Philippa Kaur

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Experiment results and regression modelThe simulation experiment results based on the design scheme are presented in Table 4, including 24 analysis factors and 7 zero-point experiments for estimating the errors. Quadratic multiple regression analysis of the results in Table 4 was performed using the Design-Expert software, and the regression models between the influencing factors and evaluation indices were established as follows:$$ Y_{{1}} = {1767.57} – {64.29}X_{{1}} + {117.46}X_{{2}} + {324.46}X_{{3}} + {107.87}X_{{4}} – {21.81}X_{{1}} X_{{2}} + {17.94}X_{{1}} X_{{3}} – {41.44}X_{{1}} X_{{4}} + {16.69}X_{{2}} X_{{3}} – {41.19}X_{{2}} X_{{4}} + {73.56}X_{{3}} X_{{4}} + {23.2}{X_{{1}}^{{2}}} – {82.42}{{X_{{2}}}^{{2}}} – {13.17}{{X_{{3}}}^{{2}}} – {53.67}{{X_{{4}}}^{{2}}} $$$$ Y_{{2}} = {1968.14} + {636.42}X_{1} + {34.42}X_{2} + {66}X_{3} + {115.17}X_{{4}} + {28.63}X_{{1}} X_{{2}} + {9.13}X_{{1}} X_{{3}} – { 45.87}X_{{1}} X_{{4}} + {1}0X_{{2}} X_{{3}} + {30.5}X_{{2}} X_{{4}} – {1.75}X_{{3}} X_{{4}} + {55.03}{X_{{1}}^{{2}}} – {8.1}{{X_{{2}}}^{{2}}} – {72.72}{{X_{{3}}}^{2}} + {61.03}{{X_{{4}}}^{{2}}} $$Table 4 Experiment schemes and results.Full size tableThe relationship between the actual values of the efficiency of conveying-soil and the distance of throwing-soil and the predicted values of the regression model is shown in Fig. 7. It can be seen from Fig. 7 that the actual values are basically distributed on the predicted curve, consistent with the trend of the predicted values, and linearly distributed.Figure 7Scatter plot. (a) Scatter plot of actual and predicted distance of throwing-soil. (b) Scatter plot of actual and predicted efficiency of conveying-soil.Full size imageVariance analysis and discussionThe F-test and analysis of variance (ANOVA) were performed on the regression coefficients in the regression models of the evaluation indices Y1 and Y2, and the results are shown in Table 5. According to the significance values P of the lack of fitting in the regression models of the objective functions Y1 and Y2 in Table 5, PL1 = 0.1485  > 0.05 and PL2 = 0.2337  > 0.05 (both were not significant), indicating that no loss factor existed in the regression analysis, and the regression model exhibited a high fitting degree.Table 5 ANOVA results of regression model.Full size tableAccording to the ANOVA, the significance values P of each influencing factor in the test could be determined28. For the evaluation index Y1, the factors X1, X2, X3, X4, X3X4, X22, X42 had extremely significant influences, while the factors X1X4, X2X4 had a significant influence. For the evaluation index Y2, the factors X1, X3, X4, X1X4, X12, X32, X42 had extremely significant influences, and the factors X2, X1X4 had a significant influence. Within the level range of the selected factors, according to the F value of each factor as shown in Table 5, the weight of the factors affecting the efficiency of conveying-soil is feeding speed  > helix angle of auger  > rotating speed of auger  > slope angle. And the weight of the factors affecting the distance of throwing-soil is slope auger  > rotating speed of auger  > feeding speed  > helix angle of auger.In addition, it is obvious that there are interactions between the feeding speed and rotating speed of the auger, slope auger and rotating speed of auger, helix angle of the auger and rotating speed of the auger on the efficiency of conveying-soil Y1. For the distance of throwing-soil Y2, there is an interaction between the slope angle and the rotating speed of the auger.Analysis of response surfaceThe fitting coefficient of the efficiency of conveying-soil is R2 = 0.9714, R2adjust = 0.9263, R2pred = 0.8082, the difference between R2adjust and R2pred is less than 0.2. The fitting coefficient of the distance of throwing-soil is R2 = 0.9873, R2adjust = 0.9742, R2pred = 0.9355, the difference between R2adjust and R2pred is smaller than 0.2. It is indicated that the response surfaces of the two models established have good consistency and predictability for the experimental results29.The response surface is created directly using the Design-Expert software. After entering the data, select “Analysis” module. In the “Model-Graph” menu bar, select “3D-surface” to switch to the 3D view. To express the interactive influence of each factor on the efficiency of conveying-soil Y1 and distance of the throwing-soil Y2, the above two quadratic regression