Step 1: Recall the species-area relationship.
Both mainland and island sites show more species as area increases, a well established ecological pattern, so both lines in the correct panel should slope upward, not flat or downward. This already rules out panel S, where the mainland (solid) line is flat, showing no increase with area, which does not match how species richness actually behaves on the mainland.
Step 2: Compare island richness to mainland richness at the same area.
Islands are more isolated, so fewer colonists arrive, and lose species faster to extinction, so for a given area, an island is expected to hold fewer species than an equally sized patch of mainland. This means the dashed (island) line should generally sit below the solid (mainland) line, at least over most of the area range shown. This rules out panel Q, where the dashed island line starts above the solid mainland line and crosses to end up below it, and it also weakens panel R, where the dashed line sits above the solid line throughout.
Step 3: Compare the steepness (slope) of the two lines.
Because islands lose species to extinction more easily as they get smaller, and rare colonisation makes small islands especially species poor, the island species-area line is empirically found to be steeper, a bigger slope on the log-log plot, than the mainland line. So the dashed line should rise faster than the solid line, gradually closing the gap as area increases, rather than the two lines being parallel or the mainland line being steeper.
Step 4: Match this to panel P.
In panel P, the solid mainland line starts higher, more species at small area, but rises gently, while the dashed island line starts lower but climbs more steeply, narrowing the gap as area grows. This matches both expectations: islands hold fewer species than mainland at a given area, and the island relationship is steeper.
Step 5: Final answer.
Panel P shows the mainland starting above the island but with the island's steeper slope catching up as area increases, the pattern ecologists actually observe.
\[ \boxed{\text{P}} \]