Butterfly location data
Butterfly species records were obtained from the Canadian National Collection (CNC) of butterflies (Layberry et al. 1998). The entire database includes nearly 300 000 records for 297 butterfly species in Canada from the late 1800s to the present. Each record included in this database is georeferenced, dated and corresponds to a verified specimen stored in one of Canada's natural history museums or in collections maintained by federal or provincial agencies. The CNC of butterflies is the largest dataset of its kind in Canada and includes remote and northern areas, where exploration was vigorous, from the earliest time periods.
Modelling species’ ranges
We modelled the ranges of butterfly species in Canada using the PC implementation of Genetic Algorithms for Rule-set Production (GARP; Stockwell and Noble 1992, Stockwell and Peters 1999, Appendix, Fig. S1). GARP operates by using a series of environmental measures to estimate species’ niches, defined as the array of environmental conditions within which the species some presence (Oberhauser and Peterson 2003, Anderson et al. 2003). This method of range identification has been used extensively to predict the species ranges among many taxa (including butterflies; Peterson and Cahoon 1999, Oberhauser and Peterson 2003, Stockwell and Peterson 2003, Anderson et al. 2003, Peterson et al. 2004) and has led to the discovery of new species in Madagascar (Raxworthy et al. 2003). Newly-developed methods may improve on the reliability of GARP (Elith et al. 2006). An example of such a method is maximum entropy (Phillips et al. 2006). However, we used GARP for this study because its strengths and limitations are better known, in contrast to very new alternatives for modelling species’ range data from presence-only observations.
There are two alternatives to using statistical means of estimating species’ ranges, such as GARP, both of which are likely to be less accurate. The first is to digitize range maps presented in field guides. Although many macroecological studies have taken this approach – for many taxa, the only option available (for example, our own studies: Kerr 1999, Kerr and Packer 1999) – this method, in practice, rarely accounts for subtle environmental variability that may affect where boundaries for species’ ranges occur. Quantitative accuracy assessments are rarely available for such maps, nor are comparisons between historical and contemporary ranges commonly possible using this mapping method. A second alternative is to estimate species’ ranges directly from point observations, either manually (Kerr 2001, Kerr et al. 2001) or by using a method like minimum convex polygons (Lees et al. 1999). The resultant ranges mirror sampling intensity unless the data are rendered very coarse (in the case of early work on Canadian butterflies, quadrats were ca 500×500 km; Kerr 2001), or advice from systematists is sought. In the last case, errors cannot be quantified and estimates of range shifts through time are difficult to interpret. Statistical range modelling methods, such as GARP, allow for detailed error estimates and can account for subtle environmental variation through time and across space.
Species selection criteria
We modelled the ranges of species that had been reasonably well-collected, using the criterion that each species’ to be modelled must have been observed in at least 20 distinct locations within each study period (1900–1930 and 1960–1990, corresponding with climate data sources, described below). The average number of sampled locations per species in the 1900–1930 period was 104 compared to 458 in the 1960–1990 period. Note that GARP attains ca 90% of its best accuracy in its modelling output with 10 observations and reaches an apparent asymptote at ca 20 observations (that is, adding more records after 20 is unlikely to change model output, provided those observations do not come from a biased set of locations within the species’ true range; Stockwell and Peterson 2002, Anderson et al. 2003), so no effect of differences in sample sizes between study epochs was anticipated. However, widespread species have been found to contribute disproportionately to overall species richness patterns (Lennon et al. 2004). There were more butterfly records in our second study period (1960–1990). Differences in our regression results between the study periods might then arise just because sample sizes caused range sizes of species to differ between study periods. To test for such an effect, it is necessary to determine whether differences in the numbers of observations between epochs in this study leads to systematic differences in butterfly range size. We calculated the best-subset of GARP model predictions (see below for details) based on 104 (the mean number of observations for species in the first epoch) randomly chosen records from 1960 to 1990 ten times each for the four most commonly observed species (Colias philodice, Celastrina ladon, Agriades glandon, and Nymphalis antiopa) for a total of 10 000 additional range simulations. These species are from three different families (Pieridae, Lycaenidae, and Nymphalidae) and have particularly extensive Canadian ranges with large numbers of records from 1960 to 1990. We compared ranges estimated from the smaller subset of available sampling records with ranges from the full set of observations to test whether different sampling sizes between epochs would be likely to generate systematic differences in range estimation. If Lennon et al. (2004) are correct, widespread species should contribute most strongly to the overall diversity pattern that would be observed. Consequently, analyses of those richness trends would be particularly error-prone if changes in numbers of sampling records caused GARP to produce systematically different range estimates.
