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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"If I had the power to-day, I should most deliberately set out to endow our capital cities with all the appurtenances of art and civilization on the highest standards of which the citizens of each were individually capable, convinced that what I could create, I could afford–and believing that money thus spent not only would be better than any dole but would make unnecessary any dole. For with what we have spent on the dole in England since the war we could have made our cities the greatest works of man in the world."

The Last Mammoth

Well, perhaps not the last last, but a fascinating study of one mammoth in the twilight of the species.

We are so far away from having another ice age at this point, that we can only look back at the last one with wonder. And one of its major wonders was that there were mammoths. One of many megafauna species, mammoths reigned through millions of years, weathering a dynamic climate of ice ages and integlacial periods with ease. Yet the arrival of humans spelled their doom. A recent paper in Science discussed the fate of one mammoth, based on atomic /isotopic analysis of its tusks and teeth, telling us where it was born, roamed, and died. 

Ice ages come and go, but something unusual caused the extinction of innumerable megafauna after the last one.

The remains of this mammoth were found north of the Brooks Range in Alaska. Tusks are teeth that grow continuously through life, so the length of a tusk represents a chronological sequence of deposition, which these researchers analyzed for strontium, oxygen, and other isotope ratios, which reflect the animal's diet and thus its location, since these ratios differ across the landscape. In this case, they were able to guess that this mammoth was born well south of the Brooks Range, around the middle Yukon river. It then spent its youth roaming the area, out to what is now the pacific coast, and eventually inland as well to what is now Fairbanks. At some point it ranged north as well, above the Brooks Range. Finally, in what the researchers surmise was a late spring in its ~28th year, this mammoth succumbed to old age just north of the Brooks range and gave us its almost complete remains.  

Figure describing the haunts of one late Pleistocene mammoth, from strontium isotopes in its tusks. The black lines are "best walks" between the various isotope identified site, and somewhat fanciful idea of how this mammoth may have ranged through its life.

It is fascinating to have such an intimate look into the life history of such a distant and mysterious creature, which clearly ranged freely and widely. But it was not really the last mammoth, living 17,000 years ago when populations were robust and humans had only begun to encroach on its realm. No, the last mammoth remains are thought to be those of St. Paul island in the middle of the Bering sea (far lower left white dot in the accompanying map), dating to about 5,600 years ago. Why an island? Well, that is clearly because they had been hunted down everwhere else, leaving only isolated populations stranded after the sea level rise ending the last ice age flooded the rest of the Bering land mass.

Humans have been causing ecological catastrophe for a very long time. But with climate change, we are operating on an entirely new scale of lethality to the biosphere. It may have begun with charismatic megafauna, but whole ecosytems are now in the crosshairs.

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• Evolution? Yes.

All Facts are Theories, But Not All Theories are Facts

Are theories and facts different in kind, or are they related and transform into each other?

During the interminable debates about "Intelligent Design" and evolution, there was much hand-wringing about fact vs theory. Evolution was, to some, "just" a theory, to others a well-attested theory, and to others, a fact, whether in the observation of life's change through time (vs the straight creationists), or in the causal mechanism of natural selection (vs the so-called intelligent design proponents). Are theories just speculations, or are they, once accepted by their relevant community, the rock-like edifice of science? And are facts even plain as such, or are they infected by theory? Our late descent into unhinged right-wingery poses related, though far more complex, questions about the nature of facts and who or what can warrant them. But here, I will stick to the classic question as posed in philosophy and science- what is the distinction and or relation between facts and theories? This follows, but disagrees with, a recent discussion in Free Inquiry.

The official scientific organs (NCSE) have generally taken the position that theories are different from facts, making a pedagogically bright line distinction where things like tectonic plate theory and evolution are theories, while rock compositions and biochemistry are facts. In this way, science is made up, at a high level, of theories, which constantly evolve and broaden in their scope, while the facts they are built on arrive on a conveyor belt of normal scientific progress, via lab experiments, field work, etc. Facts help to support or refute theories, which are such abstract, dynamic, and wide-ranging bags of concepts that they can not rightly be regarded as facts.

All very pat, but what are facts? It turns out that nothing we observe and call a fact escapes some amount of interpretation, or the need to be based on theories of how the world works. We grow up with certain axiomatic and built-in conditions, like gravity, vision, and physical cause and effect. Thus we think that anything we "observe" directly is a fact. But all such observations are built on a history of learning about how things work, which is in essence starting with a bunch of theories, some instinctively inborn, which are gradually satisfied by evidence as we grow up ... to the extent that we take many things for granted as fact, like being able to count on gravity as we are walking, that the sun comes up every day, etc. Facts are not automatic or self-attested, but rather are themselves essentially theories, however simple, that have been put to the test and found reliable.

