ASSESSING DENSITY DEPENDENCE USING INTRA-ANNUAL COUNTS

Abstract

If causes of population fluctuation vary temporally, then tests that search for density dependence in long time series cannot distinguish, at any given time, how much population change is due to density-dependent or density-independent factors. For some species' dynamics, however, it is possible to determine over a restricted period whether density-dependent factors are involved in reducing population densities. I use a new Return Trajectory Likelihood Ratio Test (RTLRT) to determine whether a population perturbed to high density (e.g., by periodic recruitment) exhibits density dependence by returning to a positive asymptote (or leveling density, L) or is density independent and, through proportional hazards, approaches zero exponentially. In a series of simulations, declines after recruitment were mimicked by creating sequences that changed due to a combination of density-dependent and density-independent factors. Until the sequence dropped below L, losses due to each mortality type were combined; after that point the density-dependent component was discontinued. The power of the test was assessed over a range of decline rates (e−b, where b = 0, 0.1, 0.25, 0.5, 0.75, 0.9, 1) to zero and to L, initial density values (2, 4, and 6 times higher than L), and observation and process errors (eσ where σ = 0.1, 0.25, and 0.5). Test size was assessed by generating trajectories with no density-dependent decline. These simulations identified four critical parameters that influence the likelihood of detecting density-dependent decline. (1) Detection rates change with the ratio of initial recruitment peak to leveling density: high peaks generally increase detection, although they may decrease detection of slow density-dependent declines. (2) High rates of density-dependent decline relative to density-independent decline also improve detection, except that populations rapidly dropping below L will appear density independent regardless of dynamics governing change prior to that time. (3) Error reduces detection of density dependence, except when declines are shallow and process error is assumed. (4) Slow rates of density-independent decline (to <10% of original value) cause the RTLRT to detect density dependence when it is not present (i.e., size is excessive for slow declines). As an example of how the RTLRT may be used, I apply it to four years of monthly counts of an intertidal isopod, Idotea wosnesenskii, which recruits annually to high densities under boulders. Based on the RTLRT, subsequent declines were density dependent in some years, although detection differed with the assumption of process or observation error, and with the use of separate or averaged samples. In addition to density dependence, selective mortality of one class of individuals or mortality balanced by continuing low immigration could also cause steep declines to L. For isopods, however, densities were higher under boulders with small depressions than under smooth controls, suggesting that declines may occur when densities exceed the number of safe sites available. The postrecruitment decline of I. wosnesenskii appears to be at least partially density dependent.