#### Posts

2018-09-10: Feeding a controversy

2018-06-11: Glow worm distribution

2018-04-23: Outlawing risk

2017-08-22: A rebuttal on the beauty in applying math

2017-04-22: Free googles book library

2016-11-02: In search of Theodore von Karman

2016-09-25: Amath Timeline

2016-02-24: Math errors and risk reporting

2016-02-20: Apple VS FBI

2016-02-19: More Zika may be better than less

2016-01-14: Life at the multifurcation

2015-09-28: AI ain't that smart

2015-06-24: MathEpi citation tree

2015-03-31: Too much STEM is bad

2015-03-24: Dawn of the CRISPR age

2015-02-09: Hamilton's selfish-herd paradox

2015-02-08: Risks and values of microparasite research

2014-11-10: Vaccine mandates and bioethics

2014-10-18: Ebola, travel, president

2014-10-17: Ebola comments

2014-10-12: Ebola numbers

2014-09-23: More stochastic than?

2014-08-17: Feynman's missing method for third-orders?

2014-07-31: CIA spies even on congress

2014-07-16: Rehm on vaccines

2014-06-20: Random dispersal speeds invasions

2014-04-14: More on fairer markets

2014-03-18: It's a mad mad mad mad prisoner's dilemma

2014-02-17: Is life a simulation or a dream?

2014-01-30: PSU should be infosocialist

2014-01-12: The dark house of math

2014-01-11: Inconsistencies hinder pylab adoption

2013-12-24: Cuvier and the birth of extinction

2013-12-17: Risk Resonance

2013-12-15: The cult of the Levy flight

2013-12-09: 2013 Flu Shots at PSU

2013-12-02: Amazon sucker-punches 60 minutes

2013-11-26: Zombies are REAL, Dr. Tyson!

2013-11-22: Crying wolf over synthetic biology?

2013-11-21: Tilting Drake's Equation

2013-11-18: Why $1^\infty != 1$

2013-11-14: 60 Minutes misreport on Benghazi

2013-11-11: Making fairer trading markets

2013-11-09: Using infinitessimals in vector calculus

2013-11-08: Functional Calculus

## Feeding a controversy

An upsetting story has been posted and is making the rounds, in relation to a theoretical evolutionary biology preprint by Hill. I place a very high value on the right to freedom of speech and expression (though I don't believe money is equivalent to either), so I don't like hearing tales of suppression of ideas.

But just because somebody says it doesn't mean it is good science. Last autumn, I had an opportunity to review Hill's article, and found it sourly lacking as a piece of science. With careful neglect, bad science will languish and be forgotten, and that is what I hoped would happen in this case. But the thing has bubbled up again, and as a theoretical biologist, I want to go on the record about nonsensical social Darwinism to stand up for my field, for myself and maybe also for others.

Perhaps the simplest and most damning criticism of the model is that under very common theoretical assumptions, the exact-opposite conclusion would be reached. Hill claims that simple evolutionary dynamics lead to greater trait variation in one gender than another. In contrast with Hill's assumptions, it is generally accepted that a good simple model of evolution is that evolution evolves to maximize mean fitness. Fitness itself may take many forms, but is often modeled as a concave, monotone increasing function of phenotype. It then follows as a trivial consequence of Jensen's inequality that evolution will prefer mating with subpopulations of smaller random trait variation because that leads to higher mean fitness. We can imagine situations where the fitness function is convex instead of concave, but they are odd situations and you'd have to explain why the convexity flips. Such simple considerations are not addressed at all by the preprint, and thus, it is difficult to see how this can be considered a serious piece of scholarship.

As with most bad scholarship, the manuscript interweaves grains of truth with incomplete ideas and incorrect notions. For example, sexual dimorphism is relatively common in the animal kingdom. Examples include the fiddler crab claw and the lions mane. There are also examples of large stable variations within a sex, such as jack (small) and hooknose (large) morphs in male salmon. But there are a variety of explanations for these large stable variations besides the "variability hypothesis". Variability is well known to be a double-edged in evolution. Too much variability can lead to quasispecies collapse in tight fitness landscapes, while too little variability slows evolution and can make it impossible for species to adapt to changing environments.

Here are some other things that looked suspicious to me, before I decided not to waste more time on my critique.

• This is a sexual-selection theory, based on a group-selection argument. Selective pressures acting on individuals are generally held to be much stronger than those acting on a population as a whole, though there are weird exceptions. It would be better to formulate the model in terms of types.

• Assumes a simple linear spectrum along which mate selection is always made without error. The existence of such a spectrum is highly suspect. Humans learn about mate selection and learn differently from different experiences as well.

• Assumes mate selection is according to a preference function and invariant with age

• Assumes offspring fitness is independent of parenting effort

• Does not allow for any consideration of fitness directly. Extremes in height, for example, can decrease absolute fitness, leading in some examples to high mortality before reaching reproductive ages.

• There's no sensitivity analysis for the consideration of heritable vs non-heritable variation.

• The definition of "variability" used is rather primitive, and can be misleading. Generally, variability is a hard effect to quantify. There is always differences which can be due to genetics, environment, or plasticity. A null hypothesis would be equal genetic variation in both groups. But many different mechanisms could lead to differences in trait distribution between sexes. Variation between sexes is primarily removed by mating.

• Assumes mating makes no contribution to the genotype of offspring, which is ridiculous

• Assumes no evolution in the distribution over time, which can have all sorts of misleading effects

• Fitness is an emergent property of phenotype, not a phenotype itself.