Eysenck described in 1951 three criteria to identify fundamental traits: they should have a biological basis, be at least partly genetic, and be observable in other primates.
Two traits that fit this bill are extraversion and neuroticism: in his view, extraversion was linked to general cortical arousability and neuroticism was linked to a lower threshold for activation in the limbic system.
Even thought these physiological views have been proven simplistic, extraversion and neuroticism have shown up time and again as important traits in several taxonomies, probably because they predict a wide collection of important social behaviors, including tendencies to approach or avoid specific classes of stimuli like positive (extraversion) and negative (neuroticism) affect.
There is lots of evidence that these two orthogonal dimensions (positive and negative affect) are a good representation of emotion.
On the positive affect (PA) dimension you find positive hedonic stimuli, safety, rewards; these can be experienced as enthusiasm, interest, pleasantness, relief.
On the orthogonal NA (negative affect) dimension you find negative hedonic stimuli, punishment and threat which can be experienced as anxiety, anger, frustration, disgust. PA emotions are related to approach motivation, NA emotions, to avoidance.
Proponents of the dimensional view of emotion in opposition to discrete categorical emotions have observed, for example, that people who are frequently angry are also frequently sad, but rarely people are sad and angry at the same time, which is consistent with an underlying dimension of general NA instead of discrete categories of emotions. At least when it comes to dispositional affect, the dimensional view of emotions wins.
Dispositional affect can be thought of as an average of all of a person's emotions over time - a person's typical amount of a certain emotion, regardless of stimuli.
People with high NA are "complainers": they will frequently experience distress, anxiety, annoyance, irritability, hostility, worry, anxiety, fear, dissatisfaction, and tend to focus on unpleasant characteristics - of themselves, the world, the future, and other people.
People with high PA are seen as enthusiastic, optimistic, and actively involved with life, tending to have optimistic expectations about the future and being highly sociable.
Some studies suggest levels of genetic inheritability between 40% (PA) and 55% (NA) for these traits, supporting Eusenck's biological basis criteria.
Over a dozen studies correlate extraversion with PA and neuroticism with NA. These links are considered as emotional reactivity: extraverts and people with high-neuroticism respond more intensely to stimuli than introverts and people with low-neuroticism.
However, there is no experimental evidence that extraversion and neuroticism represent differential reactivity to PA and NA stimuli, yet. The most important theory relating personality to affect comes from Gray's Reinforcement Sensitivity Theory, by which two separate brain mechanisms are responsible for sensitivity to cues of reward and punishment.
Gray suggests that extraversion is related to an enhanced sensitivity to cues of reward. Extraverts are motivated by pleasure and so have a strong tendency to approach. They expect rewards and are vigilant for possible sources of reward in the environment. The hypothesized neurological substrate for this individual difference is called the behavioral approach system (BAS).
On the other hand, neuroticism is responsible for differences in response to punishment or frustration. These individuals are motivated to avoid punishment and have a tendency to inhibit their behavior. His hypothesized neurological substrate for this is called the behavioral inhibition system (BIS). Strong BIS makes one vigilant for signs of punishment or frustration in the environment and sensitive to aversive stimuli.