Variation for supply driven evolution

I’ve taken a very long hiatus (nearly 5 years!) from this blog. I suppose getting married and getting an MD are good excuses, but Artem has very kindly let me return. And I greatly appreciate this chance, because I’d like to summarize an idea I had been working on for a while. So far, only two publication has come out of it (Xue et al., 2015a,b), but it’s an idea that has me excited. So excited that I defended a thesis on it this Tuesday. For now, I call it supply-driven evolution, where I try to show how the generation of variation can determine long-term evolution.

Evolutionary theoreticians have long known that how variation is generated has a decisive role in evolutionary outcome. The reason is that natural selection can only choose among what has been generated, so focusing on natural selection will not produce a full understanding of evolution. But how does variation affect evolution, and can variation be the decisive factor in how evolution proceeds? I believe that the answer is “frequently, yes,” because it does not actually compete with natural selection. I’ll do a brief overview of the literature in the first few posts. By the end, I hope how this mechanism can explain some forms of irreversible evolution, stuff I had blogged about five years ago.

The idea that variation is crucial in evolution has been expressed in many ways. I first encountered it in undergrad as constraint-based evolution (Gould, 1980). Gould observed that of all possible morphological forms, only a small fraction are actually populated with organisms. Why is this? The is the usual adaptationist answer is that only the extant forms have sufficient fitness, but the structuralist answer is that most forms were never generated (say, a leukemia that suddenly became free living and went off to become an amoebae in the sea), and therefore cannot succeed.

This was part of Gould’s salvo against adaptationism, of course, but this line of argument was soon taken up by the the new field of evo-devo (for example see Alberch, 1982; Smith et al., 1985). The idea is that animals and plants, at least, have to go through a process of development that severely constraint the type of organism that can be produced, and these constraints are not easily overcome by natural selection.

Mathematical biologists enthusiastically rose to the occasion of modelling constraints (some might say too enthusiastically; see Arnold, 1992). Active work continues here (Rice, 2004), but basically constraints were modeled using quantitative genetics; more specifically the G-matrix, which describes the additive genetic variances and covariances of the different phenotypic traits we are studying. The G-matrix describes the shape of an ellipse in high dimensional space, where the ellipse is the additive genetic variance in the current population:

Examples of G-matrices

These figures are courtesy of an”>excellent website that introduces G-matrices. In these figures, the axes measure two different traits (“breeding” values basically mean genetic values, if one’s arm is chopped off, the breeding value of one’s arm length is different from one’s actual arm length) and each red dot is a member of the population. In the left figure, the two traits are uncorrelated. In the right figure, the two traits are correlated with each other, selection increasing Trait One will also increase Trait Two.

Note that the above figures are simply what’s observed, what maintains the shape of G is not implied. Many things affect the G-matrix, including natural selection. If there is an evolutionary constraint in the generation of variation, it will also show up in the G-matrix because some types of organisms will be harder to generate than other types. The right figure above, for example, can be produced if organisms with low/high Trait Two value and high/low Trait One value are very hard to generate. Quantitative geneticists call this the M-matrix, see Rice (2004) for a good review of how it affects the G-matrix. However, it’s the G-matrix, not the M, that’s directly involved in evolution.

G-matrix that’s relatively stable over time (as we would expect if the matrix is due to constraints of novelty generation) have all sorts of interesting consequences, such as weird trajectories to evolutionary optimums. One of the consequences, however, is when they are combined with rugged, multi-peaked fitness landscapesG-matrices can determine which of the local peaks evolution goes to. Wallace Arthur (2004) calls this effect “developmental bias”.

Based on figure 1 of Arthur (2004)

Contour of fitness landscape for two traits, with G-matrices for the populations. Figure is based on Figure 1 of Arthur (2004)

In the above figures, depending on the form of the G-matrix, the population will either move to the right upper hill (left figure) or the right lower hill (right figure).

EDE_04033_f2This has very interesting consequences for long-term evolution, as Arthur realized in the adjacent figure. Depending on what the G-matrix looks like, a population can undergo long term evolution upwards (path a), or downwards (path b). Thus, the shape of the G-matrix, representing the variation in evolution, in Arthur’s (2004) words:

…variation is not merely a prerequisite for evolutionary change, which, given its existence, allows all-powerful selection to dictate the direction of change. Rather, the form of the variation is part of the “orienting mechanism” of both short-term and long-term evolution. So, development is not a passive player in the evolutionary game but an active determinant along with its partner, natural selection, of the creatures that emerge from the realm of the possible to the realm of the actual.