equations of the evaluation indices were subjected to the dimensionality reduction treatment. Two of the factors was set to level 0, while the other two underwent interaction effect analysis to study the influence law on the evaluation indices Y1 and Y2, and the corresponding response surfaces were generated, as illustrated in Fig. 8.Figure 83D response diagram effect of evaluation indices. (a) Effect of interaction between X1 and X2 on efficiency of conveying-soil. (b) Effect of interaction between X2 and X4 on efficiency of conveying-soil. (c) Effect of interaction between X3 and X4 on efficiency of conveying-soil. (d) Effect of interaction between X3 and X4 on distance of throwing-soil.Full size imageIt can be seen in Fig. 8a, when the slope angle was constant, the efficiency of conveying-soil increased with the rotating speed of the auger to a certain value, then the efficiency increase changed more gently. The reasons for this phenomenon are described as follows. On the one hand, the greater the kinetic energy of the soil when leaving the original position, and the thinner the soil was cut, resulting in the smaller the probability of blockage in the spiral blade space. On the other hand, the centrifugal force of soil arriving at the pit mouth is greater, so it does not obstruct in the pit mouth. However, if the rotation speed of the auger was too high and the soil layer cut was too thin, the subsequent soil’s driving effect to the front would be weakened, or even the flow would be interrupted, so the vertical rising speed of the soil would be reduced. When the rotational speed of the auger was constant, the efficiency of conveying-soil decreased with the increase of slope and then slightly increased. With the increase of slope, the time of slope cutting process increased, and there was more soil backfilling on the side of high altitude, which leaded to the reduction of soil discharge efficiency. However, with the increase of slope, the amount of soil slide at the pit mouth was increased, improving the efficiency of soil discharge. Further analysis demonstrated that the response surface for Y1 changed more rapidly in the direction of the rotating speed than in that of the slope angle, indicating that the rotating speed of auger X4 had a more significant influence than the slope angle X1.As can be seen in Fig. 8b, when the helix angle of the auger was fixed, the efficiency of conveying-soil continued to increase with the increase of the rotation speed. When the rotating speed of auger was fixed, the efficiency of conveying-soil increased with the increase of the helix angle and tends to decrease when it reached a certain value. The spiral blades space was the channel of soil movement. This phenomenon was caused by the increase of the gap between the two spiral blades with the increase of the helix angle of the auger, the soil was not easy to produce blockage. Meanwhile, the movement distance of soil was shorter, and the soil with higher kinetic energy was discharged more quickly from the pit. When reaching the pit mouth, the angle of soil throwing was larger and the soil backfilling rate was reduced. However, if the helix angle of auger was too large, the upward support ability and friction of the spiral blade surface to the soil would be reduced. Further analysis demonstrated that the response surface for Y1 changed more rapidly in the direction of the helix angle than the rotating speed of the auger, indicating that the helix angle of the auger X2 had a more significant influence than the rotating speed of the auger X4.When the feeding speed was fixed, the efficiency of throwing-soil continued to increase with the increase of the rotating speed. When the rotating speed of auger was fixed, the efficiency of the throwing-soil with the increase of the feeding speed (see in Fig. 8c). The phenomenon was caused by the faster the feeding speed of the auger, the thickness of soil cut per unit time increased. Furthermore, the subsequent driving force of soil increased, and the soil kinetic energy increased. However, in the actual production, excessive feeding speed would cause soil blockage on the surface of spiral blades. The reason is due to in the simulation process, the soil would not stop moving because of blockage. Further analysis demonstrated that the response surface for Y1 changed more rapidly in the direction of the rotating speed than in that of the feeding speed, indicating that the rotating speed of auger