Philippa Kaur

Assume n countries ((nge 2)) are located in a transboundary river basin and they are the players of an evolutionary game in which the countries’ strategies concerning water sharing in the basin evolve over time. Each country can choose between a cooperative strategy or a non-cooperative strategy. The game’s interactions and players’ payoffs vary with the number n and the location of the countries within the river basin, specifically, in relation to whether they are upstream-located or downstream-located countries within the river basin. The probability of country i choosing a cooperative strategy is herein denoted by ({x}_{1}^{(i)}), (i=1, 2, dots , n), and there are ({2}^{n}) payoff sets for all the combinations of the countries’ strategies. This paper assesses the interactions between three countries sharing a transboundary river basin.Problem descriptionLet 1, 2, and 3 denote three countries sharing a transboundary river basin. Country 1 is upstream and countries 2 and 3 are located downstream. Country 1 can use maximum amount of the water of the river and choose not to share it with the downstream countries. This strategy, however, may trigger conflict with the two other countries of political, social, economic, security, and environmental natures. Instead, Country 1 can release excess water to be shared by Countries 2 and 3. Countries 2 and 3 are inclined to cooperate with Country 1 unless other benefits emerge by being non-cooperative with Country 1.There are two types of benefits and one type of cost in the payoff matrix of the assumed problem that are economic in nature. The first is a water benefit earned by a country from receiving the water from the transboundary river. The set of benefits related to water use includes economic benefits earned from agricultural, urban, and industrial development benefits. It should be noted that the water benefit for Country 1 means the economic benefit of consuming more water than its water right from the river. So, water benefits of Country 2 and 3 are the economic benefit of consuming excess water of upstream which is released by Country 1.The second is a potential benefit earned from the cooperative strategy of a country. Cooperation benefits stem from sustainability conditions like social interests, environmental benefits and political conjunctures such as international alliances and harmony from amicable interactions with neighboring countries. The parameters F and E (water benefit and potential benefit, respectively) encompass a number of benefit parameters; nevertheless, parameters were simplified to two benefit parameters to simplify the complexity of the water-sharing problem. Costs forced on other countries from non-cooperation by a country involves commercial, security, political, diplomatic, military, and environmental costs. Figure 1 displays the locations of three countries and their shifting interactions in a transboundary river basin.Figure 1Schematic of the transboundary river and riparian countries with their shifting interactions.Full size imageBasic assumptionsThe evolutionary game model of interactions between riparian countries in the transboundary river basin rests on the following assumptions:
Assumption 1

There are three countries (i.e., players) in the game of transboundary water sharing, each seeking to maximize its payoff from the game.

Assumption 2

Country 1 has two possible strategies. One is for Country 1 to release a specified amount of water to the downstream countries (this would be Country 1’s cooperative strategy). The cooperative strategy by Country 1 would produce benefits F2 and F3 to Countries 2 and 3, respectively. By being cooperative Country 1 would attain a benefit E1 called the potential benefit from cooperative responses from the downstream countries. The other strategy is for Country 1 to deny water to the downstream countries (this would be Country 1’s non-cooperative strategy), in which case Country 1 would earn the water benefit F1 from using water that would otherwise be released, but would forego the potential benefit E1. Moreover, by pursuing a non-cooperative strategy Country 1 would inflict a cost C1m to the downstream countries.

Assumption 3

There are two possible strategies for Country 2. One is for Country 2 to accept the behavior of Country 1 (this would be Country 2’s cooperative strategy), which would cause earning a potential benefit E2 to Country 2. Recall that if Country 2 acquiesces to Country 1’s cooperative behavior it would receive a benefit F2. Or, Country 2 may disagree with Country 1 (this would be Country 2’s non-cooperative strategy), in which case, Country 2 would lose benefit E2, and it would inflict a cost C2m to the other countries.

