In the last section, we began to examine William Lane Craig’s arguments based on a study of a population of mouflon sheep founded by a single breeding pair. As we saw, Craig’s use of this study was twofold: to claim it as an example of natural selection increasing mutation rates (and thus provide a supposed natural explanation for accelerated mutation rates in the human lineage), as well as an example of population genetics models overestimating a known ancestral population size (since the study found the sheep population to have greater levels of heterozygosity than expected by one mathematical model). Since understanding why Craig is mistaken for both counts requires a working knowledge of what exactly “heterozygosity” is, let’s tackle this issue first.
Non-biologists are usually most familiar with organisms that have two copies of their genetic material – so-called “diploid” organisms. Humans, for example, receive two sets of chromosomes at conception – one set from mom (22 regular chromosomes plus an X chromosome), and one set from dad (22 regular chromosomes plus either an X or Y chromosome). Combined, this is what gives us our standard 46 chromosome set. What this means is that for every location (or, to use the correct genetic term, locus) in our genome, there are two copies present. For any given locus, then, the two copies may have the exact same sequence, or they may have slightly different sequences due to genetic variation in the population. Different sequences are called different alleles. In genetic-speak, then, diploid organisms can have two different alleles at any given locus – or both alleles at a locus may be the same. If an organism has two different alleles at a locus, they are said to be heterozygous at that locus. Conversely, if an organism has two identical alleles at a locus, they are said to be homozygous at that locus.
Geneticists often use uppercase and lowercase letters as symbols for different alleles at a locus. If you remember Gregor Mendel and his pea plants from your high school biology class, you were introduced to this system. For example, at the “aye” locus, we can designate two alleles: “A” and “a”. At the DNA level, these two alleles have some sort of sequence difference, though its exact nature isn’t important for this example. What is important, however, is understanding that these two alleles give us three possible genetic combinations for this locus:
- Homozygous for “A” or the AA “genotype” (note: “genotype” simply means “combination of alleles at a locus”),
- Heterozygous, i.e. the Aa genotype, or
- Homozygous for “a”, or the aa genotype.
If we now consider a population of organisms, we can determine what proportion of them are heterozygous at the “aye” locus. For example, suppose a small population of 100 individuals has the following number of each genotype:
- 25 are AA
- 50 are Aa
- 25 are aa
In this case, there are 50/100 individuals that are heterozygous, so the heterozygosity of this population at the “aye” locus is ½, or 0.5.
Now, consider how this measure might change over time. In a small population such as this one, chance effects alone might mean that one allele could become more common over time, and the other allele less common. For example, suppose we revisit the same population above several generations later, and find the following:
- 64 are AA
- 32 are Aa
- 4 are aa
In this population the heterozygosity at the “aye” locus is now 32/100, or 0.32 – a decrease from the prior measurement several generations before. What has happened is that the “a” allele has become less common, and accordingly the Aa genotype is now also less common as a result. In small populations, this sort of thing happens readily by chance, simply because each generation may not exactly reflect the allele frequencies of the prior generation. In a small population, the effects of chance can have a large effect on the population as a whole. As an example, imagine an animal population of 10 individuals that has 6 AA individuals, 3 Aa individuals, and only 1 aa individual: if something happened by chance to the aa individual (it dies in a rock slide before breeding, for instance) this event would have a large impact on the frequency of the “a” allele. In a population of 1000 individuals with the same starting proportions (600 AA, 300 Aa, 100 aa) losing one aa individual by chance would hardly have an effect at all. This is called “genetic drift” - a change in allele frequencies due to stochastic events.
In fact, the decrease in heterozygosity over time is expected to be proportional to the size of the population: smaller populations lose heterozygosity more quickly than do larger populations, due to these sort of chance sampling events. The reason for this is simple: in small populations, losing alleles is easy due to chance events, but gaining alleles over time, through mutation, takes far, far longer because new mutations are so rare. For example, our hypothetical population of 10 individuals (6 AA individuals, 3 Aa individuals, 1 aa individual) could, over time, lose the “a” allele altogether by chance. This population would then have only the “A” allele (i.e. all individuals would have the AA genotype). In order for heterozygosity to increase at this locus, we would need to wait for a mutation to convert one of these “A” alleles to a new “a” allele - and we would wait a very long time. The net result is that over time, we expect small populations to lose heterozygosity. Genetic diversity is easy to lose, and hard to gain in a small population.
It was this effect that the research group was interested in when studying the isolated mouflon sheep population. The basic prediction was that for this population, heterozygosity would decrease over time since the population size was small. (Studying these processes are important for understanding how other small populations change over time, primarily endangered species with reduced genetic diversity.)
What the research group found, however, was that heterozygosity in this population had increased over their sampling period, and at more than one locus (the study used preserved samples of animals taken from the population at different times to measure heterozygosity at different time points spanning several decades). Why then, was this population not showing a steady decline in heterozygosity over time?
One likely reason is the one the authors of the study suggest: natural selection. The equations that predict the loss of heterozygosity over time do so with the assumption that the alleles in question are not under selection. But if the heterozygous combination of alleles provides a reproductive advantage, then an increase in heterozygosity would not be surprising at all in a small population. Let’s consider a second locus, the “bee” locus. If the Bb genotype has an advantage over the BB or bb genotypes, then this locus is less likely to lose heterozygosity over time, because more Bb individuals, on average, will reproduce successfully than will the BB or bb individuals. This means that neither the “B” nor “b” alleles will become rare in the population, since the most successful genotype has both alleles in it.
So, over time we might see something like the following in a population:
What is important to notice here is that while natural selection can increase the heterozygosity of a population over time, it does not involve new alleles caused by mutation. It merely involves an allele that already exists in the population becoming more common over time, such that the population has more heterozygous individuals than it did before.
With this understanding, it is easy to see just how off base Craig’s first argument is: that the mouflon sheep study somehow provides an example of natural selection increasing mutation rates. What the sheep study shows – unsurprisingly to geneticists – is that natural selection can preserve and even increase heterozygosity in a population over time, and that mutation has nothing to do with the process.
That Craig would advance such an argument reveals he misunderstands a very basic concept in population genetics, alas – as do his sources. This means that Craig’s argument for a “natural” mechanism to explain accelerated mutation rates in the human lineage has no support. While Craig could presumably fall back on divine intervention to explain human genetic diversity, we have already discussed why that is both an ad hoc and unsatisfying approach that does not withstand close scrutiny.
Next, we’ll address Craig’s second use of this study: his claim that it demonstrates a case of population genetics models overestimating a known population size.