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& LOD scores

CRI-MAP Tutorial - Mapping & LOD scores


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4. Building a map  (build option)
Ex. 4.1 - choosing loci; editing the .par file
Ex. 4.2 - haplotying loci; choosing loci via twopoint
Ex. 4.3 - checking the map with flipsn
5. Extending a map (Using the chr2.ord file)
Ex. 5.1 - choosing and adding more loci via twopoint & instant
Ex. 5.2 - more build runs; more flipsn


4. Building a map

The build option evaluates the likelihood of possible maps (also called "locus orders") using the most informative data first. Loci are added in their order of informativeness, i.e., in their ranking of number of informative meioses. Further, the addition of loci is a two step process. In the first step, the more efficient data from phase known meioses are used to evaluate possible maps; in the second, phase unknown information is used.
Ideally, build stops when it has found the best of all possible maps incorporating all the loci. Practically, all possible maps cannot be evaluated; the memory requirements can be too great. For this reason, as build moves on to add the next locus, it discards those maps with likelihoods much lower than the current "best" map, and retains only at most a limited number of possible maps. These practical limitations can lead to incomplete or even incorrect maps; the map discarded part way through a build run due to lack of support from the loci already processed may be the correct one, when all loci are considered. Fortuantely, these parametres - how much lower in likelihood and maximum possible map number - may be changed. The best mapping strategy is to run build several times, BOTH altering these parametres until the programme takes too long to run AND changing the order in which the loci are processed. These two parametres (and others), as well as the order of locus processing, are defined in the chr#.par file.

A typical build run, adding loci D and E to an existing map of three loci, "A  B  C", might proceed like this:

To illustrate refined use of the mapping and map testing features of CRI-MAP, we need a more complex data set; please retreive chr2gen.zip to your Crimaptutl directory, "unzip" it, and run the prepare option on it for a subsequent build run. Respond to the prepare option prompts as before. (Don't know how to "unzip" a file? Check the "zip" command on the UNIX Commands Short List page.)

chr2.gen is a large file (~292 K), holding data for 65 families scored for up to 78 co-dominant (e.g., RFLP) loci*. The prepare option has determined the informativeness of these loci (chr2.loc) and ranked them as well (chr2.par). The two most informative (68 (D2S44) & 7 (CEB1/HINF)) show as the ordered loci, and the other 76 show as the loci to be inserted, least informative (8 (CEB11/HINF), 46 (D2S65), & 60 (D2S12)) last.

To save both our time and our eyes, we will build maps using only a subset of these 78 loci! In the following build exercise, there are four steps:

  1. starting with cytological evidence, choose meiotically informative loci that are also precisely located within the p arm (i.e., choose those assigned to one or only a few bands), and use these as the ordered_loci;
  2. selecting six to ten other loci, also informative and also located on p, and use these as the inserted_loci;
  3. edit the chr2.par file to effect these choices, and run the build option with the default parametres; &
  4. alter a few of these parametres, re-run build, and check the effects.

Exercise CRI-MAP 4.1: build a map - choosing loci and editting the .par file
Examine the cytological evidence to determine which of the 30 loci found on the p arm are candidates for ordered_loci. Choose loci having high meiotic informativeness and/or precise chromosome band assignment. Next choose six to ten others as the inserted_loci. When finished, see if you agree with any of my choices.

Edit the file chr2.par so the ordered_loci field specifies the index numbers of two informative loci (or three, in their correct order!), with some of the other p arm loci as inserted_loci. Save this file twice: as chr2.par and backed-up as chr201.par . Also back-up chr2.ord as chr2.ord.orig . (If you want to use sets of ordered and inserted loci that differ from the tutorial choices, please create extra chr2try#.par files matching them.)

Enter the command crimap 2 build > build201.out at the prompt. When finished, the prompt will return, and you may browse the programmes' output with the command more build201.out . (To build maps from other sets of ordered and inserted loci, first rename the chr2try#.par file to chr2.par. Next back-up chr2.ord to chr201.ord , and restore the original chr2.ord from chr2.ord.orig . Finally, re-issue the crimap 2 build > build2##.out command, naming the output file for the try#.)

