Cecil and the hunter

Like many others, I was first outraged when I heard about the death of the beloved lion in Zimbabwe at the hands of a hunter from Minnesota. But I then quickly realized that I am in no position to judge the man. Over the past week, I have dined on salmon, chicken, pork, tuna, and beef. Just because I don’t go into the brush to kill an animal I consume doesn’t mean that I am not directly responsible for its demise. The only difference between me and a hunter is that I do not find any sport in the shooting of animals. There are nearly a hundred million cows at any given time in the US waiting to be slaughtered. Is the life of a cow not as valuable as that of a lion? It is no fault of the cow that she is not an iconic symbol like the lion. Fish are wild animals and we are hunting them to extinction. Tuna can live very long lives and are partially warm blooded. Sharks exhibit very complex behavior and have live births. I would suggest that the death of a big fish is no less tragic than the death of a big cat.

The unfortunate hunter paid a lot of money to go on what he thought was a legal hunt. The guides he hired may have misled him and broken the law but hunting lions in Zimbabwe is not a crime. Remember that this is a country that was near economic collapse just a decade ago and could use an infusion of hard currency. I have argued before that hunting may ironically be a way to preserve wildlife and habitat. The interests of hunters and environmentalists could be aligned. Regulated hunting could be an antidote to illegal poaching. If the hunter broke a law then he should be prosecuted. Otherwise, his choice of recreation is protected by the First Amendment of the US Constitution.

Terry Tao in the Times

There is a nice profile of mathematician Terence Tao in the New York Times magazine this week. Tao is astonishing in his breadth and depth. He could probably master any subject in any field if he just put his mind to it. The article plays up his “normality” in contrast to the stereotype of the eccentric asocial mathematician like Gauss, John Nash or Grigory Perelman, who proved the Poincare Conjecture. However, in my experience, most mathematicians, even the very best, are reasonably normal and sociable. My guess is that the rate of personality disorder among mathematicians is no higher than the general populace. It is perhaps true that mathematicians are more introverted and absent minded than average but rarely to a pathological degree. I think the myth persists because of a few very prominent examples but also that mathematics is a pursuit where having a personality disorder is not a major handicap. One could probably not be a great lawyer, physician or statesman if they were socially abnormal. Thus, if the rate of historically great eccentric mathematicians is high compared to other fields, it is because the sample is biased.

Have we crossed peak food?

The New York Times has an article today describing the decrease in food consumption over the past decade.  Here is one primary reference. I used to joke that the obesity epidemic would eventually be curbed by either a huge increase in oil prices or a depression. The great recession of 2008 made be believe that food consumption would come down but the data shows that it may have been dropping earlier and mostly in families with children.  The biggest decrease is in sugar sweetened beverages.

Here’s Kevin’s mention:

The recent calorie reductions appear to be good news, but they, alone, will not be enough to reverse the obesity epidemic. A paper by Kevin Hall, a researcher at the National Institutes of Health, estimated that for Americans to return to the body weights of 1978 by 2020, an average adult would need to reduce calorie consumption by 220 calories a day. The recent reductions represent just a fraction of that change.

Heritability in twins

Nature Genetics recently published a meta-analysis of virtually all twin studies over the last half century:

Tinca J C Polderman, Beben Benyamin, Christiaan A de Leeuw, Patrick F Sullivan, Arjen van Bochoven, Peter M Visscher & Danielle Posthuma. Meta-analysis of the heritability of human traits based on fifty years of twin studies. Nature Genetics 47,702–709 (2015) doi:10.1038/ng.3285.

