Monday, January 30, 2012

LHC Multilepton Search Unimpressive So Far

They looked at events with at least four leptons (electrons and muons) and some missing transverse momentum. In the inclusive selection, they observed 4 events while the expectation was 1.7 ± 0.9 events; that's roughly a 2.5-sigma excess although one should include the non-Gaussianity of the distribution to get a more accurate figure.When the Z veto was imposed, they got no events while the expectation was 0.7 ± 0.8 events which is OK within 1-sigma error. So only the veto-free figure is intriguing.

From here.

Material deviations from the Standard Model, of course, tend to support Beyond the Standard Model theories. And, greater than expected numbers of multilepton events, in particular, tend to support Supersymmetry (i.e. SUSY).

Statistical Issues

But, of course, as Motl acknowledges by remarking that the distribution is non-Gaussian, estimating a statistical significance for a discrete variable with a low value, like the predicted number of multilepton events at an experiment at the Large Hadron Collider, as a continous variable, is inaccurate. The probability of a number of events less than zero is zero, which makes a two sided set of error bars problematic. There are specific, probabilities for zero, one, two, three, four, five, etc. events under the Standard Model, and you have to compare a single data point to those probabilities.

Doing the statistical significance calculations correctly is going to reduce the statistical significance of finding 4 multilepton events, when the modal result would be 2 multilepton events, 1 or 3 multilepton events would be quite routine, and neither 0 nor 4 events is wildly improbable.

With a Z veto, which is designed to filter out false positives, you have a barely modal expectation of one event, which zero events and two events being quite likely (and zero being quite a bit more likely than two events).

Of course, when you are looking at two separate measurements that have some independence from each other, the probability that one or the other will be a given amount more than the expected value is greater, also reducing their statistical significance. You expect one 2 sigma event for every twenty trials and the more trials you do, the less notable a 2 sigma or 2.5 sigma event viewed in isolation becomes when the total context of experimental outcomes is considered.

Put another way, done right, the naiive 2.5 sigma event is probably very close to and possibly below a 2 sigma event, if the statistics is done right.

Implications For SUSY Parameter Space

Of course, since there are all sorts of SUSY theories, there is no one SUSY prediction for the number of multilepton events, although the LHC results, like those before it, imply that any deviation from the Standard Model expectation in SUSY, if it exists, must be quite subtle.

To be just a bit more refined, I have never heard anyone claim that SUSY theories for a given expected value of a result, have a materially different standard deviation from that expected value. The expected values are different, but not the variability. Therefore, if you are testing two hypotheses, one that the Standard Model is correct, and the other that a particularly SUSY model is correct, SUSY models that predict, for example, six or more multilepton events (rather than the observed two), or five or more Z vetoed multilepton events (rather than the observed zero), are strongly disfavored by the LHC results. This is potentially a pretty meaningful and precise constraint on the parameter space of SUSY models.

This is not the only constraint on SUSY parameter space. The apparent Higgs boson mass of about 125 GeV imposes real constraints, as do exclusion searches setting minimum masses of the lighest supersymmetrical particle which are fast approaching the TeV mass level. We are entering the era where fine tuning is increasingly necessary to fit SUSY theories to the data, and by implication, to fit string theory vacua to the data. LHC's experimental data won't have enough statistical power to entirely rule out SUSY even if every single one of its results is negative for its entire run, but it will impose every tighter constraints of SUSY parameter space that ties the hands of string theorists trying to fit theories to the observed data.

The simpliest versions of SUSY are already ruled out, but human ingenuity's capacity to come up with more clever versions that fit new constraints abounds.

Sunday, January 29, 2012

The M Theory Conspiracy

I've heard less plausible sociology of science arguments.

The Strategic Aspects Of A Research Agenda

In designing a research program, it is useful to distinguish between uncanny and mundane predictions. An uncanny prediction is one that is incongruous with both current scientific understanding of the phenomenon and any corresponding folk models, i.e., the prediction specifies aspects of the world that are hitherto unrecognized. In contrast, a mundane prediction is one that is consistent with our current understanding of the world, be it scientific or folk. If supported, uncanny predictions have a large impact on scientific knowledge – they provide substantial prima facie evidence supporting the hypothesis from which they were derived, and they open up new areas of empirical exploration. In contrast, when mundane predictions are supported, they have far less impact on scientific knowledge. Typically, a variety of existing perspectives can account for familiar phenomena, hence supported mundane predictions provide marginal evidence for the hypothesis from which they were derived; likewise, because the given effects are already familiar, such findings do not lead to new areas of empirical exploration. Most uncanny predictions will fail, and most mundane predictions will succeed. This is because existing scientific perspectives, and many folk models, will generally be accurate, hence hypotheses that are incongruent with such knowledge will often be incorrect, while hypotheses that are congruent with it will often be correct. Phrased in cost/benefit terms, uncanny predictions are thus a high-risk, high-yield enterprise, while mundane predictions are a low-risk, low-yield enterprise.

From here.

Altaic Populations Linked Via Uniparental DNA To Native Americans

The Altai region of southern Siberia has played a critical role in the peopling of northern Asia as an entry point into Siberia and a possible homeland for ancestral Native Americans. It has an old and rich history because humans have inhabited this area since the Paleolithic.

Today, the Altai region is home to numerous Turkic-speaking ethnic groups, which have been divided into northern and southern clusters based on linguistic, cultural, and anthropological traits.

To untangle Altaian genetic histories, we analyzed mtDNA and Y chromosome variation in northern and southern Altaian populations. All mtDNAs were assayed by PCR-RFLP analysis and control region sequencing, and the nonrecombining portion of the Y chromosome was scored for more than 100 biallelic markers and 17 Y-STRs.

Based on these data, we noted differences in the origin and population history of Altaian ethnic groups, with northern Altaians appearing more like Yeniseian, Ugric, and Samoyedic speakers to the north, and southern Altaians having greater affinities to other Turkic speaking populations of southern Siberia and Central Asia.

Moreover, high-resolution analysis of Y chromosome haplogroup Q has allowed us to reshape the phylogeny of this branch, making connections between populations of the New World and Old World more apparent and demonstrating that southern Altaians and Native Americans share a recent common ancestor. These results greatly enhance our understanding of the peopling of Siberia and the Americas.

Source: Matthew C. Dulik, Sergey I. Zhadanov, Ludmila P. Osipova, Ayken Askapuli, Lydia Gau, Omer Gokcumen, Samara Rubinstein, and Theodore G. Schurr, "Mitochondrial DNA and Y Chromosome Variation Provides Evidence for a Recent Common Ancestry between Native Americans and Indigenous Altaians", The American Journal of Human Genetics, 26 January 2012 doi:10.1016/j.ajhg.2011.12.014 via Razib Khan at Gene Expression who provides one of the key tables (breaks added in closed access paper abstract above for ease of reading).

The abstract is about as clear as mud in the context of prior research in this area, because when one says "that southern Altaians and Native Americans share a recent common ancestor", it isn't at all clear which Native Americans you are discussing, and methodological issues make the genetic conclusions seen in isolation unconvincing without a rich context to support them.

Wikipedia summarizes the state of the academic literature Y-DNA of indigeneous Americans prior to the latest paper as follows (citations and some headings and portions unrelated to Y-DNA omitted, emphasis added):

Human settlement of the New World occurred in stages from the Bering sea coast line, with an initial layover on Beringia for the small founding population. The micro-satellite diversity and distributions of the Y lineage specific to South America indicates that certain Amerindian populations have been isolated since the initial colonization of the region. The Na-Dené, Inuit and Indigenous Alaskan populations exhibit haplogroup Q (Y-DNA); however, they are distinct from other indigenous Amerindians with various mtDNA and atDNA mutations. This suggests that the peoples who first settled the northern extremes of North America and Greenland derived from later migrant populations than those who penetrated further south in the Americas. Linguists and biologists have reached a similar conclusion based on analysis of Amerindian language groups and ABO blood group system distributions. . . .

Haplogroup Q . . .

Q-M242 (mutational name) is the defining (SNP) of Haplogroup Q (Y-DNA) (phylogenetic name). Within the Q clade, there are 14 haplogroups marked by 17 SNPs. In Eurasia haplogroup Q is found among Siberian populations, such as the modern Chukchi and Koryak peoples. In particular two populations exhibit large concentrations of the Q-M242 mutation, the Kets (93.8%) and the Selkups (66.4%). The Kets are thought to be the only survivors of ancient nomads living in Siberia. Their population size is very small; there are fewer than 1,500 Kets in Russia. The Selkups have a slightly larger population size than the Kets, with approximately 4,250 individuals. 2002 Starting the Paleo-Indians period, a migration to the Americas across the Bering Strait (Beringia), by a small population carrying the Q-M242 mutation took place. A member of this initial population underwent a mutation, which defines its descendant population, known by the Q-M3 (SNP) mutation. These descendants migrated all over the Americas.

Q subclades Q1a3a and Q1a3a1a . . . .

Haplogroup Q1a3a (Y-DNA) and/or Q-M3 is defined by the presence of the rs3894 (M3) (SNP). The Q-M3 mutation is roughly 15,000 years old as the initial migration of Paleo-Indians into the Americas occurred. Q-M3 is the predominant haplotype in the Americas at a rate of 83% in South American populations, 50% in the Na-Dené populations, and in North American Eskimo-Aleut populations at about 46%. With minimal back-migration of Q-M3 in Eurasia, the mutation likely evolved in east-Beringia, or more specifically the Seward Peninsula or western Alaskan interior. The Beringia land mass began submerging, cutting off land routes.

