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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

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

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

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