Excellently clear exposition. I learned something. BTW, and for what it is worth, I have always found Fisher's arguments clearer and more easily followed than Wright's, and have often wondered if this was because he had received a much better mathematical tool-kit at Cambridge than Wright could possibly have found in the Mid-West, and that Wright therefore had to use his own home-made and slightly eccentric tool kit which he had fashioned from scratch.

Wright's concept of local peaks in a fitness landscape for example -- and I know many will disagree -- strikes me as of dubious theoretical value if only because the peaks in such a landscape would not be at all stationary but more like the up-and-down surface of a wavy ocean. Thus what might be counted as a move towards a local fitness peak at one moment in evolutionary time would the next moment be a movement away due to constant fluctuations in the local topography.

Luke Lea: “Wright's concept of local peaks in a fitness landscape for example -- and I know many will disagree -- strikes me as of dubious theoretical value if only because the peaks in such a landscape would not be at all stationary but more like the up-and-down surface of a wavy ocean. Thus what might be counted as a move towards a local fitness peak at one moment in evolutionary time would the next moment be a movement away due to constant fluctuations in the local topography.”

I like having multiple models.

In the case of humans with their low birthrate the “surface of a wavy ocean” may be a good model. For fruit flies, a relatively unchanging landscape with local peaks may be more appropriate.

It also depends on the biological trait and the cluster of genes that are being studied. Some traits are stable and some genes are conserved over long time periods. Others, such as those associated with the immune system, will continually adapt to new pathogens.

Scaling is also important. Alleles of large beneficial affect become fixed and alleles of large negative affect are cleansed. So a landscape model that filtered out the “noise” from alleles of small affect should be relatively stable. When alleles of small affect are included, the wavy ocean model is more appropriate.

Maybe I am mistaken, but I thought the basic idea behind a landscape of local fitness peaks was that certain traits would get fixed on a sub-optimal peak and would have a hard time climbing down in order to climb up another better peak -- the best peak? -- nearby.

As for fruit-flies, I presume you mean under laboratory conditions not in the wild? I confess I had not considered such a highly constrained and artificial environment, and don't have any feel for what the implications are in this regard.

The immune system? Are there sub-optimal peaks in that context? Elaborate a little. I'd love to get your views.

Was Fisher using Mayr's definition of a species, or an older one under which there would be more localized species?

Luke Lea “Maybe I am mistaken, but I thought the basic idea behind a landscape of local fitness peaks was that certain traits would get fixed on a sub-optimal peak and would have a hard time climbing down in order to climb up another better peak -- the best peak? -- nearby.”

That is also how I interpret local fitness peaks.

The difference between fly and human adaptation levels should be amplified by a stable, controlled fly environment but even wild fly populations should be much more adapted to their local environment than humans. I believe the important factor is the high birthrate that results in high selection levels. High selection levels mean that the fly genome tends to occupy higher regions on local fitness peaks.

“The immune system? Are there sub-optimal peaks in that context? Elaborate a little.”

First, decompose the fitness landscape into relatively independent components. Overall fitness depends on many low-level traits. Focus on low-level trait fitness landscapes that depend directly on far fewer genes.

Some low-level traits are very important and the genes associated with those traits have been highly optimized and conserved over many millions of years. So many other traits depend on those important traits that any decrease in the important trait’s fitness lowers the total fitness for the animal. In that trait fitness landscape, the animal is stuck at a local minimum. There might be a higher fitness peak, but there is no pathway from the local peak to the higher peak. Many low-level cellular traits have been fixed for over 600 million years.

Other low-level traits had to adapt to environmental changes including pathogens. An immune system adaptation couldn’t break other critical components. The immune system evolved to be adaptable. The fitness landscape for the immune system genes might resemble a wavy ocean, with small ever-changing peaks.

So the total fitness landscape might contain both components that resemble isolated peaks and components that resemble ocean waves.



I haven’t done a good job of explaining my mental model. I’ll try to organize the concepts and get back to you. Some of the concepts I’m trying to combine are “simulated annealing”, decomposing a fitness landscape into relatively independent low-level trait fitness landscapes, scaling laws for the fitness affect of mutations, adaptation levels associated with population dynamics, gene dependency networks, and conserved vs. variable traits and genes.

"Was Fisher using Mayr's definition of a species, or an older one under which there would be more localized species?"

- Steve, I'll look at Fisher's views on species and speciation more fully in a later post. Of course, Mayr hadn't yet promulgated his 'biological species definition' when Fisher was writing, but I think Fisher was assuming something similar: a species as an interbreeding group in which there are no strong geographical or behavioural barriers to interbreeding. See the first few pages of chapter 6 of GTNS.

- Luke and Fly, I'll say more about Wright's views in later posts. I've got considerable respect for Wright, because he did the hard work on migration and population structure where Fisher just did hand-waving.