Since the discovery of Q-M3, several subclades of M3-bearing populations have been discovered. An example is in South America, where some populations have a high prevalence of (SNP) M19 which defines subclade Q1a3a1a. M19 has been detected in (59%) of Amazonian Ticuna men and in (10%) of Wayuu men. Subclade M19 appears to be unique to South American Indigenous peoples, arising 5,000 to 10,000 years ago. This suggests that population isolation and perhaps even the establishment of tribal groups began soon after migration into the South American areas.

Haplogroup R1 . . .

Haplogroup R1 (Y-DNA) is the second most predominant Y haplotype found among indigenous Amerindians after Q (Y-DNA). The distribution of R1 is believed to be associated with the re-settlement of Eurasia following the last glacial maximum. One theory put forth is that it entered the Americas with the initial founding population. A second theory is that it was introduced during European colonization. R1 is very common throughout all of Eurasia except East Asia and Southeast Asia. R1 (M137) is found predominantly in North American groups like the Ojibwe (79%), Chipewyan (62%), Seminole (50%), Cherokee (47%), Dogrib (40%) and Papago (38%). The principal-component analysis suggests a close genetic relatedness between some North American Amerindians (the Chipewyan and the Cheyenne) and certain populations of central/southern Siberia (particularly the Kets, Yakuts, Selkups, and Altays), at the resolution of major Y-chromosome haplogroups. This pattern agrees with the distribution of mtDNA haplogroup X, which is found in North America, is absent from eastern Siberia, but is present in the Altais of southern central Siberia.

Haplogroup C3b . . .

Haplogroup C3 (M217, P44) is mainly found in indigenous Siberians, Mongolians and Oceanic populations. Haplogroup C3 is the most widespread and frequently occurring branch of the greater (Y-DNA) haplogroup C. Haplogroup C3 decedent C3b (P39) is commonly found in today's Na-Dené speakers with the highest frequency found among the Athabaskans at 42%. This distinct and isolated branch C3b (P39) includes almost all the Haplogroup C3 Y-chromosomes found among all indigenous peoples of the Americas. The Na-Dené groups are also unusual among indigenous peoples of the Americas in having a relatively high frequency of Q-M242 (25%). This indicates that the Na-Dené migration occurred from the Russian Far East after the initial Paleo-Indian colonization, but prior to modern Inuit, Inupiat and Yupik expansions.

Analysis of Dating

There are a couple of different methodologies for mutation dating. Pedigree mutation rates support a most recent common ancestor between Native American and South Altaic populations ca. 5,170 to 12,760 years ago (95% confidence interval, median 7,740 years ago), and a most recent common ancestor between North Altaic and South Altaic populations that is only a bit more recent (a 95% confidence interval 3,000 to 11,100 years ago, median 5,490 years ago). Evolutionary mutation rates support a most recent common ancestor of North Altaic and South Altaic of a median 21,890 years ago, and a statistically indistinguishable most recent common ancestor of Native Americans and South Altaic of a median 21,960 years ago.

Of course, all of the interesting inferences from the dates flow from the method you use and its accuracy. The evolutionary mutation rates suggest a split just before the Last Glacial Maximum and is suggestive of a scenario in which part of a population retreats to the South from the glaciers, while the other seeks a refuge in Beringia.

The pedigree date (which usually is closer to the historical corrolates that make sense) would be a decent fit for secondary Na-Dene migration wave that is before the original Native American population of the New World, but is before more recent circumpolar population migrations in and after the Bronze Age. The pedigree date also makes the possibility that there is an authentic Na-Dene to Yenesian linguistic link far more plausible than the older evolutionary date. Linguistic connections ought to be impossible to see at a time depth of 21,000 years, but is conceivable with a link that could be less than a third as old.

The "median split time" using pedigree dates is 4,490 years ago for N. Altaians v. S. Altaians, and 4,950 years ago for Native Americans v. S. Altaians, which would coincide with Uralic language expansion and the first of three major waves of Paleoeskimo migration to the New World. The evolutionary dates give a 19,260 years ago "median split time" for N. v. S. Altaians, and 13,420 years ago for Native American v. S. Altaians, an order reversal from all the other dates apparently driven by a wide and old date biased confidence interval. The very old genetic dates don't make a lot of sense, however, given that megafauna extinction dates in Siberia suggest a modern human arrival there ca. 30,000 years ago, plus or minus.

The indications that the northern Altaians are less strongly genetically connected than the southern Altaians to Native Americans is quite surprising. Linguistically and culturally the Northern Altaic populations would seem closer, but those are things that are more succepible to change over time and the southern populations may have faced stronger cultural pressures than the more remote and isolated northern populations.

The reasoning here matters a great deal, of course, and with a closed access paper isn't easy to evaluate. The abstract seems to indicate that the linkages are being based on the phylogeny of non-recombining Y-DNA haplogroup Q (the dominant one in Native Americans) without necessarily relying much on the mtDNA part of the analysis. In particular, it isn't easy to tell from the abstract how succeptible the data are to a multiple wave, as opposed to a single wave migration model.

There are really no sensible models for the arrivals of modern humans in the New World that can fit with a split between Native Americans and Siberian populations any later than 13,000-14,000 for the predominant haplogroups of Y-DNA haplogroup Q found in South America (Q-M3 and its descendants). But, a link of a secondary subtype of Y-DNA haplogroup Q that is pretty much exclusively found in North America at a later date is quite possible to fit consistently with plausible population models. Evolutionary mutation rate dates would strongly disfavor this scenario, but pedigree mutation rate dates could comfortably accomodate this scenario.

Thursday, January 26, 2012

Deep Thoughts From Marco Frasca

Italian physicist Marco Frasca's latest paper leaves his usual comfort zone of QCD and discusses instead a deep and fundamental relationship between the Schrödinger equation (that describes how the quantum state of a physical system changes in time) and the equations of the observable stochastic (i.e. probablistic) processes of Brownian motion (which describes the dispersion of particles that flows from their random movements) from first principles via some mathematical leaps of insight that have eluded some of the best minds in math and physics for almost nine decades (counting from the publication of Schrödinger equation, which is younger than the equations that describe Brownian motion). Essentially the Schrödinger equation is the square root of the equation that describes Brownian motion, when the equations are properly formulated and the square root if defined in a clever way that gives rise to a complex number valued solution.

[T]he square root of Brownian fluctuations of space are responsible for the peculiar behavior observed at quantum level. This kind of stochastic process is a square root of a Brownian motion that boils down to the product of two stochastic processes: A Wiener process [i.e. "the scaling limit of a random walk"] and a Bernoulli process proper to a tossing of a coin. This aspect could be relevant for quantum gravity studies where emergent space-time could be understood once this behavior will be identified in the current scenarios.

Note, however, that there is at least one obvious step that has to be bridged between this conclusion and a rigorous theory of quantum gravity, since the Schrödinger equation is a non-relativistic effective approximation of quantum mechanics.

[T]he solutions to the Schrödinger equation are . . . not Lorentz invariant . . . [and] not consistent with special relativity. . . . Also . . . the Schrödinger equation was constructed from classical energy conservation rather than the relativistic mass–energy relation. . . . Secondly, the equation requires the particles to be the same type, and the number of particles in the system to be constant, since their masses are constants in the equation (kinetic energy terms). This alone means the Schrödinger equation is not compatible with relativity . . . [since quantum mechanics] allows (in high-energy processes) particles of matter to completely transform into energy by particle-antiparticle annihilation, and enough energy can re-create other particle-antiparticle pairs. So the number of particles and types of particles is not necessarily fixed. For all other intrinsic properties of the particles which may enter the potential function, including mass (such as the harmonic oscillator) and charge (such as electrons in atoms), which will also be constants in the equation, the same problem follows.

In order to extend Schrödinger's formalism to include relativity, the physical picture must be transformed. The Klein–Gordon equation and the Dirac equation [which provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity] are built from the relativistic mass–energy relation; so as a result these equations are relativistically invariant, and replace the Schrödinger equation in relativistic quantum mechanics. In attempt to extend the scope of these equations further, other relativistic wave equations have developed. By no means is the Schrödinger equation obsolete: it is still in use for both teaching and research - particularly in physical and quantum chemistry to understand the properties of atoms and molecules, but understood to be an approximation to real behaviour of them, for speeds much less than light.

Presumably, however, it would be possible to square the relativistic versions of the Schrödinger equation (such as Dirac's equation) in an analogous manner to derive are diffusion equations for Brownian motion in relativistic settings that is consistent with special relativity, while still illustrating how complex number valued underlying quantum mechanics can reflect an emergent and fluctuating underlying nature of space-time.

As a footnote, it is also worth noting that his paper was made possible only with the a collaboration with elite mathematicians that would have been much more difficult to facilitate without the crowdsourcing of part of the problem that the Internet made possible.

Monroe, Louisiana As The Source Of New World Civilization

A series of articles in Science magazine a month ago (cited below), have transformed my understanding of human civilization in the Pre-Columbian New World. Together with some secondary sources like Wikipedia, the World Almanac 2012, Jared Diamond's "Guns, Germs and Steel", and a few other websites, the implication is that the history of civilization in the New World is far more united in space and over millennia, far greater in scale, and far more sophisticated than I had believed as recently as two months ago.

In a nutshell, which will probably take multiple more lengthy posts to explore in the future, here is the conjectural narrative.

Several sites in the general vicinity of Monroe, Louisiana show the emergence of the earliest large scale mounds and earth platforms, which were part of projects on a scale comparable to the earlier Sumerian pyramids, Egyptian pyramids, Mesoamerican pyramids, and megalithic complexes of Atlantic Europe in the period from about 3700 BCE to 2700 BCE. These appear to have provided these people with a means by which to more easily endure the periodic flooding of the Mississippi River, do not show signs of large trade networks, and while they may show indications of transitional proto-agriculture, do not show signs of a full fledged food production system based upon eating domesticated plants and animals as the entire basis for their diet.

