In simplest terms, a stemma is a family tree of manuscripts (showing which manuscripts were copied from each other), and stemmatics is the preparation and analysis of such stemma. It's a genealogy, tracing relationships from "parent" to "child" to "grandchild," showing "sisters" and "nephews" and "cousins."
Historically, stemmatic work on New Testament manuscripts has proved almost impossible, due partly to the bulk of the tradition (traditional stemmatics requires a detailed examination of the manuscripts of an author, which is impossible for the number of manuscripts of the NT) but mostly to the fact that so many of the intermediate links have been lost. The largest certain stemma for the New Testament has only three members:
Dp/06 | ------- | | Dabs1 Dabs2
(That is, the manuscripts Dabs1 and Dabs2 were both copied from D/06, Codex Claromontanus.)
We should note that the word "stemma" is used in two different senses (creating the usual confusion as a result). The above is a strict stemma, with the precise location of every manuscript known. This is the usual form we see in stemma of classical manuscripts. Because the NT tradition is more complex, however, one will sometimes find the word "stemma" applied to much less certain relations, with many generations of copies intervening between the handful of surviving manuscripts. For example, the exact stemma above would be a small portion of a sketch-stemma of the "Western" uncials of Paul (of which there are five all told: D, Dabs1, Dabs2, F, and G):
[WESTERN ARCHETYPE] | ---------------------- | | * * | | F/G Type D Type | | [X] D | | --------- ---------- | | | | F G Dabs1 Dabs2
In this stemma, the links marked * represent many generations and some possible mixture. X is, of course, the lost manuscript which is the parent or grandparent of both F and G.
It is of just such situations that R. H. Rouse, in "The Transmission of the Text" (published in Richard Jenkins, ed., The Legacy of Rome: A New Appraisal, p. 39), remarks, "if survivors are few, the stemma perforce brings into proximity manuscripts that, historically, were widely separated in time and place of origin -- and it can bestow the same, unweighted semblance of stemmatic separation on two manuscripts that were in reality written within a few months' time, or within the same room." Rouse cites an example from Seneca of this phenomenon. A sketch-stemma is not a full picture. But, at Rouse goes on to add, "stemmas remain our only available road-map." We just need to be very sure to distinguish the rough from the exact. The next example shows this even more clearly, in a slightly different sort of stemma. This is for the manuscripts of Family 1739 in the Catholics, and is designed to show mixture explicitly (we will note only four manuscripts: 323, 945, 1241, 1739; others could be added)
[FAMILY 1739 ARCHETYPE] | --------------- BYZ | | : [X] [Y] /: | |--- / : 1241 1739 \ / : | 323 : \ / \ / \ / 945
Here, the mixture is represented by the dotted lines: 945 could be descended from 1739, but with mixture from the Byzantine text; 323 is not descended from 1739, but comes from its branch of the 1739 family, with Byzantine overlay; 1241 represents a separate branch of the 1739 family.
Both the above stemma are just general outlines, lacking details, and properly should be called by some other term (except that there really isn't one). The distinction is important, because a proper stemma allows you to reconstruct the archetype with precision. In the sketch stemma, there may not even be an archetype. (E.g. the stemma for Family 1739 actually goes back to two roots, the ancestor of Family 1739 and the ancestory of the Byzantine text. Somewhere further back, of course, there is an archetype which lies behind both -- but we can't reconstruct it from the members of Family 1739.)
In most of what follows, we will, of necessity, look at sketch stemma, because that's all we can do for the NT. It is likely that other precise NT stemma could be constructed (e.g. of the Kx Cluster 17 manuscripts written by George Hermonymos), but in no case would more than a small fraction of the tradition be represented. Therefore stemmatics are generally ignored in New Testament, where the "Genealogical Method" (which focuses on manuscript tendencies rather than immediate kinship) is the more normal technique. (This would better be replaced by true study of text-types, but that is another issue.) Stemmatics represent a crucial part of Classical Textual Criticism, however, and the methods involved are covered in more detail in that article, which also supplies additional sample stemma and examples of their use.
