESI) of nine provinces.Full size imageCriterion layer quantitative resultsTo further study and appraise the water ecological security of the study area, this paper quantifies the criteria layers (i.e., pressure, state, response) on account of the SMI-P method. It selects 2009, 2014, and 2019 for comparative analysis. As shown in Fig. 4, the criterion layer has undergone specific changes over time. First of all, the distribution of pressure in 62 cities has not changed much in three years. The areas with more tremendous pressure on water ecological security are mainly concentrated in eastern cities, including Shuozhou, Taiyuan, Jinzhou, Luliang, Linfen, Jincheng, and Changzhi, Anyang, Hebi, Jiaozuo, Puyang, Liaocheng, and other cities. Areas with less pressure are mainly concentrated in western and eastern cities, including Guoluo Tibetan Autonomous Prefecture, Hainan Tibetan Autonomous Prefecture, Haibei Tibetan Autonomous Prefecture, Ordos, Bayannaoer, Yulin, and other cities. In 2009, the precipitation in spring and winter in Lanzhou is less, the degree of drought is serious, and the flood disaster is more severe in flood season, which brings tremendous pressure to the water ecological security. After 2015, Lanzhou continued to implement the Action Plan for Prevention and Control of Water Pollution and then the river chief system was implemented. In 2019, The Work Plan of Lanzhou Municipal Water Pollution Prevention and Control Action in 2019 was issued and implemented. All these measures and actions have laid a foundation for water ecological security. On the contrary, with the rapid development of urbanization and economy and society, the pressure of water ecological security in Jinan has increased.Figure 4Quantitative spatial distribution map of the 62 cities in the Yellow River Basin. Note This was created by ArcMap-GIS, version 10.5. https://www.esri.com/.Full size imageThe larger the value of the status layer, the better the aquatic ecological status. On the contrary, the worse the aquatic ecological security. The overall spatial distribution of the status layer has not changed significantly in the past three years, and the changes are mainly concentrated in some cities. For example, the water ecological security status of Wuhan and Ulan Chab has gradually deteriorated in three years. The reason is that the urban population is becoming denser and sewage discharge is increasing, but related management and measures have not been fully implemented. In Dongying, the water ecological security status improved in 2014 and 2019. According to the Environmental Status Bulletin, in 2014, Dongying deepened its drainage basin pollution control system, continuously strengthened the restraint mechanism to improve river water quality, and carried out a pilot wetland ecological restoration.In the three years of 2009, 2014, and 2019, the response layer has changed more significantly than the pressure and status layers. It can be seen that the degree of response scarcity has gradually shifted from western cities to eastern cities. The reason can be understood as that due to their superior natural conditions, western cities have relatively weak awareness of water ecological protection and governance, and their ability to respond to emergencies is insufficient. However, with the increasingly prominent ecological and environmental problems, the awareness of maintaining water ecological safety is increasing, and the protection and governance measures are constantly improving. For example, Guoluo Tibetan Autonomous Prefecture, Hainan Tibetan Autonomous Prefecture, and Haibei Tibetan Autonomous Prefecture. Eastern cities are densely populated, urbanization development is faster than western cities, and environmental problems occur more frequently. Therefore, the awareness of ecological and environmental protection is more substantial, the governance system is relatively complete, and responsiveness is relatively good. However, as time progresses, some cities have somewhat slackened their ecological environment governance, and therefore their responsiveness has also weakened. For example, Shuozhou, Jinzhou, Lvliang, Linfen, and other places.Final quantitative resultsIn order to show the water ecological security status of 62 cities more intuitively, this paper shows the water ecological status level in Table 2 through the GIS spatial distribution map (Fig. 5).Figure 5Distribution map of water ecological security status in 62 cities of the Yellow River Basin. Note This was created by ArcMap-GIS, version 10.5. https://www.esri.com/.Full size imageLooking at the overall situation in the past three years, the water ecological security status is relatively stable, with little overall change. The reasons mainly include natural geographical location and economic and social development. In terms of physical geography, the safer areas are concentrated in the upper reaches of the Yellow River Basin, all of which have the characteristics of large land and sparsely populated areas and relatively superior natural conditions. They provide good conditions and foundations for the construction of water ecological security. The moderate warning cities are primarily located in the Loess Plateau and the North China Plain, where water resources are scarce, and the dense population, posing a threat to water ecological security. In terms of economic