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Various estimates for great crested newt pond occupancy rates have been published with most relating to site or regional scale assessments. A naïve occupancy rate of 0.13 has been identified for a data set from the northwest of England29, while estimates based on conventional occupancy16 modelling of 0.31 for southeast England and between 0.32 and 0.33 for mid Wales were presented by Sewell et al.13. The only other national data which the authors are aware of are within the Freshwater Habitat National PondNet Study, which estimates a naïve pond occupancy of between 13 and 18%30, and the Amphibian and Reptile Conservation Trust National Amphibian and Reptile Recording Scheme, which suggests a 12% occupancy rate for the UK31. Using data from nearly 5000 ponds sampled across England, here we provide a more extensive national-level analysis while accounting for imperfect detection in the eDNA sampling protocol. Assuming a threshold of just one positive qPCR replicate in a sample, the naïve occupancy estimate of 0.30 is similar to the localised regional estimates made by Sewell et al.13 using direct observation methods. The posterior mean estimates of 0.198 for occupancy are comparable to most other estimates for great crested newt pond occupancy in the UK, but lower than the naïve estimate. The lower modelled estimates of occupancy than the naïve estimate suggest that false positives should not be ignored and need to be accounted for statistically using methodologies such as the eDNAShinyApp package used here23,24,27.The goodness of fit analysis was based on the MCMC output for each site and observed covariate levels in the data set. Some lack of fit was observed, with a predicted peak in amplification at 10 qPCR replicates but an observed peak at 12 qPCR replicates. There are several potential causes for this. For example, variation between laboratories could not be accounted for as these metadata were not made available. The assumption that error rates are the same across all laboratories may therefore not apply and could contribute to poorer model fit. Secondly, we did not consider error rates as functions of covariates, and this may also have contributed to a poorer fit.Stage 1 error was found to be smaller than Stage 2 error for both false positive and false negative error. However, Stage 2 error operates on individual qPCR replicates and not at the site level. If there was no error at Stage 2, we would observe either zero qPCR replicates amplifying or all qPCR replicates amplifying (i.e. 12 in the case of the data presented here). The majority of samples showed zero qPCR amplification (3429 samples), and this was strongly linked to absence of newts. For sites with amplification, we observed a greater number of samples amplifying between 1 and 11 qPCR replicates (1074 samples) than we did amplifying with all 12 qPCR replicates (422 samples). The qPCR replicates that do not amplify in samples containing target DNA are erroneous, even if other replicates within that sample do amplify and contribute to this high Stage 2 false negative error in the model output. Data simulated from the fitted model show that the frequency of samples that contain DNA at Stage 2 amplifying in less than five of the 12 qPCR replicates is very low (Fig. 2b). Given that all replicates need to be erroneous to alter the naïve assignment of a sample containing DNA to negative, Stage 2 false negatives at this sampling level are unlikely. However, this does not rule out Stage 1 false negative error which we estimate to be 5.2% (with wide credible intervals between 0.1% and 25.1%).Higher levels of Stage 2 replication remove lab-based false negative error. If eDNA is present within a sample and a high number of replicates are used, it is highly unlikely that all qPCR replicates will be erroneously negative, even when the false negative rate at the replicate level is high. Conversely, high levels of Stage 2 replication increase the likelihood of false positive error occurring32. Stage 2 false positive results are of greater consequence than the 2% the model output would suggest. Unlike false negative error where all Stage 2 replicates need to be erroneous to change the naïve assignment of occupancy of a sample, when a threshold of one amplifying replicate is applied, only a single replicate needs to be an erroneous to generate a false positive. With 12 qPCR replicates at Stage 2 and a 2% false positive error per replicate, a sample with no DNA present has a 24% chance of producing at least one amplification. Assuming this error is randomly distributed through samples with no DNA present and qPCR replicates, it is more likely that samples with small numbers of replicates amplifying would be erroneous than where large numbers of replicates amplify. This was confirmed in the goodness of fit analysis with the distribution of Stage 2 false positive replicates making up all samples amplifying with one or two positive qPCR replicates, while negligible false positive amplification was seen with four amplifying replicates or above (Fig. 2a). With only a single sample at Stage 1, false positive error is limited to the 1.5% per sample, as per the ({theta }_{10}) value in the occupancy model output.We would recommend that, where possible, results from individual sites are interpreted as a probability of site occupancy, based on modelled outputs such as those produced by the eDNAShinyApp R package23,27. The precision of these models is dependent on sample size. Where sample