The Chinese customer is always right

Unless you have been sleeping under a rock you are aware that there is a controversy around China and the NBA due to different standards of political speech in the USA and China. Obviously the major issue that looms over the debate is the reality that at some point in the 2020s China will become the world’s largest economy, and one of the major consumer engines of the world. From a corporate perspective, this hangs over all the discussion and consideration. The Chinese market is like El Dorado.

But I would like to draw attention to something Joe Tsai, owner of the Brooklyn Nets and co-founder of Alibaba, said on Facebook:

The one thing that is terribly misunderstood, and often ignored, by the western press and those critical of China is that 1.4 billion Chinese citizens stand united when it comes to the territorial integrity of China and the country’s sovereignty over her homeland. This issue is non-negotiable.

A bit of historical perspective is important. In the mid-19thcentury, China fought two Opium Wars with the British, aided by the French, who forced through illegal trade of opium to China. A very weak Qing Dynasty government lost the wars and the result was the ceding of Hong Kong to the British as a colony.

The substance of the dispute here on their face-value isn’t too important. Rather, from a commercial perspective the opinions of Chinese matter because there are 1.4 billion of them. Additionally, from a commercial perspective, the “objective truth” doesn’t matter. The “customer” is always right. Whether the Chinese have legitimate grounds for their beliefs is less important than what their beliefs are, because there are so many of them. The substance of beliefs may dictate consumption. Whether those beliefs are true or not is secondary (ask the supplements industry in the USA).

But this is not a dynamic limited to this context. Do you remember the Islamic mosque and cultural center that was slated to be built near the World Trade Center? The project was abandoned after various groups, including some 9/11 victim families, felt that it was offensive. Though I didn’t believe that the center had anything to do with 9/11 as such, I do recall being vaguely sympathetic to their feelings. In hindsight, this was clearly the wrong call by me in light of broader trends in our culture.

Since that time the reign of feelings over facts has proceeded apace. In American society, the facts at hand matter less and less, than who the people are who have their own reaction, perception, and subjective experience, of the facts. The fact that 9/11 families were uncomfortable determined the ultimate course of construction. The fact that college students are uncomfortable that someone is going to speak who wrote something that offends them 20 years ago is key factor that determines if the invitation will be rescinded. The overall objective fact of something is incidental in comparison to the visceral reaction.

One of the things that I have witnessed which illustrates this trend is the way Richard Dawkins is viewed by young “enlightened” people. Dawkins has always been a bit of a brusque and direct individual in regards to what he believes are the facts irrespective of the target. In 2006 he was commissioned by Britain’s Channel 4 to take lead on a documentary titled The Root of all Evil. When The God Delusion was published Dawkins’ intellectual celebrity rose to new heights.

Not so in 2019. The reason? Richard Dawkins is 78. In fundamental ways, he has not changed. He is an old man. And, he has a naive and to my mind an overly simplistic view of the importance of truth above all things. But those are his sincere beliefs. As such, he expresses his views without much equivocation and in a simple and open manner which is now often highly offensive to many people who a decade ago admired him. The primary reason is that Richard Dawkins is an upper-middle-class white male, and the targets of his criticism, for example, a hijabi in Bradford, England, are not. How sympathetic the targets are matters a great deal. The logic or empirical basis less so.

In the late 2000s I recall a friend of mine at the time, an academic philosopher, explaining to me that in the context of the offense, the intent of the offender is irrelevant when compared to the reaction of the offended. This seemed like a bizarre view to me at the time, but in this decade this view has become more and more mainstream.

When these ideas were first being articulated several decades ago there was still a strong hope and expectation that economic liberalization in China would lead to political liberalization. I shared that hope. It seems that in many ways we were wrong. Rather than the internet as a means for free expression, it has become an essential tool of commerce and social control and manipulation. My vague impression is that most  Chinese are either politically apathetic or somewhat nationalist and anticipating warmly the geopolitical power of their nation-state on the world stage.

In contrast, in the United States I feel we are in a parochial cultural moment. On the Right, the slogan “Make America Great Again” is reflective of nostalgia for the 20th-century. On the Left, particular concerns with the failings of the American project loom larger than the larger dynamics in human history (as opposed to the mass decline of poverty in places like China over the last generation). Around the year 2000 many Americans had a view of the 21st-century where prosperity would transform the rest of the world into cultural clones of America. This would have resulted in universal particularisms and sensitivities. That is, the ascendency of post-modern thinking, and the rise of subjectivism would have been constrained by a common cultural framework directed and shaped by American and European elites. What is “problematic” here would be “problematic” there.

