How are fog-2 and natural sperm depletion related? Formally, there are four possibilities.

• fog-2 and sperm depletion through time are independent of each other (they do not affect the same genes at all)
• fog-2 and sperm depletion have additive effects. They act on the same phenotype but are otherwise independent of each other.
• fog-2 and sperm depletion share an epistatic interaction, which means they act along the same pathways. The combined effect of having a fog-2 mutation and being a 6d old adult is less than expected by additivity.
• fog-2 and sperm depletion share a synthetic interaction, which means they act along parallel pathways. The combined effect of having a fog-2 mutation and being a 6d old adult is more than expected by additivity.

In order to explore these possibilities, we decided to first ask whether these two perturbations were acting on overlapping gene modules. If so, do their effects have the same sign?

The plots below will help us answer these questions. We have plotted the biological effect of each variable versus another. Points are colored according to the logarithm of their q-value. Purple indicates a q-value closer to 0.1, whereas yellow indicates a q-value $<10^{-20}$.

fog-2 partially phenocopies changes in expression due natural sperm depletion

Indeed, the graph below shows that not only do the fog-2 transcriptome and the transcriptome of 6 day old C. elegans act on the same modules, they also share the same sign!

Changes due to sperm depletion are not additive with changes in expression associated with mutation of fog-2

Next we checked whether the interaction coefficient was positively or negatively correlated with the aging coefficient. A negative correlation indicates that, on average, mutation of fog-2 and aging are epistatic to each other and act along the same molecular pathways; whereas a positive correlation indicates that on average mutation of fog-2 and aging have a synthetic interaction and they are acting along parallel pathways.

We can see that the correlation is negative, which indicates that fog-2 and aging are acting along the same molecular pathways.

For completeness, we also show a plot of the genotype coefficient versus the interaction coefficient. Having seen the plot above, we expect a negative correlation between genotype and interaction. Indeed, that is what we see. This evidence suggests that sperm-depletion, whether natural or induced by a mutation, causes entry into a new C. elegans state.