January 1, 2003:

Dear Ken,
Program capabilities (graphlife.k): 
given a bunch of gene family trees with species
at the leaves,
we can
1. input those trees
2. derive dependency edges based on the analysis in the puzzle
3. determine which groups of species fit into single evolutionary trees.
4. Produce those evolutionary trees when possible.
5. determine which subsets of
families allow all species to fit into a single
evolutionary tree.
6. Produce interbreeding models given a base evolutionary tree.

Here is what we have found out.
The largest sets of families that are compatible in the sense that they
produce a single evolutionary tree are:
A1341, AdhC, G1121, 5SrDNA
and
A1341, CesA1b, FAD21, G1121

The first produces the following evolutionary tree:

miss0 (0)"
    miss1 (1)"
        miss4 (4)"
            davi (8)"
        miss5 (5)"
            miss9 (9)"
                miss13 (13)"
                    goss (16)"
                    miss17 (17)"
                        herb (20)"
    miss2 (2)"
        miss6 (6)"
            hirsD (10)"
            miss11 (11)"
                miss14 (14)"
                    miss18 (18)"
                        miss21 (21)"
                            miss23 (23)"
                                miss26 (26)"
                                    long (29)"
                                miss27 (27)"
                                    raim (30)"
                            miss24 (24)"
                                miss28 (28)"
                                    miss31 (31)"
                                        miss32 (32)"
                                            miss33 (33)"
                                                miss35 (35)"
                                                    miss37 (37)"
                                                        schw (39)"
                                                    miss38 (38)"
                                                        soma (40)"
                                            miss34 (34)"
                                                tril (36)"
    miss3 (3)"
        miss7 (7)"
            miss12 (12)"
                miss15 (15)"
                    miss19 (19)"
                        miss22 (22)"
                            turn (25)")


Using all families:
`ndhF `matK `rpl16 `trnT `A1341 `AdhA `AdhC `CesA1
`CesA1b `FAD21 `G1121 `G1262 5SrDNA
and ignoring hirs(A), we get three different evolutionary trees.
These can vary -- i.e. different combinations of families can work.

For example, in one execution we get the following groupings:
hirsD `raim `schw `soma `stoc
davi `herb `long `turn
goss `tril
where each line produces a single evolutionary tree.
Here is the tree for the first group, just for example:
miss0 (0)"
    hirsD (1)"
    miss2 (2)"
        miss5 (5)"
            miss8 (8)"
                miss11 (11)"
                    miss14 (14)"
                        miss16 (16)"
                            miss18 (18)"
                                miss21 (21)"
                                    miss24 (24)"
                                        miss27 (27)"
                                            miss29 (29)"
                                                raim (31)
                            miss19 (19)"
                                miss22 (22)"
                                    schw (25)"
    miss3 (3)"
        miss6 (6)"
            miss9 (9)"
                soma (12)"
    miss4 (4)"
        miss7 (7)"
            miss10 (10)"
                miss13 (13)"
                    miss15 (15)"
                        miss17 (17)"
                            miss20 (20)"
                                miss23 (23)"
                                    miss26 (26)"
                                        miss28 (28)"
                                            stoc (30)")

Here the miss denote missing species.

Here are some other combinations of compatible species again
using all gene families.

hirsD `raim `schw `soma `stoc
goss `herb `long `turn
davi `tril)

and 
schw `soma `stoc `turn
goss `herb `hirsD `long `tril
davi `raim))

Our first objective is to show that cross-breeding takes place.
A longer term objective is to show that we can produce the most
parsimonious graph: as few ancestors as possible when cross-breeding
takes place.
As of now, we do not quite make it.

For example, if the inspecies are 
`hirsD `raim `schw `soma `stoc
Then we can produce herb by interbreeding miss9, miss2, and miss0.
goss on the other hand uses miss8, miss2, miss11, miss16, miss21.

Thanks,
Dennis
P.S. One uncertainty I have is that I'm getting the gene family trees
correct. Here for example is my tree for CesA1b:
Tree: CesA1b"
 (0)"
     (1)"
        soma (2)"
         (3)"
            long (4)"
            herb (5)"
     (6)"
        goss (7)"
         (8)"
            turn (9)"
            schw (10)"
             (11)"
                davi (12)"
                 (13)"
                    tril (14)"
                     (15)"
                        raim (16)"
                        hirsD (17)")