X4 had a more significant influence than the feeding speed X3.When the slope was fixed, the distance of the throwing-soil increased with the increase of rotation speed of the auger, and the increase amplitude increased gradually, as shown in Fig. 8d. The reason for this phenomenon was that the soil had more kinetic energy when it left its original position and the centrifugal force it received when it reaching the pit mouth is greater. When the rotation speed was too low, the soil layer was thin and the subsequent soil driving force was insufficient, resulting in the soil mass per unit area at the pit mouth was light and then the kinetic energy was small. When the rotating speed of auger was fixed, the distance of the throwing-soil increased continuously with the increase of the slope. As the slope increased, the time of soil swipe down process increased and then the rolling distance on the slope increased. Further analysis demonstrated that the response surface for Y2 changed more rapidly in the direction of the slope angle than in that of the rotating speed of auger, indicating that the slope angle X1 had a more significant influence than the rotating speed X3.Comprehensive optimal designAs relative importance and influencing rules of various experimental factors on evaluation indexes were different from each other, evaluation indexes should be taken into comprehensive consideration30. The optimization equation is obtained by the Design-Expert software multi-objective optimization method with Y1 and Y2 as the optimization objective function.$$25le {X}_{1}le 45$$$$10le {X}_{2}le 22$$$$0.04le {X}_{3}le 0.1$$$$30le {X}_{4}le 120$$$${{Y}_{1}}_{mathrm{max}}({X}_{1},{X}_{2},{X}_{3},{X}_{4})$$$${{Y}_{2}}_{min}({X}_{1},{X}_{2},{X}_{3},{X}_{4})$$In practice, the best combination of parameters needs to be selected according to the terrain slope. When the slope was fixed, the Design-Expert software was applied to optimize and solve the above mathematical model. The optimal combination of working parameters affecting the efficiency of conveying-soil Y1 and distance of throwing-soil Y2 for the auger were obtained and are shown in Table 6. If the ground preparation was required before the digging operation, the digging parameters can be designed according to values of Group 6 in Table 6.Table 6 Optimal parameter combinations of several terrain slopes.Full size tableDisturbance of soilA soil disturbance is defined as the loosening, movement and mixing of soil caused by an auger passing through the soil16. In the interface of the EDEM Analyst, add a “Clipping plane” to show the movement of the auger inside the pit. The kinetic energy, soil particle velocity vector, and velocity value of soil particles is observed when the auger in the middle of the soil bin31,32, as shown in Fig. 9.Figure 9The disturbance of the soil effect by spiral blade.Full size imageThe soil was lifted to the surface and then dropped to the lower side. In addition to the volume occupied by the spiral blades, the disturbed area also included the out-of-pit disturbed area caused by the compression of the cutting end of the spiral blade, as shown in the lower left corner of the auger.The kinetic energy and velocity of soil decreased firstly and then increased along the opposite direction of the auger feeding. The cutting end of the auger and the soil-throwing section occurred in the region with high kinetic energy and velocity. This was because the maximum kinetic energy was obtained at the cutting end of the auger, which was gradually consumed in the process of rising. After reaching the dumping end, the soil lost the restraint of the pit wall. When the centrifugal force of soil lost the reaction force, the kinetic energy of soil increased. Too much kinetic energy, however, can cause the soil to spread too far, causing subsequent trouble. The kinetic energy of the soil at the cutting end was related to the rotational speed of the auger. The spiral angle affected the angle between the force and gravity, and then the kinetic energy consumption in the process of soil increased.Verification experimentsTo verify the accuracy of the optimization model for auger working, as well as to evaluate the rationality of the working parameter combination optimized by the virtual experiment, performance verification tests were carried out on the EDEM software. According to the optimized process parameter setting test (as shown in Table 6), the relative error between the theoretical value and the experimental value was obtained. The verification test results are summarized in Table 7. The average relative errors of the efficiency of conveying-soil and the distance of throwing-soil between the Theoretical value and text value were only 4.4%, 9.1%. The simulation model is fairly accurate. The field performance verification experiments were carried out in slope. Figure 10 illustrates the field test and working conditions.Table 7 Results and comparison of validation test.Full size tableFigure 10Operation diagram at the experiment site.Full size image More

