Where did all the Diversity go?

The Lewontin Paradox says that, by the neutral theory of evolution, large populations should show large molecular diversity... but they don't. Where does it go?

One of the pillars of modern evolutionary theory is the theory of neutral evolution, which is a complement to that of natural selection. It posits that most mutations have no significant effect, so most evolution on a molecular scale is a random walk of mutations appearing, disappearing, or rising in frequency in the population. Occasionally they may take over the whole population, which is called "fixing" their frequency at 100%. This in turn has given rise to the concept of the molecular clock. If the neutral evolution process is truly random and constant through time, then it can be used to date phylogenetic events, by assuming that the divergence between species in their neutral molecular sequences rises monotonically through time and reflects the time since their divergence as species, not different selective trajectories.

Molecular clocks have various problems, like mutation rates that can be variable between species, but on the whole, they have worked very well and have generated numerous successful predictions of phylogenetic branching patterns and dates of key events. But there is another corollary of neutral evolution theory that is less supported. That is its prediction of overall molecular diversity in contemporary populations. Since mutations arise constantly, the molecular diversity of a population should be roughly proportional to the population size, given as N. But that is not what is seen, at all. Natural populations actually have a small range of variation, of a couple orders of magnitude, while their actual sizes can obviously range over many, many orders of magnitude, from small populations of charismatic species like polar bears to astronomical populations of mice, ants, and protozoa.

This is called Lewontin's paradox, after a biologist who pointed it out most succinctly. And this "missing diversity" has been a topic of discussion for the five ensuing decades. Several papers over the last decade tackled it again, and are reviewed here. One would think with the flood of molecular data that this kind of molecular conundrum could be easily solved. Sequence enough members of a large population, and see what happened, or happens, over time. But the issue is not the fact of the missing diversity, but rather the mechanisms explaining why it occurs. 

A graphic statement of the paradox. The expected degree of diversity is marked in the gray band, whereas the observed diversity is marked by the colored dots.

One side of the debate is the selectionist camp. They argue that selection is the missing ingredient. Selection not only drives down the diversity of selected alleles, whether they are deleterious or beneficial, but it also has a "hitchhiker" effect where nearby molecular variation that is not itself selected is carried along during selection events and thinned out just as the selected alleles are. Hitchhiking is limited by recombination, which is the process by which parts of our chromosomes are broken apart during meiosis and stitched together with those from the other parent. Over (long periods of) time, recombination allows alleles to separate from nearby baggage so that they can be selected on their own merits. But since recombination happens on average only a few times per chromosome per meiosis, this rate of isolation by recombination is quite slow. Typically, humans inherit alleles in large batches within "haplotypes" of nearby genes and their alleles, which is one reason why some traits tend to occur together.

The authors offer their quantitative model of how much decreased molecular diversity positive selection and linkage to neighboring loci could supply, in the blue band. While this model approximates actual values for very large populations, it does not for mid-size populations, so is still insufficient as a general explanation.

While there is a lot to be said for selectionist arguments, a couple of authors have pointed out that, in quantitative terms, selectionists have not yet resolved the problem fully. There are many possible explanations, however, each contributing to the ultimate solution. The model of full population diversity is based on a variety of idealized assumptions- a fully mixed, randomly mating population, with no selection, and constant population size through time. None of these assumptions are realistic, and it falls to population geneticists to figure out how real populations relate to this ideal. They have come up with a concept called the "effective population size" to adjust for various non-idealities. For example, the effective population size of humanity is about 10,000 individuals. This is radically smaller than the actual human population, largely due the recency of our population growth. Humans went through a bottleneck of very few individuals during the glacial minimums of the last few million years, and the recent expansion in population has not substantially added to that diversity, at least yet. Numbers do not equal diversity.

Could this be a more general property? Do all populations go through enough seasonal or millennial variation in numbers that their true effective population sizes are much smaller than their current numbers lead us to believe? Could this be true for ants, and termites, and protozoa? That is unlikely, really. The paradox is universal, not only applying to big species, but to all species. One might also note that the level of the grey band in the graphs above, at large population sizes, is inherently unrealistic, positing that essentially every position in the genome varies within large populations- those with more individuals than nucleotides in their genome. Were this the case, it would be hard to define a species at all. So the very coherence of the species concept is at stake here, in finding mechanisms that keep species from exploring the entire space of molecular possibilities.

This is where the paradox rests right now, amidst some controversy in the field. But in principle, the sitution is not so unclear. The neutral theory is certainly correct in terms of the numbers of mutations arising in any population- that they are proportional to the population size, and should keep accumulating over time, up to a clearance rate by neutral (i.e. random) drift. And it is equally clear that there are no magical processes that eliminate that variation- rather, that some combination of non-ideal population dynamics and selection account for the loss, though the accounting has not reached mathematical completeness yet. I would favor putting more weight on selection, while others invoke more population dynamics such as assortive mating, seasonal bottlenecks, or winner-take-all mating systems. The most recent author states:

"Given that I find that models of linked selection are incapable of explaining the observed relationship between 𝑁𝑐 and 𝜋, this supports the hypothesis the diversity across species are shaped primarily by past demographic fluctuations."

And a prior author writes, in a similar vein: 

"... Instead, predicted diversities fall mostly along the x = y line — the result that we would expect if linked selection had only a limited impact on levels of diversity in large populations and diversity levels scaled with effective population sizes estimated in the absence of linked selection. This finding is consistent with the idea that demographic fluctuations are the principal determinant of levels of diversity among species. Interestingly, selfing species seem to show the best evidence of large reductions in diversity due to linked selection, perhaps due to their much reduced effective rate of recombination"

These authors generally grant a one or two magnitude effect to selection, which is only a partial solution. Unfortunately, leaving the remainder of the problem to population fluctuations is somewhat hand-waving. In fact, the demographic diversity of the many species affected, and the high uniformity of the loss of diversity, suggest that something more systematic is going on. 

One of the more recent analyses proposed an interesting idea along selectionist lines. This article reviewed work on fruit flies, which have vast population sizes and show the paradox most acutely. Thanks to artificial selection, fruit flies have come up with insecticide resistence traits in a matter of decades, when faced with the armamentarium of commercial fruit growers. And they have done so many times independently, generating the same mutations, a combination of which is needed for optimal resistance. This in a 140 million base pair genome that is expected to mutate at a little less than one mutation per fly per generation. What this author pointed out was that purifying selection against negative traits is fundmentally asymmetric vs positive selection for positive traits. Positive selection carries along its local hitchhiking variants to a much higher proportion of the population- i.e. to 100 %. Negative selection, which generally pares bad alleles down from already very rare frequencies, has a much lower hitchhiking effect. More importantly, positive selection ignores the "effective" population size, and can gain beneficial alleles as they arise from the entire existing population, leading to sweeps of positive selection that become more frequent the bigger the population is. Thus it may be that the rate of positive selection is higher than the modelers above have given it credit for.

• Why is biological diversity so much higher in warm latitudes? It isn't faster evolution. Perhaps slower extinction and fewer bottlenecks? This may be an argument for population fluctuations over selection as forces curtailing species diversity, if not molecular diversity.
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