Hildegunn Viljugrein, Nils Chr. Stenseth, Graham W. Smith, and Gunnhilder H. Steinbakk. 2005. Density dependence in North American ducks. Ecology 86:245–254.

Appendix E. Supplementary figures.

FIG. E1. Kernel density estimates of the posterior distribution of for (a) Mallards and (b) Canvasbacks. For both species the density curves are given for three areas (S29, S34, and S45)

FIG. E2. The relationship between mean coefficients of variation (i.e., the precision of the data) and estimates of direct density dependence obtained from (a) the state-space model (with parameters ) where numbers of ponds are not included (ci = 0) and (b) a first-order autoregressive model (with parameter ). Second rows show the similar relationships when numbers of ponds are included in the models (parameters  and ). When density dependencies are estimated according to the autoregressive approach (not taking sampling error into account), the regression lines are strongly significant. For the density-dependence estimates of mallards obtained from the state-space approach, the significance of the regression lines is dependent on including the two areas with data of particularly low precision. The relationship between the estimates of direct density dependence obtained from the autoregressive model and the state-space model are shown in (c).