We can easily identify homozygous recessive genotypes and partially-dominant traits simply by looking at the phenotypes of the progeny. Identifying carriers of recessive alleles isn’t as simple, as recessive alleles are hidden — the phenotype of an ‘AA’ animal is indistinguishable from that of an ‘Aa’ animal.
The purpose of test matings is to identify carriers of recessive alleles by forcing any such alleles that may be present to appear in progeny. It takes just one such progeny to be born to show without doubt that the tested parent is indeed a carrier. But as there is no guarantee of such a birth, it is more a matter of knowing how many offspring must be born to be sure that the tested animal is definitively not a carrier.
Before going further, let’s first summarise the calculations from last week:
The probability of homozygous recessive (’aa’) offspring when a heterozygous carrier (’Aa’) is mated to:
|Genotype of Mate||Probability|
|homozygous dominant (’AA’)||0|
|progeny (either ‘AA’ or ‘Aa’) of known ‘AA’ parent||0.125 (one in eight)|
|heterozygous dominant (’Aa’) — a known carrier||0.25 (one in four)|
|homozygous recessive (’aa’)||0.5 (one in two)|
All this table does, really, is confirm what we already know from Mendelian genetics, that the greatest likelihood of a homozygous recessive genotype will come by joining a heterozygous dominant to a homozygous recessive. This is because the homozygous recessive parent has only recessive alleles to pass on to its progeny, and the outcome is solely determined by which allele the heterozygous parent contributes. This mating scenario also requires the smallest number of matings to be sure a tested animal is not a carrier. (We’ll go over this later.)
All other probabilities will be between 0.5 and 0, depending on how prevalent the recessive allele is in the greater population. (And the number of required matings required are much higher too.)
Thus it makes too much sense to mate all test animals to homozygous recessive genotypes. This is indeed the case with alpacas, with their simply-inherited fleece type trait. Suri is dominant, huacaya is recessive, huacayas are in plentiful supply, and huacayas are indeed used to test suri genotypes.
But unfortunately it isn’t always as straightforward as that! It just so happens that huacayas happen to be popular, and in many cases preferred to suris. Their recessive genotype is desired, but this is actually not the norm for most recessive traits.
Many recessive traits are actually not wanted (eg horned cattle), or are a cause of infertility, or are lethal. Such animals either are never born, or are quickly culled if they are. Breeding age adults can be hard to find or non-existent.
The table above shows that the next-highest probability of dominant recessive genotypes comes from matings to known carriers. But this too presents challenges, as known carriers of deleterious alleles are also culled.
One easily obtained source of potential carriers, however, is a sire’s own daughters. There are several downsides to this, even apart from the time needed for the test sire to reach breeding age to produce those very daughters. Many daughters must first be born and raised to breeding age themselves, with time for gestation added to that. And a sire × daughter mating produces inbred progeny of low value.
However, the big advantage of such matings is that all the recessive alleles that potential sire may carry can be tested at once, as at least one copy of each is likely to be present across the whole daughter group.
Test matings with any random animal in a herd is likely to require the highest number of matings to ensure an animal isn’t a carrier, especially if an allele is already rare in that population. (The probabilities are 0.05 or 0.0125, depending on which assumptions are used. We’ll be going over the maths that calculates those probailities over the next few weeks.)
Yet testing with random animals is still the easiest approach of all, despite those odds. While many more females would be needed, that sire would be mated anyway if he’s being considered for testing at all. And as with mating to daughters, this method tests for all recessive alleles likely to be in the population. Sires in artificial insemination studs are routinely tested this way.
Over the next few weeks we’ll step through the maths of matings, and the number of required matings to be confident a tested animal is not a carrier — slowly!
But first, next week, an introduction to the concept of levels of confidence in statistics. The is the measure of confidence we have that a particular outcome is reliable and reproducible — and with which we can determine the number of matings required for different test mating scenarios.