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Analysing pedigrees

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  • Registered Users Posts: 2,092 ✭✭✭The Tetrarch


    In Jan/Feb 2017 I compared the previous pedigree analysis program results to horse ratings, and that is where this is heading.
    The early comparisons of the inbreeding counts to ratings are disappointing.

    The inbreeding counts are from generation 1 to generation 10
    i.e. an inbreeding in the 4th generation of both the sire and dam (4x4) and an inbreeding in the 10th generation (or any other generation) were both counted as one.
    Obviously an inbreeding group in the 4th generation should have more influence on the foal (and on a rating) than an inbreeding group in the 10th generation.
    My analysis in Jan/Feb 2017 was on six generation pedigrees, where the majority of inbreeding was in the 4th, 5th, 6th generations, and I did not feel it necessary to give weights to different generations.
    That 2017 program proved that ratings varied with the type of inbreeding and the inbreeding counts.

    H E Keylock in The Mating of Thoroughbred Horses (1942, 95 pages) suggested that the influence of ancestors on a foal is 1/2+1/4+1/8+1/16+1/32+1/64+1/128 ... , a series that approaches 1, with the two parents contributing 50%, the four grandparents 25%, the eight great-grandparents 12.5% and so on. This would have a parent four times more influential than a grandparent (50%/2 v 25%/4).

    Other books prefer 0.7 i.e. two duplicated horses in the 4th generation (2x1) are about as influential as three in the 5th generation (3x.7).

    Keylock quotes J B Robertson who agreed that the above formula (Galton's law) was true as a general statement (late ancestors have greater influence than distant ones), but is/could be untrue where characteristics are transmitted independently and show no tendency to blend (an example is coat colour).

    My next programming step is to copy all the work to new directories, and make changes there.
    I will keep the work done year to date as the extraction of inbreeding groups is sound.

    One feature I added since 2017 was a change to the analysis of a sire duplication group that produce a son and daughter (s_mf = sire producing a male and female).
    I split s_mf into s_mf and s_fm.
    The first is a sire producing a son in the sire pedigree of the foal, and a daughter in the dam side.
    The second is a sire producing a daughter in the sire pedigree of the foal, and a son in the dam side.
    Early numbers indicate that s_mf produces a higher rating than s_fm (but that is on small data).
    The reason might be that s_mf is a duplication from the sire side of the pedigree of a major sire (his son) on the sire line or broodmare sire of a top sire, with a daughter of that sire in the dam of the foal.
    s_fm could be duplication from the sire side of the pedigree of a minor sire (his daughter) on a dam line of the sire or on the dam line of the broodmare sire, or on the dam line, with a son of that minor sire in the dam of the foal.

    It would be nice if, instead of a "son and daughter of an unnamed sire", I could gather the names of the duplicated sires.
    I notice that only a small number of sires occur frequently as duplications in pedigrees.

    Time for a proverb and a quote:
    "Everything is learned by comparison."
    "I did not progress until I learned to reflect."


  • Registered Users Posts: 2,092 ✭✭✭The Tetrarch


    Since my last post three weeks ago I have been working on tidying data.
    The ratings file with 159,000+ horses needed to be reviewed.

    From Jan/Feb 2017 until now, August 2020, the names in my pedigree database have changed a little
    e.g. the sire Warning (1985) had a name change to Warning (14) because I entered another horse into the pedigree database, also Warning (1985).
    You can not have two horses with the same name.
    These were changed to Warning (14) [by Known Fact out of Slightly Dangerous] and Warning (2) [by Albaro out of Chilton Blue].
    The numbers in brackets (14) and (2) are the Bruce Lowe family numbers, useful in differentiating when the name and year of birth are identical.
    These name changes in the pedigree database, perhaps 3% of the 159,000 rated horses, had to be updated in the ratings database.

    ...........................................................................................................

    Back to the new pedigree analysis program and how to fix the poor results.