and social development, relatively safe areas are located in remote areas with inconvenient transportation. The region is dominated by agriculture and animal husbandry, with relatively backward economic development and a low level of urbanization. In addition, the threat to water ecological security is relatively tiny. Residents in the moderate warning area have a significant living demand, and the over-exploitation and utilization of natural resources have led to the destruction of the ecological environment. Therefore, it poses a more significant threat to water ecological security.Combining Fig. 5 and Table A.2 of appendix, it can be seen that in 2009, there were 8 safer cities, 22 with early warning level, and 32 with moderate warning. Relatively safe cities are concentrated in the southwest and north of the Yellow River Basin; cities with moderate warning level are distributed in the central and eastern areas. In 2014, the number of safer cities increased to 10, and the number of cities with moderate warning level decreased to 30. The means that water ecological security has received more and more attention, and cities have consciously strengthened the protection and governance of water ecology to maintain water ecological security. In 2019, there are 11 relatively safe cities, 21 cities with warning level, and 30 cities with moderate warning level. The overall situation has not changed much, and some cities have changed significantly. For example, Erdos had increased from an early warning status in 2009 to a safer status in 2014, and its safety index has risen from 0.57 to 0.65. Wuzhong has been upgraded from the warning level in 2009 (0.39) to the relatively safe in 2014 (0.44), and the safety index (0.47) in 2019 has also increased. Binzhou had improved from its early warning status (0.60) in 2009 to a relatively safe level (0.64) in 2014, and its safety index (0.66) has also increased in 2019, but the increase is not significant. On the contrary, Jinan has deteriorated from the early warning level in 2009 and 2014 to the moderate warning level in 2019, indicating that the water ecological security of Jinan has been seriously threatened in the process of rapid development.Spatial autocorrelation analysis of 62 cities in the Yellow River BasinGlobal spatial autocorrelation analysisThis paper selects 2009, 2014 and 2019, and analyzes the global spatial autocorrelation based on GeoDa. Combining Table 4 and Fig. 6, the Moran index for these three years was 0.298, 0.359, and 0.334 respectively, which were all in the [0,1] interval, indicating the water ecological security of 62 cities in the past three years showed significant spatial autocorrelation. Moreover, there is a positive spatial correlation, and the spatial autocorrelation is strong. The four quadrants of the scatter chart are high-high (i.e., first quadrant) aggregation area, low–high (i.e., second quadrant) aggregation area, low-low (i.e., third quadrant) aggregation area, and high-low (i.e., fourth quadrant) aggregation area. After testing, z-value  > 1.96, p-value  More

Detection of archival Phyllonorycter mines in historical herbariaOnly 1.5% (225 out of 15,009) of herbarium specimens of Tilia spp. examined from the Palearctic contained Ph. issikii leaf mines. These 225 herbarium specimens occurred in 185 geographical locations across the Palearctic, with the westernmost point in Germany (Hessen; the herbarium specimen dated by 2004) to the most eastern locations in Japan (on the island of Hokkaido; 1885–1974) (Fig. 1).Figure 1The localities where herbarium specimens of Tilia spp. carrying Phyllonorycter mines were collected in the Palearctic in the last 253 years. The dotted line divides Ph. issikii range to native (below the line) and invaded (above the line). The map was generated using ArcGIS 9.3 (Release 9.3. New York St., Redlands, CA. Environmental Systems Research Institute, http://www.esri.com/software/arcgis/eval-help/arcgis-93).Full size imageMost specimens with leaf mines (90%; 203/225) originated from Eastern Palearctic, in particular from the Russian Far East (RFE) (67.5%, 137/203) (Fig. 2a). In some cases, leaves were severely attacked, carrying up to 12 mines per leaf (as documented in the Russian Far East in 1930s–1960s). On the other hand, we found only 22 herbarium specimens with mines (10%; 22/225) from the putative invaded region in Western Palearctic, with the majority of herbarium specimens with mines (7% 15/225) from European Russia (Fig. 2b).Figure 2The presence of Phyllonorycter issikii mines in the herbarium specimens collected in the putative native (a) and invaded (b) ranges over the past 253 years (1764–2016). The number of herbarium specimens with and without mines and the percentage of the specimens with mines in each region or country from all herbarium specimens examined in a region or country (in brackets) are given next to each graph. The total number of herbarium specimens, including those with and without mines, is given for Eastern (a) and Western Palearctic (b) separately and altogether (a + b).Full size imageThe average number of leaf mines per herbarium specimen found in native (5.68 ± 0.77) and invaded regions (6.09 ± 1.70) was not significantly different (Mann–Whitney U-test: U = 20,145; Z = 0.43; p = 0.43). However, the infestation rate by Ph. issikii, i.e. percentage of leaves with mines per herbarium