size is large, a reduced bias and narrower credible interval range is observed24. However, using occupancy modelling, Buxton et al.24 demonstrated that studies that contain only a small number of sites are unlikely to produce accurate and precise estimates. As a result, such assessments will need to continue to rely on a threshold value of amplifying qPCR replicates to define site occupancy. A naïve amplification threshold for assigning occupancy of one positive qPCR replicate is unwise and should be increased to reduce Stage 2 false positive error. Indeed, a threshold of three positive qPCR replicates would reduce false positive error, without increasing false negative error. Alternatively, redistributing the replication between Stage 1 and Stage 224, would also reduce the credible interval width and generate a more precise posterior mean estimate at Stage 1, in turn reducing the uncertainty around the occupancy estimate. A redistribution of replication leading to two samples collected from each site, both analysed using up to six qPCR replicates, as opposed to one sample analysed using twelve qPCR replicates, has been suggested24.Equal weighting of the ten covariates used in the traditional great crested newt HSI assessment25 may be ecologically unrealistic29. This is supported by the observations here, with only some of the HSI covariates identified as important for occupancy. The model applied by the eDNAShinyApp package23,27 successfully identified several covariates known to influence great crested newt occupancy, that are included within the HSI assessment25. These included occurrence of fish, water quality, shade, pond density, macrophyte cover, frequency of drying and geographic area; although our analysis was based on Easting and Northing, rather than the broad-scale suitability map used in deriving the original HSI25. However, several traditionally used HSI variables emerged as unimportant, i.e., waterfowl, terrestrial habitat quality, and area of pond; while ground frost, rainfall, surface wind and land cover type, are not included within the HSI assessment but were important.The importance and influence of the HSI suitability indices of fish, shade, pond density, water quality, macrophyte cover, and frequency of drying on pond occupancy were all as expected with wide literature support25,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48. The negative pond occupancy response to climatic covariates of ground frost and high precipitation are supported in relation to annual survival47. ‘It is worth noting that the PIP value for wind speed was only just over the threshold for inclusion as important. Although ponds are shallow with limited stratification possible, wind speed has been shown to influence the distribution of eDNA in deeper waterbodies49,50. Estimating the presence of fish in a pond by direct observation for the traditional HSI may be problematical, and metabarcoding approaches to eDNA surveys which offer information on presence of other species would improve the accuracy of covariates, such as fish presence40. Indeed, assigning “Possible” fish presence within the HSI when scoring a pond accounted for the same percentage (33.1%) of both positive and negative eDNA samples. This suggests that when surveyors are not confident of fish presence, they are using this category in equal proportions for both occupied and unoccupied ponds. Landcover and bedrock were also important for pond level occupancy. This is expected given the importance of terrestrial habitat, and water retention to the species (Figs. S1, S3)35,51. However, with very unbalanced sample sizes between the categories (Figs. S2, S4), and influence of nearby land cover types uncaptured by the data, this variable is difficult to interpret, and we suggest further examination. Nevertheless, the positive associations with woodland and grassland reflect established knowledge of habitat preferences36. Equally, as freshwater predominantly relates to rivers and lakes rather than ponds in the landcover dataset used, negative relationships reflect the lower suitability of these habitats36.Several covariates, however, did not exhibit the expected response for pond occupancy. Terrestrial habitat was not found to be important despite the species being only semi-aquatic, and previous studies emphasising the importance of this variable36. This may be a result of the original Oldham et al.25 terrestrial habitat assessment being simplified into four subjective categories in the ARG UK26 protocol: this may not be nuanced enough to differentiate terrestrial habitat usage using statistical modelling. Waterfowl were not identified by the model as important predictors of great crested newt pond occupancy, where they have been elsewhere29,41, with one study suggesting a positive relationship between waterfowl species richness and great crested newt occupancy40. The lack of importance demonstrated in this data set may indicate that other covariates outweigh waterfowl in terms of occupancy importance, or they may only become important predictors of occupancy at very high waterfowl densities rarely observed in this data set. Similarly, pond area was not found to be an important predictor of pond occupancy. There was no difference in the mean area for occupied or unoccupied ponds; however, no occupied ponds were found above 10,000 m2. We would anticipate that both very small and very large ponds to be unsuitable for great crested newts25,52.Northing but not Easting was found to be an important predictor of pond occupancy. A