Species modelling methods
GARP was used to generate a minimum of 100 estimates for the range of each species (Appendix, Fig. S1). A set of ten “best-subset” maps were selected using criteria developed by Anderson et al. (2003). The criteria used were intrinsic commission index and intrinsic omission error. The intrinsic commission index is the total amount of range area projected to be present for a given species, consisting of the intrinsic commission error, which is mistaken over-prediction (i.e. predicting that the species will be present in an area where it is actually absent), and correct range prediction (predicting the species will be present in an areas where it truly is present). The intrinsic omission error is the proportion of training points that GARP failed to include in the estimate of the species’ range. From these models, the average commission index was calculated, and the best-subset of each species’ range predictions was determined by selecting the 10 range estimates that were closest to that average commission index value. A more conservative criterion was used in this study than the one proposed originally by Anderson et al. (2003): only models within 15% of the actual commission index value were eligible to be retained as best-subset models (for example, if the commission index was 20%, then only models with commission rates between 17 and 23% could possibly be selected). In a detailed investigation of GARP optimization, Anderson et al. (2003) report that this approach yielded the best overall accuracy by balancing range overestimation and underestimation: if commission errors are too high, the species’ range will be overestimated while an incorrectly small commission index will underestimate the species’ true range. For each species where 100 range simulations did not provide at least ten maps based on the criteria described above (and in Appendix, Fig. S1), 100 additional simulations were run. If GARP was unable to produce 10 range models meeting those criteria after 1200 simulations, that species was dropped from the analysis. A minimum of 50% of species observations were used to train the GARP models and remaining points (not less than a third of the total number) were excluded from the model for testing. The final range estimate for each species was then obtained by taking only the presence area agreed upon by at least eight of the ten best-subset maps. For theoretical and empirical details regarding this approach to GARP range modelling, see Anderson et al. (2003).
Some final range models predicted species would be present in environmental similar but geographically distant areas (always very small) where the species has never been observed in the 130 yr sampling history of the Canadian National Collection. Peterson et al. (2002) point out a species may be absent from an environmentally suitable area because of strong dispersal barriers. We removed such areas, which are almost certainly artefactual and beyond the boundaries of the species’ correct distributions, if they occurred in an ecozone where the species is thought to be absent. Ecozones are large regions (mean size ca 650 000 km2) in Canada that correspond roughly to biomes.
After applying all criteria, 102 of the initial 297 species remained for analysis. Ranges for these species could be modelled most reliably.
Eleven environmental datasets were used to generate species’ range estimates in GARP. These were selected based on plausible links to species’ biological needs, subject to the availability of reasonable historical data sources. Monthly precipitation, and minimum, maximum, and mean monthly temperature data for 1961–1990 and 1901–1930 were obtained from the Canadian Forestry Service (McKenney pers. comm.) in raster GIS format. These datasets were collected as climate normals for the two time periods, so minimum monthly temperature, for example, refers to the lowest monthly average temperature based on a 30-yr mean for a particular location. These data were aggregated to produce growing season (April–October) and annual climate datasets in raster format for all of Canada. These datasets included mean growing season and total annual precipitation, and minimum, maximum, and average temperatures for both the growing season and entire year for both study epochs. High resolution digital elevation data (1 km; Anon. 1988) were also used as butterfly species are known to respond to elevation gradients (Kerr et al. 1998). Historical land use data, derived from Statistics Canada records (Ramankutty and Foley 1999), soil texture data (Shields et al. 1991), and physical land cover data describing the broad ecosystems and major agricultural regions of Canada (described fully in Kerr and Cihlar 2003) were also included. Although these variables are temporally invariant in this study, they can contribute substantially to where the geographic limits of species’ ranges occur and excluding them would severely reduce range model accuracy.