specimen was statistically higher in the West than in the East: 35% ± 8.19 versus 23% ± 1.94 (Mann–Whitney U-test: U = 1339; Z = 2.30; p = 0.02).Leaf mines from the East were significantly older than those from the West (Mann–Whitney U-test: U = 81; Z =  − 4.4; p  400 bp) were obtained for 71 archival specimens that were between 7 and 162 years old (Fig. 4, the points in dashed frame) (Table S4). Nine of these 71 specimens were over one century old (106–162-year-old): eight originated from the Palearctic and one from the Nearctic (Fig. 4, the points in gray cloud).In the Palearctic, the oldest successfully DNA barcoded Ph. issikii specimen (obtained sequence length 408 bp) was a 162-year-old larva dissected from the leaf mine on Tilia amurensis from the RFE (village Busse, Amur Oblast, the year 1859), sequence ID LMINH119-19 (Fig. 5, Table S5). In the Nearctic, the oldest sequenced specimen (obtained sequence length 658 bp) was 127-year-old larva of Ph. tiliacella on T. americana from USA, Pennsylvania (Fig. 5, Table S5).Figure 5A maximum likelihood tree of 81 COI sequences of Phyllonorycter spp. Overall, 71 archival sequenced specimens were dissected from herbaria collected in the Palearctic and the Nearctic in 1859–2014 and ten specimens (highlighted in blue) originated from the modern range20. The tree was generated with the K2P nucleotide substitution model and bootstrap method (2500 iterations), p  More

Graded lockdowns imposed by the South African government to manage the COVID-19 pandemic27,28,29 has afforded us a unique opportunity to quantify shorebird responses to increasing human density in Muizenberg Beach over 8 months in 2020, including a 2-month period of virtual human exclusion. In spite of our study being limited to one beach over 2 years, we were able to take advantage of data collected prior to- (2019) and during the 2020 COVID lockdowns, to better understand a pervasive feature of sandy beach ecosystems (human recreation) that is predicted to intensify in future10.Findings for the 2019–2020 component of our study generally conformed to hypotheses posed. Firstly, shorebird abundance was inversely associated with human abundance and was positively related to lockdown level in 2020. Secondly, shorebird abundance was generally greatest during lockdown levels 5 and 4, when humans were effectively absent from the beach. To contextualise, shorebird abundance was roughly six times greater at the start of lockdown level 5 (2020) than the equivalent period in 2019. Thirdly, lowest shorebird abundance occurred during lockdown level 1 when human abundance was greatest in 2020. Collectively, these findings indicate a strong inverse association between shorebird- and human abundance on Muizenberg Beach and align with results of other studies36,37,38,39. Cumulatively, our findings, allied with prior research highlight the potential for human recreational activity, particularly at high intensities, to impact shorebird utilisation of sandy beach ecosystems, which may in turn affect ecological functions they provide that contribute to ecosystem multifunctionality.The inverse relationship that we recorded between human- and shorebird abundance likely manifests through the diverse ways in which recreational activity impacts fundamental processes and ecosystem components, which in turn link ecologically to shorebirds10,36,37,38,39,40. Muizenberg Beach is popular for surfing, bait-harvesting and general recreational activities, and it is these activities that likely drive the human-shorebird relationship that we report, particularly in 2020. When carried out under high human densities, such activities can lead to a reduction in space available, rendering the ecosystem less suitable as a substrate for birds36. Noise pollution and the presence of dogs may further depress habitat suitability41. Repeated trampling of sediment can negatively impact macrofaunal populations, which together with altered sedimentary biogeochemistry (e.g. increased anoxia), can reduce trophic resource availability to shorebirds, with benthic bait-collecting compounding these effects42,43. At the start of our data collection in 2020, we were unable to identify shorebird species due to lockdown levels 5 and 4 prohibiting human presence on the beach27,28,29. It is probable though that shorebird assemblages during lockdown levels 5 and 4 were not the same as those we identified between lockdown level 3 to 1 (mainly gulls; Table 3). This is based on research showing that increasing environmental disturbances can induce switches in biotic assemblages to those that can tolerate human activities44. Thus, the shorebird assemblages we identified during lockdown levels 3 to 1 is potentially the end-result of the mechanisms highlighted above (space reduction, noise, reduced resource availability) acting on shorebird assemblages in the absence of humans (lockdown levels 5 and 4) following humans being permitted onto the beach.At an inter-annual level, our data revealed idiosyncratic patterns that raise interesting questions about human-shorebird relationships. In 2019, in the absence of any lockdowns, shorebird abundance rose over the winter period (May–August). Winter peaks in abundance have previously been recorded in the literature45,46,47, including for kelp gulls (Larus dominicanus), which were the dominant shorebird in Muizenberg