distribution gradient with latitude is a common feature of biodiversity generally, and in the UK great crested newts are much more patchily distributed in Scotland than in England53,54. Pond occupancy estimates varied by year, with a greater occupancy in 2018 than the other years considered. This is likely linked to climatic conditions and may relate to the timings of ponds drying in relation to eDNA sample collection. This may therefore be an artefact of unoccupied ponds being more likely to dry early in the season and therefore being excluded from occupancy estimates for dry years, or local migration to less suitable habitat if core ponds start to dry, however long term analysis of individuals within a metapopulation shows little support for this47. As a result, in very dry years, we would expect an increase in pond occupancy to be observed in the data. Although average early spring rainfall for England in 2018 was higher than in either 2017 or 2019, rainfall during the main eDNA survey window of May and June was considerably less in 2018 than in the other two years (Fig. S5). Similar variation in year on year occupancy rate has been observed elsewhere30.As with all sampling methods, imperfect detection is a general feature of eDNA surveys. When high levels of qPCR replicates are used, false negative error is predominantly due to failure to collect DNA in a sample rather than failure to detect DNA within the lab. False positive error can occur at both stages and is exaggerated at Stage 2 by high levels of replication; Stage 2 false positive error is most likely in samples with a low proportion of replicates amplifying. We recommend using statistical models to estimate the occupancy of individual sites, taking into consideration sampling error. Failing that, a naïve occupancy threshold of two or three amplifying qPCR replicates, adjusting for total levels of replication, should be applied before assigning a site as occupied or not.With specific reference to great crested newts, we estimate approximately 20% of ponds through their natural range within England are occupied. We estimate that eDNA sampling failed to collect DNA from approximately 5% of sites where it was present. However, if eDNA is collected it is highly unlikely to be missed during the laboratory phase using the present protocol. We estimate that eDNA is erroneously collected in approximately 1.5% of water samples causing Stage 1 false positive results. However, false positives at the laboratory phase were found to be 2% per qPCR replicate; it is likely that this error would account for the majority of samples amplifying with one or two qPCR replicates, as a result these need to be treated with caution. To maximise accuracy, we recommend redistributing replication between the two stages, as is recommended elsewhere, and that thresholds to define a replicate as positive are further examined24,55. It is important to recognise that visual surveys also experience imperfect detection13, with observation errors likely to be similar to or greater than the error experienced using eDNA methods, particularly if the recommendations presented here are put in place to minimise laboratory stage false positive error. The benefits associated with eDNA over traditional methods allowing rapid collection of large scale distribution data are invaluable and should not be devalued in relation to traditional methods15. Although not identified within the models as important predictors, waterfowl, terrestrial habitat, and pond area may remain important habitat features for great crested newts. These covariates may be less important than the other HSI covariates, may not be measured in a sufficiently nuanced way to enable their importance to be identified, or may have influence on a local but not national scale29,40. However, equal weighing of the ten HSI variables is an oversimplification with the effect of some variables, for example pond area, overinflated within the HSI analysis, whereas others are undervalued, for example fish intensity. It is important to measure HSI covariates accurately and consistently to allow them to be utilised in statistical analysis such as this, and a review of the covariates and weighting is warranted now large occupancy data sets are becoming available. More

Acute cold shock causes drastic phenotypic alterationsThe duration of cold exposure for young adult hermaphrodite C. elegans at 2 °C is negatively correlated to post-shock survival rates15. Wild-type hermaphrodite worms exposed to a 4-h cold shock (CS) do not initially display high mortality rates (Fig. 1a); this allows observation of a range of phenotypic transitions as they recover from the limited-duration cold stress at their preferred temperature of 20℃. One of the most striking phenotypes exhibited in post-cold shock (post-CS) animals during the recovery period is a dramatic decrease in pigmentation in the normally highly pigmented intestine, so that the body becomes almost entirely clear (Fig. 1b, c)15. This is often accompanied by motor and reproductive disruptions such as mobility loss, withering of the gonad arms, decreased number of internal embryos, and the eventual death of about 30% of the population (Fig. 1a–d)15. It should be noted that these phenotypic responses do not appear to be due to any relative heat shock following the transition from 2 to 20 °C as the expression of GFP-tagged HSP-4 (heat shock protein) is not induced following cold shock (Fig. 1e). Neither is the reduced pigmentation following cold shock due to a period of starvation