Why reductionism DOES work: Individuals to genes

In the last couple of posts I have suggested that reductionism is for chumps. Two weeks ago I argued that gene interactions made average effects wonder around all over the place, and last week I argued that indirect genetic effects mucked up the works if there was population structure. This would seem to imply that quantitative genetics doesn’t work. Tell that to anybody who works in the agricultural breeding industry and they will laugh at you. Possibly more than any other field you can take quantitative genetics to the bank. You want lean pork, more marbling in your steak, more lysine in your corn? Quantitative genetics will do it for you. Furthermore, heritability estimates are technically only valid for the generation in which they are measured, however, the reality is that the common rule of thumb is that they are generally usable for 10 or more generations, and often appear to be pretty close after 100 generations. So, if reductionism doesn’t work why does quantitative genetics work so well? I will argue that as may be true of many complex systems, it works for the wrong reasons.

1. Within populations genetic effects will tend to be additive for statistical reasons.

In other words, selection and drift make gene interactions go away. Yes, genetic drift and selection can cause the additive genetic variance to increase, but it happens by statistically depleting the epistatic variance. After only a few generations of small population size the population can be treated as if there was no epistasis. In other words, as long as you stay within populations reductionism often provides a fairly accurate picture of the world. But you need to be careful. Another population may also act additively, but it will be a different additivity with alleles having different effects on the phenotype.

VA by generation

Twenty five generations of brother sister mating starting with equal amounts of AXA epistasis and additive genetic variance. The small population size increases the additive genetic variance, but also decreases the epistatic genetic variance, which is the difference between the green and red lines. After only a few generations of small population size there is very little epistatic variance available.

2. In a well connected metapopulation you may not see much differentiation for local average effects.

The way to detect epistasis is to look among populations either by examining the variance in local average effects (Goodnight 2000. Heredity 84:587), or the variance in local breeding values (Goodnight 1995, Evolution 49:502). This runs into two problems. First, nobody ever listens to me, so this experiment has been exactly twice (plus one in progress unpublished experiment) (De Brito, et al. 2005. Evolution 59: 2333, Drury & Wade 2011. JEB 24:168), and second, the variance in local breeding values is a function of the migration rate among subpopulations within the metapopulation.

I have not published this work, so I am violating my personal rule to not put unpublished results on my blog, but I think this is relevant, and it is part of a much larger model on speciation. Lets just say there is more than one paper coming out of this model, I am coming off of sabbatical, and well, it might be a year before this part gets written up. In any case If we look at a single metapopulation with an infinite number of demes. By the way, infinite demes is an assumption that is very suspect. For example, the approximation that equation works pretty well if there are infinite demes, but falls apart in finite metapopulations (yea, that is another paper that will out of this model. . . ).

With that in mind if we look at the variance in local breeding values as a function of Nm it becomes apparent that in order to get a significant variance in local breeding values migration rates need to be relatively low.

LBV X Nm

The effect of migration on the variance in local breeding values. Gene interaction is much more detectable among populations than within populations.   The appropriate measure being the variance in local breeding values or the variance in local average effects. Shown here is the variance in local breeding values as a function of Nm, or the number of migrants entering a deme per generation.   Note that migration rates must be below one migrant per generation before variance in local breeding values will be statistically detectable. Green dots (upper left corner) is zero migration, red dots are migration rates of 0.005. Scatter is due to different deme sizes. VAA = 1, VA = 0, generation 30,000.

To see the interplay between migration rate and deme size a three dimensional graph may help:

3d Graph

3d graph of the variance in local breeding values as a function of migration rate (M) and deme size (N). Unfortunately, JMP does not render surfaces exactly correctly. The graph should reach up to a value of 2 for zero migration.

There are a few caveats. First this is a drift model. There is no selection. If selection were to be added (good luck with that) I would speculate that selection against migrants offspring (e.g., hybrids) would mean much higher levels of population differentiation. Second, this model uses island model migration with infinite number of demes. Isolation by distance would dramatically increase the population differentiation and allow detectable gene interactions at much higher migration rates.

So this puts us in a relatively interesting situation. The models of drift and selection within demes tells that epistasis will be difficult to detect, and models of migration among demes tells us that migration rates above about 1 migrant per generation will also make gene interactions difficult to detect. Thus migration has the effect of tying the population together, and as a result preserving a lot of alleles.   The larger the metapopulations and the more the migration the more overall number alleles that will be preserved. However, such situations are ripe to explode if migration is ever restricted, or two metapopulations are separated. The variation is there, and thus no measurable epistasis, but once the populations are separated those interactions will pop out of hiding and show up again between species where migration rates are lower or non-existent. This would argue that again, the additive model is working for the wrong reasons. Just because gene interaction is statistically hard to detect doesn’t mean it isn’t there. It may simply mean that the conditions are such that it is hidden.

iceberg

Not a whole lot of ice from my view from the ships deck! (http://blogdasa.com/2012/12/27/5-documentarios-que-me-tornaram-uma-pessoa-mais-bacana/)

One last thought. This also argues that it is reasonable to speculate that Dobzhansky and Muller are wrong. You don’t need two, or even any mutations for speciation to occur, just a barrier to gene flow that can be anything from isolation by distance to a road to disruptive selection.Barriers to reproduction will naturally arise.

Next time:  I will NOT talk about why you cannot reduce group selection to individual selection.  I say this for one simple reason:  I got nothin.  As far as I can tell indirect genetic effects are so powerful that any attempt to reduce group selection to individual selection is destined to end in tears.

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