In mainstream biological thought it is held that while mutagenesis is non-random in many ways, the utility of a genetic mutation to the organism in which it occurs does not affect the rate at which it occurs. However experimental evidence exists that in some instances the rate of specific mutations arising is greater when they are advantageous to the organism than when they are not.
Such evidence was first produced by Cairns et al. in 1988. The original experiments involved a strain of E. coli that has a frameshift mutation in the lactose operon, inactivating the proteins needed for utilization of this sugar. The bacteria were then spread on an agar medium in which the only carbon source was lactose. This meant that a cell could grow only if a second mutation occurred in the lactose operon, reversing the effects of the nonsense mutation and therefore allowing the enzymes to be synthesised. Mutations with this effect appeared to occur significantly more frequently that expected, and at a rate that was greater than mutations in other parts of the genomes of these E. coli cells.
Similar results have been observed in other experiments.
These experiments suggested that mutations in bacteria are influenced by the selective pressures that the bacteria are placed under. In other words, it seems that the environment can sometimes affect the genotype, as suggested by Lamarck.
This hypothesis, if true, would modify the central dogma of molecular biology, which states that DNA defines protein expression, and that protein expression creates function in a physical environment. If the environment provides feedback to DNA to mutate in a given way, such a process would involve an information transfer from the environment to the DNA.
Genomes, T.A Brown, Second Edition ISBN 1-85996-029-4, Chapter 14.1.3 Hypermutation and the possibility of programmed mutations
The Origin of Mutants, Cairns et al 1988 Nature. 1988 Sep 8;335(6186):142-5.