Re: Haldane's dilemma
Tue, 22 Apr 1997 08:53:26 -0700

David Campbell wrote:

David, I am subsrcibed to both the ASA and Evolution lists. I don't know
where you are reading my messages from, but I will start with ASA.

> >David Campbell wrote:
> >>
> >> >
> >> >Walter Remine, in his book _The Biotic Message_ first brought my
> >> >attention to Haldane's dilemma as an unsolved problem in population
> >> >genetics (amd applies to evolution).
> >>
> >> Seems like the name was mentioned in my class, but I forget what it was.
> >> Could you post a definition?
> >
> >In 1950s, Haldane calculated the maximum rate of genetic change due to
> >differential survival. His calculations reveal that many higher
> >vertebrate species could not plausibly evolve in the available time,
> >because the reproductive capacity of the species limits the rate at
> >which new rare traits can replace old prevalent traits. Haldane
> >calculated that on average, the cost of substitution is 30, and is paid
> >off in installments of 0.1 per generation. Thus it takes about 300
> >generations to pay for the cost of substituting one trait.
> A population bottleneck or isolation of a small subpopulation could
> allow new rare traits to become prevalent.

This is the argument that Mayr used to countere Haldane. The problem, as
far as I understand is that in small populations, beneficial mutations
are exceedingly rare.

> If those with the new were a
> significant part of the small population, genetic drift could make the new
> trait dominate among the small population's descendants.

Through genetic drift, the odds are that rare beneficial mutations are
likely to be eliminated. And if you were to take inbreeding into account
the problem gets worse. You get rapid change, but the overall change is
not beneficial.

> Extreme selective
> pressure, in the unlikely event of a significantly beneficial mutation,
> could also act more rapidly.

Unlikely is the word.

> I suspect that calculation of the amount of genetic change
> necessary for generating a given species may be dificult to asses, though
> perhaps half of the difference between the most disparate modern species
> would be a reasonable approximation (assuming each evolved an equal amount
> away from the last common ancestor would minimize the maximum change to
> explain). I don't know whether this problem would increase or decrease the
> amount of time apparently needed relative to his calculation.

I don't know, but here is the example given by Remine:

Say a given prehuman ancestor species has a generation time of 20 years.
Given a span of 10 million years (which is amply generous), that's
enough time for 500 000 generations.

Imagine a population of 100 000 of these, and a scenario that wildly
speeds up evolution. Say, every generation, one male and one female
receive a mutation so beneficial that all the other 999 998 of them die
off in opne generation., and the population is replenished (back up to
100 000) in one single generation. At that crashing rate of one
beneficial mutation per generation for 500 000 generation, you get 500
000 new nucleotides - approximately .014 % of the genome. Is that enough
to get a human out of some chimp-like ancestor?

Haldane calculated that it takes on average 300 generations to pay for
the cost of one substitution. That leaves us 1667 beneficial mutations.

What is wrong with this argument?