The Phase of Mass Selection and Long Term Selection Experiments

On to Phase 2 of Wright’s Shifting Balance Process. But before I do I should probably start with a shameless attempt to up my standings in the next Carnival of Evolution World Cup Competition by alerting the committee responsible to the following figure that I found:

precambrian-rabbit-copy

Obvious evidence of Pre-Cambrian Bunnies (unapologetically lifted from http://clubschadenfreude.com/2013/02/19/not-so-polite-dinner-conversation-part-9-the-second-half-of-19-limestone-coelacanths-and-circular-reasoning/)

OK, on to phase 2: the phase of mass selection. In Wright’s words “. . . the set of gene frequencies drifts far enough to cross one of the . . . saddles in the surface of fitness values . . . There ensues a period of relatively rapid change in this deme, dominated by selection among individuals (or families) until the set approaches the equilibrium . . ..” (Page 455, Wright 1977). Evolution and Genetics of Populations. Vol. III. Univ. Chicago Press.).

There would appear not to be much controversy about this. In particular, Wright’s claim for this phase is that the population will climb the nearest peak and approach the local optimum. I doubt that Fisher would argue much with that. However, there are actually is the potential for some discussion. In particular, in an additive world the response to selection occurs strictly by changes in gene frequency of alleles with fixed effects. However, one of the points I have made before (https://blog.uvm.edu/cgoodnig/2013/07/31/drift-and-epistasis-the-odd-effects-of-small-population-sizes/) is that drift can convert epistatic variance into additive variance, and in the process change the average effects of alleles. As I mentioned last week, this may be the important role of Wright’s phase one: Drift causing shifts in local average effects. As I also discussed last week it is unlikely that these shifts will be major, since in general epistasis tends to be small as a variance component, and thus in most cases there won’t be much material for the “conversion” process to work on. This is where Wright’s phase two comes in.

To see where this is important it is useful to look at long-term selection experiments, and note two anomalies that are consistently found in such experiments. First, they work too well. That is, you typically can get 100 or more generations with a nearly linear response to selection (and MUCH more if we acknowledge the existence of laboratory selection experiments involving bacteria — Wiser, Ribeck, and Lenski 2013. Science 342:1364-1367). Second, there are typically intermediate selection plateaus.

Corn Selection copy

The results of 100 years of selection for oil and protein in corn. Note the overall long term linear response to selection (orange highlight), which is none the less punctuated by extended selection plateaus (green highlights).

Turning first to the long-term linear response to selection. This is actually expected under Fisher’s infinitesimal model, which has the odd feature that, because there are infinitely many loci of infinitely small effect, selection changes the gene frequencies of the individual loci by an infinitesimal amount, which is to say gene frequencies do not change. Of course in the real world there is a finite number of loci, nevertheless, this long-term linear response to selection implies that there are indeed a VERY large number of loci contributing to the response to selection. It turns out that there are two other possibilities. One is the ongoing input of new mutations, which due to space constraints I will not talk about, and the second is epistasis. It turns out that, as with genetic drift, selection will drive the conversion of epistasis to additive effects. The rather surprising empirical result from an old paper (Goodnight 2004 in: Plant Breeding Reviews. J. Janick, ed.) is that in epistatic systems selection seems to convert epistasis into additive effects at a more or less steady rate. Thus, this conversion of epistasis into additive variance driven by selection is a possible explanation for the extended response to selection.

VA with selection and epistasis

The additive genetic variance in four simulated populations with two loci and 100 alleles per locus under selection. Dashed lines are populations with only additive effects. Note the approximately exponential decline in the additive genetic variance. Solid lines are populations with additive-by-additive epistasis. Note that the additive genetic variance remains elevated for 10 generations before beginning an exponential decline.

The intermediate selection plateaus are also consistent with an epistatic model. The typical, and adequate, explanation for intermediate selection plateaus is that the population has run out of selectable variation, and is waiting for either a favorable mutation, or a favorable recombination event. However, consider the simple case of additive-by-additive epistasis.

VA fitness surface

The fitness surface for additive-by-additive epistasis.

 

From this fitness surface you can see that there are two possible outcomes of selection, fixation of the A1A1B1B1 or A2A2B2B2 fitness peaks. Interestingly, in a completely deterministic system there is a boundary dividing the domains of attraction for the two peaks. Thus, we can start two populations near fixation in one of the fitness valleys, such as nearly fixed for A1A1B2B2, and with arbitrarily small changes in gene frequency they will go to different peaks.

deterministic selection

The response to selection for two populations, one with a starting gene frequency of A1 = 0.99, and B1 = 0.0101 or 0.0099. Note in this deterministic model the outcome is a function of minor differences in gene frequency at the B locus. Each arrowhead represents one generation.

This simple system gives us both the results typical of long term selection experiments, that is surprisingly long responses to selection, and intermediate selection plateaus.

response to selection

The response to selection in the example described above. Note the long response to selection with an intermediate selection plateau.

Two more fun graphs, then I will conclude and leave you alone. First, the intermediate plateau is due to a lack of additive genetic variance, but not total genetic variance. The problem is that when the population nears a gene frequency of 0.5 the genetic variance is mostly expressed as epistasis, and the population cannot respond to selection. When the population is dominated by either allele at either (or both) locus the additive genetic variance increases.

VA during selection

During the selection process total genetic variance remains relatively constant (except near fixation) but additive genetic variance dominates during the early and late stages of the selection when frequencies are far from 0.5, and the epistatic variance dominates during the middle stages when the gene frequencies are near 0.5.

And, because I cannot resist, the average effects of the A1 and A2 alleles reverse over the course of the selection experiment.

figure 12 AXA LAE

The local average effects of the A1 allele. The A1 allele starts out being the low fitness allele. Half way through the response to selection the gene frequencies approach 0.5 and the local average effects reverse with the A1 allele becoming the high fitness allele.

So, returning to Wright’s phase two, the phase of mass selection, we see, again, that Fisher and Wright were seeing two sides of the same process. Within populations selection will appear to act exactly as Fisher said, as a process that refines adaptations and leading to the (locally) optimal phenotype. Between populations it must be recognized that in an epistatic world selection is a diversifying force that acts to magnify the small differences in local average effect and potentially driving populations to different adaptive peaks.

In other words, to paraphrase Dave McCauley when he was a postdoc and spiritual leader of us graduate students at the University of Chicago, it is the interaction of stochastic and deterministic evolutionary forces that give meaning to life.

One Response to “The Phase of Mass Selection and Long Term Selection Experiments”

  1. Clem says:

    Or perhaps your shameless attempt to curry favor with the judges will be regarded as biting and you will be sent off with a red card… thrown into the dust bin as it were. The bunny is cute though, so +1 for effort?

    Congrats on the second place finish – can you show us the silver medal?

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