One of the authors, Peter Visscher, is perhaps the most influential and innovative thinker in human genetics at this moment and this paper continues his string of insightful results. The paper examined close to eighteen thousand traits in almost three thousand publications, representing fifteen million twins. The main goal was to use all the available data to recompute the heritability estimates for all of these traits. The first thing they found was that the traits were highly skewed towards psychiatric and cognitive phenotypes. People who study heritability are mostly interested in mental function. They then checked to see if there was any publication bias where people only published results with high heritability. They used multiple methods but they basically checked if the predictions of effect size was correlated with sample size and they found none. Their most interesting result, which I will comment on more below was that the average heritability across all traits was 0.488, which means that on average genes and environment contribute equally. However, heritability does vary widely across domains where eye, ear, nose and throat function are most heritable, and social values were least heritable. The largest influence of shared environmental effects was for bodily functions, infections, and social values. Hence, staying healthy depends on your environment, which is why a child who may be stunted in their impoverished village can thrive if moved to Minnesota. It also shows why attitudes on social issues can and do change. Finally, the paper addressed two important technical issues which I will expand on below – 1) previous studies may be underestimating heritability and 2) heritability is mostly additive.

Heritability is the fraction of the variance of a trait due to genetic variance. Here is a link to a previous post explaining heritability although as my colleague Vipul Periwal points out, it is full of words and has no equations. Briefly, there are two types of heritability – broad sense and narrow sense. Broad sense heritability, H^2 = Var(G)/Var(P), is the total genetic variance divided by the phenotypic variance. Narrow sense heritability h^2 = Var(A)/Var(P) is the linear or additive genetic variance divided by the phenotypic variance. A linear regression of the standardized trait of the children against the average of the standardized trait of the parents is an estimate of the narrow sense heritability. It captures the linear part while the broad sense heritability includes the linear and nonlinear contributions, which include dominance and gene-gene effects (epistasis). To estimate (narrow-sense) heritability from twins, Polderman et al. used what is called Falconer’s formula and took twice the difference in the correlation of a trait between identical (monozygotic) and fraternal (dizygotic) twins (h^2 =2 (r_{MZ}-r_{DZ})). The idea being that the any difference between identical twins must be environmental (nongenetic), while the difference between dyzgotic twins is half genetic and environmental, so the difference between the two is half genetic. They also used another Falconer formula to estimate the shared environmental variance, which is c^2 = 2 r_{DZ} - r_{MZ}, since this “cancels out” the genetic part. Their paper then boiled down to doing a meta-analysis of r_{DZ} and r_{MZ}. Meta-analysis is a nuanced topic but it boils down to weighting results from different studies by some estimate of how large the errors are. They used the DerSimonian-Laird random-effects approach, which is implemented in R. The Falconer formulas estimate the narrow sense heritability but many of the previous studies were interested in nonadditive genetic effects as well. Typically, what they did was to use either an ACE (Additive, common environmental, environmental) or an ADE (Additive, dominance, environmental) model. They decided on which model to use by looking at the sign of c^2. If it is positive then they used ACE and if it is negative they used ADE. Polderman et al. showed that this decision algorithm biases the heritability estimate downward.

If the heritability of a trait is mostly additive then you would expect that r_{MZ}=2 r_{DZ} and they found that this was observed in 69% of the traits. Of the top 20 traits, 8 traits showed nonadditivity and these mostly related to behavioral and cognitive functions. Of these eight, 7 showed that the correlation between monozygotic twins was smaller than twice that of dizygotic twins, which implies that nonlinear genetic effects tend to work against each other. This makes sense to me since it would seem that as you start to accumulate additive variants that increase a phenotype you will start to hit rate limiting effects that will tend to dampen these effects. In other words, it seems plausible that the major nonlinearity in genetics is a saturation effect.

