# The Sex Ratio Riddle

Predetermining the sex of calves has been one of the most intriguing and sought-after technologies in the cattle industry for decades. Most of the attention

Predetermining the sex of calves has been one of the most intriguing and sought-after technologies in the cattle industry for decades. Most of the attention has been in “sorting” sperm into groups bearing X and Y chromosomes in order to facilitate the exclusive production of either male or female calves.

Such sexed sperm is commercially available, but the only procedure that's both accurate (about 90%) and practical uses an expensive device called a flow cytometer sorter. This equipment separates X from Y chromosome-bearing sperm. X-sperm produce females and Y-sperm produce males.

Although the procedure usually provides samples in which about 90% of sperm is the desired type on a statistical basis, what does this mean for calves born in a given herd?

### The natural way

The sex ratio of calves at birth is the number of males divided by the number of females. This average is 1.06 males per every female born in large populations of cattle. For simplicity, let's assume the true sex ratio is exactly 1.00, or 1 male born/female (50% males, 50% females). This doesn't mean, however, that in any given time period, 50% of calves born in your herd will be bulls.

Each conception/birth is an independent event, and the probability of an individual newborn calf being male or female isn't influenced by the sex of earlier pregnancies from the same cow, or concurrent pregnancies of other cows in the herd. A calf is either male or female, just as a flipped coin must land as either a head or a tail. In both cases, the rules of binominal variation (only two possible outcomes) apply.

If you flip a coin once, the odds are 1 in 2 that a tail (bull) will result. If you flip the coin six times, you could obtain from 0 up to 6 tails, though the most likely outcome is 3 tails. Repeat this exercise 100 times (each time with a set of six flips), and you'd likely find the distribution shown in Table 1.

This table is based on the rules of probability for a binominal. Although any given flip has only two possible outcomes — head or tail — with six flips per set, there are seven possible outcomes, with probabilities (percentage of flip sets) as described in Table 1.

This also is true for calf sex. If six calves were born after artificial insemination (AI) with regular semen, there would be 1-in-3 odds (32%) of obtaining three bulls and three heifers — a sex ratio of 1.00. However, there also would be about 1-in-9 odds (11%; 2% + 9% in Table 1) of obtaining 6 or 5 bulls (i.e., 0 or 1 heifer), and concurrently about 1-in-9 odds of obtaining 1 or 0 bulls. Hence, there are about 1-in-5 odds (22%) of obtaining a sex ratio outside the range of 2 to 4 bulls, even though the true population ratio is 50:50.

If your calculation of sex ratio was based on 500 newborn calves, the observed sex ratio will be closer to the expected 1:1. There would be 2-in-3 odds of obtaining a sex ratio between 0.92 and 1.08 (48-52% bulls). Indeed, with 500 newborn calves, there is only a 1-in-20 chance the sex ratio would be outside the range 0.85 to 1.17 (46-54% bulls).

### Sex ratio with sexed sperm

A flow-sorter used to prepare sexed sperm for AI usually is operated to provide about 90% of the desired sperm type (X or Y sperm). Higher accuracy is possible, but it's much more expensive because fewer sperm are sorted.

The actual percentage of Y-sperm for individual freeze codes or batches usually will fall within a range of 0-3 percentage units below or above the target (i.e., 87-93% Y-sperm). In our discussion, we'll assume semen contains exactly 90% Y-sperm.

Table 2 shows what might be expected for the first 10 calves born after the use of sexed semen. Though the semen contained 90% Y-sperm, odds are 1 in 14 you'll obtain less than 80% bull calves (calculated after summing probabilities for 0-7 bulls); for 1 in 100 unlucky cases, there will be 6 bulls and 4 heifers. Therefore, there likely will be some unhappy customers, even if sexing is truly 90% accurate.

However, a preponderance of bulls (8-10 bulls in Table 2) would be obtained in 93% of cases. Meanwhile, with regular (unsexed) semen, in only 5% of cases would there be 8-10 bulls. With regular semen, 66% of cases would include 4-6 bulls.

With a sample of 10 calves, there would be insufficient information for any meaningful prediction (beyond that in Table 2) about the sex of the next 10 calves born in this herd or the first 10 calves born in another herd using the same semen.

The impact of the number of calves in a new data set on the possible deviation of the percentage of bull calves from a theoretical 90%, assuming exactly 90% Y-sperm, is shown in Figure 1. This figure illustrates two inescapable facts:

• With about half of all data sets, the percentage of bulls will be less than that anticipated based on the percentage of Y-sperm in the semen.

• The chances of getting close to 90% bulls improve with larger sets of calves produced with sexed sperm. With 20 newborn calves, for 25% of data sets, there will be less than 85% bulls; and even with 100 newborn calves, in 15% of data sets, there will be less than 88% bulls.

Obviously, for about half the data sets for a given number of calves, the percentage of bulls will be greater than anticipated.

The take-home message is that, provided sufficient newborn calves are evaluated, after use of sexed semen prepared to provide 87-93% Y-sperm, there's a high probability the vast majority of newborn calves will be bulls. However, if a producer buys 20 doses of sexed semen resulting in 10 calves, it will not be so unusual to get only 6 or 7 bulls.

### Pregnancy rates/calf normalcy

It's imperative that producers recognize that conception/pregnancy rates with sexed semen usually are lower than rates obtained with regular semen, especially with AI of cows rather than heifers. This difference might be 10 percentage units lower with sexed sperm than conventional sperm used in the same herds, and even lower under stressful conditions or with poor management.

Importantly, in a study of 1,169 calves produced from sexed sperm, there were no excess problems in resulting calves compared to calves produced with unsexed sperm.

Rupert Amann and George Seidel, Jr., are reproductive physiologists with the Colorado State University Animal Reproduction and Biotechnology Laboratory in Fort Collins.

### See this table in a new window (.pdf)

Table 1. Distribution of “tails” within 100 sets of flipping a coin, each set consisting of 6 flips of a coin
Number tails (or bulls) % of flip sets
6 2
5 9
4 23
3 32
2 23
1 9
0 2
Table 2. Probability (as %) of different numbers of bull calves among the first 10 calves born
Number bulls Sexed semen (90% Y-sperm) Regular semen (50% Y-sperm)
10 35 0.1
9* 39 1
8 19 4
7 6 12
6 1 20
5 <0.1 26
4 <0.1 20
3 <0.1 12
2 <0.1 4
1 <0.1 1
0 <0.1 0.1
*Even though 90% Y-sperm is the true value,producers would get exactly 9 bulls and 1 heifer in only 39% of sets of 10 calves