Theory of inbreeding

Author: Jane Nemecek, published: 15 Aug 2024

The original article was written in the spring of 2023, as a reaction to a series of breakdowns, where many fans were quick to link current events to the apparent presence of Mr. Prospector in pedigrees. As an initial reaction, I made an attempt to explain that presence of Mr. Prospector in "breakdown pedigrees" correlates with his presence in the entire thoroughbred population. But the very same article introduced a couple of new thoughts, including the essential question: how does inbreeding even occur?

Knowing from population data analyses that American breeders, in fact, do NOT like to inbreed, I made a little investigation in search of how inbreeding forms in pedigrees - and if really have a 100% control over it.

Is inbreeding our biggest problem?

Over the past few months, I've heard numerous people claiming that inbreeding is a major issue in American pedigrees. Personally, I'd vote for a different statement: Inbreeding is the most noticeable effects in pedigrees. Whether it's too "close" 2x3 figures, too many cases of inbreeding to a particular stallion, or inbreeding to "wrong sires," we notice.

All these assessments seem easy and straightforward, but I'd like to invite you to see a different perspective: the one of a pedigree analyst. Now you don't have a few random pedigrees to judge, but you need to asses a whole group - tens or even hundreds of pedigrees. And suddenly, unexpected problems arise:

• - pedigree generations themselves won't tell you much because the practical difference between 4x5 and 5x5 inbreeding is one huge ZERO;
• - to find out that most horses are inbred in the 5th generation and the fewest in the 2nd generation is not surprising at all;
• - as a bonus, you can learn that most horses have the same stallion in their pedigree twice, and some three times.

Suddenly, after a lot of work, you're stuck with findings that every pedigree enthusiast suspects. And the worst part is: you have absolutely no practical conclusion.

With some analytical experience, there's one more thing you can do outside of examining these conventional inbreeding traits. With this preset group of pedigrees, you can count stallions and make a ranking. And this operation - otherwise a very non-usual thing for fans - is where things start to get thrilling.

Most people seem to think that "frequency" of inbreeding to a particular stallion reflects simply his success as a sire. Or his (over)use; or just direct preferences of breeders to inbreed to some dominant stallion. When you look at the rankings of American sires in Table 1, according to in how many pedigrees in population they form inbreeding, you may even feel that these assumptions are justified.

At the first reading, these rankings seem utterly normal. Expectable. Maybe the numbers not so much but don't get overwhelmed by the gigantic figures at the first two rows: I explained their cause in an older article. For now, there's a far more important perspective hidden behind these numbers: a perspective vital for our understanding of inbreeding. Similar numbers of Mr. Prospector and Northern Dancer don't reflect the same situation.

In short, Mr. Prospector's sireline has 2-6 generations, so we see its full strength and maximum inbreeding "live" in pedigrees. And since the sireline is dominant and widespread, the strength is enormous, yes.

On the other hand, Northern Dancer's numbers are only residual: Northern Dancer appears up to the 9th generation in pedigrees, and most of his influence is already beyond the sixth generation (this is statistically verified). In other words, we don't see more inbreeding to Northern Dancer in pedigrees simply because he already moved over. Otherwise, he'd create far bigger numbers than Mr. Prospector: While half of the Graded runners are inbred to Mr. Prospector before the fifth generation, statistically, every runner is inbred to Northern Dancer in the sixth.

So, even though the rankings show a significant dominance of Mr. Prospector as an inbreeding sire, the real situation is completely reversed. And we just got the first taste that inbreeding is not a superficial and clear strategy at all. In fact, this technique requires an extremely sensitive judgement.

The following pair in the table is not in the same league as Mr.P and the Dancer, but is very close to each other. I'm sure most American fans would understand the difference in their performance without any lengthy explanation: Secretariat was a gifted damsire, and basically all his inbreeding is created by Storm Cat, A.P. Indy, and Gone West (sometimes Dehere). Seattle Slew's inbreeding influence is created mostly by A.P. Indy's tail-male lineage and complemented by various sons of Seattle Slew, most notably Capote and Avenue of Flags.

In other words, while Secretariat appears in inbreeding exclusively via his daughters, for Seattle Slew, it's only via his sons (and further tail-male descendants). You could hardly find another pair of perfectly opposite strategies which lead to statistically identical results.

Let's continue. Nijinsky could be a surprising presence so high in the inbreeding rankings. He's a bit forgotten name in modern pedigrees, and few people could specify his type of influence - if they even notice that he IS a massive influence in American pedigrees. In fact, Nijinsky is the most frequent descendant of Northern Dancer in American pedigrees - and would almost equal Storm Cat and Vice Regent combined.

