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In the autumn (November), L. dispar egg masses were collected at two sites: unpolluted and polluted forest. The first was a mixed oak forest at Kosmaj Mountain, 40 km south-east of Belgrade (coordinates 44°27′56″N 20°33′56″E). These woods are regarded as unpolluted because they are far from direct pollution and are part of the system of protected green areas around Belgrade, where the construction of industrial facilities and traffic infrastructure with potential negative effects on the environment is prohibited by legal regulations. The second site was Lipovica Forest (coordinates 44°38′11″N 20°24′12″E), with mixed Quercus frainetto and Quercus cerris trees, considered a polluted forest since it is located along the border of State Road 22, one of the most frequently used IB-class roads in Serbia.Collected egg masses were kept in a refrigerator at 4 °C until spring (March) when 200 eggs for each experimental group were set for hatching. After hatching in transparent Petri dishes (V = 200 mL), 10 first instar larvae were transferred and reared together at 23 °C with a 12:12 h light: dark photoperiod and relative humidity of 60%, until the third larval instar. Then, five 3rd instar larvae were reared together in the same Petri dish. After molting into the 4th instar, each larva was kept individually until the third day of the 5th instar, when they were sacrificed. Larvae were fed on an artificial diet designed for L. dispar42, and food was replaced every 48 h. Each experimental group contained between 50 and 60 larvae (Fig. 7).Figure 7A schematic figure of the experimental treatments.Full size imageThe optimal temperature for L. dispar larval development is 23 °C, and the control group was reared at this temperature. The highest summer temperature (2007–2010) measured in Serbian Quercus forests at a similar elevation was 28.4 °C, and the lowest 19.6 °C, while the average summer temperature was 26.3 °C43. Thus, we established variable temperature regimens that included brief (24 h) and daily (72 h) exposures to 28 °C. The control group of larvae were reared through the whole experiment on optimal 23 °C. Results of Huey et al.44 indicate that short term (daily) exposure to higher temperatures during development can increase both optimal temperature and maximal growth rate at the optimum, an example of beneficial thermal acclimation. In our previous research we found that induced thermotolerance modifies the activity of detoxifying enzymes in larvae originating from the polluted forest. We exposed L. dispar larvae in several experimental groups to that regime at 4th larval instar, with intention of analyze the effects of induce thermotolerance on observed parameters (ALP, ACP, hsp 70) in 5th instar larvae reared on optimal or elevated temperature28.At sacrifice on the third day of the 5th instar, the caterpillar midguts were dissected out on ice (n = 8–11 larval midguts per group for each enzyme assay). Midgut from single larvae was weighed and homogenized in insect physiological saline, as insect fluids have buffer values similar to vertebrates45. Homogenization was performed in ice-cold 0.15 M NaCl (final tissue concentration was 100 mg/mL in each sample), for 3 intervals of 10 s with a 15 s pause between them, at 5000 rpm, using Ultra Turrax homogenizer (IKA-Werke, Staufen, Germany). The homogenates were centrifuged for 10 min at 10,000 g at 4 ℃, and supernatants were used for enzyme assays and NATIVE gel electrophoresis. This protocol ensured that supernatants would contain cytosol and lysosomes.On the third day of the 5th instar, larval brain tissues were dissected out on ice and weighed. Pooled brain tissue (n = 30 brain tissues per experimental group) was diluted with 0.9% NaCl (1:9/w:V) and homogenized on ice at 5000 rpm during three 10 s intervals, separated by 15 s pauses (MHX/E Xenox homogenizer, Germany). Homogenates were centrifuged at 25,000 g for 10 min at 4 °C in an Eppendorf 5417R centrifuge (Germany). The supernatants were used for Western blotting and indirect non-competitive enzyme-linked immunosorbent assay (ELISA). Protein concentrations samples were determined using BSA as the standard46.A modified method by Nemec and Socha47 was used to determine the activity of ALP. The reaction mixture contained 0.1 M Tris HCl buffer pH 8.6, 5 mM MgCl2, midgut homogenate, and 5 mM p-nitrophenyl phosphate. During 30 min of incubation time at 30 ℃, the hydrolytic release of p-nitrophenol from p-nitrophenyl phosphate (pNPP) occurred under alkaline conditions.The reaction was stopped with 0.5 M NaOH, and the absorbance of p-nitrophenol was measured at 405 nm. Blank and non-catalytic probes were included. One unit of enzyme activity was defined as the amount of enzyme that released 1 mmol of p-nitrophenol per minute under the assay conditions.The same modified method of Nemec and Socha47 was employed to determine ACP activity, but under acidic conditions (0.1 M citrate buffer pH 5.6 was found optimal for L. dispar ACP), with a prolonged incubation time of 60 min. One unit of enzyme activity was defined as the amount of enzyme that released 1 μmol of p-nitrophenol per minute per mg of total protein. Total ACP activity determined in the midgut samples came from lysosomal ACP that ended up in the cytosol and non-lysosomal ACP, typically localized in the cytosol.Lysosomal ACP were detected indirectly48, under the same conditions, in a mixture containing the specific enzyme inhibitor NaF (50 mM). The absorbance determined at 405 nm is proportional to the activity of the non-lysosomal fraction of total ACP. The activity of the lysosomal fraction was obtained by subtracting not inhibited non-lysosomal acid phosphatases from the total phosphatase activity. Specific activities of ACP are given in mU per mg of total protein.A modified method by Allen et al.49 was used to detect ALP isoforms after native PAGE. Using 12% polyacrylamide gel, 10 μg protein aliquots per well were separated at 100 V and 4 ℃. The ALP isoform activity was visualized by soaking the gel in an incubation mixture consisting of 0.13% α-naphthyl phosphate, 100 mM Tris–HCl buffer (pH 8.6), and 0.1% Fast Blue B. The gels were incubated at room temperature until bands appeared.For ACP phosphatase detection, the same method of Allen et al.49 was also modified. After electrophoresis, the gel was washed with deionized water and equilibrated in 100 mM acetate buffer (pH 5.2) at 30 ℃. The nitrocellulose membrane was pre-soaked in 0.13% α-naphthyl phosphate dissolved in the same acetate buffer for 50 min at room temperature. The gel was covered with the membrane and incubated in a moist chamber for 60 min at 30 ℃. The membrane was soaked in 0.3% Fast Blue B stain dissolved in acetate buffer until bands became visible.Gels were scanned with a CanoScan LiDE 120 (Japan). The intensities of enzyme bands in the regions of ALP and ACP activities were analyzed using the ImageJ 1.42q software (U. S. National Institutes of Health, Bethesda, Maryland, USA).An indirect non-competitive ELISA was used to quantify the concentration of hsp70 in L. dispar brain tissue. Samples were diluted with carbonate-bicarbonate buffer (pH 9.6) and coated on a microplate (15 μg of tissue/well) (Multiwell immunoplate, NAXISORP, Thermo Scientific, Denmark) overnight at 4 °C, in the dark. The indirect non-competitive ELISA for L. dispar hsp70 was performed according to general practice: samples were first incubated with monoclonal anti-Hsp70 mouse IgG1 (dilution 1:5000) (clone BRM-22, Sigma Aldrich, USA) for 12 h at 4 °C, and then for 2 h at 25 °C with secondary anti-mouse IgG1 (gamma-chain)-HRP conjugate (dilution 1:5000) antibodies (Sigma Aldrich, USA). Chromogenic substrate 3, 3’, 