Beach. Specifically, winter abundance peaks for this species have been recorded in sandy beaches in the Eastern Cape, the Swartkops Estuary and Algoa Bay in South Africa (southeast coast)45,46,47. However, the absence of a winter abundance peak in 2020 raises the possibility that the 2019 winter-peak was not seasonal but an opportunistic response to decreased human abundance (see Fig. 4A). In South Africa, coastal ecosystems generally experience greatest human numbers in summer, due to warmer conditions and long end-of-year-vacation periods, based on our observations and experiences.The second inter-annual trend worth noting in our findings is that shorebird abundance was greater in 2019 than 2020, despite lockdowns being implemented in 2020. This counterintuitive finding is likely due to lockdowns that excluded people from the beach in 2020 (levels 5 to 3) being too short in duration to facilitate increases in bird numbers in 2020 beyond the 2019 level. This is supported by our data showing that humans were excluded from the beach for a total of 2 months (April and May 2020; levels 5-4) out of the 8-month period during which photographs were analysed. It would have been expected at the onset of the study that humans would be excluded from the beach during lockdown level 329, which would have resulted in an additional two and a half months of human exclusion and potentially a higher mean shorebird abundance for 2020. However, it is clear from our data that humans were present on the beach during level 3. On closer inspection, it is evident that human numbers increased even prior to the end of lockdown level 4. In fact, human abundance was greater under lockdown level 3 in 2020 than in the same period in 2019. Such high numbers of humans on the beach despite prohibitions are likely due to a lack of compliance, confusion around regulations and/or ‘covid fatigue’, which describes the propensity of humans to grow tired of COVID-19 regulations48. An additional consideration is that human numbers on the beach increased dramatically during lockdown levels 2 and 1, being almost twice the level recorded in 2019 in the same period. The lower 2020 bird count that we recorded is thus likely a product of the short duration of human exclusions in 2020 (lockdown levels 4 and 5) and the magnitude and rate of increase in human numbers thereafter (levels 3-1). Separately, our findings additionally suggest that surrogates (lockdown levels in our case) are unreliable estimators of human presence or abundance and align with findings elsewhere24.The last noteworthy inter-annual trend in our data was the difference in strength of human-shorebird relationships. While the inverse relationship between human and shorebird numbers was evident in both years, it was only during 2020, when humans were excluded from Muizenberg Beach, that the extent of this relationship was revealed. Specifically, in 2020, human exclusion at the start of lockdown level 5 was accompanied by a six-fold increase in shorebird abundance relative to 2019 at the same period. Additional support for the difference in strength of the human-shorebird relationship is the (1) significant interaction recorded between human numbers and year in explaining shorebird abundance and (2) the almost twofold stronger negative relationship (based on regression slopes) between shorebird and human abundance in 2020 vs 2019. These findings suggest that were it not for the COVID lockdowns in 2020, the extent of increasing human numbers on shorebirds may have been masked. However, it must be borne in mind that inter-annual variation may have played some role in the difference in trends recorded for 2019 versus 2020, though we cannot quantify this, given that we only have data for 2 years. Nevertheless, we suggest that when making conservation/management recommendations, decision-makers need to be cognisant of the potential for human effects on sandy beach ecosystems to be underestimated in studies based on variation in human density, in which human exclusion at appropriate spatial and temporal scales is absent24. Concerns have been expressed in the past about the failure of studies to consistently detect large-scale changes in sandy beach ecosystems, including those induced by recreational activities19. We suggest that such deficiencies may relate in part to the scarcity of true human exclusions in disturbance studies at meaningful scales in space and time.Findings from the in situ component of our study suggested that shorebird assemblages were negligibly affected by the transition from lockdown level 3 to 1, but that spatial differences among zones were more prominent. The lack of cases in which lockdown levels interacted statistically with zones (Tables 2, 4) further reinforces our conclusion regarding lockdown effects. Shorebird assemblage structure did vary between lockdown levels 3 and 2, due mainly to increasing contributions of Chroicocephalus hartlaubii (Hartlaub’s Gull) from level 3 to 2 and the opposite for L. dominicanus. Contrary to our hypothesis, differences in assemblage (Shannon–Wiener diversity was the exception) and species metrics were not detected among lockdown levels. This was likely due to the gradient in human abundance being weak among lockdown levels 3 to 1, relative to levels 5 and 4, with there being no virtual exclusion of humans under level 3 lockdown, as would have been