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Climate and habitat data.

The aridity index was calculated as the weighted sum of the standardized April–October temperature average and precipitation totals as in ref. 13. Observed aridity index was derived from the updated Central England Temperature³¹ and England and Wales Rainfall³² monthly series, obtained from the UK Met Office. Projected aridity indices were derived from 2-m air temperature and total precipitation monthly fields, obtained from the CMIP5 project (Supplementary Table 1). All aridity index series use the same reference period (1860–2005) for standardization. To avoid bias due to the unequal number of ensemble members associated with each GCM, each GCM aridity index was calculated from the ensemble mean standardized temperature and precipitation time series for that GCM.

Semi-natural habitat was assessed as all land cover types besides urban, suburban, arable, improved grassland and saltwater from LCM 2000 (ref. 18), a UK national land cover map derived from satellite earth observation, in 3 km radii around UKBMS monitoring sites. Preliminary analyses and previous work suggest that landscape structure at this spatial scale has strong impacts on butterfly population dynamics^{20, 33}. Configuration metrics were calculated using the program FRAGSTATS (ref. 34). Three metrics were selected that reflect complementary aspects of fragmentation and potentially mediate butterfly responses to drought³³: mean ‘edge index’ (a standardized measure of area:perimeter ratio or ‘edginess’, where for each separate SNH patch the actual perimeter is expressed relative to the minimum possible perimeter for a patch of that size, and the mean taken across all patches), mean nearest neighbour distance between habitat patches and patch density (number of patches per km²).

Attribution of drought impacts on butterfly species.

We used data from the UK butterfly monitoring scheme (http://www.ukbms.org) for which annual indices of abundance at each monitoring site have been calculated³⁵. Species needed to fulfil three criteria to be categorized as especially drought-sensitive. First, a significant majority of monitoring sites should show population declines following the drought relative to expected values in 1996 from a six-year local population trajectory (for example, Fig. 1a, b; assessed using a Wilcoxon signed ranks test). Second, a significant majority of monitoring sites should also show significant population declines relative to the year immediately preceding the drought. Finally, across all years that sites were monitored the species should show a significant negative relationship between interannual growth rates and annual summer aridity index. Interannual growth rates were calculated as log(N_t/N_t−1), where N_t is the population density in year t. This was then used as a response variable in a linear mixed-effects regression against annual aridity index in year t with Site as a random effect to account for multiple observations at each monitoring site. These three tests resulted in six UK species identified as drought-sensitive under our criteria (Supplementary Fig. 1).

We analysed the effect of semi-natural habitat (SNH) on degree of population collapse from the 1995 drought event and subsequent recovery¹³, following methods used in ref. 33 and explained here. For each species at each monitoring site, the degree of population change in response to the 1995 drought was measured by the difference between the observed and expected population count in 1996 (from a six-year linear population trend; Fig. 1a). This method accounts for long-term population trajectory, which is important because long-term species declines³⁰ could lead to false attribution of drought impacts if change only from the preceding year’s count is considered. A six-year period was chosen to assess the population trajectory because preliminary analysis suggested that this time period maximized statistical power by balancing accurate assessment of pre-drought population trends with higher sample size for sites included in the analysis³³. Also in preliminary analyses, we tested for effects of density dependence on interannual growth rates (regression of log(N_t/N_t−1) versus N_t−1, where N_t is population density in year t; ref. 36). We found 43% of the population time series showed evidence of density dependence (at p < 0.05). However, in an analysis comparing linear and quadratic models to explain population trends over the six-year period (that is, regression of N_t on year), we found that linear models produced the best fit to population trends (for 92% of time series). Therefore, although density dependence may be an important regulatory demographic process for these butterfly species, over the time periods and range of densities on our sites, and relative to other factors (for example, weather and habitat quality), there is little evidence of curvature in population trends expected under a strong influence of density dependence. For all species and sites with population declines following the drought, recovery was assessed as the linear population trend in the subsequent four years (Fig. 1a), chosen to balance assessment of the population growth phase immediately following population collapse balanced with obtaining a reliable trend estimate³³. In models predicting recovery rates, extent of population collapse and starting population size following collapse were also included as covariates to account for density dependence in growth rates.

Butterfly drought responses in relation to habitat fragmentation.

To data from all monitoring sites, and for all six drought-sensitive butterfly species, we fitted one linear mixed-effects model (LMM) investigating the predictors of population collapse from drought (difference between observed and expected count) and one LMM investigating the predictors of population recovery (rate of population increase following decline in 1996). The model exploring the predictors of population collapse included expected population size and a measure of each site’s drought intensity (1995 aridity index from nearest 5 km cell) as control explanatory variables. All models exploring the predictors of recovery rates included the size of the initial population decline and population size immediately after the drought as control explanatory variables. In addition to these control variables, each of these models included four fixed effects characterizing SNH: total SNH area and the three FRAGSTATS metrics described above. Each model also included site and species as random intercepts to control for repeated measures from the same site and the same species. All habitat variables were standardized to have a mean of zero and standard deviation of one (that is, by subtracting the mean and dividing by standard deviation). Model checking confirmed the residuals from each mixed model containing all variables were normally distributed and had constant variance. To find the minimum adequate model, the least significant habitat variable was sequentially dropped until no more could be dropped without losing a significant amount of explanatory power, determined by using a χ² test to compare the model residual variances³⁷. This resulted in only SNH area and edge index in the final models for population collapse and recovery, respectively (see main text). Analyses were conducted using the program R and the lme4 package^{38, 39}.

Estimating butterfly recovery times.

We used the coefficients from the minimum adequate models for butterfly population collapse and recovery to calculate the average expected butterfly recovery time under the five different SNH scenarios (Fig. 2b, c). Recovery time was calculated as the degree of population collapse to drought (expected minus observed population count following the drought event) divided by the post-drought population recovery rate (change in population count per year). To parameterize the models we used the mean expected population size, observed population size and site aridity index across all species and sites, along with either ‘high’ (mean + s.d. across all sites), ‘low’ (mean − s.d. across all sites) or mean values for SNH area and edge index. These produced predicted population recovery times under five SNH scenarios, for example, high area and high edge index (main text and Fig. 2). We incorporated uncertainty by repeating these calculations using 95% confidence intervals for coefficients to calculate the upper of lower uncertainty bounds on recovery times. Recovery times were then considered in relation to the time-varying drought return time under the four different RCPs. Uncertainty across GCMs was accounted for by expressing the percentage of climate projections in which populations would persist (where average recovery times were less than drought return times).