    In the original Jan/Feb 2017 pedigree program I did not differentiate between inbreeding duplications in different generations.
    For example, an inbreeding group of a son and daughter of a duplicated sire, the sire in the 4th and 5th generations, 4x5, would be counted as 1.
    The same for an inbreeding group of a son and daughter of a duplicated sire, the sire in the 6th and 6th generations, 6x6, would be counted as 1.
    Obviously, the closer inbreeding 4x5 probably has more influence on the foal than the more distant 6x6.

    With almost all the inbreeding in the original Jan/Feb 2017 six generation pedigree program in the 4th, 5th, 6th generations the question of giving greater weight to inbreeding in the 4th generation over that in the 5th and 6th generations was ignored. The results were still informative.

    But with the unfinished 2020 ten generation pedigree program it is obvious that inbreeding in the 4th generation and inbreeding in the 10th generation should have vastly different influences.
    In my first results a few weeks ago I ignored this, giving every generation equal value i.e. a weight of 1.0 (see below)**

    Using my test case of Galileo (1998) I am experimenting.
    Galileo has 58 inbreeding groups in his first 10 generations. These have 199 duplicated horses.
    4th gen (1); 5th gen (3); 6th gen (6); 7th gen (22); 8th gen (34); 9th gen (56); 10th gen (77) = 199

    I know many do not agree with inbreeding analysis. 100% of the horse DNA is in the horse.
    Others say you need look no further than the sire and dam.
    I think you must agree that the DNA in the horse is also in the sire and dam. We do not know what DNA the horse received.
    The same for the grandparents. The DNA in the horse is also found in the grandparents.
    And the same for the great-grandparents, and earlier generations.
    The DNA in the horse came from ancestors. It did not come from elsewhere.

    Giving different weights to inbreeding in different generations for Galileo:

    Weight given / generation / percentage in that generation
    Weight 1.0**: 4th (0.5%); 5th (1.5%); 6th (3.0%); 7th (11.1%); 8th (17.1%); 9th (28.1%); 10th (38.7%)
    This was what was applied to Galileo's pedigree weeks ago.
    You can see far too much influence was assumed for the earlier generations (8th, 9th, 10th).

    Weight 0.3**: 4th (28.6%); 5th (25.7%); 6th (15.4%); 7th (17.0%); 8th (7.9%); 9th (3.9%); 10th (1.6%)
    Weight .05**: 4th (8.5%); 5th (12.7%); 6th (12.7%); 7th (23.2%); 8th (18.0%); 9th (14.8%); 10th (10.2%)
    Weight 0.7**: 4th (2.5%); 5th (5.2%); 6th (7.3%); 7th (18.8%); 8th (20.3%); 9th (23.4%); 10th (22.5%)
    Weight 2.0**: 4th (0.0%); 5th (0.1%); 6th (0.3%); 7th (2.4%); 8th (7.3%); 9th (24.0%); 10th (66.0%)

    Weight 0.3 - with the 4th generation given a value of 1.0, the 5th generation gets 0.3, the 6th generation 0.09. This gives far too much weight to the closer generations.
    In this case, the one duplicated horse in the 4th generation is given a value of 28.6%. 77 duplicated horses in the 10th generation get 1.6% for all of them. Nonsense.
    Weight 0.5 - this is the weighting I will use for the moment.
    It assumes influence is halved each generation i.e. a grandparent has twice the influence of a great-grandparent.
    Weight 0.7 - this is the weighting recommended in a pedigree analysis book I like. I think it gives too much influence to earlier (8th, 9th, 10th) generations.
    Weight 2.0 - this gives a nonsense valuation, with two thirds of the influence in Galileo's pedigree attributed to the duplications in the 10th generation of his pedigree. I did this calculation to show that a Weight under 1.0 must be correct.

    There have been many theories about thoroughbred pedigrees.
    My stance is to let the numbers tell me what analysis works.