Selection of surveys and extraction of dataWe selected published surveys that produced estimates of sperm whale population size or density (see Supplementary Information for methodology; surveys listed in Table 1). We extracted: the type of survey (ship, aerial; acoustic, visual), the years of data collection; the coordinates of the boundary of the study area; the estimates of g(0) and CV (g(0)) used to correct for availability bias, if given; and an estimate of sperm whale population or density in study area with CV. From these we calculated for each survey the survey area with waters greater than 1000 m deep (typical shallow depth limit of sperm whales3). When no value of g(0) was used (8 ship visual surveys) we corrected the population/density estimate using an assumed generic value of g(0) and recalculated the CV to include uncertainty in g(0) (as in Eq. 1 of8). Three ship visual surveys did calculate a single g(0) estimate: 0.62 (CV 0.35)32; 0.57 (CV 0.28)35; 0.61 (CV 0.25)37. These are consistent and suggest a generic g(0) = 0.60 (CV 0.29), also agreeing with g(0) = 0.60 estimated from pooled surveys in the California Current10.Global habitat of sperm whalesTo extrapolate sperm whale densities from surveyed study areas to the sperm whales’ global habitat, we created a one-degree latitude by one-degree longitude grid. We removed the following grid points as not being prime sperm whale habitat1,3,40: points on land or with central depths less than 1000 m; largely ice-covered points in the Beaufort Sea, and the waters north of Svalbard and Russia; the Black Sea and Red Sea both of which have shallow entrances that appear not to be traversable by sperm whales.Generally, food abundance is a good predictor of species distribution. However, this is not possible for sperm whales as we have no good measures of the abundance or distribution of most of their prey, deep-water squid57. Instead, oceanographic measures have been used to describe sperm whale distributions over various spatial scales with a moderate level of success13,14. We follow this approach. Measures that might predict sperm whale density were collected for each grid point, some at just the surface, others at the surface, 500 m depth, 1000 m depth or an average of the measures at the different depths (Supplementary Table S2). Water depth was the strongest predictor in Mediterranean encounters, when compared to slope and distance to shore13. Temperature and salinity have been used as predictors for the distribution of fish and larger marine animals, which could translate into prey availability and thus density for sperm whales58,59. Primary productivity and dissolved oxygen generally dictate the biomass of wildlife in an area, while nitrate and phosphate levels limit the amount of primary productivity in an area60. Eddy kinetic energy is a measure of the dynamism of physical oceanography which is becoming a commonly used predictor of cetacean habitat61. We did not use: latitude and longitude as these primarily describe the general geographic distribution of the study areas, and geographic aggregates of sperm whale catches62 as these proved to have no predictive power. The mean values of the 14 predictor measures were calculated over calendar months for each grid point, and then over the grid points in each study area.To obtain predictors of the sperm whale density at each grid point, we then made quadratic regressions of the density of sperm whales in each study area (i), d(i), on the mean values of the predictor measures, weighting each study area by its surface area. Because the surveys were conducted over different time periods, the densities were corrected based on the estimated trajectory of global sperm whale populations by multiplying d(i) by the ratio of the global population in 1993 over that in the mid-year of the survey (as in Fig. 4). Predictor variables were selected using forward stepwise selection based upon reduction in AIC.Sperm whale population sizeThe population of sperm whales globally, N, was then calculated as follows:$$N=sum_{k}dleft(kright)cdot aleft(kright),$$
