In Guns, Germs, and Steel, what is one important factor directly related to how agriculture styles cause societies to develop into the different political structures.
In order to answer this, I would suggest you look at Table 14.1. There, you can see a number of attributes that differ in the various political structures (bands, tribes, chiefdoms, and states). One of the attributes is food production. Diamond argues that societies move from having no food production to some food production and finally to intensive food production as they become more complex politically.
Bands, Diamond says, have no agriculture. They are hunter-gatherer societies. Tribes that are less complex have no agriculture but tribes that are complex have it. Less complex chiefdoms have simple agriculture while more complex chiefdoms have intensive agriculture. All states have intensive agriculture.
The reason for this general correlation is that societies need a great deal of excess food production in order to grow larger and more complex. In order for a society to support a number of people who do get their own food (who are government officials and priests and such), it must have farming. The larger the number of officials and priests (and eventually merchants and artisans and teachers and everyone else who's not a farmer) the more intensive the agriculture must be.
So, the major factor is the intensity of agriculture. The more complex the society, the more it needs to have agriculture and, in the most complex societies, intensive agriculture.