    From "The Mating of Thoroughbred Horses" (1942) by H E Keylock
    "The following conclusions are arrived at with regards to the inheritance of characteristics
    1. Good performers on the race course cannot be selected by their conformation or other visible characteristics.
    2. Varying characteristics do not follow the female or male line of descent, but follow an unpredictable course.
    3. Neither the sire nor the dam can convey any characteristics to their progeny and the progeny inherits all the characteristics from its four grandparents.
    4. Some animals usually pass on the necessary winning characteristics and some animals usually do not pass on these characteristics.
    If they do pass them on then these characteristics are not inherited from ancestors in the 1st, 3rd, 5th, and 7th generations, but from ancestors in the 2nd, 4th, 6th and 8th generations."


    I agree with point 1. and 2.
    H E Keylock suggested that influence in pedigrees by generation is (1/2)+(1/4)+(1/8)+(1/16)+(1/32)+(1/64) .....
    That gives each parent 1/4 influence, each grandparent 1/16 influence, each great-grandparent 1/64 influence (Weight 0.25).


  • Registered Users Posts: 2,702 ✭✭✭tryfix


    Since my last post three weeks ago I have been working on tidying data.
    The ratings file with 159,000+ horses needed to be reviewed.

    From Jan/Feb 2017 until now, August 2020, the names in my pedigree database have changed a little
    e.g. the sire Warning (1985) had a name change to Warning (14) because I entered another horse into the pedigree database, also Warning (1985).
    You can not have two horses with the same name.
    These were changed to Warning (14) [by Known Fact out of Slightly Dangerous] and Warning (2) [by Albaro out of Chilton Blue].
    The numbers in brackets (14) and (2) are the Bruce Lowe family numbers, useful in differentiating when the name and year of birth are identical.
    These name changes in the pedigree database, perhaps 3% of the 159,000 rated horses, had to be updated in the ratings database.

    ...........................................................................................................

    Back to the new pedigree analysis program and how to fix the poor results.

    In the original Jan/Feb 2017 pedigree program I did not differentiate between inbreeding duplications in different generations.
    For example, an inbreeding group of a son and daughter of a duplicated sire, the sire in the 4th and 5th generations, 4x5, would be counted as 1.
    The same for an inbreeding group of a son and daughter of a duplicated sire, the sire in the 6th and 6th generations, 6x6, would be counted as 1.
    Obviously, the closer inbreeding 4x5 probably has more influence on the foal than the more distant 6x6.

    With almost all the inbreeding in the original Jan/Feb 2017 six generation pedigree program in the 4th, 5th, 6th generations the question of giving greater weight to inbreeding in the 4th generation over that in the 5th and 6th generations was ignored. The results were still informative.

    But with the unfinished 2020 ten generation pedigree program it is obvious that inbreeding in the 4th generation and inbreeding in the 10th generation should have vastly different influences.
    In my first results a few weeks ago I ignored this, giving every generation equal value i.e. a weight of 1.0 (see below)**

    Using my test case of Galileo (1998) I am experimenting.
    Galileo has 58 inbreeding groups in his first 10 generations. These have 199 duplicated horses.
    4th gen (1); 5th gen (3); 6th gen (6); 7th gen (22); 8th gen (34); 9th gen (56); 10th gen (77) = 199

    I know many do not agree with inbreeding analysis. 100% of the horse DNA is in the horse.
    Others say you need look no further than the sire and dam.
    I think you must agree that the DNA in the horse is also in the sire and dam. We do not know what DNA the horse received.
    The same for the grandparents. The DNA in the horse is also found in the grandparents.
    And the same for the great-grandparents, and earlier generations.
    The DNA in the horse came from ancestors. It did not come from elsewhere.