presumably experienced by the worms while they are at 2 °C. At this extreme cold temperature, the worms enter a “chill coma” in which pharyngeal pumping and virtually all other movement ceases15,16; however, a total absence of food for a similar time period does not induce a comparable clearing phenotype (Supplemental Fig. S1). Interestingly, some CS wild-type animals regain pigmentation after clearing; these worms do not die and display a general reversal of the other negative impacts of cold shock (Fig. 1b)15. We sought to better understand the factors regulating the post-CS recovery program in wild-type worms, focusing particularly on the functional role of pigmentation loss and the genetic components involved in producing it.Figure 1Cold-shocked worms show decrease in survival and characteristic phenotypic alterations. N2 young adult hermaphrodites were shifted from 20 to 2 °C for a 4 h cold shock (CS) and thereafter recovered at 20 °C for 96 h with assessment of (a) survival and (b) phenotypic alterations (n = 177). Death and immobility were assayed by nose tap; worms were considered to be immobile if the tap elicited slight movement in the head region but no other body movement, and dead worms were completely unresponsive (Chi-squared Test for Homogeneity: P  More

Study site and experimental designThe study site, experimental design, and annual sampling protocol have been described in previous publications15,22,47 but a summary will be provided here. The experiment was conducted in a remote study site approximately 20 km northeast of Kangerlussuaq, Greenland, at 67.11° N latitude and 50.34° W longitude, approximately 160 km inland from Baffin Bay. Annual growing season (May through July) mean temperature and total precipitation at the study site during the duration of this experiment (2002–2017) were 8.62 ± 0.20 °C and 43 ± 6.78 mm, respectively47. The surrounding area has functioned as an important caribou (Rangifer tarandus) migration corridor, calving ground, and Indigenous Peoples hunting site for at least approximately 4000 years48, and was designated as a UNESCO World Heritage Site, Aasivissuit—Nipisat, by the United Nations in 2018. Caribou are present in greatest numbers seasonally, with most of the animals that use the site migrating into it during late winter and early spring and migrating out of it in mid to late summer; some male caribou remain at the site through winter. Muskoxen (Ovibos moschatus) are present at the site year-round. Arctic hares (Lepus arcticus) and rock ptarmigan (Lagopus muta) occupy the site in low numbers. In contrast to other locations in the Arctic where they are important herbivores, this site does not harbor voles or lemmings.In June 2002 we erected six exclosures constructed of woven wire fencing material supported by steel t-posts; each exclosure was circular and measured 800 m2. Adjacent to each exclosure, and separated from it by approximately 20–50 m, we located a comparable control site. Exclosure sites and adjacent control sites covered a range of elevations from approximately 275–300 m above sea level. In early May 2003, prior to onset of the plant growing season, we installed passive, open-topped warming chambers constructed of UV neutral glazing material on three plots inside and three plots outside of one exclosure site and three plots inside and four plots outside of a second exclosure site. In early May 2004, we added three warming chambers inside and three warming chambers outside one of the sites equipped in 2003, and we installed an additional three warming chambers on plots inside and three warming chambers on plots outside of a third exclosure site, thus resulting in a total of 12 warmed plots distributed among three exclosure sites and 13 warmed plots distributed among three control (grazed) sites. An ambient (control) plot was located near, but not closer than 2 m to, each warmed plot, thus resulting in 25 warmed plots and 25 ambient plots distributed among three exclosures and adjacent grazed sites. No plot was located closer than 2 m to the edge of any exclosure. Warming chambers were constructed according to the International Tundra Experiment (ITEX) protocol49, were 1.5 m in basal diameter, and encompassed 1.77 m2. Warming chambers were installed in early May each year, anchored to plots using metal garden stakes, and removed annually at the time of vegetation sampling, which was intended to coincide with peak aboveground abundance at mid to late July in most years (except in 2006, when sampling was conducted in mid-June, and in 2003 and 2011 when sampling was conducted in mid-August)47. Warming chambers significantly elevated near surface temperature by approximately 1.5–3.0 °C, and resulted in a non-significant reduction of soil moisture22,50.Vegetation samplingVegetation sampling was conducted non-destructively using a square Plexiglas tabletop point frame on adjustable aluminum legs. The point frame measured 0.25 m2 and was centered within each plot for sampling. The corners of each plot were equipped with hollow aluminum tubes sunk into the soil surface at the cardinal directions, and the legs of the point frame were inserted into these tubes to ensure consistent orientation and location of the frame during sampling. Once the frame was positioned, a steel welding pin was lowered through each of 20 randomly located holes in the point frame tabletop, and each encounter by the tip of the pin with vegetation was recorded until the pin struck soil, litter, or rock. In 2003 and 2004, vegetation was recorded at