Assumption 4

Similar to Country 2, Country 3 has two possible strategies. One is for Country 3 to agree Country 1’s behavior (this would be Country 3’s cooperative strategy) attaining a potential benefit E3. Recall that if Country 3 agrees with Country 1’s cooperative behavior it would gain a benefit F3. Another strategy for Country 3 is to oppose Country 1 (this would be Country 3’s non-cooperative strategy) missing the benefit E3 and forcing a cost C3m to the other countries.
Table 1 defines the benefits and costs that enter in the transboundary water-sharing game described in this work. The payoff to country (i=mathrm{1,2},3) depends on its own strategy and on the strategies of the other countries, and each country may choose to be cooperative or non-cooperative. The strategies of country (i) are denoted by 1 (cooperation) and 2 (non-cooperation). The probabilities of country (i)’s strategies are denoted by ({x}_{1}^{(i)}) and by ({x}_{2}^{(i)}), in which the former represents cooperation and the latter represents non-cooperation. Clearly, ({x}_{1}^{(i)})+ ({x}_{2}^{(i)}) = 1. The payoff to country (i=1, 2, 3) when the strategies of Countries 1, 2, 3 are (j, k,l), respectively, where (j, k,l) may take the value 1 (cooperation) or 2 (non-cooperation) is denoted by ({U}_{jkl}^{left(iright)}). Thus, for instance, the payoff to country (i=2) is represented by ({U}_{212}^{(2)}) when Countries 1 and 3 are non-cooperative and Country 2’s strategy is cooperative. Evidently, there are 23 payoffs to each country given there are three countries involved and each can be cooperative or non-cooperative. Table 2 shows the symbols for the payoffs that accrue to each country under the probable strategies.Table 1 Benefits and costs.Full size tableTable 2 Payoff matrix under cooperation or non-cooperation.Full size tableFormulation of the transboundary water-sharing strategies as an evolutionary gameThe expected payoff to country (i) is expressed by the following equation:$${U}^{(i)}=sumlimits_{j = 1}^2 {sumlimits_{k = 1}^2 {sumlimits_{l = 1}^2} } {x}_{j}^{(1)}{x}_{k}^{(2)}{x}_{l}^{(3)} {U}_{jkl}^{(i)} quad i=1, 2, 3$$
(1)
The following describe the expected payoffs of Country 1 when it acts cooperatively (({U}_{1}^{(1)})) or non-cooperatively (({U}_{2}^{(1)})):$${U}_{1}^{(1)}={x}_{1}^{(2)}{x}_{1}^{(3)}{U}_{111}^{left(1right)}+{x}_{1}^{(2)}{x}_{2}^{(3)}{U}_{112}^{left(1right)}+{x}_{2}^{(2)}{x}_{1}^{(3)}{U}_{121}^{(1)}+{x}_{2}^{(2)}{x}_{2}^{(3)}{U}_{122}^{(1)}$$
(2)
$${U}_{2}^{(1)}={x}_{1}^{(2)}{x}_{1}^{(3)}{U}_{211}^{left(1right)}+{x}_{1}^{(2)}{x}_{2}^{(3)}{U}_{212}^{left(1right)}+{x}_{2}^{(2)}{x}_{1}^{(3)}{U}_{221}^{left(1right)}+{x}_{2}^{(2)}{x}_{2}^{(3)}{U}_{222}^{left(1right)}$$
(3)
Therefore, the expected payoff of Country 1 is ({U}^{(1)}) which is equal to:$${U}^{(1)}={x}_{1}^{(1)}{U}_{1}^{(1)}+{x}_{2}^{(1)}{U}_{2}^{(1)}= sumlimits_{j = 1}^2 {sumlimits_{k = 1}^2 {sumlimits_{l = 1}^2 } }{x}_{j}^{(1)}{x}_{k}^{(2)}{x}_{l}^{(3)} {U}_{jkl}^{(1)}$$
(4)
The expected payoffs of Countries 2 and 3 can be similarly obtained as done for Country 1. The cooperative and non-cooperative expected payoffs of all countries can be expressed in terms of the payoffs listed in Table 1. The results are found in Appendix A.Replication dynamics equationsThe replication dynamics equations describe the time change of the probabilities of a player’s strategies. The replication dynamics equation of Countries (i) is denoted by ({G}^{(i)}left({x}_{1}^{(i)}right)) which is as follow22:$${G}^{(i)}left({x}_{1}^{(i)}right)=frac{d{x}_{1}^{(i)}}{dt}={x}_{1}^{(i)}left({U}_{1}^{(i)}-{U}^{(i)}right)$$
(5)
The replication dynamics equations of Countries 1, 2 and 3 are presented in Appendix B according to the benefits and costs showed in Table 1.Stability analysis of a country’s strategiesUnder the assumption of bounded rationality each country does not know which strategies may lead to the optimal solution in the game. Therefore, the countries’ strategies change over time until a stable (i.e., time-independent) solution named evolutionary stable strategy (ESS) is attained. The evolutionary stable theorem for replication dynamics equation states that a stable probability of cooperation ({x}_{1}^{(i)}) for country (i) occurs if the following conditions hold25: (1) ({G}^{(i)}left({x}_{1}^{(i)}right)=0), and (2) (d{G}^{(i)}left({x}_{1}^{(i)}right)/d{x}_{1}^{(i)} More

