Tigers originated in northeastern Asia and gradually expanded southward. They diversified from the regions of China into two major migratory streams: westward and southward. The westward branch traveled through Mongolia, China's Inner Mongolia, Xinjiang, and the Central Asian Soviet republics, reaching as far as northern Iran and southern Caucasia. However, they failed to cross the Arabian Desert to enter Africa, or surmount the Caucasus Mountains to reach Europe.
The southward movement further split into two branches. One branch entered the Korean Peninsula, extending as far south as southern Korea, where it was blocked by the sea. The other branch passed through North, Central, and South China, entering the Indochinese Peninsula. Upon reaching this region, it divided once again into two streams. The first stream continued southward along the Malay Peninsula. It crossed narrow straits to reach the islands of Sumatra, Java, and Bali, but failed to cross the wider ocean to reach other islands. The second stream turned westward, passing through Myanmar and Bengal into India, extending all the way to the southern tip of the Indian Peninsula. However, it also failed to cross the Palk Strait to reach Sri Lanka.
From this analysis, tigers can swim across relatively narrow straits, which is why they appear on islands like Xiamen, Hong Kong, and Singapore. However, they cannot cross wider and deeper straits; therefore, Taiwan and Hainan Islands have never had tigers since ancient times.