Turning to sketch stemma and the actual complications of the New Testament tradition, we face another complication: Mixture. We saw hints of the effects of this above, in the sketch of the relations in Family 1739. Of the four witnesses shown, two (323 and 945) were mixed, with Family 1739 material and Byzantine material intermingled.
And that's with only four manuscripts and two ancestors! It only gets worse as we add more. (This is in distinct contrast to classical stemma; these start with one archetype and branch. But when mixture is allowed, ancestors multiply. An analogy I saw somewhere is to genealogies showing one versus two parents. If you only look at, say, fathers, then all genealogies narrow -- one father can have perhaps six sons, and twenty grandsons, and sixty great-grandsons, so there are more names at the bottom of the genealogy than the top. But if both parents count, then ancestors multiply exponentially. Every child has two parents, and four grandparents, and -- unless one is a Habsburg -- eight great-grandparents, etc.) The same is true in the New Testament. When Stephen C. Carlson studied several dozen manuscripts of the 1 John, using the mathematical method known as cladistics, the result was almost unimaginably complex; the stemma could only have been constructed by computer. Take the case of manuscript 876. Carlson's work (which he has graciously shared with me prior to publication) led him to presume four major lines of descent for 876, contributions from four major textual groupings (Alexandrian, Byzantine, Family 1739, Family 2138), and at least 23 assorted missing manuscripts as well as three extant documents (424*, 1739, 1845). And 424, as we all know, went on to mix with Family 1739 again! The sketch stemma below shows just the ancestry of 876:
Archetype | -------------------------------- | |  (*1) | | ---------------- | | | |   | | | | 1739  | | | | (*3) ----------------- | | (*3)  | | (*3) (*2) | |   | | | --------------------- | | | | |  | | | | |  | | | --------------------- (*2) | | (*4) 1854 | | (*4)  | | (*4)  | | |  | | |  | | | 424* | | ------------------------------- | 876
Notes to the above:
*1 = Text close to
*2 = Byzantine-type text
*3 = Family 1739 text
*4 = Family 2138 text
In the stemma shown, the bracketed figures represent no-longer-extant stages of the text. They are not actual manuscripts, but phases of the text. So, e.g., the split between  and  represents the point at which the Family 1739 text (all descended from ) and the group (descended from ) split. These splits probably represent multiple generations of copying, and quite possibly many manuscripts were copied at each stage. These nodes are branch points (e.g. L splits off the Byzantine text at , while the 1739 and B texts part company at ). There are unquestionably many more manuscripts involved than those shown.
(Carlson would also note that what I have labelled the Archetype -- which was, in the sketch he sent me, node  -- is only a possible starting point; it appears to be the branch point from which all others descended, but several other nodes, including  which is the common ancestor of P74, A, B, 1739, etc., or , which is akin to , could be the root point.)
In terms of complexity, there is really no problem here. We show only 13 steps, and two stages of mixture, to produce 876. This is surely low -- there must have been more than 13 steps, and probably more than one phase of Byzantine mixture. But the above shows how incestuous the ancestry of a late manuscript may prove. Which in turn shows the difference between a New Testament and a classical stemma.
Let's do one more, just to show the complexity of the situation. For this one, I will reproduce the path to the Byzantine manuscript L, but showing where other manuscripts come off:
 (Archetype?) | -------------------------- | | |  C  | | ------------------- ----------- | | | |   | | | | ------------ -------- | | | | | | | 1739 P74  A  | | | | --------- ------ | | | | | | B Y  ------ |  | L
It appears, based on the descendants of the various texts, that  (which, despite its position, is not especially close to A) is a sort of "proto-Byzantine" text, with  being the Byzantine text proper. It will be seen that the so-called Alexandrian text is not a text-type here; in fact, , A, B, and C would appear to represent four different text-types. (And, frankly, I think this very possible; it largely concurs with my own results in the article on Text-Types.)