That has not happened. Rather, Alistar McGrath’s general prediction in The Twilight of Atheism has come to be. I say general because atheism has not collapsed in a specific sense (on the contrary, as irreligion has increased greatly in the United States). But particular cultural understandings of what is right and proper have come to the foreground with more muscular robustness as the Enlightenment ideal of a universal shared reality fades.

One of the more nihilistic aspects of the intellectual revolution triggered by the influence of Michel Foucault is to reduce perception and comprehension as simply outcomes of power relations. I would argue that what we see today in the corporate response to the rise of Chinese economic power is the reshaping of truth and sensitivities toward broadly Chinese outlines due to Chinese power. What one sees here is the convergence between capitalist kowtowing toward power, and the reality that more and more people acknowledge and accept that power determines our understanding of reality.

The world is not out there, the world is created by us.

Albion’s seeds in Arkansas

A few days ago The New York Times had a piece up that stirred a lot of comment, In the Land of Self-Defeat: What a fight over the local library in my hometown in rural Arkansas taught me about my neighbors’ go-it-alone mythology — and Donald Trump’s unbeatable appeal. It profiles the fight over the funding of (or lack) a library in Van Buren County, Arkansas. The local conflict is situated in national politics, and the gulf between rural and urban, and white Red America and cosmopolitan Blue America.

This is all fine as far as it goes, but a lot of the values expressed among the citizens of Van Buren County make a lot more sense if you take a deeper historical perspective. Long-time readers know where I’m going with this. Albion’s Seed: Four British Folkways in America, American Nations: A History of the Eleven Rival Regional Cultures of North America, and The Cousins’ Wars: Religion, Politics, Civil Warfare, And The Triumph Of Anglo-America, all highlight the deep divergences of values and variation of culture which characterize the roots of Anglo-America. That is, the America that was here at the Founding in 1776 was already a variegated thing and America that was created in the 19th and 20th-centuries may have been inflected by waves of Irish, German, and Southern and Eastern European immigrants, but the broad outlines of regional difference predate the later waves.

What is seen cannot be unseen, and once you read one of the above books, you read and perceive the expression of American cultures differently. From Theodore Parker’s The great battle between slavery and freedom (1856):

In 1850…Arkansas had 97,402 white persons under twenty, and only 11,050 attending school; while of 210,831 whites of that age in Michigan, 112,175 were at school or college. Last year, Michigan had 132,234 scholars in her public common schools. In 1850, Arkansas contained 64,787 whites over twenty, – but 16,935 of these were unable to read and white; while, out of 184,240 of that age in Michigan, only 8,281 were thus ignorant, – of these, 3009 were foreigns; while, of the 16,935 illiterate persons of Arkansas, only 37 were born out of that State. The Slave State had only 47,852 persons over twenty who could read a word; while the free State had 175,959. Michigan had 107,943 volumes in “libraries other than private,” and Arkansas 420 volumes….

The reality is that many of the southern regions of the United States have long had a deeply rooted and traditional aversion to public communal investments. This has been to the detriment of the development of broad public education as well as institutions of higher learning. In contrast, investment in primary schools in “Yankee America” was a recurrent feature of town-life in areas settled by New Englanders. This tendency does not today always lean on ideological lines. Much of Utah was settled by Yankees, and its public culture is arguably much more communitarian today than that of the South.

After Golden State, the government finally moves

More than a year after the GSK apprehension through genetic genealogy, the feds are finally moving and looking closely at what’s been going on, New federal rules limit police searches of family tree DNA databases:

The DOJ interim policy, which takes effect on 1 November, is intended to “balance the Department’s relentless commitment to solving violent crime and protecting public safety against equally important public interests,” such as privacy and civil liberties, a press release states. The policy says “forensic genetic genealogy” should generally be used only for violent crimes such as murder and rape, as well as to identify human remains. (The policy permits broader use if the ancestry database’s policy allows such searches.) Police should first exhaust traditional crime solving methods, including searching their own criminal DNA databases.

These guidelines are baby steps. They don’t impact people working in the private sector. But likely they presage more fully-fleshed responses.

