Why is CO a major species only in fuel-rich combustion? In fuel-rich combustion, my understanding is that enough fuel reacts and consumes all of the oxygen present. The combustion products $\ce{CO2}$ and $\ce{H2O}$ undergo dissociation until equilibrium is established and one of these is $$\ce{CO2 -&gt; CO + 1/2O2}.$$ 

From the graph below, the equilibrium mole fraction of combustion products are plotted vs. equivalence ratio. Why is there a sudden rise in $\ce{[CO]}$ as we move into fuel rich combustion? Is this due to the drop in $\ce{[O2]}$ such that $\ce{[CO]}$ must increase to compensate for equilibrium to be established?
I think it is quite simple: the higher the proportion of the compound that will burn in the mixture, the more oxygen will be required to a complete combustion. If you have a constant amount of oxygen (in the reactor), and more is requires while increasing the amount of fuel, the complete combustion will gradually decrease, and the ratio $CO/CO_2$ produced will increase as a result of that.

As it can be seen on the graphic, from the point that the equivalent ratio of fuel and oxygen is larger than one, the $CO$ starts being formed in a considerable proportion, and over a ratio of 1:3, starts being the major product.