A quick glance through build201.out shows the structure of the programmes' output. After a re-statement of much of the chr2.par file, the loci used to build the map are listed and described as ordered or inserted. Then a series of interim reports reveals the status of the currently ordered loci ("current orders") plus which other locus the programme is presently trying to insert into those current orders (the extra locus shown in "orders_temp"). Finally, and unfortunately for this build run, the programme exits with no loci added to the "current orders", and prints the possible maps. None of the loci to be inserted were unambiguously placed on the map of the two original ordered loci; we see the Sex_averaged map having only the two original loci, and mapping them at 100 centi-Morgans apart. This is followed by the most likely placements for each of the inserted loci.

The three other trial sets of ordered and inserted loci also fail to produce maps of the p arm. How, then, does one choose the ordered and inserted loci? As I mentioned, these naïve choices assumed the dataset has mapping information for each locus relative to all others. (They also assumed we would be lucky enough to choose loci less than 100 cM apart!) To find which loci ARE mappable with which other loci, we must use CRI-MAPs twopoint option. At the same time, and to maximise the available information, we will use "locus haplotyping" for loci with multiple polymorphisms.

Exercise CRI-MAP 4.2: build a map - haplotyping loci in prepare;
choosing loci via
twopoint
Re-run the prepare option on chr2.gen. This should overwrite the chr2.ord file. When asked

Do you wish to change any of these values? (y/n)

enter "y", if use_haps = 0 and set it to 1 ! Then when asked

Do you wish to enter any new haplotyped systems? (y/n)

enter "y". There are nine genes each scored two or more times, for two or more independent polymorphisms (unique probe-enzyme combinations). For each of these genes, enter its polymorphisms in a haplotyped system, having "inter-locus" distances of zero.

hap_sys0 0 2 4 *
hap_sys0 1 3 *
hap_sys0 23 24 *
hap_sys0 39 40 *
hap_sys0 41 42 *
hap_sys0 44 45 *
hap_sys0 53 54 *
hap_sys0 63 64 *
hap_sys0 72 73 75 76 *
done
Choose the twopoint option, respond with "n" when asked if you want LOD tables for ALL pairs of loci, and enter the index numbers of the p arm loci as ordered loci.
1 5 9 33 39 41 44 50 53 55 56 59 60 62 63 65 66 67 68 69 70 71 72 *
Enter no inserted loci. This will force the calculation of pairwise lodscores for all pairs of loci on the p arm. After accepting the new parametre file, type crimap 2 twopoint > 2p2ptlod.out.

Browse the 2p2ptlod.out file. After a re-statement of the parametres, and a listing of the haplotyped systems, this file lists pairs of loci that are genetically linked, plus their likely recombination fractions and the confidence placed in these estimates (lods). While any pair of loci in this list could be chosen as ordered_loci for the next build run, choose a pair with both a large inter-locus distance (rec. fracs.) and confidence (lods). By these criteria, good choices are locus pairs D2S43 - D2S44 or D2S6 - D2S48.

Choosing loci that are far apart for the inital map has the advantage that the build run may "reach" more distant loci on either side of the map. However, there may be more errors in the relative positions of loci mapped both between the two inital loci and on either side. For this reason, such build runs are best followed by flipsn runs. Most likely maps from these trials can then be used as ordered loci for subsequent build runs, with all remaining loci to be inserted.
Of course, ordered loci may be chosen on other criteria. Another fine choice is the set of three loci reported in the first three twopoint scores: D2S1, ACP1, & TPO. Though the interlocus distances are small, the dataset maps them with high confidence, and their most probable order (ACP1 - D2S1 - TPO) seems clear.
The best strategy, as mentioned previously, is to choose a number of different sets of ordered and inserted loci, building a map with each one, and proceding with the most successful map(s). For a third set of ordered and inserted loci, use the three loci of the second trio of twopoint scores: APOB, D2S70, & D2S48. Their most probable order is D2S48 - APOB - D2S70

