The phenotypic view: Stopping rules and Quantitative Genetics

As Henry Louis Mencken once said “For every complex problem there is an answer that is clear, simple and wrong.”  Dawkins’ gene centric view is exactly that: clear, simple and wrong.  In its place I suggested a phenotypic view of evolution in which phenotypes are viewed as creating new phenotypes with a transition equation describing this process.  The most obvious elements of the transition equation are genes, but there are numerous other factors ranging from cytoplasmic factors and vertically transmitted bacteria to culture and inherited environmental factors (e.g., taking over the parent’s nesting site when they die).

This raises the question of whether we have traded the incorrect gene centered view for one that is, while perhaps closer to the truth, nevertheless impossibly complex, and therefor intractable.  The answer lies in deciding what we want to know and what we need to know about a system.

In the gene centered view of evolution we really don’t have a good understanding of how evolution acts on a gene until we have identified that gene, know its sequence, know the allelic variants and their effect on the phenotype, and all of the pleiotropic forces acting on that gene.  This information, which might be thought of as gene ecology and gene physiology, but certainly not gene evolution, has bred a sense that if you don’t understand everything there is to know about a gene you really can’t study evolution.

A good example is the alcohol dehydrogenase gene (ADH)  in Drosophila.  Since the discovery ADH in 1964 (Johnson and Denniston Nature 204:906) and the identification of the latitudinal gradient in the ADH fast/slow allele polymorphism in 1973 (Vigue & Johnson Biochem. Genet. 13:721) an enormous amount has been discovered about the structure and function of the ADH locus.  For example, we know its structure, and the regions that are polymorphic (figure below) and that there is selection is affecting the F/S polymorphism (McDonald & Kreitman 1991 351:652):

ADH gene

Map of the ADH locus (taken from Powel 1997 Progress and Prospects in Evolutionary Biology:  The Drosophila Model.  Oxford University Press, page 423).  Note that we know the specific location of the single nucleotide polymorphism that gives rise to the fast and slow alleles.

Nevertheless, all of this knowledge of the gene structure has told us little about the selective forces acting that create maintain the ADH cline, nor has it explained the rather substantial variation in alcohol knockdown resistance that is seen within the different ADH genotypes:

ADH activity

ADH activity in 47 lines of D. melanogaster each with a different homozygous second chromosome from a natural population, but identical for all other chromosomes. (taken from Powel 1997 Progress and Prospects in Evolutionary Biology:  The Drosophila Model.  Oxford University Press, page 423).

The point is not to criticize the very fundamental and interesting work on the ADH gene.  Rather, my point is that from the perspective of understanding the evolution of alcohol tolerance at the phenotypic level, this tremendous detail concerning the gene physiology has done little to advance our understanding of either selection or inheritance of this trait.  On the other hand, from a genic perspective, it is clear we still do not know enough about the ADH gene to explain its evolution in the manner we would like.

Unfortunately, demonstrating that the genic approach is not adequate does not save the phenotypic approach.  It should be clear that using the phenotypic approach the “true” transition equation from one phenotype to the next is impossibly difficult, and almost certainly complex in the formal sense of the word.  This, however, turns out to not be too serious a problem, and one for which the solution is already known.  In particular, we need to recognize that there is a difference between what we need to know, and what we want to know.  Certainly, we would like to know everything there is to know about the factors affecting a trait such as alcohol metabolism.  From a phenotypic evolution perspective what we need to know is enough to predict the offspring phenotype from the parental phenotypes.

The point is that we can work to define the between generations transition equation in ever greater detail;  however, at some point we can decide that we know the transition equation well enough and stop at that level of detail.  The best starting point for this is classic quantitative genetics.

Anybody who has studied quantitative genetics (which, sadly is a small and dwindling number) knows that it was introduced by Fisher, and if you read the classic text of Falconer and Mackay, you know that the field was originally developed from a theoretical perspective of the phenotypic effects of numerous unmeasurable underlying loci.  However, after giving it some serious thought I realized that what Fisher really did was make the world safe for blending inheritance.

