Figure 4

(a) Joint effect of (weighted) DIN and DIP (dissolved inorganic nitrogen and phosphorus) in the previous year on long-tailed duck state population size from spring migration counts at the Söderskär observatory. Nutrient amounts were measured in the southern Baltic Sea and their joint effect was calculated with the formulation \({\left({1-w}_{D}\right)DIN}_{\left(t-1\right)}+{w}_{D}\left({-1*DIP}_{\left(t-1\right)}\right)\) designed for estimation with Eq. (4). (b) The effect of juvenile proportions estimated using Eq. (2) based on wing data from Danish hunting returns on the population growth rate (t) = \({n}_{\left(t+1\right)}-{n}_{\left(t\right)}\) of long-tailed ducks estimated using Eq. (4), and (c) the trajectories of these during 1968–2013. Values are scaled to mean zero and unit variance. (d) Observed and predicted numbers of spring migrating female long-tailed ducks at Söderskär. Population estimates and confidence interval are calculated using a hierarchical state-space model as given in Eq. (4).