Mutational robustness describes the extent to which an organism’s phenotype remains constant in spite of mutation. Natural selection can directly induce the evolution of mutational robustness only when mutation rates are high and population sizes are large. The conditions under which selection could act to directly increase mutational robustness are extremely restrictive, and for this reason, such selection is thought to be limited to only a few viruses and microbes having large population sizes and high mutation rates. However, mutational robustness may evolve as a byproduct of natural selection for robustness to environmental perturbations.
Mutational robustness is thought to be one driver for theoretical viral quasispecies formation.
Robustness and evolvability
Mutational Robustness appears to have a negative impact on evolvability because it reduces the mutational accessibility of distinct heritable phenotypes for a single genotype and reduces selective differences within a genetically diverse population. Counter intuitively however, it has been hypothesized that phenotypic robustness towards mutations may actually increase the pace of heritable phenotypic adaptation when viewed over longer periods of time. The hypothesis put forth is that connected networks of fitness neutral genotypes result in mutational robustness and reduced accessibility of heritable phenotypes over short timescales. On the other hand over longer periods of time, genetic drift combined with neutral/buffered mutations can provide mutational access to a greater number of distinct heritable phenotypes that are reached from different points of the genetic neutral network. This hypothesis is supported by simulations of biological systems. and appears consistent with the available data on biomolecular evolution Simulations have indicated that positive relationships between mutational robustness and evolvability can be facilitated by degeneracy within biological systems.
Costs and Benefits of Mutational Robustness
Being genetically robust does have advantages when they influence crucial systems to survival. Gene Regulatory networks, and many vital proteins are found to be more robust in order to preserve their functionality and maintain the survival of those systems.  The more influential a network is across the span of the organism, the more robust it becomes. 
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