And therein lies a clue to how we, and especially scientists, evaluate information and use the categories of fact and theory in a practical and dynamic way. Lawyers often talk of coming up with a theory of the case, which is to say, a story that is going to convince a jury, which has the job of finding the facts of the case. When the jury finds the theory convincing, and vote for the lawyer's side, the facts are found insofar and the law is concerned. Their determination may come far short of philosophic rigor, but the movement is typical- the movement from theory to fact. 

On the other hand, what is a theory? I think it can be described as a proposed fact. No one would propose a theory if they didn't think it was true and explanatory of reality. Whether broad or narrow, it is a set of interpretations that seek to make sense of the world in a way that we limited humans can categorize, into our store of knowledge. For instance, Freudian theories of repression, Oedipal complexes, castration fears, etc. would have been, if borne out, facts about our mental lives. Being rather vague, they may have needed a great deal of refinement before getting there, but all the same, they were proposed facts regarding what we feel and do, and the psychic mechanisms that lead to those feelings. 

In science, it is the experiment and its communication that is the key event in the alchemy of transforming theories into facts. Science is unusual in its explicit and purposeful interaction with theories that are unproven. Tectonic theory was once a mere theory, and a crackpot one at that. But as observations came in, which were proposed on the basis of that theory, or retroactively appreciated as support for it, such as the lengthy hunt for mid-ocean ridges where tectonic plates separate, and other faults where they converge, that theory gained "fact-ness". Now it is simply a fact, and the science of geology has gone other to other frontiers of theory, working to transform them into fact, or back off and try some others.

The mid-Atlantic ridge, straining to be understood by observers equipped with the theory of plate tectonics. Also, a video of the longer term.

Another example is the humble molecular biology experiment, such as cloning a gene responsible for some disease. The theory can be so simple as to be hardly enunciated- that disease X is in part genetic, and the responsible mutation must occur in some gene, and thus if we find it, we can establish a new fact about that disease as well as about that gene. Then the hunt goes on, the family lineages are traced, the genetic mapping happens, and the sequencing is done, and the gene is found. What was once a theory, if an unsurprising one, has now been transformed into a fact, one perhaps with practical, medical applications.

But the magic of experiments is usually only discernable to the few people who are sufficiently knowledgeable or interested to appreciate the transformation that just happened. The boundary between theory and fact depends on the expertise of the witnesses, and can be sociologically hazy. Does homeopathy cure disease? Well, hemeopathic practitioners regard that as fact, and have gone on to an elaborate practice and pharmacopeia of dilute solutions to effect various cures. Others disagree and regard the whole thing as not only a theory, but a stunningly wrong-headed one at that- as far as can be imagined from having gained fact-hood. Real science revolves around experiments done to what is essentially a standard of philosophical proof. Techniques are reported and consistently applied, controls are done to isolate variables of interest, materials are described and made publicly available, and the logic of the demonstration is clarified so that readers knowledgble in the arts of the field can be confident that the conclusions follow from the premises. And the practitioners themselves are culturally vetted through lengthy apprenticeships of training and critique. 

The practice of peer review is a natural part of this series of events, putting the experiment through a critique by the (hopefully) most knowledgeable practitioners in the field, who can stand in for the intended audience for whom the experiment is supposed to perform this alchemical transformation of theory. The scientific literature is full of the most varied and imaginative efforts to "factify" hypotheses, hunches, and theories. Very few of these will ever be appreciated by the lay public, but they lay the ever-advancing frontier of facts from which new hypotheses are made, new theories tested, and occasionally, some of their resulting facts are discovered to be useful, such as the advent of gene therapy via the Crisper/Cas9 gene editing system, liposomes, and associated technologies. 

Another aspect of the public nature of science and peer critique is that if a knowledgeable observer disagrees with the theory-fact transition purported by some experiment, they are duty-bound and encouraged to replicate those experiments themselves, or do other experiments to demonstrate their counter-vailing ideas. On a cheaper level, they are welcome and encouraged to ask uncomfortable questions during seminars and write tart letters to the editors of journals, since pointing out the errors of others is one of the most enjoyable activities humans pursue, and doubles as a core of the integrity that characterizes the culture of science. In this way, facts sometimes reverse course and travel back into the realm of theory, to sweat it out in the hands of some disgruntled grad student and her overbearing supervisor, destined to never again see the light of day.