the species level for deciduous shrubs (Betula nana and Salix glauca) and at the functional group level for graminoids (including grasses, rushes, and sedges of the genera Calamagrostis sp., Poa sp., Festuca sp., Hierochloë sp., Trisetum spicatum, Luzula sp., Carex sp., and Kobresia sp.), forbs, mosses, lichens, and fungi. Beginning in 2005, vegetation was recorded at the species level for forbs, in addition to deciduous shrubs, and at the genus level for lichens (Peltigera sp.), fungi [Calvatia sp.; most likely C. cretacea51], and mosses (Aulacomnium sp.). Graminoids were not resolved to the genus or species levels due to concerns about consistent identification. All taxa were identified in the field by the authors on the basis of visual inspection of live individuals in consultation with reference guides52,53,54,55. In adherence with the Guidelines for Professional Ethics established by the Botanical Society of America, sampling and identification were done non-destructively, and no voucher specimens were collected.Commonness estimationEcologically meaningful estimation of commonness is inherently relative; a taxon is only common or rare in relation to other taxa5. While there exist a considerable array of quantitative indices of commonness56, we opted for one that integrates abundance and occurrence by assigning equal weight to each. Using annual abundance sums obtained during point frame sampling, we calculated commonness for each taxon as the product of its proportional abundance across all plots within each treatment and its proportional occurrence across all plots within each treatment. Hence, the commonness (C) of an individual taxon, i, in a given year, t, can be expressed as the product of its proportional abundance (A) and proportional occurrence (O) in that year:$$C_{it} = A_{it} *O_{it}$$
(1)
in which proportional abundance of taxon i in year t is the sum of point frame pin intercepts, h, for that taxon in that year across all plots sampled that year divided by the total number of point frame pin intercepts, H, of live vegetation biomass recorded across all plots sampled that year:$$A_{it} = h_{it} /H_{t}$$
(2)
and in which proportional occurrence of taxon i in year t is the sum of the number of plots, p, on which point frame pin intercepts of taxon i were recorded in year t divided by the total number of plots, P, sampled in year t:$$O_{it} = p_{it} /P_{t}$$
(3)
This index was used to estimate taxon-specific commonness within each experimental treatment combination (i.e., exclosed ambient, exclosed warmed, grazed ambient, and grazed warmed treatments), as well as across the entire site (sitewide commonness) for derivation of baseline commonness. To derive baseline commonness for subsequent analysis of its contribution to taxon-specific trends in commonness over the course of the experiment, we used sitewide commonness of each taxon in the year 2006. As described above, greater taxonomic resolution beyond functional group was not widely applied in our sampling until the third year of the experiment, 2005. However, we decided against using 2005 as a baseline for commonness at the site because it also happened to be the final year of a two-year outbreak of caterpillar larvae of a noctuid moth, Eurois occulta, that reduced aboveground abundance of nearly all taxa on our plots22,57. Except for the fungus C. cretacea, all taxa, whether recorded by pin intercepts during point-frame sampling or not, were observed on at least one plot under each of the four experimental treatment combinations. The rarest forb in this study, Pyrola grandiflora, was observed on a single plot under each of the exclosed ambient, exclosed warmed, and grazed warmed treatments, and on two plots under the grazed warmed treatment, but was not recorded during point frame sampling of exclosed ambient or grazed ambient plots. Hence, any conclusions about the effects of warming on this species must be limited. Similarly, the lichen Peltigera sp., which was also very rare in this study, was recorded during point frame sampling on plots under each treatment combination, but was not detected by sampling on exclosed warmed plots after 2005 even though it was observed on one exclosed warmed plot after that. This might be considered corroboration of the negative effect on this genus of warming under herbivore exclusion reported in the Results, but caution may also be warranted. The fungus C. cretacea first appeared under the grazed ambient treatment in 2008 and then under the exclosed ambient treatment in 2012, but was not recorded under the grazed warmed or exclosed warmed treatments. This might in and of itself suggest a negative effect of warming on the establishment or occurrence of this species, or fungi in general, and might be consistent with limiting effects of reduced moisture availability under warming. However, we urge caution with this interpretation because fungi may not form fruiting bodies every growing season, and such fruiting bodies may emerge aboveground in different locations from one growing season to the next, thereby potentially confounding repeated detection by sampling methods such as ours.Analysis of experimental treatment effects on plant functional group abundanceWe used a Gaussian generalized linear model (GLM) with an identity link function to analyze variation in functional group abundance among experimental treatment combinations. This GLM included total annual abundance, for the period 2003–2017, of deciduous shrubs (comprising summed abundances of Betula nana and Salix glauca