One consideration is that when thinking about the intersection of genealogy and forensics we often view the latter as a black-box, with reliable technology and data. The reality is that degraded samples are not as easy to work with, and extracting information is not trivial. Because of this variation in quality, it seems possible that unless there is some self-regulation, eventually the government will exhibit greater and greater oversight on this space due to its relevance to law enforcement. There have already been enough scandals with conventional government forensic labs.

This is on my mind after a conversation with my friend David Mittelman. He founded Othram last year. It is one of the few companies that actually operate a lab targeting this space. He is very concerned about companies that sell lab services without operating a lab since they have no visibility on the data generation. He has suggested the community builds tools like Genome-in-a-Bottle to help self-regulate and verify that labs can do what they claim they can do. Obviously his interest is simple: excessive regulation on the private sector is not good for business, so he prefers that firms just get ahead of concerns and be transparent.

If genetics doesn’t self-regulate, the government surely will.

The arc of selection on polygenic traits

A very important new preprint, Polygenic adaptation after a sudden change in environment:

Polygenic adaptation in response to selection on quantitative traits is thought to be ubiquitous in humans and other species, yet this mode of adaptation remains poorly understood. We investigate the dynamics of this process, assuming that a sudden change in environment shifts the optimal value of a highly polygenic quantitative trait. We find that when the shift is not too large relative to the genetic variance in the trait and this variance arises from segregating loci with small to moderate effect sizes (defined in terms of the selection acting on them before the shift), the mean phenotype’s approach to the new optimum is well approximated by a rapid exponential process first described by Lande (1976). In contrast, when the shift is larger or large effect loci contribute substantially to genetic variance, the initially rapid approach is succeeded by a much slower one. In either case, the underlying changes to allele frequencies exhibit different behaviors short and long-term. Over the short term, strong directional selection on the trait introduces small differences between the frequencies of minor alleles whose effects are aligned with the shift in optimum versus those with effects in the opposite direction. The phenotypic effects of these differences are dominated by contributions from alleles with moderate and large effects, and cumulatively, these effects push the mean phenotype close to the new optimum. Over the longer term, weak directional selection on the trait can amplify the expected frequency differences between opposite alleles; however, since the mean phenotype is close to the new optimum, alleles are mainly affected by stabilizing selection on the trait. Consequently, the frequency differences between opposite alleles translate into small differences in their probabilities of fixation, and the short-term phenotypic contributions of large effect alleles are largely supplanted by contributions of fixed, moderate ones. This process takes on the order of ~4Ne generations (where Ne is the effective population size), after which the steady state architecture of genetic variation around the new optimum is restored.

There is a lot to take in in this preprint. If you jump to the discussion it frames its importance pretty well. A lot of selection is probably quantitative and polygenic, but a lot of the empirical investigation has been of the sweep of single-locus alleles that rise up to fixation. It strikes me that some of the results here resemble R. A. Fisher’s geometric model of adaptation (The Genetical Theory is the first citation).

I read the whole preprint, but I didn’t double-check the formulae. I have neither the ability or the time. This is where I really which there was a lot of visible post-publication review. I am very interested in the topic under discussion, but it is outside of the purview of my competency, but I know enough that I would probably benefit from extensive comments by others.

This part of the discussion jumped out at me since it echoes my thoughts:

Another implication of our results pertains to the search for the genetic basis of human adaptation, as well as adaptation in other species. Efforts to uncover the identity of individual adaptive genetic changes on the human lineage were guided by the notion that their identity would offer insight into what “made us human”. Under the plausible assumption that many adaptive changes on the human lineage arose from selection on complex, quantitative traits, this approach may not be as informative as it appears (15, 19). Our results indicate that after a shift in the optimal trait value, the number of fixations of alleles whose effects are aligned to the shift are nearly equal to the number of alleles that are opposed (Fig. 6).

Anticipating post-postcolonialism

Recently on Facebook, an old friend who is now a professor promoted a new series of essays to which she contributed. She noted that this is a history which “…place enslavement, colonialism, and indigenous removal at the center…” Some of the analyses clearly take postcolonialism for granted, where the contact with and shock of European imperialism are critical to understanding everything.

