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.