In the early part of the last century, around the time of the rediscovery of Mendel there were two schools of thought surrounding inheritance (see Provine “The origins of theoretical population genetics” 2001, U of C Press).  One of these schools was the Biometicians.  The Biometricians wanted to believe in blending inheritance, but they were caught in the statistical problem that with bi-parental inhertance the variance in a population should go down by half every generation.  This is a crippling problem for the blending inheritance model.  Fisher came along and showed that with an infinite number of Mendelian loci of infinitesimal effect (the infinitesimal model) the offspring mean would in fact be the average of the two parents, but that because of hidden variation (the segregation variance) the variance in the population would not decline.  Thus, simplistically, quantitative genetics is based on the assumption of blending inheritance with no loss of variation.

The point for our story, however, is that Fisher suggested a simple regression of offspring on midparents to describe the transition equation between generations.  The slope of this simple regression is (in theory) the heritability, and is proportional to the response to selection (yes, I am getting ahead of myself).  (By the way, I say in theory, because Fisher presented a very explicit model of additive genetic variance, and by extension heritability, in terms of the underlying Mendelian loci.  It turns out that the regression of offspring on midparents conforms to this formal definition of heritablity only under certain circumstances.)

Breeders equation

The regression of offspring on midparents.  The slope of the regression is the heritability, which is proportional to the response to selection based on the breeder’s equation.  Empirically there is ample evidence that in many cases this simple regression approach is predictive of the response to selection, often for 100 or more generations – and actually far longer than it should work if the simple genetic model on which it is based is correct.

Although Fisher (and Falconer and MacKay) developed this model on the assumption of underlying genetic effects, the truth is that the linear regression is probably a reasonable first approximation of the transition equation from parent to offspring for a wide range of possible modes of inheritance.  Although we may be very curious, we do not need to know why this regression works, we simply need to know that it does in fact work.  This simple transition equation in many cases may work well enough and we can stop there.  In other cases a more complex transition equation might be called for.  In the example of alcohol metabolism in Drosophila I would be tempted to use a linear model that had both a continuous effect (parental alcohol resistance), and a discrete effect (genotype at the ADH locus).

Thus, although the “true” transition equation is indeed impossibly complex, in almost all cases a relatively simple model will be good enough.  As evolutionary biologists the goal is to predict the phenotype in the next generation.  For this job quantitative genetics, or an extension of classic quantitative genetics, is the fundamentally correct approach.  How much detail we choose to put into describing the transition equation will be a function of how good a prediction we need to make.  Given that humans are inherently curious, we almost certainly will want to understand the details of why our transition equation works, but when we choose to do that, we need to be clear that we are studying gene anatomy, gene physiology, or gene ecology, but we are not studying the evolutionary biology of the original trait.

 

One Response to “The phenotypic view: Stopping rules and Quantitative Genetics”

  1. John Stanton-Geddes says:

    Hi Charles,
    Great to see your thoughts (Andrew directed me here)!

    I FULLY agree with you that both (a) not enough people study quantitative genetics and (b) that “as evolutionary biologists the goal is to predict the phenotype in the next generation”.

    Regarding the first point, the entire “missing heritability” debate of genome-wide association studies could have been avoided if quantitative geneticists were involved in the work (and thankfully, they are becoming involved – great work out of Peter Visscher’s group in the past few years).

    The second point seems to have been overshadowed in the rapid rise of molecular ecology fueled by cheap sequencing (this point eloquently made by Rockman (2012) and Travisano and Shaw (2013)…disclaimer that Ruth Shaw was my PhD adviser). To study evolution, we need to examine the process directly.

    To finish with a question – if our goal is to “predict the phenotype in the next generation” we are largely limited to short-lived species amenable to manipulation so we can evaluate our predictions. How well do you think the results from these studies extrapolate to long-lived species (e.g. sequioas or ants), which are the species ecologists are typically interested in (especially in regards to climate change)?

    Rockman 2012: http://onlinelibrary.wiley.com/doi/10.1111/j.1558-5646.2011.01486.x/full

    Travisano and Shaw 2013: http://onlinelibrary.wiley.com/doi/10.1111/j.1558-5646.2012.01802.x/abstract

Leave a Reply