1. Sex ratio theory
I formerly thought that when a tendency to produce the two sexes in equal numbers was advantageous to the species it would follow from natural selection, but I now see that the whole problem is so intricate that it is safer to leave its solution to the future.
- Darwin
‘The Descent of Man’,
R kids per female, s: sex ratio. A focal female has Rs daughters and R(1-s) sons. If there are N individuals in the offspring generation, and everybody has the same sex ratio allocation, then there will be Ns females and N(1-s) males to mate with. Assuming all females can be mated, daughters produce a total of R kids, while sons produce a total of r Ns/N(1-s) kids (accounting for the fraction of females that they are likely to mate get in competition with all of the males out there). Given that each generation is related by 1/2 to a parent, the total number of genes propagated is (Rs/2)(R/2) + (R(1-s)/2)(R/2 Ns/(N(1-s)) = R^2 s/2. More grandkids will be born to the focal female if she produces a highly female biased sex ratio. THIS IS THE OPTIMAL STRATEGY.

2. Why is the sex ratio 1:1? (Fisher, 1930) Frequency dependent selection
Because every individual has a mother and a father, females and males must contribute equally, on average, to the
(Fisher, 1930)

3. “The total reproductive value of the males [in a population] is exactly equal to the total value of all the females, because each sex must supply half the ancestry of all future generations of the species...The sex ratio will so adjust itself, under the influence of Natural Selection, that the total parental expenditure incurred in respect of children of each sex, shall be equal.”
Fisher 1930.

4. Why is the sex ratio 1:1? (Fisher, 1930) Frequency dependent selection
Because every individual has a mother and a father, females and males must contribute equally, on average, to the
(Fisher, 1930)

5. Why is the Canadian sex ratio at birth 1.06:1 (M:F)?
Sex allocation between the sexes should be equal
end of parental care
birth

6. Deviations from 1:1
Local Mate Competition theory (LMC) (Hamilton, 1967)
Trivers-Willard model (TWM) (Trivers and Willard, 1973)

7. Local Mate Competition (LMC)
If one sex has reduced fitness due to competition with siblings of the same sex, it is advantageous to skew the sex ratio towards the opposite sex
Prediction: where inbreeding is common, the sex ratio should be skewed towards the choosy sex (usually females)

8. LMC: fig wasp example
5%-10% of offspring are male
(Herre, 1987)

9. LMC: fig wasp example Sex ratio (M:F) Number of foundresses
0.2
0.1
West and whatever: doesn’t need to be subsequent layings, could be simultaneous
Number of foundresses
(Herre, 1987)

10. Deviations from 1:1
Local Mate Competition theory (LMC) (Hamilton, 1967)
Trivers-Willard model (TWM) (Trivers and Willard, 1973)

11. Trivers-Willard model (TWM)
Females: Low variance in reproductive success; even females with few resources can reproduce.
Males: High variance in reproductive success; males with more resources sire more offspring.
Constrained by sex determination system (XY versus haplodiploidy)
# of offspring per parent
Prediction: High fitness mothers should produce more sons and low fitness mothers should produce more daughters

12. TWM: mice example (Rosenfeld et al., 2003) Very High Fat Low Fat
Purpose: to determine if sex ratio could be altered by altering the fat content of the mothers’ diet
Fed ad libitum for 6 wks on either a very high fat or low fat (but still healthy) diet.
All mothers appeared to care for their offspring with no differences. No difference in litter size or gestation period.
Supports the TWM, that good condition (more energy) mothers will produce more sons.
Found that diet, not maternal weight, was the main variable that determined the sex of the pups.
Also, an effect of age (not pariety) - ratios become more biased as age increased (did not speculate as to a mechanism why)
(Rosenfeld et al., 2003)
Very High Fat
Low Fat

13. TWM: mice example (Rosenfeld et al., 2003) Very High Fat Low Fat
Mothers fed
high fat
More sons
Purpose: to determine if sex ratio could be altered by altering the fat content of the mothers’ diet
Fed ad libitum for 6 wks on either a very high fat or low fat (but still healthy) diet.
All mothers appeared to care for their offspring with no differences. No difference in litter size or gestation period.
Supports the TWM, that good condition (more energy) mothers will produce more sons.
Found that diet, not maternal weight, was the main variable that determined the sex of the pups.
Also, an effect of age (not pariety) - ratios become more biased as age increased (did not speculate as to a mechanism why)
(Rosenfeld et al., 2003)
Very High Fat
Low Fat

14. Conclusion
Sex ratio theory provides some of the most testable hypotheses in evolution
Why? (a) Easily measured trait, (b) Strong frequency-dependent selection, (c) Clear cut predictions about the factors that alter sex ratio

15. LMC K = rate of inbreeding (1 - K) = rate of random mating
s*:(1 - s*) = population sex ratio (M:F)
s:(1 - s) = mutant sex ratio (M:F)
T = number of s genes transmitted to grandchildren
r = family size
N = total population size
We are looking for the ESS, s*, the unbeatable sex ratio. That is, no mutant allele that alters the sex ratio will be successful in establishing itself in the population

16. LMC: malaria application
Sex ratio of Plasmodium is measured by counting the ratio of gametocytes in the blood of infected people.
Once in the mosquito, the gametocytes rupture and mate, going through different life stages and eventually producing more gametocytes in the mosquito salivary glands.
If a mosquito feeds on a host with multiple infections, this is considered outbreeding in the mosquito and the sex ratio should resemble 1:1 in the next human host
(Read, 1995)