Of Population Structure and the Adapative Landscapes

Last week I talked about adaptive topographies, and while my discussion may have done little more than add to the confusion, at least it got across Wright’s view that there are multiple selective peaks, which in essence means that there are multiple solutions to the problem of achieving high fitness.

12_EVOW_CH17

Figure taken from http://locustofauthority.wordpress.com/

Wright was interested in how a population could move from one local peak (such as the center intermediate height peak in the figure above) to another higher peak. He considered several options, which are summarized in the figure I showed last week:

SW_1988_fig4

He speculated that there were only a few ways that a population could move from one peak to another. In his figure above A, B, and C all depict very large population sizes: in the figure N is population size, U is mutation rate, and S is selection intensity, thus 4NU and 4NS large means that the population size is very large relative to the mutation and selection rates. The point of these top figures is that he thought that the only way a very large population can move from one peak to another is by a change in the environment (C).

His point is well taken in that in large populations drift will have only a small effect, and the population’s position on the adaptive landscape will be dominated by the effects of selection. Selection can only drive a population “up hill” to higher fitness, thus there is no way for the population to move down hill in fitness and cross a valley to a higher adaptive peak.

However, there are two reasons this may not necessarily be true. The first is a model put forth by Weinreich and Chao (2005 Evolution 59: 1175), that in retrospect is rather obvious (Isn’t that true of all great models?). Consider a population of bacteria (remembering they are the prokaryote equivalent of haploid) that has two loci A and B. Further imagine that A2B2 is intermediate fitness, A1B2 and A2B1 are of low fitness and A1B1 is the high fitness genotype. Based on Wright’s reasoning if we started a population off in a chemostat fixed for A2B2 it could not evolve to become A1B1 because of the mixed genotype low fitness valley. However, what Wright was not figuring on was just how large these populations are. A typical chemostat might have 106 to 109 cells per milliliter. If we imagine a mutation rate of 10-5 per locus then in each milliliter of chemostat there will be between 20 to 20000 bacteria that have mutated from A2B2 to A1B2 or A2B1. These mutants are effectively a low fitness population that is one mutation away from moving to the higher peak. Obviously it is in constant flux, new mutants are being added continuously due to mutation, but lost due to their lower division rate, and being eluted from the chemostat. Nevertheless, there is this substantial standing population of single mutant low fitness bacteria. At the higher density (109 cells) we would expect roughly 2 double mutant cells per milliliter at any given time. Note in the figure below the chemostat has 650 ml, thus such a system should have between 1.3 and 1300 high fitness individuals at any given time, even before taking into account the effects of selection.  Thus, in the very large population sizes of bacteria, two locus peak shifts, far from being rare, become nearly a certainty. Whether or not this works for the much smaller population sizes of multicellular organisms, or adaptive peaks that require the assembly of more than a few interacting loci remains an open question.

chemostat

A typical chemostat setup.  Media is added to the chamber at a constant rate, and effluent is removed.  When properly set up such chambers will maintain a constant population size of the experimental organisms. (image taken from http://openi.nlm.nih.gov/detailedresult.php?img=2906461_1471-2180-10-149-1&req=4)

The second model is Gavrilets’ “holey landscape” model (Gavrilets 1997 TrEE 12: 307). In this model Gavrilets points out that real adaptive landscapes have very high dimensionality, and that high dimension graphs do not behave the same way as the three dimensional graphs we are familiar with. He argued that with a large number of horizontal axes there would nearly always be a ridge along some dimension that connected the two points. Thus, he argued that rather than an adaptive landscape of hills and valleys we should think of adaptive topographies as flat plains with holes in them. The holes represent fitness valleys that selection would prevent the populations from entering. In this model the flat plain means that there is no selection, and the changes are neutral. Without selection all populations will drift at random over the landscape regardless of the population size (although large populations will move more slowly). For more on this check out some of Østman’s work on the evolutionary dynamics of holey landscapes. For what it is worth, my own perspective is that Gavrilets’ model may or may not be correct. Either way it does not qualitatively change Wright’s model. In Wright’s model it is necessary to cross adaptive valleys, in Gavrilets’ model there is a high dimensionality ridge connecting them. Either way it will take a combination of selection and drift to explore the landscape and move to a higher peak. After all, are we really surprised that the details of an 80 year old model may not be exactly correct?

Gavrilets-holey

Gavrilets’ holey landscape model. Taken from http://evolvingthoughts.net/2012/12/evopsychopathy-4-adaptive-scenarios/

Returning to Wright’s figure at the top of the post, parts D, E, and F consider what happens when populations are smaller. In D he imagines that a population is very small. He suspected that these would be so small that selection would be relatively ineffective, and they would be so dominated by drift, (not to mention inbreeding depression) that they would have little chance of evolving to a new peak. In figure E he suggests that a medium size population would be the ideal balance between selection and drift, with drift allowing exploration of the landscape, but selection still being strong enough to cause it to tend to climb towards peaks. The problem with the E scenario is that a single population can only explore a small part of the landscape, and it is unlikely that it would stumble upon a higher adaptive peak.

This leaves us with F, which is a metapopulation structure, that is a set of moderate size to small subpopulations that are joined together by a low level of migration. He felt that this population structure provided a set of subpopulations that were small enough to be strongly influenced by drift, and because it was a large number of subpopulations they could explore a much larger portion of the adaptive landscape. Finally, because they were tied together by low levels of migration, when a population evolved towards a new adaptive peak it could export this fitness solution to other populations.

So, this is why Wright focused on what are now known as metapopulations. He reasoned that it was only in these structured populations that you had the conditions that would allow the kind of random exploration of the adaptive landscape that he thought was essential for a population to discover and move to a higher adaptive peak.

One Response to “Of Population Structure and the Adapative Landscapes”

  1. Charles, I would be much obliged if you attended this session at Evolution:

    1A_302A Adaptation
    Date: Saturday, June 21, 2014
    Time: 8:30 AM – 9:45 AM
    Location: 302 A

    9:30 AM – 9:45 AM: Is it time to abandon the holey fitness landscape metaphor? (1228)

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