  From the proliferative mechanisms generating neurons from progenitor cells to
neuron migration and synaptic connection formation, several vicissitudes
culminate in the mature brain. Both component loss and gain remain ubiquitous
during brain development. For example, rodent brains lose over half of their
initial neurons and synapses during healthy development. The role of
deleterious steps in network ontogeny remains unclear, yet it is unlikely these
costly processes are random. Like neurogenesis and synaptogenesis, synaptic
pruning and neuron death likely evolved to support complex, efficient
computations. In order to incorporate both component loss and gain in
describing neuronal networks, we propose an algorithm where a directed network
evolves through the selective deletion of less-connected nodes (neurons) and
edges (synapses). Resulting in networks that display scale-invariant degree
distributions, provided the network is predominantly feed-forward.
Scale-invariance offers several advantages in biological networks: scalability,
resistance to random deletions, and strong connectivity with parsimonious
wiring. Whilst our algorithm is not intended to be a realistic model of
neuronal network formation, our results suggest selective deletion is an
adaptive mechanism contributing to more stable and efficient networks. This
process aligns with observed decreasing pruning rates in animal studies,
resulting in higher synapse preservation. Our overall findings have broader
implications for network science. Scale-invariance in degree distributions was
demonstrated in growing preferential attachment networks and observed
empirically. Our preferential detachment algorithm offers an alternative
mechanism for generating such networks, suggesting that both mechanisms may be
part of a broader class of algorithms resulting in scale-free networks.
