Speciation in continuous populations

I am in Brazil this week to give a talk about speciation in continuous populations, so I figure I will save a little effort by summarizing some of the stuff that is in that talk. By the way, Sao Carlos is a wonderful town, and if you can come up with an excuse to come to Brazil I strongly recommend it. Of course, if you are a vegetarian, while it SHOULD be a good place for you, man do these folks like their meat!

So, on to speciation. This is a project I did with Maggie Eppstein, currently chair of the University of Vermont Computer Science department, and Josh Payne, then a computer science graduate student and now a postdoc at the University of Zurich. In other words, it was big on computer science, and maybe a bit less big on biology, but the implications for biology are important. (Payne, J.L., Eppstein, M.J., and Goodnight, C.J. “Sensitivity of Self-Organized Speciation to Long Distance Dispersal”, Proceedings of the 2007 IEEE Symposium on Artificial Life (Alife’07), pp. 1-7, 2007.  Eppstein, M.J., Payne, J. L., and Goodnight, C.J., “Underdominance, Multiscale Interactions, and Self-Organizing Barriers to Gene Flow”, J. Artificial Evolution and Applications (special issue on Biological Applications), Volume 2009, Article ID 725049, 13 pages, 2009

This project stemmed out of a discussion I had with several people at NECSI (http://necsi.edu/). So, in talking to them I came to realize that when you had two types that were incompatible, they were distributed randomly on a plain, interactions were local, and the types spread contagiously that there would be this interesting process of coarsening. That is if you started out with the types randomly distributed the locally common type would have an advantage and increase, whereas the locally rare type would have a disadvantage and decrease. The net result would be your random distribution would devolve into regions that were primarily one type, and other regions that were the opposite type. I also found out that the boundary between these regions would wander about randomly across the plain, but it would get trapped by any sort of boundary

Sayama coarsening

Coarsening. In this example the fitness of an individual is proportional to the number of neighbors of the same color. This results in a process of coarsening in which the once uniform distribution becomes clumped with low fitness boundaries between the different color regions.

In any case the question becomes whether speciation this process of coarsening in populations with local interaction lead to speciation. We decided to look at the very simplest case, that of simple underdominance. That is, can we take a population with within locus underdominance, and have it self organize into two species.

By the way, as with any good theoretician, I will use Mayr’s biological species concept as my definition of a species. I know that this is really not a great definition, but heck, I got to meet Professor Mayr on several occasions and he said nice things about my research, so I stand by my decision. . .

First off, the trivial case is where the underdominance is so extreme that the heterozygote is lethal:

Genotype       A1A1             A1A2           A2A2

Fitness               1                   0                   1

Obviously, such a population will immediately split into two reproductively isolated “species”. Yes, this works, but it is biologically totally unconvincing.

I won’t go into the details, however, what we can show is that it is quite easy to introduce mild underdominance into a viscous population. Thus, we would be hardly surprised to see underdominance such as:

Genotype       A1A1             A1A2           A2A2

Fitness               1                   0.9                   1

The problem is that this is not an effective barrier to gene flow. Indeed we were able to show that it takes a complete reproductive isolation to prevent the movement of a neutral gene across the boundary.

gene penetration

Gene flow of a neutral gene across a underdominant boundary. Note that there is a linear relationship between the degree of underdominance and neutral gene penetration, and importantly, a discontinuity when gene flow is zero.

Thus, we are only going to allow mild underdominance, yet we want the population to divide into two completely reproductively isolated populations. It turns out that it is not that hard if we allow multiple loci with mild underdominance. To illustrate this consider two loci with underdominance of 50%, so that the double heterozygote is lethal.

two loci no epistasis

Two underdominant loci. Double homozygotes have the highest fitness, single heterozygotes (yellow) have lower fitness, double heterozygote (white) is lethal.

If we set up this system on a 100 by 100 field with nearest neighbor mating and dispersal we see “coarsening”, but because the coarsening is not focused there is no speciation: coarsening

Local mating leads to “coarsening”, patches of one double homozygous genotype (A1A1B1B1 etc) separated by hybrid zones.

In other words, simply by having localized mating and underdominance we are half way there. We get the coarsening, and regions of the two species, but in all cases there is a pathway through a viable hybrid zone between any two regions.

This is where we had to introduce some epistasis. In our next iteration we added a bit of epistasis so that the two opposite corner genotypes were favored:

Two loci, epistasis = 0.1

Two underdominant loci. Double homozygotes of the same numerical value have the highest fitness, single heterozygotes (yellow) have lower fitness, double heterozygote (white) is lethal.

This now results in coarsening and eventually speciation:


Local mating leads to coarsening, and domination of the two most fit genotypes (A1A1B1B1 and A2A2B2B2). In this case all of the hybrids are lethal, and the two populations are reproductively isolated.

This is actually very interesting, because you will note that in the early stages all four homozygous forms are formed, but the single locus heterozygous boundaries wander around randomly. When two such come into contact they coalesce into a single stronger boundary, eventually leading to speciation. Importantly, this is not limited to only two loci. It turns out that this coarsening and coalescence of leaky boundaries will continue regardless of how many loci are involved. Thus, even extremely mild underdominance at a large number of loci will eventually lead to speciation in this model:

speciation with multiple loci

The effect of number of loci on speciation. In a panmictic population (black line) the population always fixes on one of the two best genotypes, although the time to fixation changes as the number of loci increases. In spatically structured populations speciation always occurs, with the time to speciation being a function of the number of loci required and the amount of epistasis.

This is a very simple simulation, yet it makes the important point that when there are genetic incompatibilities speciation can easily occur. Indeed, this implies that the speciation may be the expected outcome for a widespread species with limited gene flow.

One Response to “Speciation in continuous populations”

  1. […] Goodnight discusses some of his own work showing that within populations similar individuals tend to cluster …to form groups and this may lead to […]

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