# Asynchrony Drives Plant and Animal Community Stability in Mediterranean Coastal Dunes
## 2 Materials and Methods
### Measures of Stability  
The most commonly used measure of community stability is temporal variability [2; 13; 32; 78; 79; 80]. A frequently used measure for temporal variability is the Coefficient of Variation (CV). This is the temporal standard deviation over the temporal mean of abundance, such that a higher CV implies lower stability [81]. We used Community variability (_CVcomm_) as an inverse measure of stability for each dune separately, referring to a community as the assemblage of species in a single taxonomic group found on a single dune.  
_CVcomm_ ranges from 0 to 1 and is a measure of the standard deviation (_s.d._) over the mean (\(\mu\)):  
\[CVcomm=s.d_{comm}/\mu_{comm} \tag{1}\]  
_CVcomm_ can also be derived using Thibaut and [PERSON]'s [18] function:  
\[CVcomm=\sqrt{\Phi}*CVpop\_av.weighted \tag{2}\]  
where \(\phi\) (or Phi) is Loreau's synchrony [14] and \(CVpop\_av.weighted\) is the CV for each species, weighted by its relative abundance and averaged across all species [18]. Synchrony (\(\phi\)) measures covariance among species within a community and ranges from 0 (highly asynchronous) to 1 (complete synchrony) [14]. Note that a value of \(\phi\) = 0.5 suggests that any synchrony between species is random.  
Dominant species contribute to _CVpop_av.weighted_, and dominance has been shown to have an important role in regulating community stability [8; 26; 35; 36; 82]. Meanwhile, communities with high levels of asynchrony could have higher community stability, irrespective of the stability of individual populations. Unless species abundances are perfectly synchronous, \(CVcomm\) must be always be smaller than \(CVpop\_av.weighted\)[27].  
We tested the relationships between parameters using \(CVcomm\), synchrony, and \(CVpop\_av.weighted\) as the inverse measures of community stability, asynchrony, and weighted population stability, respectively, in order to maintain the calculations given in Equations (1)and (2). However, when discussing the significance of relationships, we refer to stability and asynchrony, because conceptually they are easier to understand in relation to DSR theory. Community stability is considered \(CVcomm^{-1}\), population stability is \(CVpop\_aw.weighted^{-1}\), and asynchrony equates to \(1-\phi\).  
To exemplify the relationship between the various measures of stability, Figure 1 represents the simulated data for simple two-species communities, showing how community stability can be affected by the balance between population stability and asynchrony (modelled data is provided in Supplementary Materials Table S1). The temporal mean for overall (community) abundance was \(\mu\) = 45 in all cases. Low population stability coupled with low asynchrony (when species fluctuations are synchronized) created the most unstable community (Figure 1a). The combination of high population stability coupled with low asynchrony (Figure 1b) achieved the same degree of community stability as low population stability coupled with high asynchrony (Figure 1c). High population stability together with high asynchrony produced the most stable community in terms of overall abundance (Figure 1d).