  The paper deals with two interrelated topics, identifying transient
amplifiers in an iterative process and analyzing the process by its spectral
dynamics, which is the change in the graph spectra by edge manipulations.
Transient amplifiers are networks representing population structures which
shift the balance between natural selection and random drift. Thus, amplifiers
are highly relevant for understanding the relationships between spatial
structures and evolutionary dynamics. We study an iterative procedure to
identify transient amplifiers for death-Birth updating. The algorithm starts
with a regular input graph and iteratively removes edges until desired
structures are achieved. Thus, a sequence of candidate graphs is obtained. The
edge removals are guided by quantities derived from the sequence of candidate
graphs. Moreover, we are interested in the Laplacian spectra of the candidate
graphs and analyze the iterative process by its spectral dynamics. The results
show that although transient amplifiers for death-Birth updating are rare, a
substantial number of them can be obtained by the proposed procedure. The
graphs identified share structural properties and have some similarity to
dumbbell and barbell graphs. Also, the spectral dynamics possesses
characteristic features useful for deducing links between structural and
spectral properties and for distinguishing transient amplifiers among
evolutionary graphs in general.
