Explain the most likely reason that aquatic vertebrates evolved from an aquatic existence to a land based existence?
There must have been a lack of resources or some other abiotic factor acting upon that species, thus evolution takes place and the animal grows legs and walks on land in search for more nourishment. It may find food or it may not, its a game of chance.
The primmest life was of autotrophs which can synthesize their own food using light or heat energy. They were present in water initially. Some autotrophs which were in shallow water finds the problem related to drying in hot seasons. So gradually they start growing on land and the Plants were developed from it.
The first heterotrophs were present in water too. But due to overload of them in water or due to the shallow water situation or due to reasons mentioned above they gradually came out of the water like amphibians. Gradually amphibians becomes the land animals and then due to natural selection various species were formed.