According to Guns, Germs, and Steel, what is the connection between the early types of agriculture and how the modern political structures are now?

There is very little connection between these two. 
Diamond does not claim that there is any connection between types of agriculture and
types of government.  For example, he does not claim that some kinds of agriculture led
to democracy and others led to communism.  The only claim that Diamond makes is that
agriculture led to complex societies and that the areas that got these things first
became dominant in the world.  Their forms of government have come to prevail in the
world today.

For example, Diamond can help us understand
why democracy exists to some extent in countries as far apart as the US, India, South
Africa, and Australia.  His argument tells us that agriculture arose first in Eurasia
and that rise helped Europe to come to dominate the world.  Since Europe was able to
dominate the world, European countries like Great Britain were able to conquer people
across the world and either replace those people with white settlers (as in the US and
Australia) or impose their systems of government on the people they conquered (as in
India).

However, there is no way to take Diamond's
arguments and explain why some countries have developed communist governments and others
have become democratic.