Final answer:
After the 1818 joint occupation, 'Oregon Fever' led to a surge in American settlers in Oregon, strengthening U.S. claims and influencing the 1846 Oregon Treaty, which established the 49th parallel as the border, thus resolving the territorial dispute with Britain.
Step-by-step explanation:
In the years following the 1818 joint occupation of Oregon by the United States and Britain, the region saw a significant increase in American settlers, particularly during the early 1840s with a wave known as "Oregon Fever". This migration bolstered American claims to the Oregon Territory and played into the widespread belief in Manifest Destiny.
The increased American presence led to negotiations between the United States and Great Britain, culminating in the Oregon Treaty of 1846, which established the 49th parallel as the boundary between U.S. and British holdings, excluding the Vancouver Island that remained with the British. President James K. Polk, who initially advocated for control over the entire Oregon Country up to 54°40' latitude, settled for this compromise to also secure a Pacific deepwater port at Puget Sound and prepare for potential conflict with Mexico.