One some level empirically it is impossible to understand the recent history of black Americans or Native Americans without understanding the role that imperialism and colonialism played in shaping their self-understandings, and how they reacted to their oppression. But, on a purely normative level, I wonder if this diminishes the attempt to understand cultures and societies in a positive sense. As in, what defines a people beyond their reaction to other people? To be frank, often the fixation on slavery and genocide by white intellectuals allows these intellectuals to continue to focus on white people as the agents of history.

To some extent, this does reflect reality. But even in bondage and subjugation people continued to innovate, create, and flourish. The long recession of the native peoples and nations of the New World in the face of European hegemony was the work of centuries. How many people know that the last Maya kingdom was conquered by the Spaniards in 1697? Or that the Mapuche people of southern Chile were fully not conquered until the late 19th-century?

There are whole histories here that could be told which are not nearly as Eurocentric.

But the bigger issue is that outside of the context of the peoples of the New World, who felt the blunt force of European imperialism for centuries and manifested the colonialist experience par excellence, a postcolonial narrative that foregrounds the agency and action of Europeans may not be fully informative. The period between 1400 and 1800 is one where Europe became progressively more dynamic and powerful vis-a-vis other regions of the oikoumene, but until the very end of this period European powers were often marginal players except in their own imaginations.

After 1800 European hegemony truly took hold, as the Eurasian “gunpowder empires” collapsed, and the interior of Africa was finally opened up to colonization due to quinone. The question then becomes: does this century or so allow us to understand by and large the course of future history?

British rule in 1800

Consider both India and China. India was under direct or indirect British rule in totality by the middle of the 19th-century, though note that even in 1800 much of the subcontinent was under native rule. India and Pakistan were independent by 1947. China began to be impinged by European powers by the 1840s, and then underwent a series of shocks and decentralizations so that it was quasi-colonial by the early 20th-century. Like India, China’s indigenous elite shucked off foreign rule in the 1940s with the victory of the Communists.

But both India and China were strongly shaped by non-indigenous ideologies and currents after independence. China was Communist, while India’s elite was shaped by Fabian socialism. But today both China and India are arguably shifting toward more self-consciously indigenous modalities.

One way to understand the contemporary turn of both India and China is to interpret them in the lens of recent Western political history. For example, Hindu nationalism as an analog to nationalist movements in 20th-century Europe. These analogies are not without merit, but the problem is that often they are taken to extreme correspondences which are highly implausible. To me, it is important to consider the possibility, even likelihood, that deep indigenous sentiment and sensibilities are resurfacing in these societies as European ascendency recedes.

If this is the case, then it is important to understand the histories of these people beyond their interaction and engagement with the West. Beyond postcolonialism. Hindu nationalism is far more than fascism in brownface, and Salafism is more than a purely rational reaction to the Western challenge.* We must move beyond our European schemas to understand the post-European age.

* Actually, I do think Salafism is impossible to understand without its reaction and engagement with the West, but the impulse is far more ancient and goes back to Ibn Taymiyyah.

Napoleon Chagnon, R.I.P.

Napoleon Chagnon has died. It is unfortunate that Chagnon is known to many for the fact that he became involved in a controversy triggered by the activism of a polemical journalist. It will surprise none of the readers of this weblog I agree with Alice Dreger’s take on the whole issue.

If you want to familiarize yourself with Chagnon, I would recommend Noble Savages: My Life Among Two Dangerous Tribes — the Yanomamo and the Anthropologists. It was written at the end of Chagnon’s life, so it summarizes his research and overall views.

I will be frank and state that I am much more skeptical of the generality of some of Chagnon’s inferences using an evolutionary psychological framework than I was 20 years ago. If Chagnon’s critics had focused more on the science everyone would have benefited. As it is, they went the easy route with political food fights.

Chagnon asked the right questions, even if I now judge that he came to some wrong answers. Such is science.

Open Thread, 09/29/2019


Jürgen Osterhammel’s Unfabling the East is a book I really want to read someday. But I have to finish The Transformation of the World: A Global History of the Nineteenth Century first.

Ancient genomic regulatory blocks are a major source for gene deserts in vertebrates after whole genome duplications.

What Whales and Dolphins Left Behind for Life in the Ocean.

U.S. Officials Warn of Rising Threat From Qaeda Branch in Northwest Syria. Like Leftist terrorism in the 70s, this will linger for a while.