A little more than a thousand years later (flourishing 1600 BCE to 1000 BCE), however, a civilization that appears to be derived from this first wave of mound builders appears at Poverty Point, which is within a day's walk of the earlier sites in Louisiana. This urban center is much larger in scale, perhaps comparable to a medium sized archaic era Greek city state, and shows clear signs of a trade network that extends as far as Milwaukee, Wisconsin in the North and the Ozarks in the West. It used copper and engaged in fine stoneworking. Its trade network may have even extended farther still. The way that its structures are aligned with solstices and equinoxes, its burial practices, its pottery, and the arrangement of structures in the complex, appear to strongly echo and to probably be antecedent to the Mesoamerican civilizations of the Olmecs (from ca. 1200 BCE), the Mayans (from ca. 900 BCE), and the Woodlands Hopewell of Ohio (from ca. 400 BCE).

The Inca civilization, as a well organized technological large scale civilization as opposed to merely a group of people engaged in disconnected hamlet scale agriculture, fishing, hunting and gathering, appears to derive largely from Mesoamerica. For example, pottery appears in Ecuador ca. 3200 BCE, but does not appear in Peru until around 1800 BCE, and the earliest large scale states emerge in the Inca region ca. 0 CE, about a millennium after the Olmecs and the Mayans. At the point of Columbian contact, there were regular trade and communication relationships between the Aztecs who had consolidated political control of Mesoamerica in a civilization clearly derivative of the Olmec and Mayan civilizations, and the Inca civilization.

Timing and broad outlines of the way that their communities were planned also suggest that a couple of large scale village network societies in the Amazon, ca. 0 CE to 1650 CE, may have been influenced or informed to some extent by the Poverty Point culture or by Mesoamerican societies that were influenced at a formative point by the Poverty Point culture.

From the Hopi woodland culture emerged a sprawling urbanized region in the vicinity of Saint Louis, Missouri, over a region about a day's walk across along one of the main confluences of the Mississippi River basin called Chahokia around 1000 CE. This civilization took a major hit around the 1160s and 1170s during a major New World drought, and eventually collapsed as an urban complex around 1350 CE around the time of the Little Ice Age, although much declined remnants of this civilization persisted pocketed throughout its prior range up until the point of European contact at which point European diseases dealt a further blow to what was left of this civilization.

Chahokians worked copper, had fine stonework, constructed gigantic earthworks with invisible interior elements (layers of black earth, white gravel and red earth, inside mounds corresponding more or less to the layers of hell, Earth and heaven in their cosmology) on a scale comparable to the Egyptian pyramid at Giza or the largest Mesoamerican pyramids, although no traces of a written language have been uncovered at this point.

The central complex may have housed 10,000 to 20,000 people, and the larger area may have housed 75,000 people, making the complex a bit larger than the largest urbanized complexes of the Amazon (about 50,000), and in the top ten of Mesoamerican cities at their Pre-Columbian peak (the largest urban area in the Pre-Columbian New World, in the vicinity of what is now Mexico City had about 300,000 people). It was by far the largest urbanized area in what is now the United States and Canada.

The Mississippian culture of which Chahokia was a focal point engaged in maize and pumpkin farming, as well as the farming of a few domesticates or semi-domesticates later abandoned as food sources, although they may have significantly supplemented their food sources with hunting, gathering and fishing. At one major feast whose remnants were unearthed by archaeologists at Chahokia, those present dined on about 9,000 deer.

Chahokia's trading network, colonies and strong cultural influences extended throughout the entire Mississippi basin from the Rocky Mountains to the Great Lakes to the Appalachian Mountains and also throughout all or most of the American South where Chahokia's culture overlaps heavily with the Southeastern Cultural Complex. For example, trade brought Chahokia Great White shark teeth from the Atlantic, and minerals from Georgia and Alabama. The mythology and rituals of the Osage Indians correspond closely to the Chahokian ceremonial system that we know from archaeology. Indian tribes that speak the Sixouian languages, of which the Osage language is a part, were spoken in a linguistic area ca. 1500 CE that corresponds closely to the core Chahokian aka Mississippian cultural area. Their "national sport" was a game a bit like Bocci ball in which one threw of ring or disk and then tried to throw your spear as close to that point as possible, which attracted large crowds of spectators, was as popular among average people as softball or soccer, and was the subject of high stakes gambling.

Thus, as recently as two or three hundred years before Columbus arrived in the New World, almost all of the United States to the east of the continental divide and to the west of the Appalachians and the South of the Great Lakes and almost all of the American South were all part of a reasonably united cultural complex that had its most direct common origins (admittedly with a couple of intervening "dark ages") in the vicinity of Monroe, Louisiana around 3700 BCE.

It may not have been one centralized megastate, but it could fairly be compared to the kind of balkanized area with a shared culture found in Europe or in the Indian subcontinent. At a time depth of something on the order of 1600 BCE to 900 BCE, the Poverty Point culture heir in the Monroe, Louisiana area was probably one of the formative cultural contributors (together with important local innovations, particularly with the addition of the domesticated plants to the mix) to the earliest sophisticated civilizations of Mesoamerican and those civilizations, in turn were probably formative cultural contributors to the civilizations of South America in the greater Inca geographic region and in the Amazon. The successors to the Poverty Point culture in North America called the Mississippian culture centered at Chahokia, that may have bloomed via a combination of improved climate conditions, the development of a variety of maize that thrived in the North American climate (derived from the Mesoamerican version which was domesticated somewhere in the vicinity of the Pacific Coast of modern Mexico), and high profile astronomical events like Hailey's Comet and a major supernova, reinvigorated that culture.

It is also hardly a stretch to suppose that the Uto-Aztecian language speaking populations of Northern Mexico and the American Southwest (including the Ute's of Colorado) and the Anasazi (whose civilization collapsed in the megadroughts 1160s and 1170s) probably have their origins in the Aztec civilization of Mesoamerica, which may in turn have a deep time depth connection to Poverty Point, Louisiana.

There is a solid argument supported by strongly suggestive evidence that directly or indirectly, almost all of the civilized cultures in the Americans trace their roots to a significant extent to an ancient civilization of mound builders ca. 3700 BCE in the vicinity of Monroe, Louisiana.

On the other hand, we also know that the Apache and Navajo Indian tribes of the American Southwest a derived from the Na-Dene people of the Pacific Northwest and arrived in the American Southwest as a result of a migration around 1000 CE.

General Implications

This superculture spanning five millennia and providing a source that had dramatic cultural influences on large swaths of both North American and South America probably did not extent quite everywhere in the New World. The indigenous cultures to the west of the North American continental divide and to the North of the Great Lakes, and possibly also some in the American Northeast, parts of Florida, and "uncivilized" parts of South American were probably not a part of this superculture.

This also means that the vast majority of people in the New World, at the time of European contact, either were part of a Chalolithic culture, or had ancestors within the last few hundred years who had been, even if their own society had reverted to a hunter-gather mode.

The Viking presence in the New World was contemporaneous with the high point of the Mississippian culture (ca. 1000 CE to 1350 CE), which may explain both why the Vinlanders could not dominant the locals and gain sweeping control of North American the way that the Iberians of half a millennium later would further South, and this small Viking civilization collapsed at about the same time that the Chahokia did for basically the same Little Ice Age climate driven reasons.

This archaeological background also suggests that in addition to the "Guns, Germs and Steel," that Jared Diamond notes, that a critical advantage that the Europeans arriving in the New World, at least in North America, had was timing. They encountered the indigenous North Americans not at their glorious peak of ca. 1000 CE, but two or three centuries into an era of decline, comparable perhaps to the period from 1200 BCE to 900 BCE, following Bronze Age collapse, or from 476 CE to 776 CE that we call the "dark ages" following the collapse of the Roman Empire. Indigenous North American civilization has just about hit bottom and not had time to meaningfully recover yet, when it was hit anew first by devastating European diseases, and close on the heels of this devastating series of plagues, by a population with guns, swords, and military history that surpassed that of the Native Americans (including the experience of fighting distant foreign wars in the Crusades), a written language, horses and other domesticated animals, long distance sea travel, a somewhat more effective social organization.

If the North American population had managed a few hundred more years to reignite their civilization (and probably adopt the written language of the Mesoamericans in some form), they might have been far better able to hold their own, perhaps even more effectively than the Aztecs and Incas did. Yes, they were behind in a relentless march of progress and faced limitations in their domesticated plant and animal options that the European population that they encountered had not. But, the development and dissemination of a flood of new evidence in the couple of decades since Diamond wrote his book, suggests that the lag was closer to hundreds of year than several millennia as he suggested in his book.

This narrative of the emergence of New World civilization is profoundly more unified and cohesive in time and in space than was previously known. This helps to explain the mystery of why there were so few and such geographically expansive language families in North American where there had not previously been known to be such large scale societies (the advanced Inca and Aztec societies and prior existence of the Mayans and Olmecs made the modest number of languages in the geographically smaller anyway areas of Mesoamerica and Pacific South America explainable long ago). It also provides suggestive evidence regarding what kinds of linguistic relationship between known North American language families might exist at what time depths, so that linguists can know what they should expect to be the most fruitful places to look for genetic linguistic connections between known North American language families. And, these narrative suggests that the process of linguistic consolidation in North American may be more similar to that seen in the Old World and at much shallower time depth in North America, than we have previously believed.