Exercise CRI-MAP 4.3: build a map - re-edit chr2.par; re-run build;
check the map with
flipsn
Copy and edit chr2.par to reflect each of your sets of choices for ordered_loci & inserted_loci, saving back-ups as chr211.par , chr212.par , etc. Re-run the build option for each set of locus choices, re-directing the programmes output to unused filenames (e.g., build211.out, build212.out, etc.). Don't forget to back-up the chr2.ord file after each run, and restore the original version before the next build! Browse the output files to see which final set of ordered loci - which map - is biggest. Note that "biggest" may mean largest number of loci mapped, or largest span of centi-Morgans covered, depending on your goals.

Create another copy of chr2.par and place the loci of the biggest map - in their reported order - in the ordered_loci field, leaving the inserted_loci blank. Finally, put this map through a local rearrangement analysis with the flips4 option. Re-direct the programme output to flip42##.out.

Of the three sets of ordered and inserted loci suggested, the third set gives the biggest map. However, there is useful information in the results from each of these build runs, information that can help us to construct a still better interim map. Examining each of these build2##.out files ...

Notice that the map from Try 11 is contained by the map from Try 13. Notice further that both Try 12 and Try 13 manage to insert locus D2S47, yet have no other loci in common. Although all build runs had access to the same mapping data, and were attempting to map the same set of 23 p arm loci, strikingly different maps were produced. The "take-home message" is try MANY build runs!
A difference in the order in which loci were added to the current_orders gave the difference in map resolving power between Try 11 and Try 13 build runs. But why did Try 13 fail to include the ordered loci of Try 12? This seems especially odd because D2S47 - the common locus - was added to the Try 13 map BEFORE any of ACP1 D2S1 & TPO were tried. One problem could be that we have specified the least informative locus for two of the three haplotyped sets of loci in this critical region. In the programme authors' language, we are using weak loci as "primary loci", which may use the extant data less efficiently. Using the most informative haplotyped loci as "primaries" yields chr214.par with the following changes:

...
ordered_loci 56 54 50  *
inserted_loci 68 69 65 44 64 5 67 1 66 33 59 62 70 75 55 9 42 40 71 60 *

hap_sys0 75 73 72 76 *
hap_sys0 64 63 *
hap_sys0 54 53 *
hap_sys0 44 45 *
hap_sys0 42 41 *
hap_sys0 40 39 *
hap_sys0 24 23 *
hap_sys0 1 3 *
hap_sys0 0 2 4 *
END
However, these changes don't alter the resultant map. build214.out shows the most likely placements of ACP1, D2S1_2 & TPO on its map, followed by their LOD scores.
ACP1
    55  68  1   69  33  59  40  66  56  54  50  65  
                                              X   X 

-627.11
-626.89

D2S1_2
    55  68  1   69  33  59  40  66  56  54  50  65  
                                              X   X 

-614.28
-614.06

TPO
    55  68  1   69  33  59  40  66  56  54  50  65  
                                              X   X 

-645.62
-645.82
Accurate placement of these loci might require waiting for this end of the map to be "filled in" with at least one other locus showing linkage to them.

Using the hap_sys0 revisions of chr214.par , flip4215.out reveals only one local rearrangement - a switch of two neighbouring loci - with a likelihood close to the best current map. With a LOD score 1.46 worse, this rearrangement is ~28.8 fold LESS likely than the best map. All other rearrangements have LOD scores 3.000 or more worse, and are filtered out of the flip4215.out report. This gives us high confidence in most of the map, and an additional reason to focus on adding new loci to its right end; not only might we place ACP1, TPO, & D2S1, but also we could settle on the true order for "D2S48 (APOB+APOB_2) D2S70 D2S47" . So, what new loci might be insertable, and what is their best sequence in the inserted_loci parametre for efficient and effective use of the next build run?


