Draft skeleton. Stage scenarios and anchor quotes are in place; the simulator and code panels are not yet wired.
Bees: female bees are diploid, male bees are haploid. The male's sperm have no recombination — all his sperm are identical. So worker bees share 50% of their genes from their mother (recombined) and 100% of their father's haploid genome — averaging 75% relatedness to their sisters. They are more closely related to their sisters than they would be to their own kids. Any allele that drives a worker to help her mother produce more daughters increases the worker's gene frequency more than her own reproduction would. That's why worker bees don't reproduce. The math of inclusive fitness drives sterility.
— 461_lec29_01
A — Solitary individuals as the null
A population of solitary insects, each reproducing for itself. Individual-level cov(w, z) is what matters. There is no colony.
Fitness is not the number of children you have. I've never defined it that way. It's the number of copies of yourself in the next generation. If your brothers and sisters make lots of copies of themselves, there are copies of your genes in the next generation — even if you have no children of your own. Self is your genes, not just your body.
— 461_lec28_04
TODO: solitary-insect sim. Individual-level Price equation; no group structure.
B — Add haplodiploid sisters
Switch to haplodiploid genetics. Mother is diploid; father is haploid. Sisters share 75% on average (all 100% of dad's haploid genome plus 50% of mom's recombined contribution). The math now favors helping mother make more sisters over reproducing yourself.
Bees: males are haploid, females diploid. Female bees are 75% related to their sisters but only 50% related to their own kids. From a genetic standpoint, a bee can make more copies of itself by having more sisters than by having its own kids. So workers feed the queen so she can make more sisters. They make more copies of themselves through her. The whole hive structure falls out of meiotic math.
— 145_lec24_04
TODO: haplodiploid relatedness calculator. Show that r(sister) = 0.75 > r(daughter) = 0.5 makes worker sterility predicted.
C — The diagnostic at the colony level
Run the Price ratio with colonies as groups, workers as agents. Between-colony cov(W, Z) for colony productivity vs within-colony cov for worker reproductive success. When the ratio exceeds 1, the colony is the unit. Worker policing (workers killing other workers' eggs) is what keeps the within-colony cov suppressed.
What the relatedness coefficient does is take all altruism and turn it into selfish help. You're not helping your brother. You're helping your genes inside your brother. The U in the equation isn't you in the corporeal sense — it's you in the genetic sense. Which means you're more likely to help others when they're more closely related, which is really just helping yourself. If your genes are helping your genes, that's not altruism, it's selfishness.
— 202_lec32_04
TODO: colony-level Price ratio sim. Worker-policing-intensity slider; show colony as unit when policing is strong enough.
D — Honeybees and naked mole rats
Honeybees are the canonical case: haplodiploidy + worker policing = the colony is the unit. Naked mole rats are diploid, not haplodiploid — but heavy inbreeding inflates relatedness within a colony to ~0.8. Same math, different mechanism. The colony emerges in both cases when the relatedness numbers cross the right threshold.
Mouse sperm have hooks. After insemination they hook together into super-sperm — joined flagella swim faster than singletons. Only one will fertilize the egg. The rest have zero fitness. They cooperate anyway. Sperm from the same male readily form the super-sperm blob. Sperm from two unrelated males don't. Sperm from two related males do — at a lower rate. The hookup decision is driven by how related the sperm are.
— 461_lec28_03
TODO: honeybee + naked-mole-rat comparison. Predict worker sterility from relatedness in each system. .R export. Non-trivial code mod: re-derive eusociality conditions for a diploid system with given inbreeding coefficient F.