Why Gattaca is unrealistic (from a mathematical perspective)

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You know that film Gattaca. That film where, by embryo selection, they can choose to have a tall, handsome, and smart child. As someone who studies genetics, during the entire film and afterwards, I've been cringing at the storywriters entire ignoring of mathematical principles.

First of all, it's impossible to create a child with a specific genotype/phenotype if the parrents do not carry alleles for that genotype. For example, the genotype of non myopic people is mm, while the genotype for myopics is Mm or MM. If someone with genotype MM has a child, it is impoosible that their child is non-myopic (mm).

Second of all, but less obvious, is that when selecting for multiple genotypes, the odds of there being an embryo that has the desired traits within a group of embryos, becomes slimmer the more traits there are selected for.

Ignoring the effects of chromosomal linkage, the formula describing this is the following:
y=1-(1-p)^x
where y is the probability that there is an embryo with the desired genotypes/phenotypes, x is the number of embryos, and p is the probability that each embryo has all of the desired traits.
The formula from which p can be derived is the following:
p=(1/4)^m * (1/2)^n * (3/4)^q
where m is the number of genotypes that have a 0.25 chance of occuring, n is the number of genotypes that have a 0.5 chance of occuring, and q is the number of traits that hve a 0.75 chance of occuring.
These two equations can also be combined into the following:
y=1-(1-[(1/4)^m * (1/2)^n * (3/4)^q])^x

If you want to know the minimum number of embryos that will have to be created for at least a certain percentage chance of the desired genotypes appearing in one, use this equation below.

z = ceil[(ln[1-c])/(ln[1-p])]

where z is the number of embryos that have to be used, and c is the probability of that specific embryo appearing that is acceptable.


Example:
If you want at least a 90% chance of an embryo being present that has 10 specific genotypes (m=4, n=4, q=2), the number of embryos that have to be created is...
...16 766!

Based on these numbers, it seems like an unrealistic dream to be able to select for 100 traits like in Gattaca.

Simple answer: It's just a movie....

And a science fiction movie, at that. In science fiction it's usually a society far into the future that's being portrayed. The writers can do whatever the imagination allows, which is anything. The only rationalization for anything they write is that somehow the world of medicine in this pretend future has found a way around these things.

I'll say one thing, your being an aspie is definitely never going to be questioned.

I know that in fiction anything is possible. It's just that, unlike most films that use applied unobtinium to do their unexplined processes, in Gattaca, they explicitely mention using embryo selection, a technology that is currently used to select against one, two, or three undesirable phenotypes. Yet, they treat embryo selection as if it is genetic splicing. They misrepresent a technology that is already there. Yet, the way they misrepresent it is subtle enough to be cringy, at least to people who are into genetics.
Some people, after watching this film, might believe that embryo selection is really like genetic splicing.

I would imagine that people who know as much as this about genetics are very much a minority of the general population, and most people watching that movie wouldn't have a clue about any of this, no argument there.

Would it really affect anyone's life to be mistaken in what they think they glean from this movie's mistaken take on genetics though? I don't really believe so. Especially since nobody's about to be able to walk into a fertility clinic ad request precise eye attributes and no myopia please. It's interesting to be told what the realities are, as in your post, but the average movie watcher isn't going to find this mistake on the part of the writers really matters.

The whole point of the movie was to show a society based on possessing the "right" genetic characteristics is doomed to dysfunction and failure. It ignores the talents of those who are not genetically blessed and gives a free ride to people with defective characters who just happen to be genetically "perfect". However Gattaca does have one virtue. In the end decency won out.

I had assumed that the embryos were genetically engineered through gene splicing at or before fertilization, since, as you say, simple selection would be mathematically unfeasible, and also genetically impractical. Paired chromosome exchange bits of each other, sort of like trading matching socks. (e.g. one chromosome 21 swaps a bit with the other chromosome 21) Genes that are close together tend to be inherited together because they are too close together to be separated. This would mean that you'd probably have desirable genes being stuck close to undesirable recessive genes. My genetics professor said that we all carry an average of seven "deadly" recessive genes. These are fortunately rarely expressed, because our mate has a different set of recessive genes, and you have to have two of the same recessive gene for them to be expressed.

The whole premise of the movie annoyed the hell out of me--why would anyone think that genetics alone assures success? This is the point of the movie, of course--that experience and motivation are greater than inherent genetic tendencies. It ignores epigenetic factors--environmental triggers that interact with genetic predispositions, which can be very complex. It also ignores the fact that some people with disabilities, including genetic ones, have contributed greatly to society. I thought the whole thing oversimplified how genetics works, but then, eugenics tends to do that as a policy, as does murky Hollywood science.

What REALLY annoyed me is that they seemed to be training for a spaceflight to Titan by working in a typing pool or something. Whaaaaaat??

i have a pretty high suspension of disbelief when watching films, but i don't do just that very often.

i need to rewatch it.

Me too. I mean, take Jurassic Park. I just hand-waved the science for the whole thing, but it was good enough that I didn't mind so much. Gattaca was just a silly mess with a weak premise.

My understanding, as illustrated from the movie, was that they couldn't craft "perfect people" but they could "distill" the best traits of the biological parents and remove undesired traits. They never put in what wasn't possible in the first place.

Hence why a woman might want to DNA test a strand of her boyfriend's hair before marrying him...to see what potential kids would be like.

I like the movie Gattaca precisely because its basic story is ultimately one of saying "screw you" to the society depicted which places complete emphasis on genetic "perfection." The fact that the movie doesn't use realistic genetic possibilities, or that it ignored environmental influence on genetic inheritance, are minor problems to me, since the main thrust of the whole point of this movie is "Future society obsessed with perfect people forget how you don't have to be "perfect" to be valid or even to achieve great things."

That's the main message, and to put that across in the most strident way, they had to portray a pretend future of complete control over genetics the like of which is not real science.

But there's "not real science" all the time in science fiction -- that's why it's called science fiction. It's not because the story is fiction -- there are drama movies but you don't call them "drama fiction." But because the science is "fictional."