5. Extending a map

There are three sources of new loci: 1.) those known to be on the p arm but not yet located on the map (i.e., 11 loci already tried), 2.) those possibly on the p arm (i.e., 34 untried loci having no cytological location data), & 3.) those known to be on the q arm (i.e., 14 untried loci). While several of these new loci will show no linkage to the current map, when extending a map, it is acceptable to reduce the stringency used to reject other locus orders and reports of recombination fraction. We have used a stringency of LOD >=3.000 (the parametres PK_LIKE_TOL & PUK_LIKE_TOL); reducing these to 2.000 could help "filling-in" the extant map in another build run. However, to run build with a set of 12 ordered_loci against a set of 11 + 34 + 14 inserted_loci would take a VERY long time, and the result could be disappointing or brilliant, depending on the order in which the loci were tried. A better idea - to screen out loci distant from the current map and to omit loci with no information - is to first try the twopoint option again, looking for significant linkage between loci on the current map and loci we hope to insert. Then, having chosen the subset of loci to be inserted, determine the best sequence in which to insert them, using the information stored in chr214.ord and the instant option.

Exercise CRI-MAP 5.1: extend a map - selecting new loci with twopoint;
choosing the insertion order for these loci with
instant
Create chr216.par with PK_LIKE_TOL & PUK_LIKE_TOL set to 2.000, ordered_loci as the current map, and inserted_loci as the balance of the p arm loci, plus those of q or unknown cyto-location (see the cytological evidence again, and remember to omit secondary loci in haplotyped systems). Check your choices. Copy chr216.par to chr2.par.

Save the output of "crimap 2 twopoint" as 2pt216.out, and note the subset of inserted loci that shows linkage to those loci in the current map. (Spot these loci quickly as the second one in each pair.)

Of the several new loci screened for linkage to those in the current map of the p arm, 32 show a significant score at LOD 2.0 or better. Oddly, since we are working with the p arm, two loci cytologically placed on p and with high informativeness have been excluded from these 32: D2S61_2 (64) & CPSI (9). Perhaps more oddly, four of these 32 loci have been cytologically located to the q arm: LCT (49), GYPC (58), D2S17 (35), & D2S16 (34). If one or more of these can be inserted in the current map, we could have a starting point for extending our map across all of chromosome 2. (Don't worry - not part of the tutorial!)

Create chr217.par with PK_LIKE_TOL &PUK_LIKE_TOL set to 2.000, use_ord_file set to 1, ordered_loci as the current map, and inserted_loci as the newly chosen subset. Check your choices. (Note that the locus sequence for the inserted_loci parametre is NOT important at this stage; I simply added the loci in their order of occurence in 2pt216.out.) Copy chr217.par to chr2.par, and copy chr214.ord to chr2.ord.

Save the output of "crimap 2 instant" as inst217.out

The inst217.out file requires some explanation. Its form is very much like any of the build2**.out files; it re-states the parametres used and lists the loci, follows with the current map, including interlocus distances and overall LOD score, and finishes with "most likely" locations for the unmapped loci. For the loci attempted in the previous build, "most likely" locations are estimated using both LOD scores AND the locus orders database, stored in chr2.ord. For new loci, only LOD scores may be employed. Thus, the "most likely" locations for the first previously tried locus in the list, TGFA_3, are on either side of locus 59, with equally likely LOD scores of -620.34 . The "most likely" locations of the first new locus, D2S25, are shown as being in each of the thirteen possible insertion locations, but quick inspection of the LOD scores reveals that this locus is really only likely on either side of locus 33 .

Now, using these "most likely" map positions and moving from left to right, choose the sequence of loci for the inserted_loci parametre to be used in the next build runs. For loci having two or more equally likely positions, choose the rightmost. When two or more loci have the same "most likely" location, insert the loci having the highest LOD scores first. The final list will consist of 13 groups corresponding to the 13 possible insertion locations, each group having one or more loci, ranked internally by LOD scores. Check your choices, and create chr218.par .

Now for the second round of build runs.

