2.4 Niche overlap analysis using principal component analysis
In addition to assessing spatial overlap using habitat suitability modeling, we ran environmental niche overlap and niche dynamics analyses using the ‘ecospat´ package (Di Cola et al. 2017) in R 4.3.1 (R Core Team 2023). The niche overlap analysis used an ordination approach with PCA to assess how species’ niches overlap in environmental space. This was accomplished by projecting the species occurrence density across the entire range of environmental variability found in the study area (Broennimann et al. 2012). The first metric used to measure niche overlap was Schoener’s D (Schoener 1968).
\begin{equation} D\left(pX,\ pY\right)=1-\frac{1}{2}\ \sum_{i}{|pX,i-pY,i|}\nonumber \\ \end{equation}
For Schoener’s D , p X is the probability distribution for species X and and pY is the probability distribution for species Y, withp X,i being the probability assigned to cell i . Schoener’s D contains biological assumptions, where p X,i is typically used to describe prey items because it is proportional to resource availability (Warren et al. 2008). Schoener’s D varies between 0 and 1, where 0 is complete separation of niches and 1 is complete overlap. Hellinger’s H is another metric that is used without biological assumptions (van der Vaart 1998).
\begin{equation} H\left(pX,pY\right)=\sqrt{\sum_{i}{(\sqrt{pX,i}-\sqrt{pY,i})}^{2}}\nonumber \\ \end{equation}
Hellinger’s H varies between 0 and 2. Thus, an I statistic was created instead to have values for H on the same scale as Schoener’s D (Warren et al. 2008). We used both Schoener’sD and Warren’s I to measure the degree of niche overlap between the two species.
\begin{equation} I\left(pX,pY\right)=1-\frac{1}{2}H(pX,pY)\nonumber \\ \end{equation}
The niche overlap analysis tests for both niche equivalency and niche similarity, two different hypotheses for comparing niches (Warren et al. 2008, Broennimann et al. 2012). To test for niche equivalency, or whether the two species’ niches are equivalent, all occurrence records for each species are pooled and then randomly permutated into two datasets (Warren et al. 2008, Broennimann et al. 2012). This process is repeated 1000 times to get a histogram of simulated D andI values (Warren et al. 2008, Broennimann et al. 2012). The simulated values were compared to the observed D and I value, and if the 95% confidence interval for the simulated values did not include the observed values, then the two niches are equivalent (Warren et al. 2008, Broennimann et al. 2012). Niche similarity tests whether the two niches are more similar than what would be expected by chance (Warren et al. 2008, Broennimann et al. 2012). To test for niche similarity, we randomly shifted both species’ niches and then recalculated D and I . We repeated this 1000 times to gain a distribution of simulated D and I values and calculated 95% confidence intervals (Warren et al. 2008, Broennimann et al. 2012). The two niches were more similar than expected by chance if the 95% confidence interval did not contain the observed value (Warren et al. 2008, Broennimann et al. 2012). The data used for both tests included thinned occurrence records for both species, the 15 environmental predictors and randomly generated pseudo-absences. We used the number of pseudo-absences as a ratio of 10:1 pseudo-absences to presence records (Dilts et al. 2023).
We also measured the niche dynamics of eastern cottontail’s invasion in Connecticut by assessing niche expansion, unfilling, and stability. Niche expansion is the proportion of the introduced species’ niche that does not overlap with the native species’ niche, niche unfilling is the proportion of the native species’ niche that does not overlap with the introduced species’ niche, and niche stability is the proportion of the introduced species niche that does overlap with the native species’ niche (Guisan et al. 2014). Our hypotheses were niche unfilling would be less and niche stability and expansion would be more than if the two niches were random. We tested these hypotheses similar to the niche overlap hypotheses, where we compared the observed unfilling, stability, and expansion values to the ones generated by the random distribution (Di Cola et al. 2017). Our hypotheses for similarity and equivalency tests are stated in Table 1.