population genetics

Population Genetics Chpt 5 End

Chapter 5 End Problems

Problem 2

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condition <- letters[1:4]
N <- c(50,100, 50, 100)
Nm <- c(0.25, 0.5, 0.1, 0.2)
m <- Nm/N

d <- data.frame(condition,N,m)

plot(d$N, d$m, pch=as.character(d$condition))

Shifting balance favors smaller N and smaller m so C is the favored condition.

Problem 6

Start by setting r = x/ny to get the break even n. Anything larger is needed for altruistic behaviour to be favored by kin selection.

0.25 = 0.4/0.2n or n=0.4/(0.2*0.25) = 8 or greater

Problem 11

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area <- c("dark","dark","light","light")
melanic <- c(T, F, T, F)
p.eaten <- c(0.26, 0.74, 0.86, 0.14)
p.survive <- 1-p.eaten

d <- data.frame(area, melanic, p.eaten, p.survive)
d2 <- split(d, area)

lapply(d2, function(x){ x[x$melanic==TRUE,"p.survive"]/x[x$melanic==FALSE,"p.survive"]  })  #melanic/nonmelanic survival ratio
## $dark
## [1] 2.846154
## 
## $light
## [1] 0.1627907

Problem 14

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J.1 <- c(0.12, 0.8, 0.06, 0.02)

J.2 <- c(0.3,0.56, 0.1, 0.04)

J.11 <- sum(J.1^2)
J.11
## [1] 0.6584
J.22 <- sum(J.2^2)
J.22
## [1] 0.4152
J.12 <- sum(J.1*J.2)
J.12
## [1] 0.4908
I <- J.12/sqrt(J.11*J.22)  #from p408
I
## [1] 0.938709
D <- -log(I)
D
## [1] 0.06324978

Problem 15

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J.1 <- c(0.3, 0.5)

J.2 <- c(0.2, 0.3)

J.11 <- sum(J.1^2)
J.11
## [1] 0.34
J.22 <- sum(J.2^2)
J.22
## [1] 0.13
J.12 <- sum(J.1*J.2)
J.12
## [1] 0.21
I <- J.12/sqrt(J.11*J.22)  #from p408
I
## [1] 0.9988681
D <- -log(I)
D
## [1] 0.001132503
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