Every chemical reaction has a reaction rate that depends on the energy of the colliding reactants, caused in this case by the temperature and pressure. Here, the faster the fuel molecules collide with oxygen, and the more oxygen molecules surround each fuel molecule, the more likely the reaction will release enough energy per second for it to accelerate the reaction, rather than have it be cooled by the surrounding molecules. This is the threshold of combustion.

With a higher equivalence ratio, more fuel molecules are likely to react with oxygen per unit time, and there are fewer air molecules per fuel molecule to dissipate heat to.

In other words, with a higher fuel concentration, the molecules don't have to collide as hard or as often (lower temperature and pressure) to make combustion self-reinforcing.

From my point of view, the equivalence ratio is not necessarily the parameter you should look at. Instead, it is suggested to pay attention to the temperature of the mixture. There you should see that the reaction rate increases as the temperature of the mixture increases.

As far as I know there are various publications on this topic (mainly called auto ignition), e.g. by Aigner, Griebel, Meier and various other authors.

Auto-ignition temperature also influenced by the condition of air-fuel mixture: i.e. mixture formation and fuel stratification if any.

The equivalence ratio, an air-fuel mixture, increases mean more air or less fuel in the mixture. Auto-ignition temperature, fuel's characteristics, obviously varies as fuel type or compositions has changed.

Tongchit, an increase of the equivalence ratio means that the mixture gets richer in fuel, not in air.

Thank you, Mr. Francois. I should have mentioned less fuel or comparatively more air. Typically fuel used in the combustion will be rich or lean (not lean air or rich air).