Experiments crystallize most clearly the transition from theory to fact. They create, though careful construction, a situation that banishes incidental distractions, focuses attention on a particular phenomenon, and establishes a logic of causation that forms (hopefully) convincing evidence for a theory, transforming it into fact, for knowledgeable observers. They create controlled and monitored conditions where knowlegeable people can "see" the truth of a theory being put to a decisive test. Just as we can now see the truth of the heliocentric theory directly with the use of spaceships sent out across the solar system, the observation of a fact is a matter of the prepared mind meeting with a set of observations, either tailored specifically in the form of an experiment to test a theory, or else taken freely from nature to illuminate a theory's interpretation of reality. Nothing is intrisically obvious, but needs an educated observer to discern truth. Nothing is completely theory-free. Nevertheless, facts can be established.

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Covid Will Never End

But it will be a very small problem, once everyone is vaccinated.

It should be obvious by now that Covid-19 is endemic and will be with us forever. At a fatality rate of roughly 2% for the unvaccinated, it is better than the bubonic plague (50%) and smallpox (30%), but far worse than influenza (0.1%), not to mention colds and other minor respiratory infections. With vaccination, the fatality rate is reduced to, in very rough terms, 0.05%. Thus, with vaccination, Covid-19 is a much less significant public health problem, superceded by influenza, whose vaccine is much less effective.

(This calculation, of the death rate, in vaccinated people, is rather fraught, because the infection rate is hard to gauge. But assuming that over the four months when roughly one third to one half the population has become vaccinated, and exposure rates of this population similar to that of the unvaccinated and productively infected population, the overall death toll was roughly 50,000 people, of which 1,263 were vaccinated, for a ratio of 40:1)

While breakthrough infections and consequences like hospitalization and death (and possibly long covid, though that is unclear) are not impossible for vaccinated people, they are rare enough that we can resume normal activities. Current policies to limit the spread of the virus, even by vaccinated people who can carry and transmit it via light infections, is mostly aimed at the remaining unvaccinated population, who will be ending up in the hospital at much higher rates, and creating the public health burden. So no wonder patience is wearing thin with the unvaccinated, who will eventually just be cut loose to take their chances while the rest of society moves on in a new world where covid is as or even more manageable than influenza.

Why is Covid less severe in children? ACE2, the key receptor for the virus seems to have lower expression naturally, and is driven even lower by incidental conditions like asthma and allergies. Other cold viruses, to which children are widely exposed, may have "pre-vaccinated" them to the new coronavirus. And children seem to produce fewer inflammatory cytokines, producing a less exaggerated immune response, which is the main factor in later Covid pathology.

Why all the breakthrough infections? One issue is that vaccination primes the immune system, which does not prevent infection, actually. What it does is to shorten the time that the body needs to fight an infection that has already occurred, by pre-educating the immune system about the target it is facing. So vaccinated people are going to be infected at normal rates, but they just won't show symptoms nearly as frequently. And second, as widely discussed, the vaccines have great, but not perfect effectiveness. It stands to reason, as has been widely reported, that more vaccines are better than fewer, and as the virus mutates to meet our weapons of social distancing and vaccination, new editions of covid vaccines will be needed. There can never be enough education of our immune systems against these evolving threats. With the advent of successful mRNA vaccines that can be rapidly programmed with new immunogens, we have the opportunity to increase our protection against both new threats, in form of yearly (or more) covid boosters, and against old threats, like influenza, whose vaccines are stuck in a time warp of antiquated technology and poor effectiveness.

This all implies that we (the vaccinated population) will be spreading around covid on an ongoing basis. It will be endemic, and our protection will be by vaccination rather than isolation. The virus has little interest in killing us, so it will likely evolve to be more benign, as our countless cold viruses have done, thereby spreading more effectively in a well-mixed population.

The extremely urgent need for universal vaccination raises the question of why the FDA has not been faster in its authorizations. All children should have already been cleared for vaccination, and full authorization should already have been granted for adults. The safety and efficacy data is present in overwhelming amounts, and if not, (in the case of children), the studies should have been started much sooner, and run on compressed schedules. One gets the impression that this is a bureaucracy that is overly wedded to process, rather than data- particularly the critical interpretation of data that comes from actual use in the field, rather from corporate reports. And this slowness has implications for future vaccines, such as ones against influenza, as well. We deserve better from our public institutions.

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