Determining patterns of variability in ecological communities: time lag analysis revisited

All ecological communities experience change over time. One method to quantify temporal variation in the patterns of relative abundance of communities is time lag analysis (TLA). It uses a distance-based approach to study temporal community dynamics by regressing community dissimilarity over increasing time lags (one-unit lags, two-unit lags, three-unit lags). Here, we suggest some modifications to the method and revaluate its potential for detecting patterns of community change. We apply Hellinger distance based TLA to artificial data simulating communities with different levels of directional and stochastic dynamics and analyse their effects on the slope and its statistical significance. We conclude that statistical significance of the TLA slope (obtained by a Monte Carlo permutation procedure) is a valid criterion to discriminate between (i) communities with directional change in species composition, regardless whether it is caused by directional abundance change of the species or by stochastic change according to a Markov process, and (ii) communities that are composed of species with population sizes oscillating around a constant mean or communities whose species abundances are governed by a white noise process. TLA slopes range between 0.02 and 0.25, depending on the proportions of species with different dynamics; higher proportions of species with constant means imply shallower slopes; and higher proportions of species with stochastic dynamics or directional change imply steeper slopes. These values are broadly in line with TLA slopes from real world data. Caution must be exercised when TLA is used for the comparison of community time series with different lengths since the slope depends on time series length and tends to decrease non-linearly with it.