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An Analogy for Gene Distribution
In this case, the card game is an analogy. Think of the deck of cards as a genome, with each card representing a single gene and each hand representing a chromosome; thus, in this example, we're looking at an organism with 52 genes distributed among four chromosomes. The pattern of dealing in this analogy is representative of mitosis—here, each deal (cell division) involves a precise, repetitive set of mechanical operations that ensures that the same cards (genes) get distributed to each player (daughter cell). The rules guarantee that the same hands (sets of genetic information) will be preserved in each successive round of the game (generation of cells).
However, this situation leads to an interesting question of logic. What happens if the dealer and the hands are imperfect, and a mistake occasionally occurs? Say that every once in a while, the hands are dealt and the card distribution is slightly different. For instance, assume you see the results in hand 3. (Hint: Look carefully at the cards in hand 3.) Here, you didn't get to see the event that led to the change; rather, you are only able to observe the result. How, then, could you explain what happened in the prior round in the simplest way possible?
To describe what happened, you might say that it looks like some of the cards in hand 3 (specifically, the 5, 6, 7, and 8 of diamonds) were reversed in order. That's all—it's a simple change that can be logically deduced from the observed outcome. Note also that from this point forward, every round dealt from this deck will propagate this new arrangement—we will always have this inversion in hand 3, unless another accident rearranges them again. (In keeping with the analogy, this rearrangement can be thought of as a chromosomal inversion, in which small blocks of genes get flipped around.)

In hand 4, it appears that the last five cards that were dealt to hand 2 were swapped with the last five cards in hand 3. Once again, there is an analogous process in genetics—it's called a reciprocal translocation.

To make this game more difficult, you could have been asked to compare the last set of hands with the first, without receiving any information about the intermediate inversion error. Despite this omission of information, you still would have been able to figure out the simplest explanation for this result: that there was an inversion and then a translocation, in that order. Based on this explanation, you then would have been able to puzzle out the series of slow, small accidents that generated the final card arrangement. (Of course, this won't always be true—some combinations of rearrangements will be ambiguous, so you will only be able to approximate what happened.)
This game could be complicated still further. After all, here are plenty of other genetic operations that could be added. For instance, two hands could be fused together, or we could split one hand so that a total of five (rather than four) hands are dealt during each round. We could also add duplications—maybe one of the players has an ace of hearts up his sleeve, and he slips it into the deck. Deletions are also possible—perhaps someone tosses out the 2 of spades. The important thing is that these little distortions happen relatively rarely, leading to a slow rearrangement of the cards in the deck. There is nothing like a series of shuffles that scramble all of the cards at once.
Mapping Genetic Synteny
This particular game is one that is played in comparative genomics all the time, only the magnitude of complexity is much, much greater. When discussing comparative genomics, we're now dealing with tens of thousands of "cards" in the "deck," slowly rearranged in a series of "rounds" that have been played over hundreds of millions of years. Indeed, the only thing that makes it possible to play this game is that the changes have been relatively slow—in other words, not every generation and not every speciation event has been accompanied by an error. In addition, in whatever game the real species are playing, some arrangements of cards are advantageous and therefore conserved. Obviously, the game is now so difficult that not every rearrangement can be figured out, so what we often settle for is mapping synteny.
But what is synteny? In classical genetics, syntenic genes were originally defined as genes that lie on the same chromosome. Today, however, biologists usually refer to synteny as the conservation of blocks of order within two sets of chromosomes that are being compared with each other.


Real genes are not nicely labeled with suit markings to make it easy to see how they are related, but what we see here in the background colors are blocks of conserved order. Those blocks are regions of synteny. For instance, the region in hand 2 of species 2 that contains the 7, 8, 4, 3, and 2 of diamonds corresponds coarsely to a region of hand 3 in species 1—it's not perfect, because it's missing the 5 and 6 of diamonds, and the 7 and 8 are reversed, but we can at least say there's a kind of macrosynteny at play here, a larger block of rough correspondence with a whole chromosome. Within that syntenic region, there is some local scrambling, so if we wanted to go into more detail, we could say that the 7 and 8 of diamonds in hand 2 preserve the microsyntenic order of a piece of hand 3 in species 1, and the 4, 3, and 2 of diamonds in hand 2 are another microsyntenic region conserved from hand 3 of species 1.
This is a simple example. In the real world of comparative genomics, there are much more elaborately scrambled examples, and researchers don't get to see the ancestral species. Rather, they have two independently evolved species, and they have to puzzle out the minimal set of separate operations that would generate the two products. Next, the researchers must infer the ancestral chromosomal arrangement from this set of operations. Computers are essential for working out the possible permutations.
Using synteny mapping to trace evolutionary history is a combination of molecular archaeology and an elaborate logic game. It's an approach that has considerable power to let us look back into the genetic state of long-extinct organisms that have not left us their actual, intact DNA, but only the somewhat scrambled strands of their descendant's chromosomes.
References and Recommended Reading
Mulley, J., & Holland, P. Comparative genomics: Small genome, big insights. Nature 431, 916–917 (2004) doi:10.1038/431916a (link to article)