5, 5’-Tetramethylbenzidine (TMB) was used as a visualizing reagent. Absorption was measured on a microplate reader (LKB 5060-006, Austria) at 450 nm. To enable statistically valid comparisons of experimental groups across multiple microplates, each microplate contained serial dilutions of standard hsp70 (recombinant hsp70, 50 ng/mL), used for the hsp70 standard curve, and homogenized brain tissues pulled by each treatment that were loaded on the microplates in a matched design, ensuring that each data point represented the mean of three replicates from each experimental group.Western blots were used to detect the presence of heat-shock protein 70 isoforms. Brain tissue homogenates were separated by SDS PAGE electrophoresis on 12% gels, according to Laemmli50. Protein transfer from the gel to the nitrocellulose membrane (Amersham Prothron, Premium 0.45 mm NC, GE Healthcare Life Sciences, UK) was left overnight at 40 V and 4 °C. Monoclonal anti-hsp70 mouse IgG1 (1:5000 dilution, clone BRM-22, Sigma Aldrich) and secondary mouse anti-mouse Hsp70 horseradish peroxidase conjugate antiserum (1:10,000 dilution, Sigma-Aldrich) were used for detection of hsp70 expression patterns in L. dispar larval brain tissue. Bands were visualized using chemiluminescence (ECL kit, Amersham).This study identified the hsp70 concentration in brain tissue and specific activities of total ACP and ALP in the larval midgut as the most promising biomarkers, which are sensitive and have consistent responses to thermal stress. These three biomarkers were combined into an IBR analysis according to Beliaeff and Burgeot51. The value of each biomarker (Xi) was standardized by the formula Yi = (Xi − mean)/SD, where Yi is the standardized biomarker response, and mean and SD were obtained from all values of the selected parameters. The next step was describing Zi as Zi = Yi or Zi = − Yi, depending on whether the temperature treatment caused induction or inhibition of the selected biomarkers. After finding the minimum value of Zi for each biomarker (min), the scores (Si) were computed as Si = Zi + |min|. Scores for biomarkers were used as the radius coordinates of the studied biomarker in the star plots. Star plot areas for the three-biomarker assembly, positioned in successive clockwise order—Hsp70, total ACP, and ALP, were obtained from the following formulas: ({A}_{i}=frac{{S}_{i}}{2*mathrm{sin}beta }left({S}_{i}*mathrm{cos}beta + {S}_{i+1}*mathrm{sin}beta right)), (beta = {mathrm{tan}}^{-1}left(frac{{S}_{i+1}*mathrm{sin}alpha }{{S}_{i}-{S}_{i+1}*mathrm{cos}alpha }right)),(alpha =2pi /n) radians (n is the number of biomarkers). The IBR values were calculated as follows:(IBR= sum_{i=1}^{n}{A}_{i}), where Ai is the area represented by two consecutive biomarkers on the star plot. Excel software (Microsoft, USA) was used to calculate IBR values and generate star plots.Statistical analyses were conducted in GraphPad Prism 6 (GraphPad Software, Inc., USA). Mean values ± standard errors of mean values (SEM) were calculated for the activity of enzymes, larval midgut mass, and the hsp70 concentration in brain tissue. D’Agostino-Pearson omnibus and Shapiro–Wilk tests were used to check the normality of data distribution. The effects of thermal treatments and their interaction on the variance of analyzed biomarkers in larvae from the polluted and the unpolluted forest were tested using two-way ANOVA with thermal treatments as fixed factors. For all comparisons, the level of significance was set at p  More

