Catching ghosts with a coarse net: use and abuse of spatial sampling data in detecting synchronization

Petrovskaya N, Petrovskii S. 2017 Catching ghosts with a coarse net: use and abuse of spatial sampling data in detecting synchronization. J. R. Soc. Interface 14: 20160855. http://dx.doi.org/10.1098/rsif.2016.0855

Synchronization between sub-populations is a commonly observed phenomenon in natural populations. The cross-correlation between populations over time is used to determine synchrony. But while theoretical studies assume information about population sizes is available, estimating it field data is not always straightforward. The authors examined how conclusions about synchrony between different populations in different habitats were affected by “coarse sampling”. They defined coarse sampling as a finite number of samples taken across space which give an incomplete picture of the true population dynamics. The averaged population density of a few samples across space can be a bad estimate if the species distribution is aggregated and consequently, this poor estimation affects the estimation of synchrony between populations. They simulated invertebrate populations with linear growth as well as more complex population dynamics (chaos and multi-period cycles).

To determine the impact of spatial population aggregation on the number of required samples to approach the true correlation between populations, they varied the number of peaks over space, p, and assumed each peak follows a superpositioned normal distributions. To get true population size estimates, they integrated under these superpositioned normal curves. They simulated sampling by choosing points within an interval of a uniform distribution. They found not surprisingly that distributions with more superpositioned “peaks” needed more sampling sites to approach the true correlation coefficient (fig 4). If the population was aggregated in a single “hot-spot” (i.e., one normally distributed peak) more sampling points were also needed to approach the true level of synchrony.

 

As more samples are added (i.e., the sampling grid is less coarse), the estimated correlation approaches the true correlation. For more complicated distributions (larger number of peaks, p), the estimated correlation can be much lower than the true value.

To determine the number of spatial data points to sample without losing any accuracy, some ecologists have used the Nyquist frequency. However, this statistic did not work well for complicated patterns (i.e., those with more peaks) in this study. They examined realistic distributions (specifically Poisson, exponential, log normal, gamma, and power law) of species and showed that when the variance was larger (for each respective distribution) and the number of samples isn’t large enough, estimated correlation can be lost (i.e., much smaller than the true level). Alternatively, in some of these distributions and with too few sampling points, “Ghost correlations” can result, which they describe as the situation when real populations are anti-correlated but your samples say they are strongly positively correlated.

A take home message from this paper was that spatial resolution of sampling grid can’t be determined based on just one universal rule. Instead, it is context dependent on the focus of the study.