We can't waste time constructing an approach from scratch. So let's borrow from other disciplines. Our theory proposes memes are replicators just like genes, so strategies of studying genetic populations should be adaptable to the study of memeplexes.
Just as we can track the introduction and spread of invasive species, we can use principles of ecological mapping to see how new memeplexes spread and impact other memes. We could visualize the waves of the First and Second Great Awakenings. We could see how Cold War concerns led world leaders to actions which primed certain populations for religious memeplexes spread by US missionaries. We could see the memeplex of non-violence spreading from India to South Africa and the United States or the exponential growth of the Anti-Slavery Movement as it confronted and then co-opted religious language.
[There are other visual tools from the biological sciences which we can borrow. To see how some theologians & religious studies scholars have applied phylogenic trees to religious traditions, check out this truncated phylogeny of Christianity . Scroll down to see the diagram.]
But this approach has a broader application than simply the study of religions and social movements. We can apply it to the history of Science. We can visualize the paradigm shifts Kuhn wrote about, mapping the spread of scientific revolutions and how they correlate to the spread of communications technologies.
We can also use satellite imagery to study the spread of agricultural memeplexes, to see how Western Monoculture has overtaken the diverse systems of traditional farming, even where monoculture is ill-adapted to the traditional landscapes (signifying a complex memetic story). We can see the growth and spread of cities & artificial light. We can see the mines, supply routes and industrial centers, how the geography of our planet has channeled the flow of certain memeplexes, aided in their development or stifled them.
We could, with our new information technologies, demonstrate that cultures are natural phenomena.
Continue to Focusing on Language: Our Minds Are Not Our Own 
Continue to Focusing on Language: Our Minds Are Not Our Own