We investigate how scale-free (SF) and Erdos-Renyi (ER) topologies affect theinterplay between evolvability and robustness of model gene regulatory networkswith Boolean threshold dynamics. In agreement with Oikonomou and Cluzel (2006)we find that networks with SFin topologies, that is SF topology for incomingnodes and ER topology for outgoing nodes, are significantly more evolvabletowards specific oscillatory targets than networks with ER topology for bothincoming and outgoing nodes. Similar results are found for networks with SFbothand SFout topologies. The functionality of the SFout topology, which mostclosely resembles the structure of biological gene networks (Babu et al.,2004), is compared to the ER topology in further detail through an extension tomultiple target outputs, with either an oscillatory or a non-oscillatorynature. For multiple oscillatory targets of the same length, the differencesbetween SFout and ER networks are enhanced, but for non-oscillatory targetsboth types of networks show fairly similar evolvability. We find that SFnetworks generate oscillations much more easily than ER networks do, and thismay explain why SF networks are more evolvable than ER networks are foroscillatory phenotypes. In spite of their greater evolvability, we find thatnetworks with SFout topologies are also more robust to mutations than ERnetworks. Furthermore, the SFout topologies are more robust to changes ininitial conditions (environmental robustness). For both topologies, we findthat once a population of networks has reached the target state, furtherneutral evolution can lead to an increase in both the mutational robustness andthe environmental robustness to changes in initial conditions.
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