Visibility of the impact of environmental noise: a response to Kaitala and Ranta

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Abstract
Based on simulation modelling, Kaitala and Ranta (2001 Proc. R. Soc. Lond. B 268, 1769–1774) have argued that detecting the statistical relationships between environmental variability and population fluctuations will be difficult. However, their study was limited in that only one pattern of density dependence and one detection method were used. Here, we show that their conclusion is in part a consequence of their choice of population model and in part a consequence of using relatively weak or inappropriate statistical methods. Other patterns of density dependence respond differently to environmental fluctuations, and the impact of the disturbance on these is clearly visible using their methods. For some patterns of population dynamics, environmental impacts are more readily detectable by correlating running–average environmental conditions with the population time–series or by correlating the first differences of the population time–series with environmental noise. When more appropriate statistical methods are used, environmental forcing is detectable in the majority of cases used by Kaitala and Ranta. The interplay between environmental stochasticity and density–dependent population growth means that there is no single best method to detect the influence of environmental forcing, even when population dynamics are approximately linear. But environmental forcing will often be detectable, contrary to Kaitala and Ranta's assertions.