Exercise CRI-MAP 5.2: extend a map - inserting the new loci via build, using a variety of insertion sequences for these loci
Improve the current map by trying two or three new build runs using the subset of loci discovered above. (Don't forget to back-up the chr2.ord file after each run, and to restore an original version before the next build!)
In addition to chr218.par from above, create chr219.par with PK_LIKE_TOL & PUK_LIKE_TOL set to 2.000, use_ord_file set to 1, ordered_loci as the current map, and the inserted_loci in sequence of their informativeness (recall this is CRI-MAPs default choice). Lastly, create chr220.par with the entire current map in reverse order, and inserted_loci similarly switched around (i.e., use "most likely" map positions and move from right to left.) NB: You must set use_ord_file back to 0 in chr220.par!

(NB: These build runs are LONG, requiring lots of memory, and the build*.out files are LARGE; be sure you want to wait for them to come!).

Run flips2 on the biggest map.

These final attempts at map building yield significantly different results. Try 218 produces a map of 26 loci, Try 219 builds a longer map of only 24 loci, losing six loci from the 218 map but adding four different ones, and Try 220 links 27 loci, combining pieces of the two previous maps & showing two locus pair reversals. The details of the differences are summarised in the tables below, but the important conclusion for CRI-MAP users is to process the data in as many ways as possible.
Try 219 represents the standard approach, with inserted_loci added in the sequence of their informativeness. Try 218 was an attempt to insert the problematic p arm loci (those still unmapped after Try 214) only after first inserting any other new loci. The attempt failed, perhaps because the cumulative multipoint linkage evidence was conflicting. However, inserting loci in a sequence that follows more closely their likely places in the current map (Try 218 & Try 220) introduces changes to the default map. The new maps both have more loci, and one is slightly longer. Finally, note that the simple trick of reversing locus order in both inserted_loci and current_loci (Try 220) does lead to insertion of the problematic p arm loci, and also gives the "best" map of the three build runs.

Details of the final build runs
build ID# loci mapped ID of loci addedmap length (cM) LOD scorecomments
Try 2182622 21 13 77 58 49 20 10 24 26 28 31 17 70 220.8-929.87LOD=2.000; inserted by "most likely" loc'n & by inf. rank
Try 2192422 61 49 20 10 24 26 28 31 44 42 5 221.7-902.96LOD=2.000; inserted by inf. rank
Try 2202721 61 77 49 20 10 24 26 28 31 17 70 44 42 5 232.9-1033.71LOD=2.000; inserted by "most likely" loc'n (Try 218 sequence reversed)

Maps of the final build runs (initial ordered_loci in first row)
      55    68 1             69    33    59       40    66       56 54 50    65     
22 21 55 13 68 1 77 58 49 20 69 10 33 24 59 26 28 40 31 66 17 70 56 54 50    65
22    55 61 68 1       49 20 69 10 33 24 59 26 28 40 31 66       56 54 50 44 65 42 5
   21 55 61 68 77 1    49 20 69 10 33 24 59 26 28 40 31 66 17 56 70 54 50 44 65 42 5

Running the flips2 option on the map produced in Try 220 shows that this map isn't the best one! flip2221.out lists one locus pair that, when reversed, increases the overall LOD score of the map (i.e., the LOD score relative to the accepted map is negative). This locus pair, 56 70, increasing the LOD score by 1.27, is also one of the two locus pairs that differed between the maps of Try 218 and Try 220. Reversing this pair will increase the overall LOD score of the map from -1033.71 to -1032.44. While this is not a statistically significant reduction, it may have an effect on the relative LOD scores of nearby locus pair reversals. A check on this - running fixed on the revised map - confirms the improvement in LOD score. flips2 on the revised map reveals no other significantly better rearrangements, though a good number of pair reversals are within a LOD score of 3.000 of this best map.


Please continue with the all & chrompic options, in
Part 3 - Testing & X-overs   Testing & X-overs


* I use the term a locus here to mean a polymorphism at a locus, detectable via a unique restriction endonuclease plus probe combination. Thus, a gene with two (or more) polymorphisms detected by different methods will count as two (or more) loci.



Comments? Questions? Accolades?
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Updated on Wednesday, 22 January, 2005
Copyright 1995-1996 by David W. Featherston. Updated for the MacOSX by Erik Bongcam-Rudloff