(1)
where a{k} are the parameters of the regression; the summation is over k, the grid points; d(k) is the estimated sperm whale density at grid point k from the habitat suitability model; and a(k) is the area of the 1° cell centred on grid point k. Population estimates for other ocean areas (North Atlantic, North Pacific, Southern Hemisphere) were calculated similarly.The CVs of these population estimates were calculated following the methodology in8, (although there is an error in Eq. (3) of8 such that the squareroot symbol covers both the numerator and denominator rather than just the numerator). The error due to uncertain density estimates for the different surveys is:$$CVleft({D}_{T}right)=frac{sqrt{sum_{i}{left(CV({n}_{i})cdot {n}_{i}right)}^{2}}}{sum_{i}{n}_{i}}.$$
(2)
This is combined with the uncertainty in the extrapolation process (output from the linear models), CV(extrap.), to give an overall CV for the population estimate:$$CVleft(Nright)=sqrt{{CV({D}_{T})}^{2}+{CV(mathrm{extrap}.)}^{2}.}$$
(3)
Post-whaling trend in population sizeWe compiled a database of series of surveys producing population estimates of the same study area during the period 1978 (by which time most commercial sperm whaling had ceased) and 2022. Each series had to span at least 10 years, and all of the surveys in the series had to be comparable in terms of area covered throughout the time span. There also had to have been at least 3 surveys for a data set to be included.The data consisted of the survey area, A, the estimated population in area A in year y (for multi-year surveys, y would be the midpoint of the data collection years), nE(A,y), and the provided CV of that estimate, CV(nE(A,y)). The data series used for these analyses are summarized in Table 3.For each survey area, A, we calculated the trend in logarithmic population size, r(A), over time using weighted linear regression:$${text{Log}}left( {n_{E} left( {A,y} right)} right) , sim {text{ constant}}left( A right) , + rleft( A right) cdot y. left[ {{text{weight }} = { 1}/left( {{1} + {text{ CV}}left( {n_{E} left( {A,y} right)} right)} right)^{{2}} } right]$$
(4)
Table 3 also includes other published estimates of sperm whale population trends, from sighting rates or mark-recapture analyses of photoidentification data, with these estimates also having to span at least 10 years of data collection, and include data collected in three or more different years.Population trajectoryTo examine possible trajectories of the global sperm whale population following the start of commercial whaling in 1712, we used a variant of the theta-logistic, a population model that has been employed in other recent analyses of the population trajectories of large cetaceans45,63. The theta-logistic model is:$$nleft(y+1right)=nleft(yright)+rcdot nleft(yright)left(1-{left(frac{nleft(yright)}{nleft(1711right)}right)}^{theta }right)-fleft(yright)cdot cleft(yright).$$
(5)

Here, n(y) is the population of sperm whales in year y, r is the maximum potential rate of increase of a sperm whale population, and θ describes how the rate of increase varies with population size relative to its basal level before whaling in 1711, n(1711). The recorded catch in year y is c(y) and f(y) is a correction for bias in recorded catches.Whaling reduced the proportion of large breeding males64, likely disrupted the social cohesion of the females3, and may have had other lingering effects which reduced pregnancy or survival, and thus the rate of increase. Poaching has been found to reduce the reproductive output of African elephants, Loxodonta Africana, which have a similar social system to the sperm whales3, and this effect lingers well beyond the effective cessation of poaching46. There is some evidence for these effects of what we call “social disruption” on sperm whale population dynamics20,46,65. We added a term to the theta-logistic to account for such effects:$$nleft(y+1right)=nleft(yright)left[1+rcdot left(1-{left(frac{nleft(yright)}{nleft(1711right)}right)}^{theta }right)-qcdot frac{sum_{t=y-T}^{y}f(t)cdot c(t)}{nleft(y-Tright)}right]-f(y)cdot c(y).$$
(6)

