2.2. Data analyses

Functional diversity was calculated using functional dispersion (FDis), which calculates the mean distance of each species to the centroid of an ordination plot of the first three axes of all species within the community and allows for both missing data and mixed variables (Laliberté & Legendre, 2010). Previous studies have shown that β‐diversity is underestimated when completing analyses at intervals of a decade or more (Diamond & May, 1977; Russell et al., 1995); thus, to analyze fine‐scale patterns and maintain high temporal resolution, we used a 10‐year temporal interval for all analyses. FDis was calculated for the regional source pool by decade and was calculated for each lake by decade. To determine whether functional space had increased, decreased, or remained the same over time regionally (basin), by community (lake), and locally (habitat), differences in FDis were calculated between: i) each time period and the previous time period; and, ii) each time period and 1870. For each decade, the mean FDis for species present in each habitat type was calculated, and a species could occupy more than one habitat type depending on its habitat preferences as an adult.

To evaluate whether the observed patterns of functional diversity are more or less extreme than expected in the absence of an ecological mechanism, a null model was constructed for the basin and each lake. We completed a randomization simulation by decade on the species by trait matrix by randomly selecting species without replacement from the regional species pool, such that species richness was held constant between the observed and simulated communities. Additionally, at the lake level, the time of arrival for each invasive species was constrained so each invasive species could be selected only once the opportunity for establishment and dispersal was possible. For each decade at the basin and lake level, we calculated mean FDis for each randomization and completed this for a total of 1,000 times; we then calculated the overall mean, 95% confidence interval (CI), and standard error. This enabled us to determine whether an ecological mechanism, competition or environmental filtering, regulates diversity patterns in the Great Lakes, giving us the ability to analyze Darwin's naturalization conundrum. Observed values of FDis above the upper threshold of the 95% CI indicate that species are more overdispersed than expected under the null model, which suggests that competitive interactions are more important in regulating diversity patterns, whereas observed values of FDis below the lower threshold of the 95% CI indicate that species are more underdispersed than expected under the null model, suggesting that an environmental filter regulates diversity patterns and selects for more similar species. All analyses were completed using the FD package in R (Laliberté & Legendre, 2010).