Final answer:
Native Americans did not have a significant wave of migration into Texas; instead, other groups including European settlers, African American slaves, and Asian Americans experienced notable migration patterns to the area.
Step-by-step explanation:
The group that did not have a significant wave of migration into Texas is the Native Americans. The major movement of Americans into the Mexican province of Texas began in 1821 with American settlers outnumbering Mexicans leading to the Texas Revolution and ultimately the independence of Texas as a Republic. European, African American, and Asian American (namely Chinese during the Gold Rush) communities had significant migration flows into Texas during different periods. Europeans migrated in large numbers, with many Germans settling in Texas. African Americans were brought as slaves by American settlers, and their population grew substantially. Asian Americans, although the majority settled in California, still represent a significant immigration wave during the 1800s.