The structure and strength of environmental variation modulate covariance patterns. A reply to Houlahan et al. 2008


E. Ranta, V. Kaitala, M. S. Fowler (, J. Laakso, L. Ruokolainen, Dept of Biological and Environmental Sciences, PO Box 65 (Viikinkaari 1), FI–00014 University of Helsinki, Finland. – R. O'Hara, Dept of Mathematics and Statistics, PO Box 68 (Gustaf Hällströmin katu 2b), FI–00014 University of Helsinki, Finland.

Using the approach by Ranta et al. (2008) we generated a series of realistic community scenarios. For these communities we calculated mean and 95% confidence limits for the community covariance (Box et al. 1978). The results (Fig. 1) suggest that unravelling the significance of competition or environmental modulation influencing dynamics of the community members using the community covariance approach does not always succeed Ruokolainen and Fowler 2008. The results are in clear contrast to what Houlahan et al. (2007, 2008) are proposing, but correspond to our previous results (Ranta et al. 2008, p. 000): “negative community covariance can be absent even in strongly competitive communities and can be found present in communities without competitive interactions”. This makes scoring community covariance an ineffective tool in terms of finding out what actually causes natural populations to fluctuate.

Figure 1.

Community covariance scores (mean with 95% confidence limits; 100 replications for each parameter combination) under various scenarios. Each community has five species following Ricker dynamics (r from uniform random distribution between 1 and 2, K=1 for all). The panels (a) and (b) show community covariance against increasing strength of the modulating noise (w), the off-diagonal αij being all 0.5, noise equivalency is either E=0 or E=0.5, noise autocorrelation is κ=0 (white), or κ=0.5 (red). The panels (c) and (d) show community covariance against increasing strength of competition (see also Ranta et al. 2008). Note, it is impossible to tell what the ‘null-hypothesis’ parameter values should be in real world.

Analysis of natural time series can highlight interesting temporal and spatial patterns that occur in the dynamics of real systems. Without more detailed information of the system, e.g. auxiliary time series (e.g. weather) or information about shared predators, pathogens or spatial processes, little can be understood about the significance of different exogenous variables forcing fluctuations. Using the community covariance method tells us only about the covariance structure of the focal time series, not about the mechanisms driving those patterns.


  • Deceased August 2008