However, Nijinsky was a second-crop son of Northern Dancer, and almost two-thirds of his influence are also beyond the five-generation pedigrees already. Tapit is inbred to him, but Tapit's sons and daughters move Nijinsky to the fifth generation, and the "inbreeding slot" they create for Nijinsky is not that big. A good part of Nijinsky's inbreeding is created by Scat Daddy, Carson City, and numerous other horses, mares and stallions alike. Nijinsky is probably the prime example of unintentional inbreeding: none of his influence is created by a tail-male lineage, and few of his sons are important elements in American pedigrees. One of the rare exceptions can be seen in the pedigree of Admission Office, but the influence on his paternal side is much more typical for Nijinsky.

Two great American colts were Nijinsky's contemporaries: Damascus and Buckpasser. Both have a similar type of inbreeding influence, based on some strong modern stallions combined with other pedigree elements. Buckpasser is a more exemplary case: Empire Maker, Super Saver, or sons of A.P. Indy reliably carry Buckpasser's blood on the top of pedigrees, and they meet Seeking the Gold, El Gran Senor, Woodman, or A.P. Indy on the bottom. The best modern successor of Damascus is equally famous: Medaglia d'Oro. A lot of work for both Damascus and Buckpasser is still done by Private Account, who was by Damascus out of a Buckpasser mare.

One thing worth pointing out here. Neither Teddy nor Tom Fool, as sirelines, play a significant role in modern pedigrees. It's barely 3% of bloodlines at the background of pedigrees, yet their descendants appear high in inbreeding rankings. As you can notice from the mentioned names, it's almost exclusively thanks to other bloodlines, modern ones: Mr. Prospector, Native Dancer, Northern Dancer, Nasrullah. The significant conclusion here is - inbreeding doesn't have to say almost anything about the concerned stallions and their own sirelines.

And then we have A.P. Indy, a 1989 colt, at the same level as old-timers Damascus and Buckpasser. As you might expect, most of his inbreeding is created by his tail-male descendants, positioned as both sires and damsires. Super Saver and Bodemeister can be seen in combination with A.P. Indy's tail-male line, and Justify's foals will carry A.P. Indy in the fifth generation. There's still one specific for A.P. Indy: despite the thick sireline formation, only one of his inbreeding cases is a direct linebreeding. Still, A.P. Indy vs. Buckpasser is another fine example of the old saying - when two do the same, it's not the same thing after all.

And for the record, the same is true for Hail to Reason, a colt born in the late 1950s - 40 years before A.P. Indy. He finds his way into pedigrees with both current stallions like Into Mischief and Distorted Humor, but his tail-male descendants are an important part of American pedigrees as well - whether sons of Roberto, or the Southern Halo - More Than Ready lineage. Hail to Reason has probably the most universal influence from all inbreeding stallions that you can find.

The last name I want to mention is In Reality. He was a chain link of the Man o'War sireline, and you'd probably expect his modern descendants, Tiznow and Honour and Glory, to play the biggest part in his inbreeding figures. Instead, half-brothers City Zip and Ghostzapper carry Relaunch as a damsire, and as you could notice before, Empire Maker was 3x4 inbred to In Reality. Valid Appeal does the rest of the work, while Tiznow is not present in In Reality's inbreeding at all.

Do you want to meet Tiznow as a part of inbreeding in pedigrees? You need to look for Seattle Slew: Seattle Song via Tiznow is involved in almost one-fifth of Seattle Slew's inbreeding figures.

I wanted to put you through this little exercise so that you can see for yourself how many factors influence inbreeding and its frequency. Let's summarize some conclusions from the previous text:

Possible inbreeding conclusions

1. Inbreeding is not proportional to the success of a stallion.

With all due respect, Seattle Slew was a better sire than Secretariat. So was Alydar, who has only a fragment of Secretariat's inbreeding incidence.

2. Inbreeding is not proportional to the success / incidence of a sireline.

This assumption is especially tempting to accept because the inbreeding rankings seem to correspond with the real situation: Mr. Prospector and Northern Dancer are leading sirelines, and A.P. Indy is very successful, too.

It's a gross simplification of the whole situation, and since we have statistical data, it turns out completely incorrect after a detailed examination:

First of all, Mr. Prospector is not a leading American sireline. It's been Northern Dancer for several generations already. More importantly, Mr. Prospector's sireline doesn't produce almost 50% of the thoroughbred population! It's only about one-third of current crops.

