Partial auto-correlation plots for aerial density against the four explanatory variables.

<p>“ACF” is the auto-correlation function, and “AD” Aerial density. Peaks that cross the dotted blue lines are considered significant at the 5% level. All explanatory variables show at least some significant peaks suggesting some influence on aerial density, however patterns for temperature, wind speed and aphids are particularly strong (Figure 3 a, b and d).</p

Aerial density summarized by a) month and b) altitude for 2000–2010.

<p>Figure 1a Box plot for ladybird aerial density summarized by month. Boxes correspond to the 25^th and 75^th percentile, horizontal bars within boxes to means, and whiskers to maximum values or 1.5 times the interquartile range (when there are outliers present, represented by open circles). For boxplots of aerial density by year, or number of target species records in the VLR database, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082278#pone.0082278.s001" target="_blank">Figure S1</a>. Figure 1b Barplot of percentage total aerial density by altitude. The majority (roughly 85%) of ladybirds were detected in the first 5 range gates. Gate numbers correspond to the following altitudes (AGL): 1: 150–195; 2: 221–266; 3: 292–337; 4: 363–408; 5: 434–479; 6: 505–550; 7: 576–621; 8: 647–692; 9: 718–763; 10: 789–834; 11: 860–905; 12: 931–976; 13: 1002–1047; 14: 1073–1118; 15: 1144–1189.</p

Linear regression of aerial density against all explanatory variables.

<p>Graphs show the relationship between monthly mean aerial density and each of the explanatory variables (also monthly means). Units for the explanatory variables are: temperature: °C, wind speed: m/s, rainfall: mm, aphids: absolute number counted in suction trap. Note aerial density, rainfall and number of aphids are not normally distributed and are therefore log transformed (see main text). “Rsq”  =  adjusted <i>R²</i> (<i>R²_adj</i>). Temperature and aphids are both significant predictors of aerial density (see main text).</p

Time series plots for each variable.

<p>Results of time series analysis for aerial density and each explanatory variable for May to October 2000–2010. Note the correspondence between peaks in temperature and aerial density, and the lag between peaks in aerial density and aphid abundance.</p

Predictors of aerial density: Minimal (optimal) model.

<p><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082278#pone.0082278.s012" target="_blank">Tables S6</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082278#pone.0082278.s013" target="_blank">S7</a> for results of full model including wind speed and partial model excluding wind speed, respectively). For the qpGLMs, both <i>t</i> statistic, and <i>F</i> statistic with corresponding and <i>P</i> values are given. The qpGLM dispersion parameter, ρ = 0.374, and residual deviance  = 22.932 on 57 degrees of freedom (df). Residual df  = 57 for each model. Note that the GLM deviance, <i>F</i> and <i>P</i> values correspond to the full model, where residual deviance is 21.777 on 55 df. GLS without autocorrelation is equivalent to standard multiple linear regression. Results for minimal qpGLMs and GLS models (See </p><p><i>P</i> value codes: ^***<i>P</i><0.000; ^**<i>P</i><0.001; ^*<i>P</i><0.01; ⁺<i>P</i><0.05.</p

The most important broad drivers of species’ population changes, 1970–2012.

<p>Positive (green) and negative (blue) impact for each broad driver of change accounting for two percent or more of the total in absolute terms, ordered by absolute impact. Results are presented using all strengths of evidence available and weighting species in the three major taxonomic groups equally (insects, plants and vertebrates).</p

Overview of the review process.

<p>The relevant sections of the manuscript and supplementary material to go to for further information are shown in the right-hand and left-hand columns respectively.</p

The most important broad drivers of species’ population changes, 1970–2012, by higher taxonomic group.

<p>Positive (light green) and negative (dark blue) impact for each broad driver of change accounting for two percent or more of the total in absolute terms, ordered by absolute impact; by higher taxonomic group. Impact is shown as a percentage of the impact on that group, i.e. absolute impact sums to 100 for each of the three groups. Results are presented using all strength of evidence available.</p

The most important broad drivers of species’ population changes, 1970–2012, showing constituent specific drivers.

<p>Positive (green) and negative (blue) impact for each broad driver of change accounting for three percent or more of the total in absolute terms, ordered by absolute impact. Specific drivers (narrow bars) are listed under their associated broad driver (broad bars, italicised text); the impact of specific drivers sum to the total for the broad driver in each case. Results are presented using all strengths of evidence available and weighting species in the three major taxonomic groups equally (insects, plants and vertebrates).</p