expected given government regulations29. It is also possible that under lockdown levels 3, 2 and 1, the shorebird assemblage was simplified and comprised species tolerant of human activities44. The increase in Shannon–Wiener diversity value from lockdown level 3 to 2 was counter expectation, but likely reflects increased evenness during lockdown level 2, brought on by the declining dominance of L. dominicanus and a greater contribution of C. hartlaubii.Taken in its entirety, our findings provide valuable perspectives on human-shorebird interactions in sandy beaches. Based on our 2020 data spanning lockdowns of decreasing severity, our findings suggest that shorebirds are likely to benefit from human-free periods. This benefit is in reality likely to extend across multiple-trophic levels and is unlikely to be shorebird-specific, based on prior research reporting positive organism metrics at lower trophic levels in low human and/or human-free conditions in beach ecosystems20. Broadly, our findings attest to the value of using current and future lockdowns associated with managing the global COVID-19 pandemic to provide data on responses of birds and other organism groups to human-free spaces and times25,26,49. These human-free conditions can additionally provide invaluable data on sensitivities of ecosystem components and processes to increasing human density25,26,49. Data collected during lockdowns can provide better approximations of baseline conditions in sandy beach ecosystems, thereby providing a more meaningful basis for (1) evaluating future ecosystem change in response to human and global change stressors and (2) developing ecosystem restoration programs. This would be central to preventing long-term ecosystem degradation through the shifting base-line syndrome, where successive generations of decision makers/scientists judge the magnitude of change experienced by ecosystem components against increasingly deteriorating conditions over generational time-scales50. We also advocate for data emanating from COVID lockdown studies to be used in public education initiatives, so that beach users are made aware of the ways in which recreational activities can influence beach ecosystems. Such initiatives can improve involvement of public stakeholders in management of sandy beach ecosystems, which has been shown to provide cost-effective and sound decision-making, while increasing support for conservation initiatives51,52,53.Lastly, our findings have shed light on the sensitivity of shorebirds to increasing human numbers, mainly for recreational purposes. By moving beyond binary contrasts of human presence/absence, our work has also shown the magnitude of increasing human numbers on shorebirds, by virtue of the 34.18% increase in human abundance in our study corresponding with a 79.63% decline in bird numbers during the transition from lockdown level 4 to 3 in 2020. This finding is highly relevant considering that our work was based on an urban ecosystem—such systems are thought to have avian communities that are more disturbance tolerant relative to rural or suburban ecosystems54. Broadly, our work emphasises the need for environmental managers and city planners to be cognisant of the sensitivity of shorebirds to human recreational activities, even in urban settings, and to develop appropriate management plans in conjunction with scientists and stakeholders51,52,53. It should be noted that bird responses that we recorded in 2020 are unlikely to be driven solely by changing human numbers in Muizenberg Beach. Processes influencing bird assemblages in beaches surrounding our focal study area, including changes in human numbers and behaviour, may also have been influential determinants of trends recorded. We lack the data to comment meaningfully on this, but is an area worth exploring in future studies.Concluding perspectivesThe global COVID-19 anthropause has been described as the greatest large-scale experiment in modern history. This period has afforded scientists a unique opportunity to refine understanding of the consequences of human activities on Earth’s natural environments25,26,49. This is particularly relevant for human-dominated ecosystems such as sandy beaches, which are arguably the most utilised of Earth’s ecosystems for recreational purposes. In the absence of the COVID-19 anthropause, it is doubtful whether human exclusions could be carried out at scales that would allow meaningful detection of responses to human recreational disturbance. Our findings broadly attest to the points raised thus far, illustrating not only the potential for conventional approaches to underestimate human effects in sandy beaches, but also the sensitivity of shorebirds to human recreation and the magnitude of human influence. We hope that our findings stimulate further research on human recreational effects on sandy beach ecosystems, particularly with a view towards quantifying disturbance sensitivities and response thresholds of fundamental processes that drive multifunctionality in these heavily utilised, yet highly significant coastal ecosystems. We suggest that this is an imperative, given the exponential human population growth expected in the future, particularly along the coast, and the increasing demand predicted on sandy beach ecosystems from recreation, tourism and commercial sectors10,18. At its broadest level, our work dovetails with prior calls for scientists to capitalise on current and future COVID lockdowns to refine our understanding of human-nature interactions25, so that ecosystems and socio-ecological services provided can be sustainably utilised in the future. More