The same type of proportion works - or better say doesn't work - for Damascus and Buckpasser. Damascus barely survives with a rather accidental 0.3% of the population, and Tom Fool is not even alive anymore. Yet, you can still see their inbreeding in pedigrees of tens of Graded horses. On the other hand, A.P. Indy's population incidence is 15% - a far greater number than his inbreeding incidence, a mere 2%.

I'm talking about direct tail-male lineages here, but even when transposed to the total incidence of sirelines in pedigrees, any correlation between inbreeding and the success of a bloodline simply doesn't work. Table 2 summarizes all these aspects and you can take your time to analyze them after my brief explanation.

For that, I'll point out the most outrageous example: Hail to Reason has 1.8% of Graded runners inbred to him (Column 2), but his sireline covers 9.6% of all bloodlines in American graded pedigrees (Column 4). Mr. Prospector is not that far from Turn-To with 12.1% share of all bloodlines in pedigrees (Column 4 as well), but with the hypothetical same ratio as Hail to Reason, he should have had 2.3% of inbred runners (Column 2), not 46.7%!

There are other, smaller inconsistencies within the table, but we can clearly see that there's no direct proportion between the strentgh of a sireline and inbreeding incidence as an universal rule. This theory really doesn't work and it's a stunning conclusion in all its consequences.

3. Inbreeding does not have to be a primary intention.

Nijinsky simply says it all. And inbreeding to Damascus is a nice bonus but definitely not a goal when you breed a Tapit mare to a son of Medaglia d'Oro.

4. Inbreeding is not dependent on the stallion's own sireline.

Not just on its succes, but even on its own presence. We tend to be blind to this aspect in such an obvious case as Secretariat, but when talking about a rare lineage like Tom Fool, it becomes significant. Buckpasser's inbreeding influence in pedigrees is created by four other major bloodlines, including Mr. Prospector, Northern Dancer, and Nasrullah. And it works similarly for Hail to Reason via Into Mischief or In Reality via Empire Maker.

These last two points make inbreeding, in general, a very indirect and difficultly controlled technique.

Now we know what doesn't work. But what does, then? What does have a significant effect on the incidence of inbreeding in pedigrees?

5. One of the aspects directly influencing inbreeding is TIME.

And it's a very logical and natural aspect. Inbreeding can't occur too early when a stallion has one or two generations of tail-male descendants. And it can't occur too late either because once the sireline (let's use this model for simplification) slips to the sixth generation, it starts to lose its possible inbreeding incidences. Once 3x5 moves one generation further, it's not inbreeding anymore; it's just a fourth-generation incidence.

This aspect seems more damaging for sirelines than we think - and certainly distorts our perspective on inbreeding far more than we think.

Time explains why A.P. Indy has 15% tail-male incidence in the population but only 2% inbreeding - barely 16 cases. Except for Pulpit, A.P. Indy has mostly only grandsons at stud, who put A.P. Indy to the third generation of their foals: way too early for a full exploitation of inbreeding by breeders.

The second extreme is equally important. I mentioned Northern Dancer, where time moved the whole part of the gigantic sireline out of our reach in five-generation pedigrees. But, of course, this works also for particular sires. The legacy of stallions like Tom Fool, Native Dancer, Ribot, or Round Table is far further than five generations, so even though we can meet them in random pedigrees, their inbreeding incidence today is only a few residual names.

It goes without saying that all stallions and sirelines go through these three stages: too early for inbreeding - a major period of inbreeding in pedigrees with most progeny between the 3rd and 5th generation - too late for inbreeding. Since there are no observations and the author's own research covers only several years, I will safely "assume" that inbreeding works as a curve: it continually grows, culminates, and fades away.

If I failed to say it before when discussing various types of influence for particular stallions, now it's a good place to emphasize: any inbreeding picture we see is a momentarily one. It can't be of absolute value - it only represents "various places on the inbreeding curve" for particular stallions.

Still, the time aspect can't explain everything. Especially not Mr. Prospector.

Modern excessive inbreeding

As I described in the previous article, time definitely is a part of Mr. Prospector's inbreeding success: he is the only living, modern American sireline with top stallions in the right "inbreeding slot" between the third and fifth generations of pedigrees. A.P. Indy is too young, and Northern Dancer is getting too old. But Mr. Prospector is neither the strongest living sireline - nor the one most common in pedigrees. Why is he the leading stallion when it comes to inbreeding, then?

