The expected degree distribution in transient duplication divergence models

We study the degree distribution of a randomly chosen vertex in a duplication-divergence graph, under a variety of different generalizations of the basic model of Bhan et al. (2002) and Vazquez et al. (2003). We pay particular attention to what happens when a non-trivial proportion of the vertices have large degrees, establishing a central limit theorem for the logarithm of the degree distribution. Our approach, as in Jordan (2018) and Hermann and Pfaffelhuber (2021), relies heavily on the analysis of related birth-catastrophe processes, and couplings are used to show that a number of different formulations of the process have asymptotically similar expected degree distributions.