Preying on Children: The Emerging Psychology of Pedophiles. “The biological clues attached to pedophilia demonstrate that its roots are prenatal,” said James Cantor, director of the Toronto Sexuality Center. “These are not genetic; they can be traced to specific periods of development in the womb.”

“CCR5-∆32 is deleterious in the homozygous state in humans” – is it?. The paper that inspired this blog post will be retracted now, as some of the concerns expressed by the author of the post seem to have been warranted.

Adaptive Tree Proposals for Bayesian Phylogenetic Inference.

Removing reference bias in ancient DNA data analysis by mapping to a sequence variation graph.

Is Yamnaya overrated? I think a lot of the time these “ancestral” populations are just good proxies for the “true” ancestral group. That is, they are sister groups to the ancestral group. This is clear.

“The Aryans”.

ASHG 2019 meeting soon. Excited.

Humans are basically invasive weeds

One of the somewhat surprising things we have learned over the last decade is that massive admixture and homogenization has occurred between distinct human lineages over the last 10,000 years. By this, I mean that we’re not talking simply about continuous gene-flow between neighboring populations, but massive expansions of small groups and assimilation of very different groups from the expanding groups. As a stylized fact, it looks like “Early European Farmers” we as distinct from Mesolithic hunter-gatherers as modern Northern Europeans are from Han Chinese (pairwise Fst ~0.10). The fusion of these two groups later merged in much of Europe with migrants from the east, the western edge of the forest-steppe.

The empirical pattern seems to be that cultural innovations (e.g., agriculture) trigger demographic revolutions, which homogenize and admix vast regions. This is a story of demographic history. Phylogeography.

But there is another aspect, natural selection. Humans are not exempt from this. Selection operates upon genetic variation, which is preexistent (“standing variation”), or, comes from new mutations (de novo).

It seems plausible that cultural innovation has resulted in a great deal of selection over the last 10,000 years. So where did the raw material come from? One argument that has been playing out is between those who argue that it’s from variation within human populations that is ancestral and shared, and new variation. This is where admixture comes into play.

A new preprint on bioRxiv uses the 1000 Genomes data in the New World to suggest that admixture resulted in the introduction of a lot of adaptive alleles into populations of mostly European and Native background from African ancestry. Basically, it seems likely that the American tropics were colonized by African tropical diseases, which entailed adaptations which were already existent within African populations. Admixture-enabled selection for rapid adaptive evolution in the Americas:

Background: Admixture occurs when previously isolated populations come together and exchange genetic material. We hypothesized that admixture can enable rapid adaptive evolution in human populations by introducing novel genetic variants (haplotypes) at intermediate frequencies, and we tested this hypothesis via the analysis of whole genome sequences sampled from admixed Latin American populations in Colombia, Mexico, Peru, and Puerto Rico. Results: Our screen for admixture-enabled selection relies on the identification of loci that contain more or less ancestry from a given source population than would be expected given the genome-wide ancestry frequencies. We employed a combined evidence approach to evaluate levels of ancestry enrichment at (1) single loci across multiple populations and (2) multiple loci that function together to encode polygenic traits. We found cross-population signals of African ancestry enrichment at the major histocompatibility locus on chromosome 6, consistent with admixture-enabled selection for enhanced adaptive immune response. Several of the human leukocyte antigen genes at this locus (HLA-A, HLA-DRB51 and HLA-DRB5) showed independent evidence of positive selection prior to admixture, based on extended haplotype homozygosity in African populations. A number of traits related to inflammation, blood metabolites, and both the innate and adaptive immune system showed evidence of admixture-enabled polygenic selection in Latin American populations. Conclusions: The results reported here, considered together with the ubiquity of admixture in human evolution, suggest that admixture serves as a fundamental mechanism that drives rapid adaptive evolution in human populations.

The period after 1492 is easy for us to think about. But what ancient DNA has shown us is that it’s not as uncommon a phase as we might have thought.

Why I am very bearish on Netflix

I’ve been a subscriber to Netflix for 15 years. It’s a small cost. There are months I go without watching anything. But it’s there. And that’s how I want it.

That being said, I just want to put it on the record (again) that I’m bearish on the future of Netflix. The proximate reason is that major competitors with deep pockets and huge corporate backing are coming into the field of streaming (hello Disney!). But the ultimate rationale is that I think Netflix’s “superstar” system in relation to employees is going to kill any ability to navigate a tough patch with all hands on deck.

