Accounting for long-term directional trends on year-to-year synchrony in species fluctuations

What determines the stability of communities under environmental fluctuations remains one of the most debated questions in ecology. Scholars generally agree that the similarity in year-to-year fluctuations between species is an important determinant of this stability. Concordant fluctuations in species abundances through time (synchrony) decrease stability while discordance in fluctuations (anti-synchrony) should stabilize communities. Researchers have interpreted the community-wide degree of synchrony in temporal fluctuations as the outcome of different processes. However, existing synchrony measures depend not only on year-to-year species fluctuations, but also on long-term directional trends in species composition, for example due to land-use or climate change. The neglected effect of directional trends in species composition could cause an apparent increase in synchrony that is not due to year-to-year fluctuations, as species that simultaneously increase (or decrease) in abundance over time will appear correlated, even if they fluctuate discordantly from year to year. The opposite pattern is also conceivable, where different species show contrasting trends in their abundances, thus overestimating year-to-year anti-synchrony. Therefore, trends in species composition may limit our understanding of potential ecological mechanisms behind synchrony between species. We propose two easily implementable solutions, with corresponding R functions, for testing and accounting for the effect of trends in species composition on overall synchrony. The first approach is based on computing synchrony over the residuals of fitted species trends over time. The second approach, applicable to already existing indices, is based on three-terms local variance, i.e. computing variance over three-years-long, movable windows. We demonstrate these methods using simulations and data from real plant communities under long-term directional changes, discussing when one approach can be preferred