Human groups show a variety of leadership dynamics ranging from egalitarian groups with no leader, to groups with changing leaders, to absolutist groups with a single long-term leader. Here, we model transitions between these different phases of leadership dynamics, investigating the role of inequalities in relationships between individuals. Our results demonstrate a novel riches-to-rags class of leadership dynamics where a leader can be replaced by a new individual. We note that the transition between the three different phases of leadership dynamics resembles transitions in leadership dynamics during the Neolithic period of human history. We argue how technological developments, such as food storage and/or weapons which allow one individual to control large quantities of resources, would mean that relationships became more unequal. In general terms, we provide a model of how individual relationships can affect leadership dynamics and structures.