    Giving different weights to inbreeding in different generations for Galileo:

    Weight given / generation / percentage in that generation
    Weight 1.0**: 4th (0.5%); 5th (1.5%); 6th (3.0%); 7th (11.1%); 8th (17.1%); 9th (28.1%); 10th (38.7%)
    This was what was applied to Galileo's pedigree weeks ago.
    You can see far too much influence was assumed for the earlier generations (8th, 9th, 10th).

    Weight 0.3**: 4th (28.6%); 5th (25.7%); 6th (15.4%); 7th (17.0%); 8th (7.9%); 9th (3.9%); 10th (1.6%)
    Weight .05**: 4th (8.5%); 5th (12.7%); 6th (12.7%); 7th (23.2%); 8th (18.0%); 9th (14.8%); 10th (10.2%)
    Weight 0.7**: 4th (2.5%); 5th (5.2%); 6th (7.3%); 7th (18.8%); 8th (20.3%); 9th (23.4%); 10th (22.5%)
    Weight 2.0**: 4th (0.0%); 5th (0.1%); 6th (0.3%); 7th (2.4%); 8th (7.3%); 9th (24.0%); 10th (66.0%)

    Weight 0.3 - with the 4th generation given a value of 1.0, the 5th generation gets 0.3, the 6th generation 0.09. This gives far too much weight to the closer generations.
    In this case, the one duplicated horse in the 4th generation is given a value of 28.6%. 77 duplicated horses in the 10th generation get 1.6% for all of them. Nonsense.
    Weight 0.5 - this is the weighting I will use for the moment.
    It assumes influence is halved each generation i.e. a grandparent has twice the influence of a great-grandparent.
    Weight 0.7 - this is the weighting recommended in a pedigree analysis book I like. I think it gives too much influence to earlier (8th, 9th, 10th) generations.
    Weight 2.0 - this gives a nonsense valuation, with two thirds of the influence in Galileo's pedigree attributed to the duplications in the 10th generation of his pedigree. I did this calculation to show that a Weight under 1.0 must be correct.

    There have been many theories about thoroughbred pedigrees.
    My stance is to let the numbers tell me what analysis works.

    From "The Mating of Thoroughbred Horses" (1942) by H E Keylock
    "The following conclusions are arrived at with regards to the inheritance of characteristics
    1. Good performers on the race course cannot be selected by their conformation or other visible characteristics.
    2. Varying characteristics do not follow the female or male line of descent, but follow an unpredictable course.
    3. Neither the sire nor the dam can convey any characteristics to their progeny and the progeny inherits all the characteristics from its four grandparents.
    4. Some animals usually pass on the necessary winning characteristics and some animals usually do not pass on these characteristics.
    If they do pass them on then these characteristics are not inherited from ancestors in the 1st, 3rd, 5th, and 7th generations, but from ancestors in the 2nd, 4th, 6th and 8th generations."


    I agree with point 1. and 2.
    H E Keylock suggested that influence in pedigrees by generation is (1/2)+(1/4)+(1/8)+(1/16)+(1/32)+(1/64) .....
    That gives each parent 1/4 influence, each grandparent 1/16 influence, each great-grandparent 1/64 influence (Weight 0.25).



    I'm interested in the lack of inbreeding in the first few generations of Galileo's pedigree.

    In the first 5 generations the only inbreeding is via Native Dancer in his 4th and 5th generations. Galileo's half brother Sea The Stars ( Cape Cross) has no inbreeding in the first 5 generations at all. His dam Urban Sea has no inbreeding until back in the 5th generation where she has loads, Nasrullah twice on her Sire side, Alchemist twice on her dam side and Prince Rose once on each side.

    If you take the view that repetition proves something, ye can look at the Galileo x You'resothrilling cross that has produced a steady stream of G1 winners and G1 placed horse. Northern Dancer appears in the 3rd ( Sire) and 4th ( dam) generations as well as Hail To Reason on both sides in the 5th generation of that perfect niche cross.

    How do you apportion inbreeding influence as it dilutes through the generations? Edit I see.


