Thursday, November 24, 2011

What William the Conqueror's Companions Teach Us about Effective Population Size

My mother has been working on genealogy for several decades. She recently gave me a little book called My Ancestors Came with the Conqueror by Anthony J. Camp, first published in 1988. Camp is a professional genealogist. Before discussing this book, I should let you know that the relationship between professional genealogists and the amateur genealogy found on is similar to the relationship between scientists and Intelligent Design Creationism.

It's estimated that half the population of Great Britain claims to have descended from William the Conqueror who defeated King Harold at the Battle of Hastings in 1066. Not all claims meet the rigorous standards of professional genealogists but it's quite reasonable that there are millions of direct descendants of William.

Back in 1400 it was less likely that you were a descendant of William because there were fewer generations and fewer descendants. This was a problem for aspiring nobility and minor landholders so they tended to settle for the next best thing—they claimed descent from one of the companions of William who accompanied him from Normandy and fought at the Battle of Hastings. Gradually the list of companions grew and grew because if you couldn't prove you were related to an existing companion, you just made one up.

Many genealogists and historians have analyzed the various lists of companions. Some lists have over three hundred names but there are only about 20 companions who are definitely known to have been present at the Battle of Hastings in 1066 [William the Conqueror's Companions, The Companions of the Conqueror]. The Order of the Conqueror’s Companions is part of a genealogical society that traces descendants of the companions of William the Conqueror. They list 39 known companions.

Let's assume that there are 20 well-documented companions. Only one of these (William Mallet) has possibly passed on his Y chromosome to the present time and even that male line of descent is disputed. This is fully consistent with our understanding of genetics when you consider that most male lines are likely to die out in a few generations. Those that survive ten generations or so are unlikely to become extinct since there will likely be several male lines at that time.

Only 10 of the companions have descendants who are alive today. This could be due to the fact that genealogists don't have perfect records for all the companions and their families but it's also quite in line with expectations.1 You don't expect that all 20 families will avoid extinction. What this means is that for a random "population" of 40 individuals (20 companions plus their wives), only 20 of them contributed alleles to the present population after 50 generations.2

The take-home lesson from these genealogical studies is that the actual population size at a given point in time is not the same as the actual number of individuals who contribute to the gene pool over the long term.

This has long been known to population geneticists. They define a new term, Ne, called the "effective population size." In order to understand the definition of effective population size, you have to keep in mind that most of the variation in a given population is due to the presence of nearly neutral alleles whose frequency is fluctuating under the influence of random genetic drift. The parameter of interest, Ne, represents the theoretical number of individual in a population of size N who actually contribute to the variation in a population.

The definition is from Sewell Wright [Effective Population Size] ...
Effective population size is "the number of breeding individuals in an idealized population that would show the same amount of dispersion of allele frequencies under random genetic drift or the same amount of inbreeding as the population under consideration."
The effective population size is always less than the actual population (Ne < N). Sometimes it's a lot less. In most vertebrates, for example, the long-term effective population size is calculated to be about 10,000.

Why is this important? It's important because evolution is important for understanding biology and in order to understand evolution you need to understand population genetics. One of the important lessons from population genetics is that the relative important importance of natural selection and random genetic drift is dependent on effective population size. This is a major theme in Michael Lynch's book The Origins of Genome Architecture.

He argues that the effective population size of most large multicellular animals (e.g. Homo sapiens) was small enough to render natural selection impotent for most alleles that might have been somewhat beneficial in larger populations. This led to loss of such beneficial alleles by random genetic drift and to frequent fixation of mildly deleterious alleles by drift. Thus, even if the accumulation of large amounts of junk DNA, for example, was slightly deleterious, it cannot be eliminated by natural selection when the effective population size is small.

Furthermore, many alleles with small beneficial effects cannot possibly become fixed in such a population so it's silly to construct a model that relies on fixation of alleles with a small advantage. This leads to his theory of the evolution of genome complexity by nonadaptive processes. According to Lynch, the default explanation is random genetic drift and because this accounts for much of genome architecture, there's no reason to invoke natural selection to explain what we observe.