The existence of more advanced than previously known civilizations in the Amazon also helps explain why such a seemingly hunter-gatherer dominated, population fragmenting jungle could possibly have any language families that have as much geographic extent as the ones we have observed do (although, of course, vast numbers of South American languages are unclassified isolates or micro-language families) and gives us a relatively recent event (linguistically speaking) to explain why their connections can have a relatively shallow time depth relating them to each other. Again, this supports the conclusion that linguistic unity really does flow from the same expanding society with a technological edge process we've seen in the Old World, rather than following some different rule, which makes the inference that any unexplained large language families is the product of a lost prehistoric culture that will eventually be discovered stronger.

Implications For Population Genetics

Finally, before I make a final conjecture, this unified narrative has implications for efforts to cast light on prehistoric Native American populations from modern population genetic data. The assumption that a person with Native American genes was representative of a stable genetic population at the place where his or her 16th century Native American ancestors are known to have lived for tens of millennia prior to that point in time is manifestly contrary to what our emerging understanding of the archaeological evidence reveals. We know that there were dramatic ebbs and falls of archaeological cultures in particular regions at least for the past six thousand years or so, that were driven by more than random chance factors governing individual hunter-gatherer tribes in an unstructured way. These cultures were large in extent, wide in geographic distribution, engaged in some documented folk wanderings supported by archaeological and oral historical and early explorer historical evidence, and we now have some generalized context within which to know what direction any influence on 16th century population genetics due to Pre-Columbian migrations would have flowed if the cultural impacts of the known archaeological cultures had a demic component.

Now, as a matter of practicality, the small founding population of the New World, the limited demic impact of the known later waves of migration from Asia in most of the New World, and the serial founder effects applicable to even broad geographic regions that have been a partial cause of genetic distinctions between Latin American indigenous peoples and certain groups of North American indigenous peoples, mean that huge swaths of North American Indians in the geographic range of the Mississippian Superculture and its antecedents may have been so genetically homogeneous after seven thousand or so years of a nomadic hunter-gatherer existence in the region of people all derived from the same small founder population, that any subsequent impacts of demic migration and/or replacement may be virtually invisible at all but the most fine grained levels in modern genetic data.

Also, the existence of the Mississippian superculture with its known ups and downs, materially alters the kind of demographic models that are a plausible fit to reality for North American Indians. The most plausible demographic model given current evidence is that in the post-Clovis, pre-Mound Builder United States that there was a rapid early expansion of perhaps three thousand years or less from a small Beringian founding population that filled the continent at a low hunter-gatherer population density, that there was probably a peak as more effective Clovis hunting methods expanded human populations at the expense of prey populations over a thousand years or so, that there was probably a human population crash over a few centuries immediately after the Clovis era when overhunting and ecological collapse related to overhunting reduced the carrying capacity of the environment using a Clovis culture "business model" and didn't stabilize until the surviving Native Americans found a new way to survive in harmony with their megafauna free environment, that a quite low effective population baseline of pure hunter-gatherers (which would be mutationally limited due to a small effective population) whose numbers ebbed and flowed meaningfully with medium and long term climate conditions and prey population health for about seven thousand years (providing lots of occasions for minor bottlenecks that could shed low frequency genetic mutations), and that there was a population expansions attributable to Poverty Point from ca. 1600 BCE to 1000 BCE followed by some degree of population decline followed by gradually rebuilding populations until a much more dramatic population expansion ca. 1000 CE to 1160 CE, followed by a population crash across the New World at that point, followed by gradual recovery or gradual slump in population until about 1350 CE, followed by a Little Ice Age and civilization collapse population slump that is only starting to recover at the point of European contact, at which point there is another well documented slump and massive episode of intra-Native American and Native American-European admixture where historically documents and modern population genetics provide solid estimates of population sizes at given points in time, the impact of deadly diseases and admixture percentages. Both Poverty Point era and the Chahokian era provide particularly likely contexts for unusually high admixture, migration and replacement events. We can produce similar big picture, moderately detailed, archaeologically driven demographic histories using the latest available discoveries in Mesoamerica and in differing parts of South America.

This is obviously a much more complex demographic history than one could produce with a simple back of napkin exponential approximation of the kind very often used in actual published papers on prehistoric population genetics, but now that we know quite a bit about what actually happened, over simplifying that demographic history when we try to extrapolate modern population genetic data to prehistory with implicit assumptions about that demographic history that we know not to be true are inexcusable if we want to have the best possible evidence regarding the population genetics of the Americas in prehistory.

Did Asian Ideas Help Trigger New World Civilization?

While none of my sources mention the possibility, I also offer up one conjecture, which I myself don't actually necessary believe is more likely than not, but which is, given the timing of the events in question a far more plausible possibility than would have been at all supportable a couple of decades ago.

This is the possibility that some of the rise in New World civilization that started to emerge at Poverty Point could have been given a critical boost from exposure to Asian ideas.

The case of a cultural influence from Leif Erikson's 1000 CE on the culture centered around Chahokia is still so devoid of evidence, and even more weak in plausibility, since there don't seem to be any recognizable similarity in kinds of ideas or cultural features that could have been transmitted, even though it is possible that an idea could have been passed from person to person from Vinland to Chahokia, and there would have even been established trade routes in the Great Lake basins and Mississippi River basin which would extend to the Saint Lawrence seaway and Upstate New York, to carry those ideas, in a manner akin to the Eurasian Spice Road. Since, there is some evidence to suggest may have brought some Bronze Age technologies (and even simple versions of Tartan weaving patterns) to Mongolia and China from Europe and West Asia. While it could have happened, it didn't seem to have happened.

But, we know that Bronze Age Asian artifacts made it to Alaska from Asia with Paleoeskimos ca. 2500 BCE, and again with another wave of Dorsett Paleoeskimos ca. 1500 BCE, that there was a Thule (i.e. proto-Inuit) wave of migration that was possible an outgrowth of a culture that was also the source of the Uralic language family around 500 CE, and that there is suggestive evidence for a Na-Dene migration to the Pacific Northwest sometime before 1000 CE, but probably many millennia after the first wave of Native American migration to the New World across the Beringian land bridge around the time of the last glacial maximum when sea levels were lower. A time span for Na-Dene migration of ca. 4000 BCE to 1500 BCE would have been technologically possible in terms of maritime travel technology, and would have been early enough to allow transmission of Asian ideas (probably with minimal demographic impact, if any) to Poverty Point. All of these populations, unlike Leif Erikson's encounter, were substantial enough to give rise to substantial populations, two of which survive to this day in North America (the Na-Dene and the Inuit), and the other two of which each lasted at least a millennium and has left genetic traces of admixture in some of the surviving Arctic and near Arctic North Americans.

Poverty Point is an almost inevitable early destination for anyone exploring North American via the kind of canoe or kayak that Paleoeskimos and the Na-Dene culture had at their disposal. All one needs to do is put your boat in any navigable tributary in the Mississippi River basin that makes up a large share of the entire North American continent and eventually the river will take you there without even having to hazard all that many impassable rapids - these Native American explores lacked nothing that young Huckleberry Finn had. And, a wealth of historical and prehistorical evidence tend to show that exploration and migration frequently run up and down major river systems, be they the Nile, the Danube, the Tigress and Euphrates, the Indus, the Ganges, the Yellow or the Yangtze. Sooner or later, some representative of any exploring new civilization was likely to end up on their shores and carry with him the stories of his travels.

All four of the likely pre-Columbian, post-Clovis waves of migration of new people's to North America were very likely to have happened at a time when someone in Northeastern Siberia who was at least advanced technologically enough to have a boat that could get him to North America from there was likely to be aware to some extent of some of the technological innovations that had taken place in the North Chinese Neolithic of ca. 7,000 BCE - 8,000 BCE that hadn't existed with North American was originally settled by modern humans. Someone even modestly familiar with the ideas associated with that Neolithic cultural complex (or perhaps even a Chalcolithic or Bronze Age cultural complex in North China), while they wouldn't have been able to reproduce the North Chinese civilization in full (just as few people and perhaps no one knows enough individually to reproduce modern American civilization in its entirety), could have provided enough ideas to set the people of Poverty Point on the track towards developing a semi-urbanized, food producing, copper age, stone carving civilization.

As I explained at the start of this conjecture, I'm merely noting that this kind of chain of culture influence is possible, even a plausible possibility that isn't obviously contradicted by what we already know, without actually claiming that it actually happened.

But, the mere possibility that the rise of civilization in the New World might not have been the completely independent innovation that it is widely credited with having been is so paradigm shifting in our understanding of prehistory, and motivated by fact that could not have been known by people investigating this possibility even a couple of decades ago, that it bears further investigation.

Principal Sources (an incomplete list)

Andrew Lawler, "America's Lost City", 334 Science 23 December 2011: 1618-1623 (DOI: 10.1126/science.334.6063.1618).

Andrew Lawler, "Preserving History, One Hill at a Time", 334 Science 23 December 2011: 1623.

Andrew Lawler, "Does North America Hold the Roots of Mesoamerican Civilization?", 334 Science 23 December 2011: 1620-1621.

Jared Diamond, "Guns, Germs and Steel" (1997).

Sunday, January 22, 2012

Archaeology Broadway Style

The linked post has a You Tube video that is the most epic broadway style rock anthem testament to nerdiness (in this case, the kind that is at the root of archaeology), since the musical "Chess" (which was itself composed by a Swedish ex-Abba member). The post is not in English, but the video (which is not entirely safe for work), by a Norwegian singer who has a show a bit like Saturday Night live in Norway, is in English.

Quantum Field Theories Defined

Lubos helpfully defines various terms which include the words "quantum field theory."

