A retired European geneticist, Wolf-Ekkehard Lönnig, has made a point that he feels is devastating to population genetic arguments about the effectiveness of natural selection. In a post at the Discovery Institute’s blog Evolution News and Views. He pointed to an argument he made in 2001 in an encyclopedia article. The essence of his criticism is that many organisms produce very large numbers of gametes, or of newborn offspring. Most of those must die. Then
If only a few out of millions and even billions of individuals are to survive and reproduce, then there is some difficulty believing that it should really be the fittest who would do so.
In addition, he was interviewed two days ago by Paul Nelson, in a podcast posted very recently by the Center for Science and Culture of the Discovery Institute, on their blog Evolution News and Views. You will find it here. He makes the same point (while Nelson misunderstands him and keeps raising an unrelated point about protein spaces).
It is a stunning thought that evolutionary biologists have ignored this issue. Have they? Have population geneticists ever thought about this? Well, actually they have, starting nearly 90 years ago. And the calculations that they made do not offer support to Dr. Lönnig. Let me explain …
The standard model
In population genetics, the standard model of genetic drift in finite populations is the Wright-Fisher model, introduced in 1930 and in 1932 by those two founders of that discipline. The other great founder, JBS Haldane, used a nearly equivalent model in 1927, though discussed less explicitly.
In a Wright-Fisher model there are N parents, each of whom produces a very large but equal number of gametes. So large, that it is assumed that there are an infinite number of them, each parent contributing equally. These gametes then combine at random to form all possible genotypes, each in exactly its expected frequency.
If natural selection occurs, it then shifts the genotype frequencies in precisely the expected way. Finally, density-dependent mortality occurs, leaving only N survivors, so that the population size is maintained. It impacts all genotypes equally, so that the N surviving adults are in effect a random sample from the genotypes that survived natural selection. This sampling of adult survivors causes the genetic drift.
A numerical example
For example, if we have a population of a haploid species with N = 10,000 individuals with two alleles A and a at equal frequencies, each of them will produce a vast number of gametes, equal numbers from the two genotypes. Among the gametes they will be in a 1:1 ratio. Now if the a genotype has viability 1% lower, after that mortality their numbers will stand in the ratio of 1 : 0.99. So after this mortality the frequency of the A genotype is 1/(1+0.99) = 0.50251256.
These young individuals then die randomly in freak weather, are eaten randomly by predators, are run over by trucks, and so on. All the haphazard random mortality that Lönnig is worried about. Finally a random 10,000 of them are chosen to win the lottery and survive.
As Lönnig says, there are all sorts of outcomes possible. Will the natural selection be effective? Lönnig obviously thinks not. But we can do the calculations. Will the frequency of the A genotype increase? Each of the 10,000 survivors is a randomly drawn offspring, and 0.50251256 of those are A. So it’s just like tossing a coin 10,000 times, when the probability of Heads is 0.50251256.
A simple binomial distribution shows that among the adult survivors the probability that the A genotype is more frequent than a is 0.681725. In all the random dying and random survival, the frequency of A rises more often than it falls.
Now that is one generation. Further rounds of reproduction and survival, with the same fitnesses, will ultimately lead to the frequency of A either rising to 100% or falling to zero. What is the probability that, starting with equal frequencies, we end up with A winning out? For that we move from Fisher and Wright’s models to calculations by PAP Moran (1958) and Motoo Kimura (1962). Let’s leave out the details, and open the envelope. And the probability is … 0.999999… and so on until there are 43 of those 9s.
We can conclude that Dr. Lönnig is not familiar with theoretical population genetics. He is a retired plant breeder at the Max Planck Institute for Plant Breeding Research, who specialized in mutation effects in such plants as the “husk tomato” Physalis pubescens. I can understand why he might not have studied population genetics thoroughly.
But why then is he holding forth on the topic? This is easily explained. He is also a creationist, associated with the German creationist organization Wort und Wissen. He formerly posted creationist material on his homepage at his Max Planck Institute. In a controversial move, the Institute forbade him to do this.
If Dr. Lönnig wants to understand these matters more, I recommend to him that he visit a gambling casino – in spite of the wild uncertainty of individual gambles, he might be surprised at how often he would lose his pocket money playing games that are mostly random, but slightly biased in favor of the house.