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Study areaThe important river Damodar (563 km) originates from Khamarpat hill under Palamau district of Jharkhand state (India). It flows toward east direction and ultimately it joins with river Bhagirathi-Hooghly in West Bengal. Upper and middle parts of the river basin have rich diversity of minerals and standard quality coal reserve of Gondwana formations. Abundant supply of fresh river water with high mineral and energy resources attracts many large, medium and small-scale industries since historical time. River Damodar is the principal supplier of water resource to drinking, industrial and domestic purpose in its catchment area. Therefore, such favourable environment attracts huge population along with industrial integration in this area. The present study area is bounded by 23° 28′ 28.7″ N to 23° 40′ 52.5″ N and 86° 49′ 26.8″ E to 87° 18′ 42.4″ E and 65.37 km river stretch has been selected for the study. In this section high, agglomeration of industries and allied human works intensively developed along the riverside. Many iron and steel plants, thermal power plant, sponge iron factory, chemical industries, coal mining fields and urban centres have been developed through the evolution of time. As a result, huge untreated waste (solid/ liquid), hot water, coal dust and urban effluents are being regularly discharged to the riverbed through various connecting channels which are locally called nallas (Fig. 1)10,11.Figure 1source QGIS 3.16 software (https://qgis.org/en/site/forusers/download.html).Location map of the study stretch of a tropical river Damodar (India). The diagram is prepared by openFull size imageSample collection and data analysisWater samples were collected from eleven discharged points of industrial effluents on main riverbed. First, samples were taken on December 2019 (pre-lockdown/ normal period), again second, samples were collected in June, 2020 (during lockdown) to assess the changes on river water quality due to temporarily closing of industries. Third, samples were obtained in November, 2020 (after unlock phase) to get clear idea about effects of industries on the river water quality. Samples were obtained from 0.5 m below the surface water level within 5 m influencing radius zone. Pre cleaned polyethylene bottles (500 ml) were used for the collection of five subsamples from each sampling site and mixed up to get a bulk contain (1 l). All samples were carried properly for further analysis in laboratory. Sample containers were labelled as S1, S2, S3… to S11 for properly identification (Fig. 1). Total 20 parameters were analysed from each sample of each period. Important parameters such as pH, electrical conductivity (EC), total dissolved solids (TDS), turbidity, magnesium (Mg2+), calcium (Ca2+), chloride (Cl-), sulphate (SO42–), nitrates (NO3−), Biological Oxygen Demand (BOD), Dissolved Oxygen (DO), zinc (Zn2+), cadmium (Cd2+), lead (Pb2+), nickel (Ni2+), chromium (Cr), iron (Fe2+), chlorophyll a (Chla), total phosphorus (TP), and Secchi disk depth (Sd) have been considered. Consequently, pH and EC were measured at the sampling sites using Thermo probe, Hanna HI9811-5 potable meters respectively. DO was determined through Winkler’s method at the sampling spot immediately28. EC denoted by microsiemens per centimetre. TDS was determined following the procedure given by Hem (1991). Turbidity was denoted by Nephelometric Turbidity Unit (NTU’s). All cation, anions, BOD and DO were expressed in mg/l while all heavy metals, TP and Chla denoted as microgram/l. All other physico-chemical parameters and heavy metals were analysed by standard procedure which was prescribed by American Public Health Association (APHA)29. Chla and total phosphorus were estimated following APHA29 standard procedures. Secchi disk (Sd) with 8 in. diameter and attached cord in disk centre was used for depth measurement and expressed in meters at the maximum limit of depth where disk was seen from the above into the water.Modified water quality index (MWQI)MWQI of the 33-sample water was conducted for 11 sample sites by important water quality parameters namely pH, TDS, EC, turbidity, Mg2+, Ca2+, Cl-, SO42–, NO3–, BOD and DO. We considered 11 variables per sample in the index. The calculation of MWQI was conducted following the method of Vasistha and Ganguly30.At first, pre defined weightage was assigned for each selected parameter. The weightage of each parameter was obtained from previous literatures. After that, relative weight of each parameter was derived by the formula.$$ RW = AW/sumlimits_{i = 1}^{n} {AW} $$
(1)
where RW is relative weight of each parameter, AW is assigned weight obtained from past literature (AW of pH = 1, TDS = 1.79, EC = 1.78, turbidity = 1.09, Ca2+  = 0.8, Mg2+  = 0.72, Cl– = 1.28, SO42– = 1.60, NO3– = 2.32, BOD = 1.72, DO = 2.85) and n is total number of parameters considered for analysis.Second, quality assessment (Qi) of each parameter was obtained following the formula.$$ Q_{i} = (C_{i} times S_{i} ) times 100 $$