Thursday, January 19, 2012

Woit On Symmetry In Physics

Peter Woit has a really worthwhile answer to this year's Edge Website question of the year, which is "What is your favorite deep, elegant, or beautiful explanation?" He says:

Any first course in physics teaches students that the basic quantities one uses to describe a physical system include energy, momentum, angular momentum and charge. What isn’t explained in such a course is the deep, elegant and beautiful reason why these are important quantities to consider, and why they satisfy conservation laws. It turns out that there’s a general principle at work: for any symmetry of a physical system, you can define an associated observable quantity that comes with a conservation law:

1. The symmetry of time translation gives energy
2. The symmetries of spatial translation give momentum
3. Rotational symmetry gives angular momentum
4. Phase transformation symmetry gives charge

In classical physics, a piece of mathematics known as Noether’s theorem (named after the mathematician Emmy Noether) associates such observable quantities to symmetries. The arguments involved are non-trivial, which is why one doesn’t see them in an elementary physics course. Remarkably, in quantum mechanics the analog of Noether’s theorem follows immediately from the very definition of what a quantum theory is. This definition is subtle and requires some mathematical sophistication, but once one has it in hand, it is obvious that symmetries are behind the basic observables.

Here’s an outline of how this works, (maybe best skipped if you haven’t studied linear algebra…) Quantum mechanics describes the possible states of the world by vectors, and observable quantities by operators that act on these vectors (one can explicitly write these as matrices). A transformation on the state vectors coming from a symmetry of the world has the property of “unitarity”: it preserves lengths. Simple linear algebra shows that a matrix with this length-preserving property must come from exponentiating a matrix with the special property of being “self-adjoint” (the complex conjugate of the matrix is the transposed matrix). So, to any symmetry, one gets a self-adjoint operator called the “infinitesimal generator” of the symmetry and taking its exponential gives a symmetry transformation.

One of the most mysterious basic aspects of quantum mechanics is that observable quantities correspond precisely to such self-adjoint operators, so these infinitesimal generators are observables. Energy is the operator that infinitesimally generates time translations (this is one way of stating Schrodinger’s equation), momentum operators generate spatial translations, angular momentum operators generate rotations, and the charge operator generates phase transformations on the states.

The mathematics at work here is known as “representation theory”, which is a subject that shows up as a unifying principle throughout disparate area of mathematics, from geometry to number theory. This mysterious coherence between fundamental physics and mathematics is a fascinating phenomenon of great elegance and beauty, the depth of which we still have yet to sound.

Most of this is familiar to me, but I had not lodged in my head the deep connection between the notion of energy and the notion of time translation.

More Higgs Boson Mass Numerology

There are some constants other than the Higgs boson mass in the Standard Model that have been measured that can be combined in very simple formulas to give numbers that are within the margin of error of current Higgs boson mass estimates.

One is that experimental indications for the Higgs boson mass in the vicinity of 123-125 GeV are remarkably close to precisely one half of the Higgs field vaccum expectation value of 246 Gev. The other is that experimental indications for the Higgs boson mass are remarkably close to precisely half of the sum of the masses of the W+ boson, the W- boson and the Z boson (or alternatively, the sum of the masses of the W+ boson, the W- boson, the Z boson and the photon, since the photon mass is zero; or alternatively, the sum of the masses of all of the fundamental fermions, since the gluon rest mass is also zero). The sum of these masses is about 250.3 GeV, half of which would be about 125.15 GeV.

One could get an intermediate value by adding the sum of the relevant boson masses to the Higgs field vev and dividing by four (a result suggestive of a linear combination of the four electroweak bosons, the W+, W-, Z and photon).

Another way to bridge the gap would be to use the "pole masses" of the W and Z bosons, rather than their conventional directly measured masses. This basically adjusts the masses of unstable fundamental particles downward by a factor related to their propensity to decay in an amount proportional to half of their decay width, which at a leading order approximation is about 1.8 for these bosons. This would give us a sum of the three pole masses which is equal to roughly 248 GeV, which would be a fit to a 124 GeV Higgs boson pole mass if there is such a simple relationship, although the match would presumably have to be to the pole mass of the Higgs boson (something not yet possible to estimate with any meaningful accuracy as we have considerable uncertainty in both the Higgs boson mass and its decay width).

These pole mass calculations are approximate, and an exact calculation has significant terms at two loop level and probably beyond, so coming up with an exact pole mass calculation figure is a bear of a calculation. But, the notion that the Higgs field vacuum expectation value might be equal to the double the Higgs boson pole mass, and to exactly the W+ boson pole mass, the W- boson pole mass, the Z boson pole mass, and the possibly the (zero) masses of the photon and/or the eight gluons, is an attractive one. It is also suggestive of the idea that the Higgs boson itself might be understood as a linear combination of four spin one electroweak bosons to get a Higgs boson, whose pairs of opposite sign spins combine to produce an aggregate combined spin of zero, in line with the scalar character of the Higgs boson. One would need some reason to come up with a factor of two, or alternatively, some reason to add in the Higgs vev to the sum of the four electroweak boson masses which would naturally be divided by four since it is derived from a linear combination of four bosons.

The Z boson mass is related exactly to the W boson mass by the Weinberg angle aka weak mixing angle (an angle, for which the sin squared is about 0.25, which Rivero has some interesting numerological speculations in a 2005 paper and whose possible origins are discussed in terms of a heuristic set forth in a 1999 article). So, if there is some simple relationship between the Higgs boson mass, the Higgs field vacuum expectation value, the W boson mass and the Z boson mass, such that the Higgs field vacuum expectation value and Higgs boson mass can be calculated from the W boson and Z boson masses, it ought to be possible to derive all of these constants exactly, in principle at least, from the W boson mass and the Weinberg angle (which is definitionally derived from the relationship between the weak and electromagnetic gauge couplings).

Of course, even if the experimental values come to be known with sufficient precision to rule out such simple relationships, one is still left with the question: why should this simple relationship be such a near miss? For example, does the simple relationship capture the first order terms of an exact relationship whose next to leading order and beyond terms are unknown?


This all becomes even more exciting if one can come up with a generalization of the Koide formula to account for all of the charged fermion masses from just a couple of constants. Both the W boson mass and Z boson mass were predicted from other constants known at the time before they were discovered, and one could conceivably get the number of free constants in the Standard Model down to a much smaller number.

While not precisely on point, this is also as good a point as any to ask, why have string theory and SUSY so utterly failed to provide accurate predictions of the mass constants or mixing matrix values in the Standard Model? Isn't that the very least that we should expect of any purported grand unification or theory of everything scheme?

Monday, January 16, 2012

Picture Of Lost Civilization In The Amazon Emerging

The Amazon is home to more groups of uncontacted hunter-gatherers than anyplace else in the world, with the possible exception of Papua New Guinea. But, it isn't generally known as a center of pre-Columbian advanced civilizations comparable to that of the Aztecs of Mesoamerica and the Incas of the Pacific Coast of South America. The only real traces found among contemporary Amazonians of a possible lost civilization are a few legends and some very geographically broad linguistic groupings that don't fit the usual geographically confined hunter-gatherer mold.

But, new pieces of evidence increasingly show signs of a civilization that did greatly modify its environment in the Amazon.

Alceu Ranzi, a Brazilian scholar who helped discover the squares, octagons, circles, rectangles and ovals that make up the land carvings, said these geoglyphs found on deforested land were as significant as the famous Nazca lines, the enigmatic animal symbols visible from the air in southern Peru. . . . parts of the Amazon may have been home for centuries to large populations numbering well into the thousands and living in dozens of towns connected by road networks, explains the American writer Charles C. Mann. In fact, according to Mr. Mann, the British explorer Percy Fawcett vanished on his 1925 quest to find the lost “City of Z” in the Xingu, one area with such urban settlements. . . . So far, 290 such earthworks have been found in Acre, along with about 70 others in Bolivia and 30 in the Brazilian states of Amazonas and Rondônia.

Researchers first viewed the geoglyphs in the 1970s, after Brazil’s military dictatorship encouraged settlers to move to Acre and other parts of the Amazon, using the nationalist slogan “occupy to avoid surrendering” to justify the settlement that resulted in deforestation.

But little scientific attention was paid to the discovery until Mr. Ranzi, the Brazilian scientist, began his surveys in the late 1990s, and Brazilian, Finnish and American researchers began finding more geoglyphs by using high-resolution satellite imagery and small planes to fly over the Amazon.

Denise Schaan, an archaeologist at the Federal University of Pará in Brazil who now leads research on the geoglyphs, said radiocarbon testing indicated that they were built 1,000 to 2,000 years ago, and might have been rebuilt several times during that period. . . . So far, 290 such earthworks have been found in Acre, along with about 70 others in Bolivia and 30 in the Brazilian states of Amazonas and Rondônia.

Researchers first viewed the geoglyphs in the 1970s, after Brazil’s military dictatorship encouraged settlers to move to Acre and other parts of the Amazon, using the nationalist slogan “occupy to avoid surrendering” to justify the settlement that resulted in deforestation. But little scientific attention was paid to the discovery until Mr. Ranzi, the Brazilian scientist, began his surveys in the late 1990s, and Brazilian, Finnish and American researchers began finding more geoglyphs by using high-resolution satellite imagery and small planes to fly over the Amazon.

Denise Schaan, an archaeologist at the Federal University of Pará in Brazil who now leads research on the geoglyphs, said radiocarbon testing indicated that they were built 1,000 to 2,000 years ago, and might have been rebuilt several times during that period. Researchers now believe that the geoglyphs may have held ceremonial importance, similar, perhaps, to the medieval cathedrals in Europe. This spiritual role, said William Balée, an anthropologist at Tulane University, could have been one that involved “geometry and gigantism.”

