If you get to know me, you'll soon learn that I hate roaches so very, very much. Maybe it has to do with my childhood, or something. I don't know. But I know this: millions of years from now, when my body is nought but dust, my works (huge pyramid tomb, obelisks, and statues of me) utterly destroyed, and my name forgotten, I want my legacy to be the complete and permanent extinction of all roaches. That's how I want to make my unmistakable and timeless mark on the universe. And here's how to do it.
We need to create a mutation in them that has the following two effects.
1) If the individual receives only one copy, then the gene affects meiosis such that ALL of the individual's offspring receive a copy of the gene, rather than just half.
2) If the individual receives two copies (one from each parent), then the individual is stillborn or sterile.
We only need to introduce a small number of these mutated individuals into the world to start the process. The first effect will cause this gene to spread among any population of roaches. No matter how quickly they multiply, even if every female lays ten million eggs, they cannot escape this gene forever. The second effect makes sure all of them die once they have this gene. If you work out the differential equations, the result is an exponential decline, approaching zero. Of course, at low numbers, stochastic effects dominate, and it's possible that all 10 of the "diseased" individuals will die in an accident, leaving 3 "healthy" ones. But then a lack of genetic variation should help us, and the same stochastic effects might favor us by just finishing them off.
Another effect which might harm our efforts is the mixed-ness of roach populations. If we introduce this gene into a population, and it kills that entire population before any leave to other groups to infect them, then we fail. Just like the ebola virus, our gene might be too lethal to spread successfully. In addition, we have to consider that there are several roach species. We'd have to execute this process for each species. But that gives us an opportunity to perfect our method of extermination.
Finally, we examine the possibility of ecological harm. Would the sudden disappearance of roaches disturb the environment? Yes. They are plentiful, eat stuff nothing else wants (dead leaves), and lots of other things eat them. But is it worth it? Lack of roaches, or ecological stability? I don't think it's that simple; the ecosphere can cope, other less repulsive things will start eating leaves and living in our walls (like cute little kitten-shaped insects, perhaps). But to make our difficult choice a little bit easier, I leave you with the (paraphrased) words of the late Reverend Dr. Martin Luther King, Jr.:
"I have a dream that my four little children will one day live in a nation where they will not [have to deal with roaches] but [can play with kittens all day long]. I have a dream today!"
I'd start with mosquitoes, which do actual harm beyond just the creepiness, and are even less useful in the Circle of Life. But I'd argue that any one type of insect isn't really important. As you say, there are other things that would eat leaves; in fact, there already are thousands of other bugs that fill the same ecological niche, without feeling the biological drive to come inside and lay eggs in our cupcakes. Kill them all, and godspeed in engineering that gene.
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