  • Registered Users Posts: 2,092 ✭✭✭The Tetrarch


    tryfix wrote: »
    I'm interested in the lack of inbreeding in the first few generations of Galileo's pedigree.
    A few minutes ago I did a quick analysis of Sea The Stars. There are similarities with Galileo.
    They are from the same dam, but different sires.
    I am interested in how the two sires, Cape Cross and Sadler's Wells, match with Urban Sea. The matching will be different.

    Sea The Stars has 55 duplication groups (224 horses) in 10 generations. Galileo has 58 groups (199 horses).
    The similarity is that few of the early inbreeding groups of either i.e. those close to the horse, have the usual two sons (or more) of a duplicated sire found in the majority of modern pedigrees.

    Sea The Stars:.......... f.m; m.mf; f.f; f.f; m.m; m.f; ff.f; mmf.f; f.m; mmmff.m; mfff.fff; f.ff; m.f; mmmmmmmmmmmmmmff.m. (bold are from duplicated dams)
    Galileo:.................... f.m; mm.f; mf.ff; mf.m; mf.ff; m.f; mmmf.m; f.m; f.f; f.f; mff.mfff; f.mmf; f.f

    I took two colts rated 25 and 14 at random.
    Random Colt 1: ........... m.m; m.mf; f.f; m.m; m.fff; m.m; f.f; m.m; f.mfff; m.mmmmmmmmmmfffff; m.mmfff
    Random Colt 2: ........... f.f; m.mm; f.m; m.mm; f.f; f.ff; f.mmmm; m.mmmmmf; f.mff; f.f; ff.f; m.mmmmmmmmm; f.mmmfffff

    The thing I expect and notice is the lack of duplicated sons of sires close up in Sea the Stars and Galileo.
    In the poor horses there are (1) m.m x 4 (2) m.mm x 2 close up.


  • Registered Users Posts: 2,092 ✭✭✭The Tetrarch


    The yearling sales are starting, and will be run over the next few weeks.
    I downloaded Excel files from Tattersalls and Goffs, and am working on extending the pedigrees of 2,969 yearlings to six generations.
    I will probably finish the pedigree extensions today.

    My plan is to analyse those yearlings with
    (1) the pedigree program I wrote in Jan/Feb 2017
    (2) the pedigree program (unfinished) I have been writing since March 2020.

    (1) will probably be done today.
    (2) will be done in the next few months.

    I will rank the yearlings by ability based on the pedigree analysis.
    The yearlings will run over the next few years, and I will use their ratings and earnings to compare my analysis with the results.

    Harold Hampton analysed yearling sales catalogues in New Zealand in the mid-1950s, writing out 1,400 six generation pedigrees by hand, and analysing them.
    Hampton's results were good, identifying most of the quality runners. He used his failures to refine his analysis.


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  • Registered Users Posts: 2,092 ✭✭✭The Tetrarch


    This morning I got out a book on statistics and tried to get a bit of sense out of my ratings file.
    I copied into Excel 69,215 horses that have a rating, and also have a sire rating, and a dam rating.

    Average runner rating: 77.10 (median 76.00); Average sire rating: 122.54 (median 126.00); Average dam rating: 83.42 (median 84.00)
    The correlation coefficients are: Runner with dam 0.271; Runner with sire 0.131
    The correlation coefficient is a number from +1 to -1. +1 would be a perfect relationship between two numbers. As one number increases the other number increases. -1 one number decreases as the other increases.

    You might think sending a dam rated 83 to a sire rated 122 would give a runner rated possibly (83+122)/2 = 102. That does not happen.
    What might surprise people is that the runner average of 77 is well below their dam average of 83.

    Surely the top sires do better than that? I had a look.