(2)
where Ci is concentration of particular parameter in sample water, Si is standard permissible limit of each parameter as suggested by BIS31 and WHO31 (Table 1).Table 1 Descriptive statistics of twenty variables of physio chemical, heavy metals and biological parameters in three period.Full size tableQi for pH and DO was obtained through some modification of Eq. (1.2) because optimum concentration of these two parameters are little different from others. The optimum value of pH and DO is considered as 7.0 and 14.6 mg/l (100% saturation at 23 °C), respectively32. Thus, Qi for these two parameters were performed using the formula.$$ Q_{i} = (frac{{C_{i} – V_{i} }}{{S_{i} – V_{i} }}) times 100 $$
(3)
where Vi denotes optimum values of pH and DO.Third, in this step sub index (SIi) was calculated for each considered parameter by multiplication of relative weight (RW) with quality assessment (Qi) value of each parameter using formula below.$$ SI_{i} = RW times Q_{i} $$
(4)
At last, MWQI was obtained for each sample site by summation of SIi of each parameter as below:$$ MWQI = sumlimits_{i = 1}^{n} {SI_{i} } $$
(5)
Water quality (based on MWQI values) has been categorised into 5 classes such as excellent (≤ 50), good (50–100), poor (100–200), very poor (200–300) and unfit for drinking (≥ 300) as suggested by BIS31 (IS:10500).Heavy metal index (HMI)Analysis of heavy metal index was done using 6 parameters as Cd2+, Zn2+, Cr, Pb2+, Ni2+, and Fe2+. Calculation was conducted through this formula33.$$ Wi = K/Si $$
(6)
where Wi suggests weightage of ith parameter, K means constant value (1), Si means standard value of ith parameter as per BIS31, and WHO32. In the next step, sub index calculation (Qi) was done through this formula.$$ Qi = sumlimits_{i = 1}^{n} {frac{Mi}{{Si}}} times 100 $$
(7)
where Mi is the value of heavy metal concentration in sample water, Si is maximum limit of permissible of ith parameter in µg/l according to BIS31 and WHO32 (Table 1). At last, HPI was calculated using this formula which is given below.$$ HPI = frac{{sumlimits_{i = 1}^{n} {WiQi} }}{{sumlimits_{i = 1}^{n} {Wi} }} $$
(8)
where n indicates total number of parameters used for calculation of HPI. HPI can be classified into five categories such as excellent (0–25), good (26–50), poor (51–75), very poor (75–100) and unfit for drinking ( > 100).Potential ecological risk (RI)To assess the environmental response of heavy metal contamination, a new index was applied from sedimentological perspective and it was proposed by Hakanson33. In this method, effects of heavy metals on environment and possibilities to ecological risk can be determined by a single contamination coefficient, toxic response coefficient of heavy metals and comprehensive contamination of metals for any aquatic or soil environment using this formula34.$$ C_{f}^{i} = C_{s}^{i} /C_{n}^{i} ,;c = sumlimits_{i = 1}^{n} {C_{f}^{i} } $$
(9)
$$ E_{r}^{i} = T_{r}^{i} times C_{f}^{i} ,;RI = sumlimits_{i = 1}^{m} {E_{r}^{i} } $$
(10)
where Csi specifies heavy metal contamination value, Cni indicates reference value of heavy metals, C stands for degree of contamination by toxic heavy metals, Eri represents ecological risk factor of any single substance, Tri indicates ‘Toxic- response’ of any particular metal and RI denotes potential ecological risk index of all measured toxic metals. In this study, reference value of heavy metals was taken from standard preindustrial values of heavy metals as Cd = 1.0, Pb = 70, Cr = 90 and Zn = 175. Toxic response of heavy metals was used as follows: Cd = 30, Pb = 5, Cr = 2 and Zn = 1 (Hakanson33). Values of RI can be classified into four categories such as Practically uncontaminated ( 600).Trophic State Index (TSI)Trophic status of river was identified by Trophic State Index (TSI) considering three parameters such as Secchi disk depth (Sd), Chlorophyll-a (Chla), Total phosphorus (TP). Trophic State Index (TSI) was calculated by Carlson method35.$$ TS(Sd) = 60.0 – 14.41 times Ln(Sd) $$
(11)
$$ TS(TP) = 14.42 times Ln(TP) + 4.15 $$
(12)
$$ TS(Chla) = 30.6 + 9.81 times Ln(Chla) $$
(13)
$$ {text{TSI }}left( {text{Trophic State Index}} right) = left[ {TS(Sd) + TS(TP) + TS(Chla)} right]/3 $$
(14)
Values of TSI were classified into seven categories such as low oligotrophic ( 80).Statistical and spatial analysisA meta analysis such as descriptive statistics, Pearson correlation coefficient, analysis of variance (ANOVA test), principal component analysis (PCA) of all physico-chemical parameters, biological and heavy metals were applied to quantify the significant changes in three phases using least significant difference (LSD) at 0.05 level. All statistical analysis has been performed using SPSS 20 and MS-excel software while R programming language v. R 4.1.1 is used only for diagrammatic presentation. Inverse Distance Weightage (IDW) technique was performed on QGIS v.3.16 software for revealing spatial variation of water quality in three periods on the basis of different indexing method. More