In 2008, National Geographic reported on a somewhat similarly developed civilization in a part of the Amazon remote from these geoglyphs.

Dozens of ancient, densely packed, towns, villages, and hamlets arranged in an organized pattern have been mapped in the Brazilian Amazon. . . . In 1993, Heckenberger lived with the Kuikuro near the headwaters of the Xingu River. Within two weeks of his stay, he learned about the ancient settlements and began a 15-year effort to study and map them in detail.

So far he has identified at least two major clusters—or polities—of towns, villages, and hamlets. Each cluster contains a central seat of ritualistic power with wide roads radiating out to other communities.

Each settlement is organized around a central plaza and linked to others via precisely placed roads. In their heyday, some of the settlements were home to perhaps thousands of people and were about 150 acres (61 hectares) in size.

A major road aligned with the summer solstice intersects each central plaza.
The larger towns, placed at cardinal points from the central seat of power, were walled much like a medieval town, noted Heckenberger. Smaller villages and hamlets were less well defined.

Between the settlements, which today are almost completely overgrown, was a patchwork of agricultural fields for crops such as manioc along with dams and ponds likely used for fish farms.

"The whole landscape is almost like a latticework, the way it is gridded off," Heckenberger said. "The individual centers themselves are much less constructed. It is more patterned at the regional level."

At their height between A.D. 1250 and 1650, the clusters may have housed around 50,000 people, the scientists noted.

According to Heckenberger, the planned structure of these settlements is indicative of the regional planning and political organization that are hallmarks of urban society.

"These are far more planned at the regional level than your average medieval town," he said, noting that rural landscapes in medieval settlements were randomly oriented.

"Here things are oriented at the same angles and distances across the entire landscape."

Charles C. Mann, in his book 1491, argued that these civilizations collapsed because they came into contact with old world diseases despite limited direct contact with Europeans, and that there was a rewilding of the Americans in response to this population collapse.

This is a possibility that shouldn't be ruled out. But, I'm not necessarily sold on that as the only possible cause, because we have other examples of relatively advanced societies like the irrigation agriculture based societies of the Four Corners area of Colorado that rose and fell due to climate conditions in the Pre-Columbian era, and civilizations like the Mayans and Olmecs that preceded the Aztecs that were interrupted by successor civilizations that were more successful. We have have old world examples like the Harappans of the Indus River Valley and the Western Roman Empire, who apparently managed to experience the collapse of their societies without the assistance of an influx of superlethal Old World diseases.

Still, clearly these civilization did collapse, and clearly they did have some level of urban organization and agriculture in the pre-Columbian era in the Amazon.

Lubos v. Koide

Lubos, at his blog, makes the case for Koide's formula for the lepton masses, which has been expanded by later investigators, being mere numerology. While he is pretty out of the mainstream when it comes to climate change and cultral sensitivity, he is quite mainstream and credible in his specialty of theoretical physics from a SUSY/String Theory perspective and his post makes the argument against Koide's formula being deeply significant about as well as it is possible to do so in a blog post sized exposition. His argument is not a straw man and deserves serious consideration.

Koide's Formula, recall, is the observation that the sum of the masses of the three charged leptons, divided by the square of the sum of the positive square roots of the charged leptons, is equal to two-thirds. It has been confirmed to five signficant digits which is consistent with experimental evidence, predicts a tau mass to a couple of significant digits more than the currently most precise value, has held up even though it was quite a bit off the most precise values at the time it was formulated several decades ago, and is interestingly exactly at the midpoint of the highest possible value for that ratio (1) and the lowest possible value for that ratio (1/3).

His main points are as follows:

(1) It is much easier to find approximate, but surprisingly close, mathematical coincidences than you would think but manipulating a handful of constants in every conceivable way.

(2) Since the formulation is dimensionless, it is actually a function of two lepton mass ratios, rather than three independent mass values, which makes it somewhat less remarkable.

(3) If the ratio 2/3rd is conceptualized as a 45 degree angle, rather than a ratio, it is not at the midpoint of the possible values, making it less special.

(4) Koide's formula uses the real valued numbers for charged lepton masses, rather than the complex valued charged lepton masses, called "pole masses" that include an adjustment for the decay width of unstable particles (basically, their half lives, converted into mass units), and when Koide's formula is applied to pole masses, the 0.79 ratio that results don't seem as special. Lubos thinks it is unnatural to use something other than pole masses in anything that expresses a fundamental relationship of charge lepton masses.

In the Standard Model, the masses of charged leptons arise from the Yukawa interaction term in the Lagrangian, [which is a simple function of] y . . . a dimensionless (in d=4 and classically) coupling constant; h . . . the real Higgs field; [and] Ψ,Ψ ¯ . . . the Dirac field describing the charged lepton or its complex conjugate, respectively. To preserve the electroweak symmetry – which is needed for a peaceful behavior of the W-bosons and Z-bosons – one can't just add the electron or muon or tau mass by hand. After all, the electroweak symmetry says that the left-handed electron is fundamentally the same particle as the electron neutrino. Instead, we must add the Yukawa cubic vertex – with two fermionic external lines and one Higgs external line – and hope that Mr Higgs or Ms God will break the electroweak symmetry which also means that he will break the symmetry between electrons and their neutrinos. . . . [In turn] In the vacuum, the Higgs field may be written as h=v+Δh. Here, v is a purely numerical (c -number-valued) dimensionful constant whose value 246 GeV was known before we knew that the Higgs boson mass is 125 GeV. The value of v is related to the W-boson and Z-boson masses and other things that were measured a long time ago. The term Δh contains the rest of the dynamical Higgs field (which is operator-valued) but its expectation value is already zero. . . . [And,] m e is just a shortcut for m e =y e v where the Yukawa coupling y e for the electron and the Higgs vev v= 246 GeV are more fundamental than m e. If you write the masses in this way, v will simply cancel and you get the same formula for Q where m is replaced by y everywhere. However, this is not quite accurate because the physical masses are equal to yv up to the leading order (tree level diagrams i.e. classical physics) only. There are (quantum) loop corrections and many other corrections. Moreover, the values of y that produce Q=2/3 are the low-energy values of the Yukawa couplings. Even though the Yukawa couplings are more fundamental than the masses themselves, their low-energy values are less fundamental than some other values, their high-energy values.

In other words, both arguments (4) and (5) are arguments that in the ordinary formulation of the Standard Model, the charged lepton mass inputs into Koide's formula are not fundamental and therefore have no business exhibiting profound and mysterious relationships to each other that have any basis in fundamental physics and hence are probably just numerological coincidences.

I'm not sold on the argument Lubos makes, for a few reasons, that I'll note with Roman numerals to avoid confusion with his reasons:

(I) Koide's formula has come into closer alignment with the experimentally measured values of the charged lepton values as they have been discovered more precisely, while most numerical coincidences (e.g. efforts to describe the electromagnetic coupling constant as a simple integer valued number) fall apart as the experimentally valued number becomes known with more precision. A five significant digit match to a simple, dimensionless, rational number shouldn't be dismissed lightly.

(II) Lots of well motivated Standard Model derived constant predictions (e.g. the W and Z masses, the proton and neutron masses) are not know to any more precision than Koide's formula, so judged by its fit to empirical evidence, Koide's formula is holding its own.

(III) Almost everyone who understands particle physics well enough to be a professional in the field intuitively agrees that the many constants of the Standard Model are not simply random and have deeper interrelationships to each other than we have yet come up with well formulates laws of physics to explicate. Put another way, there is clearly some formula out there that if discovered would derive particle masses, particle decay widths, CKM/PMNS matrix phases, coupling constants of the fundamental forces, and the constants of the running of the fundamental force coupling constants, from a much smaller set of more fundamental constants, and there is no a priori reason that we aren't capable of discovering that relationship.

If you start from the assumption that there is some deeper relationship between these constants, then the question is which are the proposed relationships between these constants has proven most fruitful so far and has tended to become more rather than less accurate as more empirical evidence has become available.

Put another way, if you assume that these constants do have a deeper relationship, then any other empircially relationship between them that is observed necessarily derives in some way from the deep relationship and hints at its nature. The empirical validity of the dimensionless Koide's formula to great precision, at the very least, is proof of a no go theorem for other proposed deeper relationship between charged lepton masses that does not observe that relationship. It fairly tightly constrains the universe of potentially valid deeper theories.

At the very least, Koide's formula poses an unsolved problem in physics akin to the Strong CP problem, i.e. "why is no there observable CP violation in the physics of the strong force?"

In the same vein, the phenomenological and predictive success of the modified gravity theory "MOND" as originally formulated by Milgrom in describing galactic rotation curves with a single numerical constant, doesn't necessarily mean that this phenomena is really caused by the law of gravity being misformulated rather than dark matter. But, it also necessarily implies that any dark matter theory that takes multiple unconstrained numerical constants to produce results that MOND can match with one numerical constant with similar accuracy is missing some very important factors that cause real galaxies to have far more tightly constrained structures than their formulation permits. The fact that a strong phenomenological relationship exists doesn't tell you its cause, but it does generally establish that there is some cause for it.

(IV) Lots of phenomenological relationships in physics that aren't fundamental at the deepest sense and can be derived from mere approximations of theoretical physics formulas which are known to be more accurate are still remarkably accurate and simple in practice.

For example, the phenomenological fact that planets follow orbits around the sun that are ellipses with foci at the planet in question and the sun, turns out to be extremely accurate, and possible to express with high school algebra and derive with elementary first year calculus, even though it ignores all sorts of more accurate physics such as the corrections between general relativity and Newtonian gravity for objects that are in motion, and the fact that planetary orbits are actually determined via supremely difficult to calculate many bodied problems that include the gravitational effects of every little bit of matter in the solar system and beyond, not just a two body problem and a formula in the form F=GmM/r^2. Before Kepler figured out that the orbits were ellipses, Copernicus came up with a simpler approximation of the orbits as spheres around the sun (which are degenerate forms of the equations for ellipses), which while also wrong, was still an immense leap relative to the prior formulations.

