Scott Alexander (Slate Star Codex), Garrett Jones (Hive Mind), and Razib Khan (GNXP) alerted me (via Twitter) of this post by PZ Myers.
Myers is both confused and insulting in his blog post, but I'll refrain from ad hominem attacks, and just focus on the science.
Myers seems to think that humans with much better cognitive abilities than our own can't exist. Sort of like a farmer in 1957 claiming that chickens that are bigger and faster maturing than his own could not exist (see figure below). I urge Myers to read some books on population genetics before returning to this discussion.
The argument for why there are probably genomes not very different from our own, but which lead to much better cognitive ability, is very simple, and I went through it in a post called Explain it to me like I'm five years old, excerpted below:
1. Cognitive ability is highly heritable. At least half the variance is genetic in origin.
2. It is influenced by many (probably thousands) of common variants (see GCTA estimates of heritability due to common SNPs). We know there are many because the fewer there are the larger the (average) individual effect size of each variant would have to be. But then the SNPs would be easy to detect with small sample size.
Recent studies with large sample sizes detected ~70 SNP hits, but would have detected many more if effect sizes were consistent with, e.g., only hundreds of causal variants in total.
[ Myers seems to be confused about the difference between specific (protein coding) genes, of which there may be only ~20k in the human genome, and the set of all variations in the DNA code, of which there are many, many more. Thousands of variants (or 10k) out of this much larger number is a tiny fraction much less than one. ]
3. Since these are common variants the probability of having the negative variant, with (-) effect on g score, is not small (e.g., like 10% or more).
4. So each individual is carrying around many hundreds (if not thousands) of (-) variants.
5. As long as effects are roughly additive, we know that changing ALL or MOST of these (-) variants into (+) variants would push an individual many standard deviations (SDs) above the population mean. Such an individual would be far beyond any historical figure in cognitive ability. [ This is exactly what has been accomplished via selection in the chickens below. ]
Given more details we can estimate the average number of (-) variants carried by individuals, and how many SDs are up for grabs from flipping (-) to (+). As is the case with most domesticated plants and animals, we expect that the existing variation in the population allows for many SDs of improvement (see figure below).For references and more detailed explanation, see On the Genetic Architecture of Cognitive Ability and Other Complex Traits.
Attention PZ: The basic population genetics used above is recapitulated by famous geneticist James Crow (Wisconsin-Madison) here and here. You can take his word over mine, since I'm only a physicist. But note that Crow cites Feynman PhD student (i.e., theoretical physicist) Thomas Nagylaki (later a famous geneticist at Chicago) for proving a tour de force result in evolutionary genetics of additive traits. Do your HW next time.
Note Added: See this August 2016 post for more discussion, in response to some comments by Greg Cochran.
References: There are some requests for references in the discussion thread below. The place to start is On the Genetic Architecture of Cognitive Ability and Other Complex Traits, but see below.
In this paper Crow discusses the prevalence of additive genetic effects, and the consequent (in the case of highly polygenic traits) large pool of variance upon which selection can act. I have merely pointed out that cognitive ability is an example of the kind of complex polygenic trait that Crow described.
Nagylaki's paper The Evolution of Multilocus Systems under Weak Selection extends Fisher's Fundamental Theorem of Natural Selection (fundamental to our theoretical understanding of evolution, but unknown to most biologists; note the role of additive variance). Evidence for additive genetic architecture in, e.g., mice, yeast, cows, etc. Additive models are used extensively in agricultural breeding.
Nagylaki's textbook on population genetics is free.
Physicists can master these results quickly via Statistical Genetics and Evolution of Quantitative Traits (Neher and Shraiman).