It doesn't make much sense, so let's take a look at what distinguishes Mr. Prospector and Northern Dancer - two stallions with truly excessive inbreeding incidence - from other sirelines. For those unaware, except for the second place in the American inbreeding statistics, Northern Dancer dominates the European inbreeding in a far more dramatic way than Mr. Prospector in America:

First, let's add two more pieces in this jigsaw puzzle. Seattle Slew was born only four years after Mr. Prospector, and the time aspect is not an issue here - nor is the success because Seattle Slew is a greatly influential stallion. Still he has only 5.7% of the population inbred to him, compared to roughly 40% of the previous two titans. In Reality is the fourth stallion with his own sireline, and although he was born between Northern Dancer and Mr. Prospector, he's even nowhere near the Seattle Slew with only 1% of the American population inbred to him.

Now, what's the crucial difference between Northern Dancer, Seattle Slew, and In Reality? We could call it a magnitude of success but, in my opinion, there's a more fitting term when we talk about pedigrees: the development of a sireline. Or even better - its expansion.

Inbreeding is not about a tail-male line in pedigrees - In Reality has one; nor about the individual success of a stallion, like Seattle Slew. Technically speaking, inbreeding can occur on 28 male positions of the 3rd, 4th, and 5th generation of pedigrees - and that's a lot of space. The more positions a stallion can cover with his progeny, the more inbreeding he can create.

Now, let's imagine a young stallion like A.P. Indy, whose inbreeding incidence covers mostly a tail-male lineage in pedigrees, or less commonly, a damsire line / 3rd sire line positions. Let's forget about the youth for a while: when you look at the attached pedigree diagram, you can see that this type of inbreeding (magenta) is a deadly disadvantage against a stallion who can, somehow, cover ALL male positions in pedigrees (pistachio).

How can you achieve the second type of inbreeding - the overall influence in pedigrees? Since success alone is not the key here - Seattle Slew and his descendants earned several leading sire titles - you need something else. Something that Mr. Prospector and Northern Dancer have and others quite don't.

This "something" can be a significantly branched sireline.

Is branching the key?

For a sireline, its success and strength go hand in hand. Northern Dancer could have never grown into such monstrous proportions if it wasn't the world-class bloodline. However, Northern Dancer and Mr. Prospector have something more than racing talent: the unusual ability to proliferate in multiple lineages.

This talent was not common in the thoroughbred history. Many lineages lacked it completely - you won't see much branching in Commando, Plaudit, or Man o'War. Blandford could branch his sireline through five sons; Hyperion had many good sons but some like Pensive, High Hat, or Hornbeam ended quickly. What we see nowadays in Northern Dancer and Mr. Prospector is not just unusual: it's extreme branching power, consisting of TENS of sons and subsequently numerous viable lineages.

When taking a look at their rivals in this comparison, the only branch that A.P. Indy has so far is Pulpit, and In Reality's American successors were Relaunch and Valid Appeal. The army of Mr. Prospector's sons - Fappiano, Conquistador Cielo, Gone West, Gulch, Forty Niner, or Smart Strike, to name just a few - were simply out of their league as inbreeding competitors.

These are very subtle details, but they can change the whole definition of the problem. The branching of a sireline and its presence in the "inbreeding slot" between the third and fifth generations are clearly developmental aspects. They are characteristics of a sireline, its development and its abilities, rather than of our breeding programs and measureable success at stud.

This change of definition should also shift our expectations. If we accept the hypothesis that excessive inbreeding is, in fact, related to the development of bloodlines, we must also retire from our attempts to address breeders to "stop inbreeding," especially to certain sires. Instead, we would need to focus on controlling bloodlines.

"Study case:" Northern Dancer in Europe

In my articles, I've mentioned many dramatic numbers describing the current European incidence of Northern Dancer. Let's sum them up quickly:

• - 78% of Group performers are (in a tail-male line) Northern Dancers;
• - 64% have another Northern Dancer stallion as a damsire;
• - Northern Dancer is a dominating sireline of the 1st to 4th sires already;
• - his overall incidence among ALL bloodlines in current Group pedigrees is almost 30% (the remaining 70% are created by over THIRTY other bloodlines).

This enormous incidence of Northern Dancer leads to an enormous amount of inbreeding as well:

• - 48% of European Group horses are born from direct linebreeding to Northern Dancer. To provide a direct comparison, linebreeding to Mr. Prospector is only 8% of American performers.
• - 42% of European runners have at least three Northern Dancer stallions from the first five sires, and 5% of horses carry four consequent lineages (three nicks) of Northern Dancer;
• - there's not a single runner without Northern Dancer in the pedigree;
• - in fact, the average incidence of Northern Dancer is way beyond a presence: it's five times per pedigree. (The maximal incidence is even far higher: twelve times.)

