Final answer:
Increased histone deacetylase activity leads to greater histone affinity for DNA and decreased gene transcription due to tighter nucleosome packing and reduced accessibility for transcription machinery.
Step-by-step explanation:
A mutation that causes an increase in the activity of histone deacetylase would most likely result in histones having a greater affinity to DNA, and there would be a decrease in transcription.
This is because the deacetylation of histones by histone deacetylase leads to tighter packing of nucleosomes, making the DNA less accessible for transcription factors and RNA polymerase to bind to the DNA, resulting in decreased transcription of genes.