Human population density is often used as an indicator of human environmental impacts (Kerr and Currie 1995, Konvicka et al. 2006). Census data have been collected regularly since the early part of the 20th century for all of Canada while relatively few alternative measures of environmental change are available. This situation is rather different in many European countries with remarkably long and detailed records of environmental trends. However, scientific data collection for most of Canada is quite a recent phenomenon – indeed, it is only since the early 20th century that settlers of European descent arrived in large numbers to most of the regions of Canada that are now agricultural or urbanized. Population density in Canada was measured as the average number of people per square kilometre in each of 238 census divisions for the years 1921 and 1981 (corresponding to the two study epochs and maintaining the same 60 yr gap as the climate data; Anon. 1973, 1982). Human population data were log-transformed in order to improve linearity. We note that early population data for British Columbia were collected from the 1941 census rather than 1921 because the 1921 census division boundaries in British Columbia were markedly different and not comparable to the post-1921 census division boundaries. However, human population sizes there are very small in the early part of the 20th century and expanded rapidly only after the second world war. Consequently, the expansion of human population in British Columbia (and thus our capacity to detect an effect of changing human population size) occurred almost entirely after the 1941 sampling period for this province. The change in population from 1921 to 1941 (ca 293 000; Anon. 1999), is the lowest for any twenty year gap from 1901 to 1991, and an order of magnitude lower than the population change from 1921 to 1991 (ca 2 757 000), or from 1941 to 1991 (ca 2 464 000; Anon. 1992).
Data for species richness, human population density, and climate were measured as the arithmetic mean in census divisions in the two time periods 1900–1930 and 1960–1990, respectively. After estimation by GARP, species ranges were also extracted individually (102 species in total) and added together to create a map of species richness for both time periods. Differences between climate, human population density, and butterfly species richness in the two time periods were then measured using ArcGIS (Anon. 2005) and extracted into the Statistical Analysis for Macroecologists package (Rangel et al. 2006).
We tested the dependent variable (butterfly species richness change) for spatial autocorrelation using Moran's I and, unsurprisingly, found that it was strongly spatially autocorrelated (for a particularly useful discussion of spatial autocorrelation in geographical ecology, Diniz-Filho et al. 2003). This observation indicates that ordinary least squares regression is inappropriate for the analysis unless, minimally, corrections to the number of degrees of freedom are applied. However, autocorrelation also biases regression coefficients, so statistical models were constructed using conditional autoregressive models (CARs) following normal data exploration and visualization (particularly observation of variable distributions and scatterplots). CARs allow for regression coefficients to be calculated in the presence of spatial autocorrelation. A detailed discussion of conditional autoregressive models is presented elsewhere (Lichstein et al. 2002, Tognelli and Kelt 2004). Akaike's information criterion was used to guide model selection (Kerr and Cihlar 2004, Rangel et al. 2006).
Finally, we tested for relationships between the species richness patterns within each study epoch based on the 51 least extensive (i.e. most range-restricted) species and 51 most extensive (i.e. largest range) species. This additional analysis allowed us to assess the degree to which commonness or rarity (from a purely geographical perspective) might affect regression results. Previous studies have noted that geographically extensive species contribute more to patterns than do range-restricted species. Although we modelled only species with large numbers of records, many of these were not geographically extensive. We did not expect to observe similar patterns among subsets of geographically restricted versus geographically extensive species. The degree to which different subsets of species exhibit consistently similar patterns when compared is a separate issue from the main ones addressed here.