Similarly, the classical ideal gas law, PV=NkT, involves physics that aren't fundamental (it can be derived from first principles from statistical mechanics and a few simplifying assumptions, and statistical mechanics, in turn, relies on classical mechanics that have to be derived at a fundamental level in far from obvious way from quantum mechanics). Yet, we still teach high school and lower division physics and chemistry students the ideal gas law because it, and non-ideal gas variants of it that use empirically determined physical constants to fit real gases, turn out to be useful ways to develop quantitative intuition about how gases behave and approximate that behavior with accuracy sufficient for a wealth of applications. The ideal gas law, in turn, was derived from even simpler observations about two variable proportionality or inverse proportionality relationships (e.g. V=cT for a gas of a constant volume) that were observed phenomenologically, long before all of the pieces were put together.

Thus, the fact that Koide's formula doesn't naturally and obviously correspond in form to current physically well motivated electroweak unification models doesn't necessarily count as a strike against it. It may be that the terms in more complex formulations of fundamental sources of charged lepton masses, either cancel out or have insignificant physical values that are swamped by other terms. For example, I suspect that a more exact formulation of Koide's formula for leptons may require the inclusion of all six lepton masses. But, the neutrino masses are so negligible relative to the charged lepton masses that their impact on Koide's formula may be invisible at the currently level of precision with which we know the charged lepton masses.

Odds are that a some level of precision, Koide's formula will cease to hold. But, for example, if the amount by which it is off is at an order of magnitude that could be accounted for via the inclusion of neutrino masses and tweaking the sign of electron neutrino mass term (a Brannen suggested possibility), then Koide's formula starts looking like an incomplete approximation of more exact theory that holds for reasons considerably deeper than coincidence, rather than merely a fluke.

(V) A notion of what is fundamental and what is derived, with a set of constants that are all tightly constrained to be related to each other mathematically, is to some extent a matter of perception. The notion that inferred Yukawa coupling constants, or pole masses of particles must be more fundamental than observed particle rest masses without adjustment for rates of decay, is not at all obvious. There is nothing illogical or irrational about described Yukawa coupling constants and pole masses as derived values, and charged lepton rest masses as fundamental.

My strong suspicion, for example, given the strong patterns that are observed in decay widths, is that the decay width of a particle is a derived constant that is the product in some manner or other of rest masses and some other quantum numbers, rather than having a truly independent value for each particle. Pole mass may be a more useful description of a particle's mass in some equations, just as a wind-chill adjusted temperature may be a more useful description of the ambient temperature in a location for some purposes. But, that doesn't necessarily mean that it is truly more fundamental.

And, reliance upon Standard Model formulations of particle masses as a source of the "true" nature of particle mass is also questionable when one of the deepest problems of the Standard Model is that its formulations can't provide particle masses from first principles for fermions or the Higgs boson (although the photon, W and Z boson rest masses can be derived from it).

(VI) Lubos ignores the relatively productive recent efforts that have been made recently to express other Standard Model particle mases (where the true values are often known to just one or two signficant digits) in Koide-like triples or other Koide-like formulations, an apparent three to one relationship between Koide-like formulations for quarks and for leptons (that fits the three to one relationship betweeen quarks and leptons seen in precision electroweak decay products), possible derivations of fermion mass relationships from CKM/PMNS matrix elements and visa versa (often finding links via the square root of fermion masses to be more natural), the phenomenological observation of quark-lepton complementarity in CKM/PMNS matrix elements, and so on. If there was just one Koide triple in the fermion mass matrix, it might just be a fluke. When there are multiple Koide triples in the fermion mass matrix that all seem to take on some kind of integer value to well within the range of empirically measured masses, dismissing the result as a fluke is problematic.

The implied angle of forty-five degrees from Koide's formula, for example, also comes up in quark-lepton complementarity, which relates to CKM/PMNS matrix element relationships.

(VII) Lubos also puts on blinders to the potential relevance of the square root of fermion mass as a potentially fundamental matter having some relationship to emerging evidence in his own string theoretic field of the similarity between gravity (which is a force that acts on mass-energy) and a squared QCD type gauge group, in which color charge is replaced with kinematic terms.

Thursday, January 12, 2012

Dim Matter Strikes Again

More accurate observations of globular clusters have turned up low luminosity stars, with masses of about 0.18 times that of the sun, that account for a large proportion of the globular cluster's previously estimated dark matter which was based on brighter observed stars and lensing observations for the entire cluster.

These clusters are considerably more rich in dark matter than individual galaxies and the phenomenological predictions of modified gravity theories derived from an early version called MOND consistently underestimate the amount of dark matter in these clusters. But, this new result finding that there is considerable luminous ordinary matter in these clusters that had not previously been seen by astronomers because their instruments weren't powerful enough to see them suggests that MOND's shortcoming in its estimates of the magnitude of effects due to something other than Newtonian gravity acting on observable luminous matter may be much smaller than previously believed.

This result should be considered together observations in late 2010 that revealed that the amount of low luminosity ordinary matter in elliptical galaxies had been grossly underestimated. The more accurate ellipical galaxy census suggested that the true amount of dark matter in the universe due to that revision in the estimate amount of normal matter in ellipical galaxies alone was closer to 50% of all ordinary and dark matter combined, rather than the frequently quoted 80% figure.

Other recent theoretical studies have shown that some portion of the effects attributed to dark matter in spinning galaxies is actually attributable to general relativistic corrections to models that estimate the effects of gravity with a Newtonian approximation, although different theorists have reached dramatically different estimates of the magnitude of these effects by using different methods to simplify the description of a spinning galaxy to which the equations of general relativity are applied.

This new result on globular clusters, combined with the prior work on dim matter in ellipical galaxies and general relativistic effects, suggests that the actual percentage of matter in the universe which is dark matter may be considerably less than 50%. Dark matter may actually end up being one third or less of all of the matter in the universe.

If one takes the position that a cosmological constant is a perfectly acceptable and respectable alternative to a hypothesis that 80% of the universe is made out of "dark energy" observed in no other way, and that it represents a property of space-time itself, and that the actual proportion of matter which is dark is much smaller than previous estimates, then dark matter candidates like neutrinos (perhaps in condensate form) that don't require the discovery of new fundamental particles, begins to look more plausible.

Pinning Down Archaic Admixture Population Models

There are many outstanding disputes, critical to understand the demographic history of Eurasian modern humans in the Upper Paleolithic era, related to the population models that are used to describe how Neanderthal genes could have ended up in almost all modern Eurasians at frequencies on the order of 2%-4% of our autosomal genome in a sample made up of many thousands or tens of thousands of individuals, despite a complete absence of Neanderthal mtDNA or Y-DNA in any genetically tested modern human, from a large sample of tens or hundreds of thousands of individuals, including hundreds of ancient DNA samples. This population genetic data has been accumulated in a collective scientific enterprise that has deliberately oversampled populations that are likely to be genetically diverse outliers in both data sets, although there are far more outlier populations and ancient DNA populations that are undersampled for autosomal genetics than there are that have been undersampled for mtDNA.

One of the confounds in estimating what kind of process gave rise to the introgression of Neanderthal DNA into modern humans is the question of how much of the Neanderthal DNA originally present in hybrid individuals has been purged over time from modern humans, either due to random genetic drift in admixed modern human populations, or due to selective disadvantage associated with particular Neanderthal genes.

It helps, in comparing possibilities that we have significant shares of the Neanderthal genome from ancient DNA to compare against modern genomes.

Neanderthal genes that could have introgressed into modern humans can be broken into one of four categories: (1) genes in which the Neanderthal genome and modern human genome are indistiguishable (which is a very substantial share of the total, probably on the order of 95% or more), (2) Neanderthal genes with a positive selective advantage (there is some early indication that this may mostly consist of HLA genes which are related to the immune system, (3) Neanderthal genes that have a selective disadvantage relative to modern human genes, which statistically should have been removed from the human genome over the relevant time spam of at least 30,000 years or so, and quite possible two to four times as long as that, even if the selective disadvantage is very modest, particularly as disadvantageous genes slowly become separated from nearby genes that may have selective advantage through the recombination process over many generations, and (4) Neanderthal genes that are selectively neutral.

One can determine in modern populations which Nenderthal genes are present at elevated frequencies indicative of selective advantage and which are only present at a baseline level, in order to both estimate the true selectively neutral baseline level of admixture before selection started to act on the genes in modern humans with Neanderthal ancestry, and to estimate the magnitude of the advantage associated with those genes present at elevated frequency. This task is somewhat harder than it seems because one has to address statistical noise that elevates the frequency of some random genes for reasons unrelated to selective advantage, but is well within the capabilities of well established statistical methods.

One can also search, by direct comparison, for distinguishably Neanderthal genes that have not ended up in any modern human at all. There are basically three ways that this could happen: (1) the genes were never transferred in an admixture event because there were a finite number of admixture events and only an approximately random half of the Neanderthal genome was transferred in each event, so some genes may never have been transferred in any of the events, (2) the genes were transferred in an admixture event and left the modern human genome via random genetic drift, (3) the genes were transferred in an admixture event but due to selective disadvantage associated with the genes, they were culled from the modern human genome. The percentage of Neanderthal specific genes known to exist which are found in no modern human populations can provide a very accurate estimate of the combined impact of these three factors, although by itself, it doesn't do much to tell you how much of each factor plays a part.

