Niche and community metrics
The analysis required the calculation of four niche-based metrics and three measures associated with stability. For clarity, we provide again the hypotheses and then describe the associated metrics. Starting with hypothesis one, species richness is predicted to increase if a site is located nearer to the centre of the niches of more of the total species pool (i.e. all 145 species). Species richness was the number of species observed at the monitoring site during the study period. To construct the average distance between the site location in niche space and the species pool niche centres, we took the average of the Euclidean distance between the site’s location in 6D and the niche centroid of every species, hereafter referred to as overall niche distance. Thus a site with a larger overall niche distance is further away from the niche centre of the total species pool.
Hypothesis two predicts that mean abundance will increase as species are nearer the centre of their fundamental niche. Therefore we calculated a mean abundance across all species for each site – density was used to account for differences in transect length between study sites. To calculate the distance of species to their niche centres, we took the weighted average Euclidean distance between the niche centroids of each species found at a site and the location of the site in 6D. The weighting means that the distance of the most abundant species in a community is weighted most highly. This was applied so that niche distances account for differences in evenness across communities. We term this measure niche-mismatch as we refer to it repeatedly in the analysis.
Hypothesis three states that asynchrony will increase with species richness and if species have lower niche-overlap. To measure asynchrony (synchrony) at a site we follow the summary measure detailed in Thibaut and Connolly (2013):
Synchrony =\(\frac{\sum_{\text{ij}}{V(i,j)}}{(\sum_{i}{\sqrt{V(i,i)})}^{2}}\)
Here i and j refer to species at a site, the numerator is the sum of all elements of the covariance matrix of the species at a site, and the denominator is the species level variances in the presence of perfect synchrony. This measure is therefore standardised, accounting for differences in richness and variance. The synchrony index always takes a score between 0 – no synchrony or population variance, and 1 – perfect synchrony. To measure niche-overlap we utilised Jaccard Similarity which is the intersection of a pair of species niches divided by their union, once again always scoring between 0 and 1. This was calculated for all pairwise comparisons (Blonder et al., 2015) and the mean was used to give an overall niche-overlap score.
Hypothesis four states that average population stability will be highest when the site is nearer the centre of the species niches, when the niche breadth of species is larger, and when the abundance of the species is higher. To calculate average population stability, we again follow Thibaut and Connolly (2013):
Average population stability =\(\sum_{i}{\frac{m(i)}{\text{mc}}\frac{m(i)}{\sqrt{V(i,i)}}}\)
Here m(i) refers to the mean abundance of species i and mc refer to the sum of species mean abundances in the community, thus the score is abundance weighted. The second term is the mean of the species abundance divided by the standard deviation – the inverse coefficient of variation (Tilman 1999). For distance to the centre of the niche, we utilised niche mismatch as calculated above. For niche breadth, we took the abundance-weighted mean volume of the niches at the site.
Hypothesis five predicts that asynchrony and average population stability will explain differences in community stability. For community stability, we again utilised the inverse coefficient of variation.
(3) Community stability = \(\frac{\mu}{\sqrt{V(i,i)}}\)
Where µ refers to mean abundance for all species at the site.