Appendix A. A table presenting the selection of the capelin index used in the study.

A table presenting the selection of the capelin index used in the study

Appendix B. A table presenting the full model selection.

A table presenting the full model selection

The extent of kelp recovery within the study area.

<p>Size of the predicted area (in km² on the left axis and in percent of the study area on the right axis) modeled to be areas with recovery of kelp (<i>Laminaria hyperborea</i>, lh) and with persistence of sea urchins (<i>Strongylocentrotus droebachiensis</i>, sd), given different cut-off probabilities for the best GAMs and for the BRT models. The low and high optimal threshold lines show the lowest and highest cut-off value according to the Youden index for the best models.</p

The study area.

<p>Map of the study area along the north Norwegian coast 65°–68°N, within the northeast Atlantic, coded for sampling year. Large points (n = 1220) are model data for the statistical analyses, whereas small yellow points (n = 403) are test data for evaluation of the models.</p

GAM for kelp recovery.

<p>The partial response plots of the best GAM (lowest AICc) for presence of the kelp <i>Laminaria hyperborea</i>.</p

The Influence of Physical Factors on Kelp and Sea Urchin Distribution in Previously and Still Grazed Areas in the NE Atlantic

<div><p>The spatial distribution of kelp (<i>Laminaria hyperborea</i>) and sea urchins (<i>Strongylocentrotus droebachiensis</i>) in the NE Atlantic are highly related to physical factors and to temporal changes in temperature. On a large scale, we identified borders for kelp recovery and sea urchin persistence along the north-south gradient. Sea urchin persistence was also related to the coast-ocean gradient. The southern border corresponds to summer temperatures exceeding about 10°C, a threshold value known to be critical for sea urchin recruitment and development. The outer border along the coast-ocean gradient is related to temperature, wave exposure and salinity. On a finer scale, kelp recovery occurs mainly at ridges in outer, wave exposed, saline and warm areas whereas sea urchins still dominate in inner, shallow and cold areas, particularly in areas with optimal current speed for sea urchin foraging. In contrast to other studies in Europe, we here show a positive influence of climate change to presence of a long-lived climax canopy-forming kelp. The extent of the coast-ocean gradient varies within the study area, and is especially wide in the southern part where the presence of islands and skerries increases the area of the shallow coastal zone. This creates a large area with intermediate physical conditions for the two species and a mosaic of kelp and sea urchin dominated patches. The statistical models (GAM and BRT) show high performance and indicate recovery of kelp in 45–60% of the study area. The study shows the value of combining a traditional (GAM) and a more complex (BRT) modeling approach to gain insight into complex spatial patterns of species or habitats. The results, methods and approaches are of general ecological relevance regardless of ecosystems and species, although they are particularly relevant for understanding and exploring the corresponding changes between algae and grazers in different coastal areas.</p></div

GAM for sea urchin persistence.

<p>The partial response plots of the best GAM without interactions for presence of sea urchin <i>Strongylocentrotus droebachiensis</i>.</p

Summer sea water temperature along latitude in the period 1990 to 2007.

<p>Modeled sea water temperature at 10(left) and July (right) at latitudes between 63–70°N in the period 1990 to 2007, at an intermediate position along the coast-ocean gradient. The analysis is based on data from the Temperature Atlas developed by <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0100222#pone.0100222-Ottersen1" target="_blank">[28]</a>.</p

Estimates of recovered kelp area within 5 regions.

<p>Predicted area (in km²) of kelp (<i>Laminaria hyperborea</i>, Lh) recovery and sea urchin (<i>Strongylocentrotus droebachiensis</i>, Sd) persistence in each of five regions along the Norwegian coast, where region 1 is the southernmost region. Areas with regrowth of other macroalgae were estimated as 100% minus the area with kelp recovery and the area with sea urchin persistence. We used the cut-off probability values equal to the Youden index (YI) for the BRT model for kelp recovery (0.27) and sea urchin persistence (0.31). The numbers in brackets are the size of the area in percentage of the total study area.</p