Another variable is the type of community where the disaster occurs. If it is one where people know each other and have had long term relationships with their neighbors, they are much more likely to cooperate and take care of those who can't take care of themselves.
In a large city where most people remain strangers to each other, anonymity is a key factor. When a person believes that they are not known, and will remain anonymous, they are much more willing to commit antisocial acts and to not take responsibility for the community's welfare.
There are other triggers that can make the prevailing mood swing either way: leadership can go either way, acts of violence may reduce people to perceiving they are in survival mode and make them less cooperative, prevailing cultural norms and values can push in either direction, perception of other people cheating in access to resources.
Every situation can be very different from every other. One more reason why preparedness is so important. If everyone prepared a little, they would not be so likely to be reduced to antisocial actions. If you are viewed as a good neighbor and you are prepared, your neighbors will look to you for guidance and leadership. Demonstrated skills will carry you a long way in keeping your community working together and taking care of each other. You are reducing their stress and fear.
Another reason, as I have posted in the past on other threads, why communication skills are important. In a community suffering from a disaster your ability to communicate, and understand other people, can make all of the difference.