Lesson 31 — When workers stop reproducing — the colony emerges UNIT 5 BRANCH · individual → superorganism

The same accounting, one scale up: workers where the cells were, the colony where the body was.

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 worker does better raising sisters than daughters. — 145_lec24_04

A — Sisters or daughters

A female bee can raise her own daughters, or help her mother raise more sisters. Fathers are haploid, so every one of a father's sperm carries the same half of him. Set how many males the queen mated with and read what two workers share.

Locked — confirm your name above to begin.

What two workers share, against how many males the queen mated with

two workers share: —  |  a worker and her own daughter share: 0.500
so raising sisters is worth: —
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 genome identically from their father.— 461_lec29_01

Prediction

Q. A queen mated with one male gives workers who share more with a sister than with a daughter. As she mates with more and more males, that number will:

Controls

1

R code — where the number comes from

# two workers have the same father with probability 1/k# same father  -> full sisters, share 0.75# different    -> half sisters, share 0.25r <- (1/k)*0.75 + (1 - 1/k)*0.25r                                  # compare with 0.5, a daughter

B — Put that number into the colony accounting

Lesson 26's two-level split again, with workers where the individuals were and colonies where the groups were. What two workers share sets how much colonies differ from each other, and that is the only thing this stage takes from Stage A.

Δz̄  =  cov(Wcolony, Zcolony)  +  E[ cov(wworker, zworker) ]

The two terms, to scale

between colonies: —  |  within a colony: —  |  Δz̄: —
worker sterility: —
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.— 461_lec28_04

Prediction

Q. Honeybee queens mate with something like fifteen males. Set the dial there. Kinship among workers alone will:

Controls

1
0.30
0.90
0.00

C — Does the colony carry it?

Sweep the policing dial at the mating number you chose, and watch where the sum crosses zero.

Both terms across the policing sweep

policing needed before the colony carries it: —

Prediction

Q. Take two species with the same costs and benefits, one whose queen mates once and one whose queen mates fifteen times. The policing needed before the colony carries worker sterility will be:

Controls

15

D — Two real colonies

Two species where the mating numbers are known. Load each, read the policing Stage C says it needs, and put that beside what the animals actually do.

what two colony members share: —
policing this predicts they need: —
what they are observed to do: —

Prediction

Q. Naked mole rats are diploid — no three-quarters anywhere, and no haplodiploidy to appeal to. Against honeybees, what two colony members share will be:

Where the numbers come from

Honeybee: queens mate with ten to twenty males, so Stage A's formula applies directly. Naked mole rats: diploid and heavily inbred, so what two colony members share is raised by inbreeding instead — a different route to the same place, and Stage C does not care which route it was.