Lynch devotes an entire chapter (Chapter 4) to Why Population Size matters. I'm hoping to get more people interested in this subject by giving them a simple example of the difference between actual population size (N) effective population size (Ne).

This isn't only important in genome evolution. As most of you know, the effective population size is an important consideration in recent human evolution [From genes to numbers: effective population sizes in human evolution] and many other disciplines.

1. The reason we focus on nobility isn't because they are more important, genealogically, than the 8,000 other soldiers at the battle. It's because we don't have any records of those other potential ancestors.

2. This doesn't mean that all of the alleles in the other 20 individuals were lost because many of them could have been passed down from siblings, aunts, uncles etc.


  1. After reading this and "The Logic of Chance", I think it may be time to put Lynch on the reading list.

    I do have a bit of a quibble of with the example though... from what I recall of my population genetics, even if N = Ne, you'd still expect to see inter-individual variation in the number of offspring; each individual should produce off-spring following a Poisson distribution; that means that you'd expect occasional lineage extinction even when N = Ne. It also means you can get Ne > N, if you reduce inter-individual variance ( obligatory Wikipedia reference).

  2. Going by the article you may find this interesting though you will have to copy and paste it into your address bar.

  3. "The effective population size is always less than the actual population (Ne < N)"

    This is not true. You can have instances when Ne > N.

  4. Just as a follow up. As pointed out by Eric underdispersion in the Poisson model can lead to Ne > N. In addition, there are several structured population models that can also lead to Ne > N. The traditional one from Wright is when there are independent demes that are equally productive in offspring numbers (i.e., local population regulation). This leads to no among-group variance at the demic level and thus drift cannot act at this level with the basic result that Ne > N (usually, this is accompanied, however, by an increase in homozygosity). With interdemic selection (differences in reproductive output among demes) you get N > Ne.

    Other structured models that incorporate sex-biased dispersal can also produce Ne > N.

    Under the Poisson model of family size, any factor that can reduce the variance in relation to the mean can produce higher Ne than N. For example, if country imposed and could enforce a two-child-policy in family size this would elevate Ne > N.

  5. Re the illustration caption, the good Bishop Odo probably used his mace too, as he also appears to have unabashedly fathered illegitimate children, something else that clerics weren't supposed to do (and yet there is a long history of them doing).

  6. Thus, even if the accumulation of large amounts of junk DNA, for example, was slightly deleterious, it cannot be eliminated by natural selection when the effective population size is small.

    I'm a bit wary of arguments promoting the causal role of population size - particularly when comparing prokaryotes, say, with eukaryotes. I think the concept of an effective population size for a clonal, LGT-dominant organism such as a bacterium is fraught, and in any case I don't think junk scales with population size within these groupings.

    Direct mechanistic constraints and immediate neighbours seem a more pressing issue than the selection-drift balance imposed by membership of a wider 'population' of a particular size.

    A prokaryote has one or two origins of replication, an energetic constraint determined by its surface area, a reliance upon diffusional transfer of metabolites.

    A eukaryote has multiple origins, a much greater ratio of energetic membrane to cell volume, engulfment of food and active transport, and, crucially, meiosis.

    For a multicellular eukaryote there is the addition of a largely quiescent germline phase - for most of the life cycle, DNA replication time and cost is a constraint on somatic cells alone.

    These factors, to me, have far more bearing upon the relative impact of junk upon DNA replication than does population size.

  7. Thanks for mention of the Augustan Society lineage group, "Order of the Conqueror's Companions". Sadly, the link above no longer works. This is the result of this group merging with the "Order of the Conqueror".

    The new group is called the "Society of Descendants of the Conquest", and the correct web page is ... something the system apparently won't let me post. You should be able to Google it, and I'll try to set up forwarding to the link above.

    Membership in this group is open to all who can document descent from either the Conqueror or his known Companions. We welcome your inquiries.

    Bruce A. Metcalf
    SDC Administrator
    The Augustan Society