It is mathematically trivial to relate the impact of the first factor to the number of admixture events that took place, and the relationship between the percentage of genes never transferred in admixture events and the number of admixture events is highly non-linear. For one admixture event, the percentage of 50%. For two it is 25%. In general, the never transmitted proportion of the genome is 1/(2^n) where n is the number of admixture events. In any scenario where there are seven or more admixture events in all of human history, the percentage of Neanderthal specific genes never transmitted in admixture events is below 1% and at somewhere on the order of twelve to fourteen admixture events ever in all of modern human history, the impact of this factor would be completely undetectable with any level of statistical significance in an autosomal genome data set as large as the one that is currently in existence.

If the effective population size of the modern human populations that admixed with Neanderthals was on the order of four hundred to seven hundred and fifty individuals, the effect of non-transmission of specific genes in any admixture event should be negligable, and even at an effective population size as low as two hundred, the impact of this factor should be a very small proportion of the total number of Neanderthal genes not observed in any modern human population. Yet, most estimates of the effective population size of the founder population of modern human Eurasians are at least in the single digit thousands, and archaic admixture itself, while it would inflate the apparent effective population size of the founder population of modern human Eurasians, at the 2.5%-4% of the total population size would not have an effect so significant that it would bring the effective population size of the founding population of modern human Eurasians to the low three digits, particularly to the extent that the estimates are corroborated by mtDNA and Y-DNA based estimates that have on archaic component.

This means that essentially all of the "missing" Neanderthal DNA (at least outside the sex chromosomes where there are clearly population structure and demographic history factors that are non-random at play) must statistically derive from either genetic drift or selective disadvantage.

We can then work to estimate both components separately using a variety of population genetic parameters, and work to look at the parameter space of assumptions that can produce outcomes consistent with the percentage of missing Neanderthal DNA that we observe.

Random drift of selectively neutral genes is easy to model with very accurate results using just a handful of parameters, either analytically, or numerically with Monte Carlo methods. Some of the key parameters are generation length, effective modern human population size at the time of admixture, number of admixture events, spacing of admixture events, boom and bust variability in effective modern human population size, and population growth (which can be quite accurately estimated in the long run from a variety of evidence, even if fine grained variability in this rate is hard to determine).

For populations that experience growth in the long run (as modern humans in Eurasia obvious did), where the number of generations is very large, it turns out that generation length doesn't actually matter very much, because when you have a number of generations in excess of one thousand with a population that reaches the many millions sometime in the Upper Paleolithic, and an overall percentage of admixture that is at least on the order of the 2.5%-4% it has reached at long term fixation, which has apparently been reached for all Eurasian given the supercontinental uniformity present in that percentage, the amount of genomic loss that takes place due to random drift bceomes insensitive to the number of generations because random drift is much more powerful an effect, in a non-linear manner, when populations are small. At a leading order estimate, the likelihood of losing a gene entirely from a population in any given span of generations is a non-linear function of the absolute number of individuals in the population who carry that gene. Basically, the percentage likelihood that a gene will leave the population by random drift is roughly proportional to the probability that a random sample from the effective population equal to the absolute number of gene carriers in the population would be zero. Once the absolute number of carriers and zero is several sample error standard deviations apart from a sample of that size, the probability of loss of a gene entirely due to random drift approachees zero.

Complicating this is a factor that also looks like random drift, which is mutation. While not listed as a separate factor, another way that a gene can be removed from the gene pool is through a mutation at that locus. The probability of this happening is a function of the number of generations involved and the effective population size of each generation, divided by the number of carriers of a particular gene, and discounted for the fact that lots of mutations are lethal and never enter the gene pool. This is the method used to make estimates of the age of mtDNA and Y-DNA haplogroups and it isn't very accurate, but there is a considerable body of empirical evidence that put order of magnitude bounds on the size of this effect. So, whlle the error bars on this component of the random loss of selectively neutral genes from the population might have extremes that vary by as much as a factor of two to ten if we were really being realistic about who precise our methods of mutation dating have proven to be in practice (perhaps more, given that the timing of the admixture event has something on the order of a factor of two uncertainty in it to begin with and that our estimates of generation length in Upper Paleolithic modern humans aren't terribly accurate and our effective population chart also has a pretty fuzzy line), if the effect is at an order of magnitude lower than other sources of removals of genes from the population's genome, we can safely ignore it, even if the precise magnitude of the effect is not known with a great deal of certainty.

From the other direction, there have been a number of reasonably useful estimates of the proportion of genes in the human genome, and the proportion of genes in a variety of other species, which do, or do not, show indications of having a selective effect at any given time (which basically consists of genes that have not reached fixation in the species for which there is no good reason to believe that selection produces multiple varieties in stable proportions as it does for HLA genes). In general, these studies have shown that the proportion of genes that are currently experiencing active selective pressures at any given time appear to be fairly modest, but not negligable either.

There is no really good way to estimate the relative numbers of selectively advantageous archaic genes to selectively disadvantageous archaic genes. There argument for more good genes than bad is that Neanderthals had more time to adapt to the new environment that modern humans were entering. The argument for more bad genes than good is that Neanderthals went extinct while modern humans didn't, so overall, modern humans had a selective advantage of some form over Neanderthals. But, it isn't unreasonable to infer that there should be an order of magnitude similar number of each. There is also no particularly good reason to think that the proportion of the genome that is selectively neutral at any given point in time has changed very much or was much different from Neanderthals than it is for modern humans. So, an examination of the number of Neanderthal genome genes present in elevated levels that hence show signs of selective advantage could cast some light, at least, on the proportion of Neanderthal genes that gave rise to selective disadvantages and were purged from the modern human genome. The early indications from this kind of analysis are that the proportion of Neanderthal genes still in the modern human genome which show signs of having been positively selected for is small relative to the total number of Neanderthal genes in the modern human genome.

Despite the fuzziness of all of these reasoning, from a quantitative perspective, the bottom line in all of this analysis is that we would expect a significantly disproportionate share of the proportion of missing genes from Neanderthal genome to have been lost due to selectively neutral random drift rather than natural selection, and that even this crude bound allows us to make fairly specific numerical estimates of the proportion of Neanderthal specific genes that were lost because they were selectively disadvantageous and the proportion of Neanderthal specific genes that were lost due to one of a couple of forms of random genetic drift.

Placing numerical bounds and maximum likelihood estimates on the proportion of Neanderthal specific genes that were lost due to random genetic drift with this kind of analysis, in turn, allows us to significantly narrow the parameter space of population model assumptions that could produce the observed amount of random genetic drift. The observed proportion of random genetic drift in the Neanderthal genome would be particularly relevant in placing bounds on the paramater space for assumptions about effective modern human population size at the time of admixture, number of admixture events, spacing of admixture events, and the boom and bust variability in effective modern human population size. And, there are independent ways to provide additional bounds on many of these parameters from other lines of population genetic data and anthropology and the physical anthropology of Neanderthal remains, so the flexibility in one paramater doesn't inject too much flexibility into other paramaters.

Also, a reasonably tightly bound overall estimate of the magnitude of random genetic drift from the proportion of the Neanderthal genome that has been purged from modern humans provides a robust, and fairly direct estimate, from the longest time period for which ancient DNA is available for hominins, that can be used to inform estimates of the rate at which selectively neutral genes are purged by genetic drift in modern humans that is relatively population model independent for use in analysis of non-Neanderthal admixture population genetics (e.g. in estimates related to Denisovian admixture, putative African archaic admixture, admixtures of modern human populations in the Upper Paleolithic era, and the accuracy of estimates of the probability that a chance in the proportion of a particular gene in a population was due to random genetic drift or selection), since the error bars on this direct measure of random genetic drift in autosomal genes over that time period would be much smaller than the error bars around estimates of any of the specific parameters in parameter space that could be used to estimate it from first principles using population models alone. Thus, making this estimate in the Neanderthal case would materially improve the statistical power of all of our long term population genetic estimates, a contribution that may be unique and may not be available with greater precision from any other set of data for the foreseeable future.

Explicitly estimating the impact of selective effects and the loss of genes due to random genetic drift is also likely to establish that the total number of archaic admixture events was larger than an estimate that ignores these effects, because, on balance, these effects tend to reduce the number of Neanderthal genes in the modern human genome. Thus, the process of estimating these numbers of likely to reveal that Neanderthals and modern humans had sex more often that a crude back of napkin estimate would suggest. And, if the kind of process assumptions (Haldane's rule which also impacts fertility assumptions, and predominantly female modern human mothers for hybrid children born into modern human tribes that averted extinction, which implies that there are large numbers of uncounted cases where Neanderthal mothers that were erased from modern human populations in the present) that most naturally explain the disconnect between autosomal genetic data and uniparental genetic data are also incorporated into the analysis, the amount of cross species sexual activity between Neanderthals and modern humans may have been quite a bit higher indeed than the current percentage of our autosomal genome attributable to Neanderthal genes would suggest, probably on the order of a factor of two to five, which would be roughly the difference between a once in a generation event (a crude estimate without these considerations) and something like a once every few years event.

My intuition is that the amount of allele loss due to random genetic drift acting on selectively neutral genes that is actually observed in the Neanderthal case would suggest that the magnitude of the impact of random genetic drift in purging selectively neutral genes from modern human populations is quite a bit smaller than could safely be inferred by a naiive estimate based on other existing data and pure population modeling not supported by this kind of empirical calibration. Thus, I suspect that this data will, generally, favor findings that it is more likely that a given chance in gene frequency was a selective effect rather than a random one, and that populations not subject to selective pressures are more genetically stable than one might naiively expect even with a fairly careful theoretical analysis.