Here, (frac{sum_{t=y-T}^{y}f(t)cdot c(t)}{nleft(y-Tright)}) is the proportion of the population killed over the last T years, and q is the reduction in the rate of increase when almost all the whales have been killed. This reduction is modelled to fall linearly as the proportion killed declines to zero.The global sperm whale population has some geographic structure18. Females appear to rarely move between ocean basins, and males seem to largely stay within one basin. Furthermore, sperm whaling was progressive, moving from ocean area to ocean area as numbers were depleted4. We model this by assuming K largely separate sperm whale subpopulations of equal size. Exploitation in 1712 starts in subpopulation 1 and moves to subpopulations 1 and 2 when the population 1 falls to α% of its initial value, and so on for the other ocean areas. The catch in each year in each area being exploited is pro-rated by the sizes of the different subpopulations being exploited. The population model for subpopulation k, which is one of the KE subpopulations being exploited in year y, is:$$nleft(k,y+1right)=nleft(k,yright)left[1+rcdot left(1-{left(frac{nleft(k,yright)}{nleft(k,1711right)}right)}^{theta }right)-qcdot frac{sum_{t=y-T}^{y}C(k,t)}{nleft(k,y-Tright)}right]-Cleft(k,yright),$$
(7)
where the estimated catch in year y in subpopulation k is given by: (Cleft(k,yright)=f(y)cdot c(y)cdot n(k,y)/sum_{{k}^{mathrm{^{prime}}}= More

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Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.This is a summary of: Zhang, S. et al. Sustained productivity and agronomic potential of perennial rice. Nat. Sustain. https://doi.org/10.1038/s41893-022-00997-3 (2022). More

Study siteWe conducted laboratory studies at the field site in Finca Irlanda, which is a 300-hectare organic shaded coffee farm located at 1100-m altitude, in the municipality of Tapachula, the state of Chiapas in Southern Mexico (92° 20′ 29″ W and 15° 10′ 65″ N). For the laboratory experiments, all organisms were freshly collected from Finca Irlanda or reared in the lab from insects collected from the field close by. The lab and field work was performed with a permit from the farm owner the Peters family.Ant aggression testTo examine the effect of phorid flies (P. lascinosus) on the aggressivity of ants (A. sericeasur) towards the parasitoids of the beetle larvae (A. orbigera), we conducted an ant aggression test with two treatments: with and without phorids. In the first treatment, a small coffee branch containing two leaves with scale insects (C. viridis) and 20 ant workers were both introduced into a one-liter plastic container. This was done to mimic as much as possible field conditions where the ants are tending scale insects. After waiting for at least 15 min for the ants to calm down and start tending the scale insects, one third- or fourth-instar larva of the beetle was introduced. In the second treatment, all settings were the same except for the addition of 3–4 phorid flies. Once the two treatments were established, one female parasitoid wasp (H. shuvakhinae) was released into each container. During a forty-minute trial, each time that a parasitoid wasp encountered an ant worker, the response of the ant individual was recorded. Ant responses to parasitoids were classified into two categories: (1) the ant ignores the wasp; (2) the ant attacks the wasp. All insects were used for a single replicate and then discarded. A total of four replicates were completed for both the presence and absence of phorids. For each trial, we calculated the proportion of actions (either aggressive or none) by ants when encountering the parasitoid wasp in the treatments with and without phorid flies. We used R36 to conduct a two-sample Mann–Whitney U test on the proportion of ant actions.Parasitism experiments and analysesTo examine the parasitoid wasp’s host preference and the effect of the 1st degree and the 2nd degree HOIs on the beetle’s parasitism and sex ratio, we conducted a laboratory experiment in insect tents (60 cm × 60 cm × 60 cm) with three treatments: (1) no ants (no HOIs but only the wasp and the beetle larvae), (2) ants (1st degree HOI), and (3) ants and phorids (1st and 2nd degree HOIs) (Fig. 1-B). We randomly assigned insect tents to each treatment in each trial, and the tents for each treatment were also shuffled in each trial. All beetle larvae used for these experiments were reared in the laboratory for at least two generations from freshly collected beetle adults. In each tent we placed a coffee branch with 4–6 leaves infested with approximately 100 scale insects inside a plastic container at