I was watching The Martian, and there is a scene with Mark harvests his potatoes and says that he keeps the larger ones for his food supply and replants the smaller ones.
Wouldn't this create a genetic propensity for the next harvest to favor smaller potatoes on average?
Great question, this is one of the cool things about potatoes!
Mark is creating clones of the mother plant when he uses the small potatoes as seed potatoes. All of the plant's potatoes have the same genetics, it doesn't matter which particular potato is used as the seed potato.
The small potatoes are smaller for non-genetic reasons, which won't be passed on.
My high-school biology textbook (~1985) contains exactly potatoes as an example for a bad strategy for selection because the new potatoes all carry the same genes as the one seeded and one gets the same distribution of sizes.
This is why here, on Earth, we use the same strategy when planting potatoes - we use the smaller ones for seeding.
What is less known about potatoes is that they also have a real seeds. This is what you get from their flowers. The seeds do have some genetic diversity because the potato flowers are cross-polinated by bees.
If one does the whole hassle of collecting and planting the potato seeds, one COULD exert selection pressure on them and (at least, in theory) select them for favorable properties.
From the comments: Getting potato seeds implies polination of their flowers and thus having bees. I am yet to see the movie, but one of the comment stated that the movie character had no bees.
Potato (and almost all other) flowers could be hand-polinated. This is routinely done in indoor gardening and this is also how an important discovery was made long ago by Gregor Mendel.
Hand-polination does not scale well, but it looks like potatoes in fact do need sexual / seed-based reproduction once in a while (few years) in order to maintain health and yield.
Gardener here.
Planting small potatoes will yield bigger potatoes. Planting big potatoes will yield smaller potatoes.
That's because potatoes are tubers that grows along the stem of the plant, if the stem is underground. And bigger potatoes have more sprouts than small potatoes (each "node" or "eye" on a potato will give you a sprout => a stem), so they have more stems, so they grow more "units" of potatoes, so the energy of the plant is divided among more of them, so each of them grows smaller (that's similar to how fruit trees bearing a lot of fruits will tend to yield smaller, less sweet fruit, hence thinning apples for instance).
So if you want to grow early potatoes, you'll likely plant big potatoes, whereas if you want storage potatoes, you'll likely plant smaller ones.
Also, early potatoes are often planted earlier than storage potatoes. I haven't seen the movie, but depending on where you live, this could mean risk of frosts (and potato plant doesn't handle it very well). I think that potentially, if the potato you're planting is bigger, this means that there's more energy for the plant to bounce back to health if the first shoots were affected by frost.
I'm a bit interested in botany but aren't a botanist (only horticulturist). From my basic understanding of it, other answers are quite right about the whole genetic aspect of potatoes.