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Empirical dataWe applied our theory to two datasets (Table 1): the plant survey dataset and the biodiversity-manipulated experiment dataset. The plant survey dataset contains nine sites of long-term grassland experiments across the United States (see also Hallett et al.10, and Zhao et al.23). Five of nine sites are from the Long Term Ecological Research (LTER) network (see Table 1). Plant abundances were measured either as biomass or as percent cover. In percent-cover cases, summed values can exceed 100% due to vertically overlapping canopies. All sites were sampled annually and were spatially replicated. We only used data of the plant survey dataset from unmanipulated control plots. Methods for data collection were constant over time.The biodiversity-manipulated experimental dataset comprises two long-term grassland experiments, BigBio and BioCON, at the Cedar Creek Ecosystem Science Reserve. Both experiments directly manipulated plant species number (1, 2, 4, 8, 16 for BigBio; and 1, 4, 9, 16 for BioCON). BioCON also contains different treatment levels for nitrogen and atmospheric CO2, but here only data from the ambient CO2 and ambient N treatments were used. We excluded plots with only one species. BigBio comprises 125 plots over 17 years, and BioCON comprises 59 plots over 22 years (Table 1).TheoryLet xi(t) denote the biomass of species i = 1, …, S at time t = 1, …, t and let μi = mean (xi (t)), σi = ({{mbox{sd}}})(xi (t)), and ({v}_{i}={sigma }_{i}^{2}) be the mean, standard deviation and variance of species i, computed through time. Let vij = cov (({x}_{i}left(tright),, {x}_{j}left(tright))) be the covariance, through time, of the dynamics of species i and j. Let xtot (left(tright)={sum }_{i}{x}_{i}(t)), ({mu }_{{{mbox{tot}}}}={sum }_{i}{mu }_{i}), ({v}_{{{mbox{tot}}}}={sum }_{i,j}{v}_{{ij}}), and ({{{{{{rm{sigma }}}}}}}_{{{{{{rm{tot}}}}}}}=sqrt{{v}_{{{{{{rm{tot}}}}}}}}). When population time series are uncorrelated, ({v}_{{{{{{rm{tot}}}}}}}={sum }_{i}{v}_{i}).As defined previously10,15, community stability is the inverse coefficient of variation of ({x}_{{{mbox{tot}}}}left(tright)), ({S}_{{{{{{rm{com}}}}}}}={mu }_{{{{{{rm{tot}}}}}}}/{sigma }_{{{{{{rm{tot}}}}}}}). Population stability is the inverse of weighted-average population variability9, ({sum }_{i}frac{{mu }_{i}}{{mu }_{{{{{{rm{tot}}}}}}}}{{CV}}_{i}={sum }_{i}frac{{mu }_{i}}{{mu }_{{{{{{rm{tot}}}}}}}}frac{{sigma }_{i}}{{mu }_{i}}={sum }_{i}frac{{sigma }_{i}}{{mu }_{{{{{{rm{tot}}}}}}}}), i.e, ({S}_{{pop}}={mu }_{{{{{{rm{tot}}}}}}}/{sum }_{i}{sigma }_{i}). The ratio of community stability over population stability is the Loreau-de Mazancourt asynchrony index14, Φ = ({sum }_{i}{sigma }_{i}/{sigma }_{{{{{{rm{tot}}}}}}}), so that$${S}_{{{{{{rm{com}}}}}}}=varPhi {S}_{{{{{{rm{pop}}}}}}}.$$
(1)
Now we suppose a hypothetical community with the same species-level variances and means as the original community but with species covariances equal to zero. Then, (1) becomes Scom_ip = (SAE)Spop, where ({S}_{{{{{{rm{com}}}}}}_{{{{{rm{ip}}}}}}}=frac{{mu }_{{{{{{rm{tot}}}}}}}}{sqrt{{sum }_{i}{v}_{i}}}=frac{{mu }_{{{{{{rm{tot}}}}}}}}{sqrt{{sum }_{i}{sigma }_{i}^{2}}}) is the value of community stability in the case of uncorrelated or independent populations and SAE is the component of Φ due to statistical averaging (here, “ip” stands for “independent populations”). The equation Scom_ip = (SAE)Spop can be interpreted as a definition of SAE. We then have$$SAE=frac{{S}_{{{{{{rm{com}}}}}}_{{{{{rm{ip}}}}}}}}{{S}_{{{{{{rm{pop}}}}}}}}=frac{{sum }_{i}{sigma }_{i}}{sqrt{{sum }_{i}{sigma }_{i}^{2}}}.$$
(2)
The compensatory effect is then the rest of Φ, i.e.,$$CPE=frac{{S}_{{{{{{rm{com}}}}}}}}{{S}_{{{{{{rm{pop}}}}}}}times SAE}=frac{{sum }_{i}{sigma }_{i}}{{sigma }_{{{{{{rm{tot}}}}}}}left({sum }_{i}{sigma }_{i}/sqrt{{sum }_{i}{sigma }_{i}^{2}}right)}=frac{sqrt{{sum }_{i}{sigma }_{i}^{2}}}{{sigma }_{{{{{{rm{tot}}}}}}}}.$$
(3)
Considering the classic variance ratio ({{{{{rm{varphi }}}}}}=frac{{V}_{{{{{{rm{tot}}}}}}}}{{sum }_{i}{V}_{i}}=frac{{sigma }_{{{{{{rm{tot}}}}}}}^{2}}{{sum }_{i}{sigma }_{i}^{2}}), our CPE is (1/sqrt{varphi }). Values CPE  > 1 (respectively, More

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