the center of an insect tent. The set up for the three treatments of species combinations were as follows: (1) 4–5 third or fourth instar beetle larvae and a parasitoid wasp; (2) 4–5 third or fourth instar beetle larvae, a parasitoid wasp, and about 60–80 ant workers; (3) 4–5 third or fourth instar beetle larvae, a parasitoid wasp, about 60–80 ant workers and 3–4 phorid flies. Organism densities in these treatments were close to those observed in the field. To allow for acclimation, we introduced organisms into the tents in the following order: first, we introduced the coffee branch containing scales, immediately followed by the ants (in treatments 2 and 3). After the ants settled down and started tending the scale insects, we introduced the beetle larvae. Once the larvae began moving on the coffee leaves, we introduced the phorids (in treatment 3). When the three treatments were established, and the organisms exhibit normal behavior, we released one lab-reared female parasitoid wasp (H. shuvakhinae) in each tent (treatments 1, 2, and 3). We allowed the organisms to interact for 24 h. After 24 h, we collected all beetle larvae in each treatment and reared them with sufficient scale insects as food, until beetle adults emerged or parasitism symptoms appeared (parasitized larvae turned into hardened black mummies). The treatments of no HOI and 1st + 2nd degree HOI were repeated for 10 consecutive times, and the treatment of 1st degree HOI was repeated for 11 consecutive times, with new individuals of each organism. We recorded parasitism instances and beetle sexes upon emergence. To estimate the sex ratio without parasitoid influence, 78 randomly selected beetle individuals were reared on coffee leaves with scale insects without any interaction with other organisms.To analyze the effect of the parasitoid, the ant and the phorid fly on the parasitism rate and the sex ratio of the beetle, we developed a nested model, starting from$$logitleft(widehat{P}(S)right)=a+bA$$where (widehat{P}(S)) is the probability of an individual being parasitized, A is a binary variable, standing for the absence (0) and presence (1) of ants, a is the baseline probability of parasitism, and b is the magnitude of parasitism altered by ants in the logistic function. We further hypothesized that phorid attacks modify the strength of the interaction modification that ants exert upon the host-parasitoid interaction. Therefore,$$b=g+hP$$where P is another binary variable, standing for the presence (1) and absence (0) of phorids. Substituting b, we obtain the following function,$$logitleft(widehat{P}(S)right)=a+gA+hAP$$where g represents the effect of ants on the parasitism rate of A. orbigera larvae, and h represents the effect of the fly’s facilitation, via interfering with the ant’s interference on the parasitism rate of A. orbigera larvae. We used binary responses (1: survival; 0: parasitized) of all available beetle individuals across the three treatments. We performed model selection based on the Akaike Information Criterion (AIC) and likelihood ratio tests. For the latter, we started model selection by fitting the full model and preceding each step by eliminating the term that had the least significance (the greatest p-value) on the explanation of the dependent variable. The analysis was performed with the application of the bbmle package in R. By doing this, we determined the maximum likelihood estimates of survival probability of the beetle, (widehat{P}(S)), in the three treatments: (1) A = 0, AP = 0 (no HOI); (2) A = 1, AP = 0 (one HOI: ant interference) and (3) A = 1, AP = 1 (interacting HOIs: phorid interference with ant interference), and errors associated with these estimates.The same idea applies to the sex ratio of the beetle under the influence of various organisms. We developed the following equation,$$logitleft(widehat{P}(F|S)right)= r+mA+nAP$$where (widehat{P}(F|S)) is the probability of a parasitism survivor being female. A and P are both binary variables. Respectively, they represent the ant and the phorid fly, and the numeric attributes, 0 and 1, denote their absence and presence. As before, model selection and parameter estimates were conducted with AIC. By doing this, we determined (widehat{P}(F|S)), the estimate of being a female beetle given survival, for the three treatments: (1) A = 0, AP = 0 (no HOI); (2) A = 1, AP = 0 (one HOI: ant interference) and (3) A = 1, AP = 1 (interacting HOIs: phorid interference with ant