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A biodiversity simulation frameworkWe have developed a simulation framework modelling biodiversity loss to optimize and validate conservation policies (in this context, decisions about data gathering and area protection across a landscape) using an RL algorithm. We implemented a spatially explicit individual-based simulation to assess future biodiversity changes based on natural processes of mortality, replacement and dispersal. Our framework also incorporates anthropogenic processes such as habitat modifications, selective removal of a species, rapid climate change and existing conservation efforts. The simulation can include thousands of species and millions of individuals and track population sizes and species distributions and how they are affected by anthropogenic activity and climate change (for a detailed description of the model and its parameters see Supplementary Methods and Supplementary Table 1).In our model, anthropogenic disturbance has the effect of altering the natural mortality rates on a species-specific level, which depends on the sensitivity of the species. It also affects the total number of individuals (the carrying capacity) of any species that can inhabit a spatial unit. Because sensitivity to disturbance differs among species, the relative abundance of species in each cell changes after adding disturbance and upon reaching the new equilibrium. The effect of climate change is modelled as locally affecting the mortality of individuals based on species-specific climatic tolerances. As a result, more tolerant or warmer-adapted species will tend to replace sensitive species in a warming environment, thus inducing range shifts, contraction or expansion across species depending on their climatic tolerance and dispersal ability.We use time-forward simulations of biodiversity in time and space, with increasing anthropogenic disturbance through time, to optimize conservation policies and assess their performance. Along with a representation of the natural and anthropogenic evolution of the system, our framework includes an agent (that is, the policy maker) taking two types of actions: (1) monitoring, which provides information about the current state of biodiversity of the system, and (2) protecting, which uses that information to select areas for protection from anthropogenic disturbance. The monitoring policy defines the level of detail and temporal resolution of biodiversity surveys. At a minimal level, these include species lists for each cell, whereas more detailed surveys provide counts of population size for each species. The protection policy is informed by the results of monitoring and selects protected areas in which further anthropogenic disturbance is maintained at an arbitrarily low value (Fig. 1). Because the total number of areas that can be protected is limited by a finite budget, we use an RL algorithm42 to optimize how to perform the protecting actions based on the information provided by monitoring, such that it minimizes species loss or other criteria depending on the policy.We provide a full description of the simulation system in the Supplementary Methods. In the sections below we present the optimization algorithm, describe the experiments carried out to validate our framework and demonstrate its use with an empirical dataset.Conservation planning within a reinforcement learning frameworkIn our model we use RL to optimize a conservation policy under a predefined policy objective (for example, to minimize the loss of biodiversity or maximize the extent of protected area). The CAPTAIN framework includes a space of actions, namely monitoring and protecting, that are optimized to maximize a reward R. The reward defines the optimality criterion of the simulation and can be quantified as the cumulative value of species that do not go extinct throughout the timeframe evaluated in the simulation. If the value is set equal across all species, the RL algorithm will minimize overall species extinctions. However, different definitions of value can be used to minimize loss based on evolutionary distinctiveness of species (for example, minimizing phylogenetic diversity loss), or their ecosystem or economic value. Alternatively, the reward can be set equal to the amount of protected area, in which case the RL algorithm maximizes the number of cells protected from disturbance, regardless of which species occur there. The amount of area that can be protected through the protecting action is determined by a budget Bt and by the cost of protection ({C}_{t}^{c}), which can vary across cells c and through time t.The granularity of monitoring and protecting actions is based on spatial units that may include one or more cells and which we define as the protection units. In our system, protection units are adjacent, non-overlapping areas of equal size (Fig. 1) that can be protected at a cost that cumulates the costs of all cells included in the unit.The monitoring action collects information within each protection unit about the state of the system St, which includes species abundances and geographic distribution:$${S}_{t}={{{{H}}}_{{{t}}},{{{D}}}_{{{t}}},{{{F}}}_{{{t}}},{{{T}}}_{{{t}}},{{{C}}}_{{{t}}},{{{P}}}_{{{t}}},{B}_{t}}$$