But how to formalize this intuition? We have no idea how real-world fitness landscapes look like, how rugged they are, how variable over time they are, etc. Artem had a good pair of post about it here and here. In fact, he suspects local fitness optima cannot be reached at all! Beyond fitness landscapes, we barely have any idea how real world G-matrices look like, and we don’t really know how plastic they are over time (although there is excellent work going on here, such as Arnold et al. (2008) and all its extensions (Jones et al., 2004, 2007)).

Next post, I will write about the evolution of mutation rates (related to Xue et al., 2015b), where how new variants are generated carry grave consequences.


Alberch, P. (1982). Developmental constraints in evolutionary processes. InEvolution and development (pp. 313-332). Springer Berlin Heidelberg.

Arnold, S.J. (1992). Constraints on phenotypic evolution. American Naturalist, S85-S107.

Arnold, S.J., Bürger, R., Hohenlohe, P. A., Ajie, B. C., & Jones, A. G. (2008). Understanding the evolution and stability of the G-Matrix. Evolution, 62(10), 2451-2461.

Arthur, W. (2004). The effect of development on the direction of evolution: toward a twenty‐first century consensus. Evolution & development, 6(4), 282-288.

Jones, A.G., Arnold, S. J., & Burger, R. (2004). Evolution and stability of the G-matrix on a landscape with a moving optimum. Evolution, 58(8), 1639-1654.

Jones, A.G., Arnold, S. J., & Bürger, R. (2007). The mutation matrix and the evolution of evolvability. Evolution, 61(4), 727-745.

Gould, S.J. (1980). The evolutionary biology of constraint. Daedalus, 39-52.

Rice, S.H. (2004). Evolutionary theory: mathematical and conceptual foundations. Sunderland: Sinauer Associates.

Smith, J.M., Burian, R., Kauffman, S., Alberch, P., Campbell, J., Goodwin, B., … & Wolpert, L. (1985). Developmental constraints and evolution: a perspective from the Mountain Lake conference on development and evolution. Quarterly Review of Biology, 265-287.

Xue, J.Z., Costopoulos, A., & Guichard, F. (2015a). A Trait-based framework for mutation bias as a driver of long-term evolutionary trends Complexity DOI: 10.1002/cplx.21660

Xue, J.Z., Kaznatcheev, A., Costopoulos, A., & Guichard, F. (2015b). Fidelity drive: A mechanism for chaperone proteins to maintain stable mutation rates in prokaryotes over evolutionary time. Journal of Theoretical Biology, 364: 162-167.

6 Responses to Variation for supply driven evolution

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  6. I feel like there is a pattern in 5-year returns.

    I’ve been recently coming back to this post of yours, both as I read your new manuscript on SDE (I will email you soon!) and finish up my own on punctuated disequilibrium. In particular, I’ve been trying to make sense of the G-matrix. And here, and for long-term evolution, I really don’t think we should be interested in the G-matrix but in the M-matrix (which you mention briefly but dismiss as just a factor that shapes G).

    Here is what I think is the reason why. I might be completely wrong, but I just wanted to think out loud.

    As far as I’m gathering from more and more reading, the G-matrix is just a description of the standing variation in the population. It matters mostly in sexual populations.

    In many of our models, we are basically looking at selective sweeps through basically monomorphic populations. Or at least many of the ‘main ideas’ can be stated without reference to sex or how standing variation interacts with itself. Thus, for us the G-matrix might as well always be single point. What matters for us, and for long-term versions of the peak selection you describe here, is not the G-matrix but the M-matrix that shows where the next competitor point will spring up.

    Now, of course, if we aren’t focused on selective sweeps and (nearly) monomorphic populations then the M-matrix would be mapping one G-matrix to the next (as the M-matrix creates new mutations) and thus it would shape subsequent G-matrices and their shapes. So in that sense, the M-matrix is ‘in’ the G-matrix as you say above. But I think the G-matrix is actually the superficial (and overly complicated) part for many of the things we are interested in, and just thinking/talking about the M-matrix is sufficient for many of the points we make?

    Or am I missing something? I will be thinking more about this as I try to read more genetics.

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