    Sire ..................rated runners ..........runner average ........ dam average
    Sadler's Wells.............888........................ 89.34.................100.91
    Rainbow Quest...........403........................ 84.76 ................100.55
    Darshaan..................264 ........................88.62 ..................94.78
    Danehill....................424 ........................91.81...................91.72
    Barathea...................397.........................76.92..................87.74
    Cadeaux Genereux.....435.........................80.93..................88.09
    Cape Cross................502.........................81.79..................87.38

    On a larger group of 159,232 rated horses the average rating is 78.95.
    One standard deviation of that group is 23.64, and 65.67% of horses are within+/- 1 SD (from 55.31 to 102.59).

    One conclusion is that commonly regarded good sires are not exceptional.
    They get highly rated mares to star their careers at stud.
    Afterwards they attract quality mares through a combination of high fees, and selectivity by the sire owner accepting only quality mares.

    How many runners were rated better than their dam in the 69,215 sample?
    Better 26,594 or 38.4%; better by 10+ ratings points 24.8%; better by 20+ rating points 14.80%; better by 30+ rating points 8.28%

    How many runners were rated better than their sire in the 69,215 sample?
    Only 67,871 sires were rated, probably because the missing ratings were from sires who ran in the USA or Australia.
    613 runners (0.90%) were rated better than their sire.


  • Registered Users Posts: 2,092 ✭✭✭The Tetrarch


    About half an hour ago I started the first real run of my new pedigree analysis program.
    It took seven months in 2020 to get this far.
    Often a program runs for a while and stops when it hits an problem. Then a fix is made, and the process starts again.
    Fingers crossed. It is still running.

    A big difficulty is trying to reduce a 10 generation pedigree to one number (or a few numbers) to indicate the quality of the pedigree.
    The load file is 159,208 horses with ratings.
    The program picks a horse, analyses its pedigree, gives the horse numbers, and outputs those into a 159,208 horses results file. Then it steps down to the next horse and repeats.
    At about 0.5 seconds each horse, it will take 22.1 hours to run.
    It is running on my 2016 PC, but in 2020 I bought two more PCs that should be a lot faster.
    I plan to split the load file in three and run the program on three PCs at the same time.
    If I compare all the 3,000+ mares on offer at the breeding stock sales in IRE, GB, FR in Nov/Dec against 500+ stallions that gives about 1,500,000 "foals" those mares could produce.
    To analyse 1.5 million test-mating foals would take 278 hours (11.5 days) on the 2016 PC.
    I will probably use a cut down version of the program to pre-analyse the large numbers, and then run the full program on the best from the pre-analysis.

    It will soon be time to get out the statistics books, and write a program to produce a statistics file from the results file.
    If the results are not good, it will be back to reassessing and probably dismantling parts of the program.


  • Registered Users Posts: 2,092 ✭✭✭The Tetrarch


    My new inbreeding analysis program is running.
    The first time I ran it if stopped 23 times when it hit an incomplete pedigree.
    Most of those incomplete pedigree were for horses born between 1900 and 1910
    It was not surprising that preparing ten generation pedigree for those found a few gaps.
    Ten generations back from 1910 is around 1801 (10 x 10.9 years = 109 years).
    I would prefer that the program stops when it hits a snag. I can check the problem.

    I used my own number for each generation: 16 for the horse (unused); 8 for each parent; 4 for each grandparent; 2 for great-grandparents, and so on.

    Using the last horse analysed, ZYZXX (2003) as an example
    (Yes, that is a real horse name (AUS) 35 starts, 4 wins)

    Buckpasser is the first* sire duplicated in his pedigree, one in the 4th generation, once in the 5th generation.
    *I use the date of birth of the duplicate sire to determine which is first (01dup group).
    Buckpasser (1963) is group 01dup and Northern Dancer (1961) is 02dup, even though the Northern dancer duplications are closer to the foal/runner.
    There is an obscure (but necessary) reason for doing this.