Here is a positive view of the firm’s system, How Netflix Reinvented HR.

Basically, Netflix’s culture is hyper-rational and takes for granted that its employees are similar. “Grown-ups.” This is fine during a growth phase, or when times are good. But if Netflix seems like it might not be the future, why wouldn’t all the superstar employees find better opportunities? And once some superstars start leaving, that will reduce Netflix’s prospects, meaning all the superstars will leave en masse, accelerating the decline. And according to Netflix’s credo, they would be behaving entirely rationally.

The company doesn’t make a pretense of loyalty to its employees beyond what they can bring to the table for the company. Similarly, the company won’t be able to lean on any sentimental loyalty from its employees if it needs to right its ship or seems like anything less than a sure bet.

Phenotype does not imply ancestry (always)

One of the questions I often get relate to whether “trait X comes from population Y and does that mean if one has trait X that one has more ancestry from population Y.” To give an illustration, I have had people ask “I have blue eyes, does that mean I am more ‘Western Hunter-Gather’ than other people?”

One issue is that though the WHG tended toward high frequency of the derived OCA2-HERC2 haplotype, other populations clearly carried it, the other is that admixture is so far in the past that having blue or brown eyes is not informative to any degree of ancestry. There were probably relict populations of WHG less than 4,000 years ago (David has mentioned of a sample less than 3,000 years ago in Scandinavia), but the admixture of WHG into other groups was very long ago. More than 1,500 generations ago. To a great extent, it seems plausible that even within populations variation in ancestral fractions should be marginal to non-existent.

But this is a verbal model. A new preprint on bioRxiv has posted a formal model that outlines the different parameters that shape the trajectory of this decoupling between phenotype and ancestry. Assortative mating and the dynamical decoupling of genetic admixture levels from phenotypes that differ between source populations:

Source populations for an admixed population can possess distinct patterns of genotype and phenotype at the beginning of the admixture process. Such differences are sometimes taken to serve as markers of ancestry—that is, phenotypes that are initially associated with the ancestral background in one source population are taken to reflect ancestry in that population. Examples exist, however, in which genotypes or phenotypes initially associated with ancestry in one source population have decoupled from overall admixture levels, so that they no longer serve as proxies for genetic ancestry. We develop a mechanistic model for describing the joint dynamics of admixture levels and phenotype distributions in an admixed population. The approach includes a quantitative-genetic model that relates a phenotype to underlying loci that affect its trait value. We consider three forms of mating. First, individuals might assort in a manner that is independent of the overall genetic admixture level. Second, individuals might assort by a quantitative phenotype that is initially correlated with the genetic admixture level. Third, individuals might assort by the genetic admixture level itself. Under the model, we explore the relationship between genetic admixture level and phenotype over time, studying the effect on this relationship of the genetic architecture of the phenotype. We find that the decoupling of genetic ancestry and phenotype can occur surprisingly quickly, especially if the phenotype is driven by a small number of loci. We also find that positive assortative mating attenuates the process of dissociation in relation to a scenario in which mating is random with respect to genetic admixture and with respect to phenotype. The mechanistic framework suggests that in an admixed population, a trait that initially differed between source populations might be a reliable proxy for ancestry for only a short time, especially if the trait is determined by relatively few loci. The results are potentially relevant in admixed human populations, in which phenotypes that have a perceived correlation with ancestry might have social significance as ancestry markers, despite declining correlations with ancestry over time.

There are a lot of words and math. It’s quite gnarly. But the figure at the top of the post shows the major effect.

Basically:

– loci in a trait (e.g., height) means that association between ancestry and trait decays more slowly
– stronger assortative mating of phenotype means that the association between ancestry and trait decays more slowly
– stronger assortative mating on ancestry means that the association between ancestry and trait decays more slowly

Since historically people did not have individualized genome-wide ancestry results “assortative mating on ancestry” means by physical appearance in the generality. To me panel E above is really what you should focus on. About 10 genes impact the phenotype, and assortative mating is at 0.5 (between 0 and 1.0). You see the correlation is already only ~0.50 between genome-wide ancestry and the trait in about 10 generations.

Anyway, dig into the math. I read the whole thing but didn’t go over the math in detail. The model and simulations make intuitive sense. I’d be curious how they fit empirical results (which are cited in the paper).