William Lane Craig, Mouflon Sheep, and Heterozygosity

| By on Letters to the Duchess



In the last few posts in this series, we have been examining William Lane Craig’s arguments based on a study of a population of mouflon sheep founded by a single breeding pair. Craig uses this study in two ways, both of which are intended to cast doubt on the conclusion that humans descend from a population rather than uniquely from an ancestral couple. First, as we have already discussed, Craig mistakenly argues that an increase in heterozygosity over time in the mouflon sheep population is evidence that natural selection can increase mutation rates. (As we saw, it is rather the case that due to natural selection over time more sheep in the population became heterozygous for previously existing alleles – not that mutation produced new alleles). Secondly, Craig cites this study as an example of a population where population genetics models overestimate a known ancestral population size. This last point understandably has significant rhetorical impact: If population genetics models can overestimate the population size of a population we know was founded by only two sheep, then it naturally follows that population genetics models may similarly be overestimating the ancestral human population size as well. The importance of this point for Craig’s apologetic that humanity descends uniquely from an ancestral pair is evident in the following exchange between Craig and a questioner – a questioner who wonders if the mouflon sheep study causes scientists to accept the idea that humans may in fact descend from two individuals rather than a population:

Question: … when they did the sheep on the island, does the scientific community embrace that as an indication that perhaps there were a pair rather than a population?

Craig: I don’t know the answer to that. As I said, this is an area in which I have only a surface knowledge. So I am sharing with you some of this information to just give you a familiarity with the issue. But you can bet that obviously evolutionary biologists who study population genetics will not be persuaded by the example of the sheep on Haute Island.

Follow-up: Because they don’t want to be.

Craig: What I think we can say is that given this data the traditional view is defensible. But I am not suggesting that this proves it. It is just that we are looking here as to whether it is defensible in light of the data.

Craig, then, feels that this study gives scientific warrant to defend the idea that humans descend uniquely from Adam and Eve.

Summarizing the argument

Craig’s argument (which is based on the work of Reasons to Believe) is relatively simple to understand:

  1. A population genetics model applied to the mouflon sheep population overestimates the known ancestral population size by up to a factor of 4.
  2. Population genetics models may similarly overestimate the ancestral population size of the human population.
  3. As such, the position that humans descend uniquely from an ancestral couple remains scientifically tenable.

The problems with this argument, however, are not readily apparent to a non-specialist. While it will take some effort to understand the details, here are summaries of the main problems with Craig’s line of argument, which we will explore in more detail in turn:

The “population genetics model” applied to this population is in fact nothing more than using a measure of heterozygosity – how many alleles are present for a few selected DNA sequences. However, Craig embraces the notion that natural selection is acting in the mouflon population, because he (erroneously) thinks it provides a mechanism for increasing mutation rate, as we have discussed. The action of selection, however, means that estimating population size using heterozygosity – as this study does – will return an inflated value, as the authors of the study rightly point out. Using heterozygosity to estimate population sizes in this way only works if the alleles being studied are not under selection. For Craig to argue that selection is acting means that he should expect the population size value to be inflated. That he argues both for selection and that the model is unreliable for this population is a non-sequitur: if selection is acting, then the model is working exactly as it should.

Human population genetics is much, much more advanced than this limited study, since it relies on numerous ways of estimating population sizes (rather than merely heterozygosity) and draws on the full genome sequence of thousands of humans. In contrast, the sheep study looks at only a handful of sequences in a small number of sheep. 

Even if human population genetics was similarly limited to a simple estimate based on heterozygosity of a few genome locations (which it is most certainly not), the resulting estimate would range in the thousands, not close to 2 as Craig requires for his argument.

Having summarized the problems with Craig’s argument, let’s take a closer look at each.

Using heterozygosity to estimate population size, and its limits

You may recall that we previously discussed the concept of heterozygosity using letters to represent alleles (you may wish to re-read that section if you need a quick refresher). In this example, the population had two alleles of the “aye” locus, represented as “A” and “a”. Individuals in this population could either be homozygous for either allele (i.e. either “AA” or “aa”) or heterozygous (Aa). The proportion of individuals in the population that are heterozygous gives us the heterozygosity value for that locus. If all members of the population are Aa, the heterozygosity is 1; if one quarter are heterozygous the heterozygosity is 0.25, and so on.

A few factors can the change the heterozygosity value for a given locus in a population over time. New mutations can increase heterozygosity by adding new alleles to a population– though over the short timeframe that the mouflon population has been isolated it is not at all likely that heterozygosity has increased through mutation, since the probability of new alleles arising through mutation in only a few generations is very small. Selection for the Aa combination—i.e. if the Aa combination has a reproductive advantage—would also increase heterozygosity, and this sort of effect seems to have been occurring in this population. If a locus is not under selection, however, it is expected that its heterozygosity will decrease over time. The reason for this is straightforward: alleles can be lost by chance in a small population much more easily than they can be gained by (rare) mutation events. In the absence of selection there is nothing to stop this loss – known as “genetic drift” – from happening over time. With the knowledge of this effect, then, it is possible to obtain a rough estimate of a past population size by measuring the present-day heterozygosity. If heterozygosity declines at a certain rate over time due to chance, and we can measure present-day heterozygosity, we can infer how much heterozygosity was present in the past, and use that value to estimate a population size.

If selection is acting, however, this way of estimating population size simply will not work. For example, if the Aa combination is reproducing at a greater rate than the other two possibilities (AA or aa) then neither the “A” allele nor the “a” allele will be lost from the population over time by chance, since both alleles are being selected for in Aa individuals. In this case, we would expect heterozygosity to be stably preserved in the population over time, since neither allele will be lost due to chance. If we naively tried to calculate a prior population size without recognizing the effects of selection, we would be assuming that present-day heterozygosity was the left-over remnants of once greater levels that had been dropping over time due to genetic drift, and thus overestimate the ancestral size of the population. Compare the following two graphs: on the left, heterozygosity drops over time without selection. On the right, heterozygotes are selected for, resulting in relatively stable heterozygosity over time:

If we were to calculate the expected level of heterozygosity at a certain time in the past, assuming no selection when in fact selection was at work, we would overestimate it – and thus overestimate the size of the population at that time.

Of course, the question remains why the effects of selection are so pronounced in this sheep population, and more importantly, why we can be confident that similar effects are not at play in human populations. We'll address those issues next. 




Venema, Dennis. "William Lane Craig, Mouflon Sheep, and Heterozygosity "
https://biologos.org/. N.p., 28 Oct. 2015. Web. 18 February 2019.


Venema, D. (2015, October 28). William Lane Craig, Mouflon Sheep, and Heterozygosity
Retrieved February 18, 2019, from /blogs/dennis-venema-letters-to-the-duchess/william-lane-craig-mouflon-sheep-and-heterozygosity

About the Author

Dennis Venema

Dennis Venema is professor of biology at Trinity Western University in Langley, British Columbia. He holds a B.Sc. (with Honors) from the University of British Columbia (1996), and received his Ph.D. from the University of British Columbia in 2003. His research is focused on the genetics of pattern formation and signaling using the common fruit fly Drosophila melanogaster as a model organism. Dennis is a gifted thinker and writer on matters of science and faith, but also an award-winning biology teacher—he won the 2008 College Biology Teaching Award from the National Association of Biology Teachers. He and his family enjoy numerous outdoor activities that the Canadian Pacific coast region has to offer. 

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