Northern Dancer is currently impossible to avoid in European pedigrees - and inbreeding to him is not about "wanting" it anymore.

Why am I mentioning all these statistical data? His European role aside, Northern Dancer provides an extremely valuable comparison. He's literally two steps further than the American inbreeding scene, and if people are smart enough, it's possible to see the consequences of the situation that North America isn't at yet.

What exactly defines this situation?

• - the absolute dominance of a tail-male lineage: 80%.
• - overall population incidence of a sireline in pedigrees SO HIGH that any random mating creates inbreeding.
• - in fact, any mating cumulates inbreeding!
• - population incidence of a sireline so high that this single bloodline creates 1/4 of pedigrees and sends us on a previously unseen and totally unpredictable way toward uniformity within the breed.

Table 4 summarizes the difference between European and American incidence of Northern Dancer, and you can see for yourself how a) local development of a bloodline, and b) its exploitation by breeders influences other parameters within the breed, inbreeding itself included. For a better description of a way how Northern Dancer's sireline is treated in Europe vs. North America, read an older article.

Especially notice that while the incidence of the Northern Dancer sireline among sires of European runners is "only" twice as high, its direct cumulation in pedigrees (the last three rows) is beyond any linear growth: it's totally out of control compared to North America.

What's a possible conclusion here?

With American bloodlines like In Reality and A.P. Indy, we've seen that breeders can't create enough inbreeding when they don't have enough stallions from the same sireline: members of the right generations to create inbreeding, and preferably, from multiple branches of the sireline, to cover as many positions in pedigrees as possible. As we've seen: one lineage really can't do.

And with Northern Dancer, we've learned that with too many stallions from the same bloodline, inbreeding is impossible to avoid. And possibly leads to dangerous effects for the entire population - or at least to effects we know nothing about yet.

The general conclusion could be that mass inbreeding is really not a matter of any particular stallions. It's also a matter of sons and their progeny, of daughters and their progeny, and of the whole bloodline and its branches. It's probably possible to say that inbreeding reflects, if anything, the overall influence of a stallion in the population, via all "channels" available.

If you need one last hint - one last subtle proof that inbreeding is not the critical aspect here - look at the modified Table 4a below this paragraph. This time, the table adds Mr. Prospector to the comparison with Northern Dancer, and as you can see, Mr. Prospector's enormous American inbreeding itself doesn't imply cumulation of his bloodline in pedigrees.

As undesired effect as it surely is, massive inbreeding is not yet any "danger" marker for the population. The magnitude of a sireline seems to be.

Controlling the excessive inbreeding

Let's suppose that this theory works. That excessive inbreeding, indeed, does depend on the excessive incidence of a bloodline in the population. What's the way to control it?

The answer suggests itself: we need to take care of bloodlines in pedigrees. To avoid one of them blowing out of proportion, we probably need the broadest and best-balanced scale of sirelines as possible. Preferably for several generations.

Let's be clear: that's what we don't have. Racing fans are watching the last stallions of several historic bloodlines fighting for survival, and many of us can't stay calm about the subject anymore. For Blandfords, Djebels, Hyperions - it's now or never, and Djebel doesn't look good. Man o'Wars and Commandoes have few last chances. Teddy and St. Simon still exist, but they seem beyond salvation already.

Still, in theory, we have no other chance than to support the variability of bloodlines, using old or modern ones.

Either way, it's not up to fans. Only one group of people in the breeding business can affect the scale of available bloodlines: stallion owners.

Breeders can prefer this or that stallion for their mare, but they can only breed to sires that are available. And a group of available sires is the ultimate definition of the scale of available bloodlines.

Now, all of us can do the 4th-grade math: $150K of the stud fee multiplied by 200 mares - who would trade it for a $5K stallion from a minor sireline, attracting 35 mares?

It's time to ask industry leaders HOW to do precisely this painful step. We need to breed to minor bloodlines, we need to give them a proper chance, and we need them alive. We need to have such stallions in rosters.

I know that calls for regulating business are unpopular and unwanted, but the business is destroying the breed. We saw Pleasantly Perfect (Ribot) and Super Saver (Native Dancer) leaving to Turkey; we saw four sons of Tiznow sold to South Korea. Probably the last Ribot (and St. Simon) in the world has no attention, and the last Teddy in the world, a Gr.1 sire, left 120 foals during his entire career. And we're clearly running out of time.

Thoroughbred breeding is business, but THE BREED IS NOT. Who is going to explain this to businessmen?