leaf and stem point frame pin intercepts), graminoids (comprising all grass, rush, and sedge tissue point frame pin intercepts), forbs, mosses, lichens, or fungi, in separate models with the two experimental treatments (warming and herbivore exclusion) and their interaction as factors, year as a factor, and day of year of sampling as a continuous covariate. Significance of individual treatment effects of warming and herbivore exclusion, as well as their interaction, was determined based on Wald Chi-square statistics and associated two-tailed P-values (with significance indicated at P ≤ 0.05).Analysis of experimental treatment effects on commonnessAnalyses of commonness data were performed at higher taxonomic resolution than were analyses of abundance data, and so were limited to analysis of data from the last 12 years of the experiment, 2006–2017. Using Eq. (1), commonness was estimated for 14 taxa, including two species of deciduous shrubs, Betula nana and Salix glauca; graminoids, comprising at least eight non-distinguished genera of grasses, rushes, and sedges listed above in the sub-section Vegetation sampling; eight species of forbs, including Equisetum arvense, Stellaria longipes, Cerastium alpinum, Bistorta vivipara, Draba nivalis, Campanula gieseckiana, Viola canina, and Pyrola grandiflora; one genus of moss, Aulacomnium sp.; one genus of fungus, Calvatia sp.; and one genus of lichen, Peltigera sp.We first investigated general characteristics of and treatment effects on commonness across the study site. We examined the skewness of commonness to determine whether the distribution of the 14 focal taxa was significantly right-skewed, indicating greater numbers of rare than of common taxa2. We obtained an estimate of skewness and its standard error across pooled data for the period 2003–2017, derived a 95% confidence interval, and compared it to zero. Next, we examined experimental treatment effects on sitewide commonness. To do this, we used a Gaussian GLM with identity link function to analyze pooled commonness of all taxa for the period 2006–2017, with commonness as the dependent variable and the two experimental treatments and their interaction as factors, year as a factor, taxon as a factor, and day of year of sampling as a covariate. We determined significance of individual treatment effects and their interaction by examining Wald Chi-square statistics, with significance indicated if the two-tailed P ≤ 0.05. We then tested for experimental treatment effects on individual taxa using the same analytical approach, but with taxon-specific commonness as the dependent variable, and treatment and year as factors, with day of year of sampling as a covariate.Analysis of trends in commonness and skewness of commonness over the last 12 years of the experimentWe next investigated whether common and rare taxa displayed different trends in commonness over the course of the last 12 years of the experiment. This was motivated by a presupposition that warming and/or herbivore exclusion might have differentially altered commonness of common vs. rare species. We first examined linear trends in sitewide commonness of all 14 taxa pooled across experimental treatments by testing for significance of linear regressions of taxon-specific commonness vs. year for the period 2006–2017. We then conducted the same analysis for each taxon individually under each experimental treatment combination to determine whether our experimental manipulations contributed to trends differentially in common vs. rare taxa. We then investigated whether the distribution of commonness across the 14 focal taxa displayed directional change over the course of the final 12 years of the experiment, and whether it might have done so differently in relation to experimental treatment combinations. To do this, we tested for significance of linear regressions of treatment-specific skewness of commonness vs. year for the period 2006–2017. Finally, we examined whether trends in commonness were related to baseline commonness for the 13 taxa resolved to the genus or species level, excluding graminoids because this group comprised multiple unresolved genera. This analysis was motivated by interest in determining whether taxa that were common at the beginning of the experiment tended to become more common and taxa that were rare at the beginning of the experiment tended to become rarer, thus indicating that degree of commonness itself might be an important driver of changes in commonness over the course of a multi-annual experiment such as ours. To do this, we fit a non-linear regression model using a von Bertalanffy equation to quantify the relationship between taxon-specific commonness trend (standardized coefficient from the regression of commonness vs. year, ranging between − 1 and 1) and baseline commonness by treatment. This equation took the form:$$Y = 1 – left( {1 – a} right)e^{ – bX}$$
(4)
In which Y = taxon- and treatment-specific commonness trend, estimated in this case using the standardized coefficient from a linear regression of commonness of taxon i under a given experimental treatment combination vs. year; a = the Y-intercept; b = the slope; and X = baseline commonness of taxon i under the same treatment combination in 2006. Significance of regressions for each treatment was determined by calculating an F-statistic using corrected model sums of squares, error sums of squares, model degrees of freedom, and error degrees of freedom. Non-linear regression models were considered significant if the F-associated P ≤ 0.05. More