There is a gene for race. Our biological make up in regards to genetics is the cause of what race we are. Our parents genes determine our race. Many people disagree with this, but the only way to determine what race we will end up is by our genetics and our parents genetics.
There may not be a single gene that determines the race but there is definitely a set of genes that determines the features of races. Genes that determine various features like eye color, skin color and hair color are different for people in different ethnic groups and parts of the world. With more research, there will be more answer in the future.
There is only one heavily connected gene pool that humans have. Every individual is just a collection of those genes. There may be more people in one part of the world with more of one gene or even a set of such genes, but they are not fixed on something called race. Any gene from any group can be transferred the same way between groups as it is within them.
The gene that makes Jamaicans more likely to run really fast can and probably already is carried by many whites. Eventually and at some point when the situation and combination of HUMAN genes is right, a white boy will be the fastest 100m runner.
Thus no race.
Although people argue back and forth about the connection between race and genetics, the truth is there is no connection between anything other than skin tone that separates humans from each other. Besides physical attributes attained through thousands of years of a people adapting to survive in a particular environment, there is no other separation, physical or mental, between "races".
Race is has absolutely no biological connotation. Race is 100% a social convention that was designed to keep people categorized within a class-based system, it is a complete illusion. If you know anything at all about biology and/or genetics, you would know that underneath a microscope, droplets of human blood do not portray any signs of a persons "race."
There is no single gene that makes someone European, African, Asian, etc, rather there are many genes that differ between human populations based on their ancestral origins. These genes determine all sorts of human characteristics, including the ones traditionally used to determine someones race, physical build and eye/hair/skin color. These genes are unique to their populations.