As I wrote this the eclipse was passing through the US and people were gathering outside across the nation to stare at the sun as day briefly turns to night. During the National Championship game (NCAA) later that night Charles Barkley highlighted the idea, that day turns to night every day and didn’t understand what all the excitement was about.
For many the eclipse excitement was simply the rarity of the occurrence, while others enjoyed the opportunity to wear funny glasses and see the edges of the sun. For me I’m amazed daylight persists when 95% of the sun is covered. The eclipse provided a unique opportunity to experience a highly improbable event, day and night at nearly the same time.
Amos Tversky and Daniel Kahneman were economists who famously illustrated the math behind multiple events or conditions occurring at the same time. This illustration is often called the Linda problem, also known as the conjunction fallacy[1]. Rather than use the original bank teller illustration we are going to consider a cow to highlight the challenge of two events happening at the same time. I’ll give you a scenario and then two statements to evaluate. Your challenge is to decide which is more probable.
D385 is an easy fleshing, commercial cow who calves early in the calving season, tends to her calf without being aggressive and has an ideal udder. She follows a bucket, leading the group to the corral and moves through the working alley with ease.
Which is more likely to be true?
- D385 is polled
- D385 is polled and raises one of the heaviest calves at weaning.
If my scenario follows the same pattern as the Linda problem of Tversky and Kahneman, most of you will select statement two as most likely. Given the “maternal” details I outlined about the D385 cow you are inclined to think she would have a big calf at weaning. Whether she is polled or not is a complete guess from the information given. Now for the math.
Let’s assume the odds of D385 raising a big calf at weaning are 80%. The odds she is polled are likely better than a coin flip so assume they too are 80%. With no additional information the odds statement 1 is true is 80%. The odds of statement 2 being correct rely on both statements being true (in conjunction) so we multiply the odds (80% x 80%) to discover the probability D385 produces a heavy calf at weaning and is polled is 64%.
Two events happening simultaneously are the combination of their odds. You can change the probabilities above in several ways, but the single condition will be more likely than the combined. For another example, change the condition “polled” to “horned” in both statements and decrease the horned probability to 10% and the odds D835 is horned are still greater than horned and raising a big calf at weaning (8%).
This helps explain why elite genetics are rare. Animals who excel in multiple traits are challenged by conjunction, where each trait you add to the scenario lowers the odds the animal will excel in all selected traits.
Genetic progress by breeds and seedstock breeders has helped improve our odds of making improvements in multiple traits by raising the average in specific traits. The incremental changes across the commercial beef industry such as increased calving ease, fewer horns, increased weaning weight and carcass traits improvement enables breeders make greater changes to other traits.
The odds are improved by either raising the average toward the goal or quantifying the trait, so we know it’s true value (100% probability).
There are several other factors such as genetic variation, heritability, and selection intensity that will impact the ability to make genetic progress. Many of us were first exposed to genetics using the color of pea flowers, because the example was simple and there was only one trait. Unfortunately, few traits are simply inherited and very few herds have only one trait they want to make progress in.
As you evaluate fall-born replacement prospects or spring-born heifer calves this summer, consider the probability the following is true: her dam calved early, her dam is an above average cow I want to keep heifers out of, and that heifer calf will be an above average cow herself.
There are heifers with traits you are 100% certain you don’t want to retain, those single traits you can quantify for your operation or management. After culling those 0% probability females, consider using the genomic selection tools available to improve your odds by objectively quantifying heifer’s genetic potential.
[1] https://en.wikipedia.org/wiki/Conjunction_fallacy