(1)
where Ht is the matrix with the number of individuals across species and cells, Dt and Ft are matrices describing anthropogenic disturbance on the system, Tt is a matrix quantifying climate, Ct is the cost matrix, Pt is the current protection matrix and Bt is the available budget (for more details see Supplementary Methods and Supplementary Table 1). We define as feature extraction the result of a function X(St), which returns for each protection unit a set of features summarizing the state of the system in the unit. The number and selection of features (Supplementary Methods and Supplementary Table 2) depends on the monitoring policy πX, which is decided a priori in the simulation. A predefined monitoring policy also determines the temporal frequency of this action throughout the simulation, for example, only at the first time step or repeated at each time step. The features extracted for each unit represent the input upon which a protecting action can take place, if the budget allows for it, following a protection policy πY. These features (listed in Supplementary Table 2) include the number of species that are not already protected in other units, the number of rare species and the cost of the unit relative to the remaining budget. Different subsets of these features are used depending on the monitoring policy and on the optimality criterion of the protection policy πY.We do not assume species-specific sensitivities to disturbance (parameters ds, fs in Supplementary Table 1 and Supplementary Methods) to be known features, because a precise estimation of these parameters in an empirical case would require targeted experiments, which we consider unfeasible across a large number of species. Instead, species-specific sensitivities can be learned from the system through the observation of changes in the relative abundances of species (x3 in Supplementary Table 2). The features tested across different policies are specified in the subsection Experiments below and in the Supplementary Methods.The protecting action selects a protection unit and resets the disturbance in the included cells to an arbitrarily low level. A protected unit is also immune from future anthropogenic disturbance increases, but protection does not prevent climate change in the unit. The model can include a buffer area along the perimeter of a protected unit, in which the level of protection is lower than in the centre, to mimic the generally negative edge effects in protected areas (for example, higher vulnerability to extreme weather). Although protecting a disturbed area theoretically allows it to return to its initial biodiversity levels, population growth and species composition of the protected area will still be controlled by the death–replacement–dispersal processes described above, as well as by the state of neighbouring areas. Thus, protecting an area that has already undergone biodiversity loss may not result in the restoration of its original biodiversity levels.The protecting action has a cost determined by the cumulative cost of all cells in the selected protection unit. The cost of protection can be set equal across all cells and constant through time. Alternatively, it can be defined as a function of the current level of anthropogenic disturbance in the cell. The cost of each protecting action is taken from a predetermined finite budget and a unit can be protected only if the remaining budget allows it.Policy definition and optimization algorithmWe frame the optimization problem as a stochastic control problem where the state of the system St evolves through time as described in the section above (see also Supplementary Methods), but it is also influenced by a set of discrete actions determined by the protection policy πY. The protection policy is a probabilistic policy: for a given set of policy parameters and an input state, the policy outputs an array of probabilities associated with all possible protecting actions. While optimizing the model, we extract actions according to the probabilities produced by the policy to make sure that we explore the space of actions. When we run experiments with a fixed policy instead, we choose the action with highest probability. The input state is transformed by the feature extraction function X(St) defined by the monitoring policy, and the features are mapped to a probability through a neural network with the architecture described below.In our simulations, we fix monitoring policy πX, thus predefining the frequency of monitoring (for example, at each time step or only at the first time step) and the amount of information produced by X(St), and we optimize πY, which determines how to best use the available budget to maximize the reward. Each action A has a cost, defined by the function Cost(A, St), which here we set to zero for the monitoring action (X) across all monitoring policies. The cost of the protecting action (Y) is instead set to the cumulative cost of all cells in the selected protection unit. In the simulations presented here, unless otherwise specified, the protection policy can only add one protected unit at each time step, if the budget allows, that is if Cost(Y, St)  More

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