Some horses are fast, and some horses are Secretariat. After the great horse's death an autopsy revealed that his heart was about three times as big as it should have been, certainly a prescription for early mortality. The greatest racer of them all seems likely to have been a biological freak, where some developmental or genetic quirk allowed him to pound away with a macro-heart. None of Secretariat's offspring replicated his magnificence. This makes sense, a classic case of regression to the mean. If one assumes that Secretariat's massive but healthy heart was the byproduct of an exceedingly rare combination of beneficial genes, then sexual reproduction will likely break apart such favorable variations.

But there could be other reasons that Secretariat's offsprings weren't quite what he was, circulatory physiology aside. A new study has just come out which concludes that mitochondrial genetics might play a crucial role in the respiratory performance of a horse.

Importantly, we have observed that there is also independent and extensive functional mitochondrial gene variation in the current thoroughbred racehorse population and that significant associations exist between mtDNA haplotype, as defined by functional genes, and aspects of racing performance.

Mitochondria are of course only passed through the female line, so none of Secretariat's offspring would have had his particular respiratory engine. You can read the full paper on the site of the company that is sponsoring this research. I can't help but wonder if some Arab sheikh knew this all along....