    01dup Buckpasser 4x5 ... values 1.0000+0.5000 = 1.5000
    02dup Northern Dancer 3x4 ... values 2.0000+1.0000 = 3.0000
    03dup Native Dancer 5x5.6 ... values 0.50+0.50+.025 = 1.2500
    04dup Alibhai 5x7 ... values 0.500+.0125 = 0.625
    05dup War Admiral 7x8.8.9 ... values 0.125+.0625+0.625+0.03125

    All the 10 generation inbreeding of ZYZXX totals 11.984375

    .................................................................................................................

    Review
    At this stage it is difficult to separate the wood from the trees.
    What inbreeding is important? What inbreeding is a negative?

    Galileo (1998) has a total inbreeding of 11.828125 (the summation of 58 duplication groups)
    Zyzxx (2003) has a total inbreeding of 11.984375 (the summation of 46 duplication groups)
    Can we conclude from this that inbreeding is not a guide to class?
    If we look at the type of inbreeding closely we can see differences.

    Galileo (1998) has inbreeding groups that produce a son(s) and daughter(s) (mf) of 5.656250
    Zyzxx (2003) has inbreeding groups that produce a son(s) and daughter(s) (mf) of 3.187500

    Galileo (1998) has inbreeding groups that produce only sons (mm) of 0.343750
    Zyzxx (2003) has inbreeding groups that produce that produce only sons (mm) of 3.812500

    Galileo (1998) has inbreeding groups that produce only daughters (ff) of 1.796875
    Zyzxx (2003) has inbreeding groups that produce that produce only daughters (ff) of 3.062500

    Galileo (1998) has inbreeding groups that have extra sons 1.750000, and groups that have extra daughters 2.281250
    Zyzxx (2003) has inbreeding groups that have extra sons 0.968750, and groups that have extra daughters 0.953125
    (an extra daughter would be a duplicated sire, e.g. Hyperion, that appears three times in the pedigree (a group).
    That group is one son and two daughters (mxmf)- an male/female duplication group (one son; one daughter) and with one extra daughter.

    ..................................................................................................................

    The most inbred horse the program found was Akazie (GER) (1938) (f).
    Akazie gets a 16.000000 from the program.
    Her sire Alchimist is by Herold out of Aversion (by Nuage out of Antwort)
    Her dam Artischocke is by Herold out of Arachne (by Nuage out of Antwort)
    Herold's dam Hornisse is by the sire Ard Patrick.
    Antwort is by the sire Ard Patrick.

    Another way of stating this pedigree is that the fourgrandparents of the sire are the same as the four grandparents of the dam.

    ..................................................................................................................

    I am thinking of changing my valuation system to Wright's Coefficient
    https://en.wikipedia.org/wiki/Coefficient_of_relationship


  • Registered Users Posts: 2,092 ✭✭✭The Tetrarch


    High numbers my program (and Wright's Coefficient) calculate from close inbreeding in the 1st, 2nd, 3rd generations are not desireable.

    In Thoroughbred Breeding, Notes and Comments (1987) by Mordaunt Milner page 103
    "Dr Q P Campbell, lecturing at the Animal and dairy research Institute in Bloemfontein, stated that 'Generally speaking, performance in a horse starts to deteriorate when inbreeding exceeds 3-8%*'. Dr Campbell suggests that for performance to be affected it would require an inbreeding as close as two free generations**. If it requires inbreeding as close as that to produce an adverse effect, it is logical that inbreeding should be as close as that before it can be beneficial."

    * does he mean > 3% ?
    ** two free generations is 3x3 or 1/32 (or 3.125%) Wright's Coefficient


  • Registered Users Posts: 2,092 ✭✭✭The Tetrarch


    Wright's Coefficient

    For example, is there is a 5x5 inbreeding to Nureyev as in the example below the calculation is
    100 x (1/2 ^((5-1)+(5-1)+1))% ....
    100 x (0.5 to the power of 9)% ....
    100 x 0.001953125% ....
    0.1953%

    This is the calculation for the planned mating (and hopefully a foal) of my 3yo filly Ahlam with a stallion in 2021