The most striking result was that the average heritability across all of the traits was about 0.5. Is an average value of 0.5 obvious or deep? I honestly do not know. When I told theoretical neuroscientist Fred Hall this result, he thought it was obvious and should be expected from maximum entropy considerations, which would assume that the distribution of h^2 would be uniform or at least symmetric about 0.5. This sounds plausible but as I have asserted many times – biology is the result of an exponential amplification of exponentially unlikely events. Traits that are heritable are by definition those that have variation across the population. Some traits, like the number of limbs, have no variance but are entirely genetic. Other traits, like your favourite sports team, are highly variable but not genetic even though there is a high probability that your favourite team will be the same as your parent’s or sibling’s favourite team. Traits that are highly heritable include height and cognitive function. Personality on the other hand, is not highly heritable. One of the biggest puzzles in population genetics is why there is any variability in a trait to start with. Natural selection prunes out variation exponentially fast so if any gene is selected for, it should be fixed very quickly. Hence, it seems equally plausible that traits with high variability would have low heritability. The studied traits were also biased towards mental function and different domains have different heritabilities. Thus, if the traits were sampled differently, the averaged heritability could easily deviate from 0.5. Thus, I think the null hypothesis should be that the h^2 = .5 value is a coincidence but I’m open to a deeper explanation.

A software tool to investigate these results can be found here. An enterprising student could do some subsampling of the traits to see how likely 0.5 would hold up if our historical interests in phenotypes were different.

Thanks go to Rick Gerkin for suggesting this topic.

New paper on global obesity

We have a new paper out in the World Health Organization Bulletin looking at the association between an increase in food supply and average weight gain:

Stefanie Vandevijvere, Carson C Chow, Kevin D Hall, Elaine Umali & Boyd A Swinburn. Increased food energy supply as a major driver of the obesity epidemic: a global analysis, Bulletin of the WHO 2015;93:446–456.

This paper extends the analysis we did in our paper on the US food supply to the rest of the world. In the US paper, we showed that an increase in food supply more than explains the increase in average body weight over the duration of the obesity epidemic, as predicted by our experimentally validated body weight model. I had been hoping to do the analysis on the rest of the world and was very happy that my colleagues in Australia and New Zealand were able to collate the global data, which was not a simple undertaking.

What we found was almost completely consistent with the hypothesis that food is the main driver of obesity everywhere. In more than half of the countries (45/83), the increase in food supply more than explains the increase in weight. In other mostly less developed nations (11/83), an increase in food was associated with an increase in body weight although it was not sufficient to explain all of the weight gain. Five countries had a decrease in both food and body weight. Five countries had decreases in food supply and an increase in body weight and finally three countries (Iran, Rwanda, and South Africa) had an increase in food but a decrease in body weight.

Now by formal logic, only one of these observations is inconsistent with the food push hypothesis. Recall that if A implies B then the only logical conclusion you can draw is that not B implies not A. Hence, if we hypothesize that increased food causes increased obesity then that means if we see no obesity then that implies no increase in food. Thus only three countries defied our hypothesis and they were Iran, Rwanda, and South Africa where obtaining accurate data is difficult.

The five countries that had a decrease in food but an increase in body weight do not dispute our hypothesis. They just show that increased food is not necessary, which we know is true. Decreased activity could also lead to increased weight and it is possible that this played a role in these countries and the 11 others where food was not sufficient to explain all of the weight increase.

I was already pretty convinced that food was the main driver of the obesity epidemic and this result puts it to rest for me. This is the main reason that I don’t believe that the obesity epidemic is a health problem per se. It is a social and economic problem.

Hopfield on the difference between physics and biology

Here is a short essay by theoretical physicist John Hopfield of the Hopfield net and kinetic proofreading fame among many other things (hat tip to Steve Hsu). I think much of the hostility of biologists towards physicists and mathematicians that Hopfield talks about have dissipated over the past 40 years, especially amongst the younger set. In fact these days, a good share of Cell, Science, and Nature papers have some computational or mathematical component. However, the trend is towards brute force big data type analysis rather than the simple elegant conceptual advances that Hopfield was famous for. In the essay, Hopfield gives several anecdotes and summarizes them with pithy words of advice. The one that everyone should really heed and one I try to always follow is “Do your best to make falsifiable predictions. They are the distinction between physics and ‘Just So Stories.’”