It will be noted that, under this stemma, there is no guaranteed rule for determining the original text. P74 is a fragment, so we can largely ignore it, but our task, based on this stemma, would be to reconstruct  and  and compare them with C. The consensus (however we determine it) of these three witnesses would be , the archetype.
To reconstruct , we must reconstuct  and .  is relatively straightforward; we compare B and Y to find , then compare  with 1739 (or, properly, 1739 and its allies) to find . But  is complicated. We have one witness in A (had Carlson had collations for 33, 436, etc., this would probably turn out to be another group needing reconstruction), but there is another in .  gives rise to , represented by L, but L is mixed with .  has other descendents (=family 623), but these are also mixed (with family 2138; I decided to spare you that part). Thus  can only be determined by trying to guess which elements of  and  come from  and which parts come from somewhere else. And  will be even less secure than . So any reconstruction of  will be insecure. And for  we must compare  with . And so forth. It's a new and complex situation.
This is not to imply that stemmatics is useless for the New Testament. If Carlson's work is brought to completion, and we have a full sketch stemma for any particular section of the text, we have gained a great deal. A number of manuscripts will be shown to be descended entirely from other types, and so need not be studied further. Others will be placed in their proper relationships. But we will likely need a whole new approach to move from that stemma to our final text.
We might add as a footnote that stemmatics as a concept has wide application outside textual criticism. There is perhaps some irony in that one of these areas is evolutionary biology (see the article on evolution and genetics). Stemmatics is, in a formalist sense, the link between the science of historical biology and biblical studies -- and yet evolutionary theory is often viewed as a anti-Christian discipline.
However, the analysis based on evolutionary biology gives us an interesting warning. The following data on Darwin's famous Galápagos finches comes from Peter R. Grant and B. Rosemary Grant, "Adaptice Radiation of Darwin's Finches," American Scientist, March/April 2002, from a chart on page 133. It groups fifteen species of finch into an evolutionary tree based on genetic analysis. However, we can also classify based on physical characteristics. If we take as characteristics beak size (large, medium, small), bird size (small = 13 grams or less, medium = 14 to 20 grams, large = more than 20 grams), and coloration (light, mixed, dark), we see the following pseudo-stemma:
ANCESTOR | ------------------------------------------- | | | A | | | ------------------------------------- | | | | | B | | | | | ------------------------------- | | | | | | | C | | | | | | | ------------------------- | | | | | | | | | D | | | | | | | | | ------------------------------------- | | | | | | | | | | E F | | | | | | | | | | ------------------- --------------------- | | | | | | | | | | | | G H | J | | | | | | | | | | | | -----?- ---------- | --------------- | | | | | | | | | | | | | | | | | | K | L M | | | | | ? | | | | | | | | | | | | ------- | ------ --------- | | | | | | | | | | | | | | | | | | | | | | | | | | | N | | | | | | | | | | | | | | | | | | | | | | | | | | | ------- | | | | | | | | | | | | | | | C.oli P.ino C.fus P.Cra C.pal C.hel C.pau C.psi C.par G.dif G.con G.sca G.mag G.for G.ful Beak small small small large mediu mediu mediu large mediu mediu large large large large mediu Size small small small large large large large mediu small mediu large large large mediu mediu Color light dark light mixed mixed light mixed mixed mixed dark dark dark dark dark dark
Evolution is not stemmatics; the pressures on the transmission are different. And physiology is a continuous phenomenon; a manuscript either has a reading or it doesn't, but a bird can be 8 grams, or 8.1, or 8.2.... But we note with interest that, if you started with just these three "readings," you certainly would not get the stemma shown! (Indeed, even the biologists have some trouble with it -- observe that the genus indications do not match the family tree. Also, there is speculation that C. olivaceas and C. fusca -- the first and third species shown -- might still be capable of interbreeding. There is also a curious form of mixture: When birds hybridize, as they occasionally do, they "choose" their species by adopting the song sung by their fathers, whichever species he belongs to.)
Simply put, a stemma depends on the technique you use and the data you examine. With a large enough data set, you should of course get a consistent stemma. But it depends very much on what you examine.