Factors influencing detection of density dependence in British birds

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Abstract
We question why density dependence has remained elusive in series of annual abundances of British birds. In particular, an earlier study reported that significant temporal trends in abundances occur in up to 74% of time series from the Common Birds Census. Several studies showed that such trends can hinder detection of density dependence. Temporal trends do not preclude the presence of density dependence and two published tests for density dependence include temporal trends in the null hypothesis model. We explore the extent to which detection of density dependence was hindered by temporal trends in bird abundance data. We used a conservative method to test for trends, which found significant (P0.05). This shows that density dependence may be falsely rejected or detected when trends are present, even when these trends are weak and not statistically significant. To circumvent this problem we detrended the time-series prior to testing for the presence of density dependence. To minimize subjectivity we used simulated time series to check that this procedure did not increase the level of type I error (false rejection of density independence). Additionally, we confirmed that the method gave acceptable levels of type II error, where the test fails to reject density independence in series generated using a density dependent model. This showed that the detrending method was acceptable and represents a major improvement in our ability to detect density dependence in time series that contain temporal trends. Detrending the bird time series increased the number of series in which significant (P<0.05) density dependence was found from 10 (17%), when trends are ignored, to 27 (45%) when series are detrended. However, this rate of 45% is still surprisingly low by comparison to other taxa, and we believe that other factors may contribute to this, which we explore in the second of this pair of papers.