    Stallion*-Ahlam
    Inbreedings are
    1) Sadler's Wells 4x6 = 1/512 x 100 = 0.20%
    2) Fairy King 4x6 = 1/512 x 100 = 0.20% (I am treating Sadler's Wells and Fairy King as the same horse as they are full siblings / have the same parents)
    3) Nureyev 5x5 = 1/512 x 100 = 0.20% (5x5 is the same strength as 4x6)
    4) Millieme 4x5 = 1/256 x 100 = 0.39% (I am treating Millieme and Shirley Heights as the same horse as they are full siblings / have the same parents)
    5) Shirley Heights 6x5 = 1/1024 x 100 = 0.10%

    These total up to 1.07%
    (0.20+0.20+0.20+0.39+0.10=1.07%)


    Taffeeite

    1) Rainbow Quest 4x4 = 1/128 x 100 = 0.78%
    2) Danzig 4x5 = 1/256 x 100 = 0.39%
    3) Ribot 6x6 = 1/2048 x 100 = 0.05%
    4) Flower Bowl 6x6 = 1/2048 x 100 = 0.05%
    5) Buckpasser 6x6 = 1/2048 x 100 = 0.05%
    6) Sir Ivor 6x6 = 1/2048 x 100 = 0.05%
    7) Best In Show 6x6 = 1/2048 x 100 = 0.05%
    8) Northern Dancer 6x5 = 1/1024 x 100 = 0.10%
    9) Northern Dancer 6x5 = 1/1024 x 100 = 0.10%

    These total up to 1.61%

    Note: Taaffeite has Northern Dancer twice in her 6th generation on the sire side, and once in the 5th generation of her dam.
    These are calculated as two inbreedings, 6x5 + 6x5. (8) and (9)

    It is suggested that inbreeding is slightly greater than the above figures if you then compare inbreeding groups e.g. compare Buckpasser to Sir Ivor. I ignored that.


    Inbreeding calculation
    1x1 = 50% [1/2]
    1x2, 2x2 = 25% [1/4]
    2x2 = 12.5% [1/8]
    2x3, 3x2 = 6.25% [1/16]
    3x3, 2x4, 4x2 = 3.125% [1/32]
    3x4, 4x3 = 1.5625% [1/64]
    4x4, 2x6, 6x2= 0.78125% [1/128]
    4x5, 5x4. 3x6, 6x3 = 0.390625% [1/256]
    5x5, 4x6, 6x4 = 0.1953125% [1/512]
    5x6, 6x5 = 0.09765625% [1/1024]
    6x6 = 0.048828125% [1/2048]

    Any inbreeding that adds up to the same number has the same percentage
    e.g. 6x6, 5x7, 7x5, 4x6, 8x4 all give the same 0.048828125%

    You can see that if your horse contains one 3x3 inbreeding that is 3.125%, and you are into the territory that is not recommended i.e. 3% inbreeding or more.
    If there is another inbreeding to the 3x3 you add that to the 3.125% from the 3x3.

    Enable, recently retired, is 3x2 Sadler's Wells and 6x6 Nasrullah: 6.25%+0.05% = 6.30%.
    I mentioned before that close inbreeding like this occasionally works if the horse (in this case a filly) is the opposite sex to the close inbreeding (Sadler's Wells, a male). In this case that is true.
    Another is Fatherland (1990) (a colt, rated 115). He is inbred 3x1 to the full sibling sisters Special and Lisadell (both by Forli out of Thong), a 12.5% inbreeding. The sex of the inbreeding, females.
    (you could say the inbreeding here is two inbreedings, 4x2 to Forli (m), and 4x2 to Thong (f).)
    Interesting to me, is that the two males in the Enable inbreeding are on the sire line of her sire, and on the sire line of her dam.
    In Fatherland the female inbreeding is on his two dam lines, the dam line of his sire, and the dam line of his dam.


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