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Conjugative plasmids confer important traits to microbial communities, with both deleterious and beneficial effects on human health, the environment, and biotechnology [1,2,3]. The spread of virulence and resistance to antimicrobial agents [1, 2] and the facilitation of specific pollutant biotransformations exemplify the importance of conjugative plasmids [3, 4]. Understanding the mechanisms governing the transfer and spread of conjugative plasmids is therefore critically important. Although substantial research efforts have been made toward understanding the molecular mechanisms and biological determinants of plasmid conjugation [5], the underlying driving forces from physical and ecological aspects remain unclear.Many microbial communities exist in environments that are periodically or continuously exposed to unsaturated water conditions. For example, the communities residing in the vadose zone of soils are periodically exposed to saturated conditions after rainfall events and irrigation, and thereafter to unsaturated conditions upon soil draining. The microbial communities inhabiting the outer surfaces of various hosts such as skin, teeth, leaves, or roots also experience frequent hydration dynamics. The air-water interfaces of such soil particles or host surfaces are subject to water evaporation when the ambient relative humidity (RH) is More

Climate dataThermal profiles showed considerable diel variation at each field location (Fig. 3). Soil temperatures on the ground surface fluctuated the most, reaching maximum temperature (Mt Ginini, 45.5 °C; Piccadilly Circus first season, 46.5 °C; Piccadilly Circus second season, 46.0 °C; Cooma, 42.1 °C; Dartmouth, 47.5 °C) during the day (1330–1730 h) and dropping to low level (Mt Ginini, 4.0 °C; Piccadilly Circus first season, 8.5 °C; Piccadilly Circus second season, 6.5 °C; Cooma, 7 °C; Dartmouth 12.5 °C) at night (2330–0400 h) (ANOVA, F4, 6521 = 279.4, P  More