interference), and errors associated with these estimates. We employed the mle2 function in the bbmle package in R to estimate the female probability (1) in the absence of HOI (the beetle and the parasitoid alone), (2) in the presence of the 1st degree HOI (the beetle, the parasitoid and the ant), and (3) in the presence of the 1st and the 2nd degree HOIs (the beetle, the parasitoid, the ant and the phorid fly).Probabilities of per capita female and per capita male survival from parasitism under the influence of ant and the phorid flyTo test whether the sex ratio of beetle survivors’ population is due to sex-differential survival probability, Bayes’ theorem was employed. Per capita female survival probability from parasitism in each treatment of the parasitism experiment was derived based on (widehat{P}(F)), (widehat{P}left(F|Sright),) and (widehat{P}(S)), and per capita male survival probability was derived based on (widehat{P}(M)), (widehat{P}left(M|Sright),) and (widehat{P}(S)). According to the Central Limit Theorem, the estimates of proportions, (widehat{P}left(S|Fright)) and (widehat{P}left(S|Mright)), are approximately normally distributed,$$widehat{P}left(S|Fright)sim Nleft(widehat{P}left(S|Fright), sqrt{frac{widehat{P}(S|F)times left(1-widehat{P}left(S|Fright)right)}{{n}^{*}}}right)$$$$widehat{P}left(S|Mright)sim Nleft(widehat{P}left(S|Mright), sqrt{frac{widehat{P}(S|M)times left(1-widehat{P}left(S|Mright)right)}{{n}^{*}}}right)$$with means (widehat{P}left(S|Fright)) and (widehat{P}(S|M)), and standard deviations (sqrt{frac{widehat{P}left(S|Fright)times (1-widehat{P}left(S|Fright))}{{n}^{*}}}) and (sqrt{frac{widehat{P}left(S|Mright)times (1-widehat{P}left(S|Mright))}{{n}^{*}}}), where (widehat{P}(S|F)) and (widehat{P}(S|M)), respectively, are the population proportions of females and males. Here we employ n*, the smallest sample size among those of the three variables in the Bayesian formulas for males and females. Since the three variables have different sample sizes, n* guarantees a conservative estimate of standard error, and thus confidence interval, of each derived probability. More

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The plots of Igeo, PERI, and PLI of HMs in the topsoil of the tourist area of Sayram Lake (Fig. 5) reveal the degree of HM pollution and eco-risk in this study area on the one hand and, on the other hand, indicate the direction for the relevant agencies to target soil environmental protection and HM pollution prevention and control measures. In this study, the Igeo results showed that Cd was the most highly enriched HM, and Pb, Zn, Cd, and Ni were slightly enriched in a few sample sites. The unnatural accumulation of these elements is usually closely associated with human activities in the area34. Tourism is the main economic activity in the district, and published studies have reported that tourism infrastructure construction (e.g., roads, buildings, etc.) and tourism wastes (e.g., plastic bags, batteries, hotel wastewater) release Cd into the soil35. Additionally, the accumulation of Pb, Zn, Cu and Ni in soils is usually associated with traffic emissions36. The PERI showed that the study area was at low risk overall, with only point ss04 exhibiting medium risk; however, this result was caused by the abnormally high Cd concentration value (Fig. 4) at point ss04 (Cd (concentration): 1.08 mg/kg, Cd (background): 0.34 mg/kg). This anomalous concentration value has a large influence on the PERI calculated based on the measured concentration, the background value and the toxicity coefficient. Therefore, references to this point can be appropriately removed when considering eco-risk. The PLI of each sampling point was greater than 1 and less than 2, which means that the area was in a moderately contaminated state. In general, the degree of soil HM contamination in this area was low; however, due to HM toxicity, bioaccumulation, and persistence37, the HM contamination of this area still requires sustained attention.Figure 5Contamination and ecological risk indices: (a) geoaccumulation index (Igeo) of HMs; (b) ecological risk of individual HMs; (c) potential ecological risk index (PERI) of HMs; (d) pollution load index (PLI) of HMs.Full size imageCorrelation analysis is an efficient way to reveal correlations among HMs through Pearson correlation coefficients, and HMs with significant correlations may originate from the same source38. As shown in Table S5, the elemental pairs Cd-Cu (p  More