Table S1 Distributional trends for eight nativeladybird species, using different thresholds for including data inthe analysis. nYr is the number of years in which a1-km2 needed to be ‘well-surveyed’ in orderto be considered in the analysis. nFocal is the thresholdnumber of focal species (including Harmonia axyridis) toconsider a 1-km2 ‘well-surveyed’ in any1 year. Setting both thresholds to zero includes all possiblecombinations, including those based on incidental records frompoorly-sampled areas. Setting nYr = 3 andnFocal = 2 (the penultimate model for each species)correspond to the results shown in the main document. Columns b(Y),z(Y) and p(Y) are the slope, effect size and P-value for thetrend in the absence of H.  axyridis; b(H), z(H)and p(H) are comparable values for the effect ofH.  axyridis on the distribution trend. nis the sample size (number of 1-km2-year combinations)generated by the thresholds applied; obs is the number ofcombinations in which the focal species was present.

Appendix S1 Table of distributional trends foreight native ladybird species, using different thresholds forincluding data in the analysis. nYr is the number of yearsin which a 1-km2 needed to be‘well-surveyed’ in order to be considered in theanalysis. nFocal is the threshold number of focal species(including Harmoniaaxyridis) to consider a 1-km2‘well-surveyed’ in any one year. Setting boththresholds to zero includes all possible combinations, includingthose based on incidental records from poorly-sampled areas.Setting nYr = 3 and nFocal = 2 (thepenultimate model for each species) correspond to the results shownin the main document. Columns b(Y), z(Y) and p(Y) are the slope,effect size and P-value for the trend in the absence ofH.  axyridis; b(H), z(H) and p(H) are comparablevalues for the effect of H.  axyridis on thedistribution trend. n is the sample size (number of1-km2-year combinations) generated by the thresholdsapplied; obs is the number of combinations in which the focalspecies was present.

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