Abstract: In this paper, we show that differences in dominance and spatial centrality of individuals in a group may arise through self-organisation. Our instrument is a model, called DomWorld, that represents two traits that are often found in animals, namely grouping and competing. In this model individual differences grow under the following conditions: (1) when the intensity of aggression increases and grouping becomes denser, (2) when the degree of sexual dimorphism in fighting power increases. In this case the differences among females compared to males grow too, (3) when, upon encountering another individual, the tendency to attack is 'obligate' and not conditional, namely 'sensitive to risks'. Results resemble phenomena described for societies of primates, mice, birds and pigs.