case2102 {Sleuth3}

Moth Coloration and Natural Selection

Description

This data was collected by J.A. Bishop. Bishop selected seven locations progressively farther from Liverpool. At each location, Bishop chose eight trees at random. Equal number of dead (frozen) light (Typicals) and dark (Carbonaria) moths were glued to the trunks in lifelike positions. After 24 hours, a count was taken of the numbers of each morph that had been removed—presumably by predators.

Usage

case2102

Format

A data frame with 14 observations on the following 4 variables.

Morph

Morph, a factor with levels "light" and "dark"

Distance

Distance from Liverpool (in km)

Placed

Number of moths placed

Removed

Number of moths removed

Details

Population geneticists consider clines particularly favourable situations for investigating evolutionary phenomena. A cline is a region where two colour morphs of one species arrange themselves at opposite ends of an environmental gradient, with increasing mixtures occurring between. Such a cline exists near Liverpool, England, where a dark morph of a local moth has flourished in response to the blackening of tree trunks by air pollution from the mills. The moths are nocturnal, resting during the day on tree trunks, where their coloration acts as camouflage against predatory birds. In Liverpool, where tree trunks are blackened by smoke, a high percentage of the moths are of the dark morph. One encounters a higher percentage of the typical (pepper–and–salt) morph as one travels from the city into the Welsh countryside, where tree trunks are lighter. J.A. Bishop used this cline to study the intensity of natural selection.

Source

Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed), Cengage Learning.

References

Bishop, J.A. (1972). An Experimental Study of the Cline of Industrial Melanism in Biston betularia [Lepidoptera] Between Urban Liverpool and Rural North Wales, Journal of Animal Ecology 41: 209–243.

Examples

str(case2102)
attach(case2102)
   
## EXPLORATION  AND MODEL BUILDING
proportionRemoved <- Removed/Placed
myPointCode <- ifelse(Morph=="dark",21,22)
myPointColor <- ifelse(Morph=="dark","blue","gray")
plot(proportionRemoved ~ Distance, pch=myPointCode, bg=myPointColor, cex=2, lwd=2)

binResponse <- cbind(Removed, Placed-Removed)
Morph <- factor(Morph, levels=c("light","dark"))  # Make "light" the ref  level
myGlm1 <- glm(binResponse ~ Distance + Morph + Distance:Morph, family=binomial)
summary(myGlm1)  # Residual deviance:  13.230  on 10  degrees of freedom
1 - pchisq(13.230,10)  # No evidence of overdispersion
myGlm2  <- update(myGlm1, ~ . - Distance:Morph)
anova(myGlm2, myGlm1) # Drop in deviance statistic = 11.931 on 1 d.f.
1 - pchisq(11.931,1)  # p-value = 0.0005520753 => strong evidence of interaction
# It appears that the intercepts are the same for both light and dark morphs, 
# that there is no effect of Distance for light morphs, but there is an effect 
# of Distance for dark morphs.
 

## INFERENCE AND INTERPREATION
myTerm  <- Distance*ifelse(Morph=="dark",1,0) # Create indicator var for "dark"
myGlm3 <- glm(binResponse ~ myTerm, family=binomial)
summary(myGlm3)


## GRAPHICAL DISPLAY FOR PRESENTATION
myPointCode <- ifelse(Morph=="dark",22,24)
myPointColor  <- ifelse(Morph=="dark","blue","orange")
plot(proportionRemoved ~ Distance, ylab="Proportion of Moths Taken",
  main="Proportions of Moths Taken by Predators at Seven Locations",
  xlab="Distance from Liverpool (km)", pch=myPointCode, bg=myPointColor, cex=2, 
  lwd=2) 
beta  <- myGlm3$coef
dummyDist <- seq(0,55,length=50)
lp <- beta[1] + beta[2]*dummyDist
propDark <- exp(lp)/(1 + exp(lp))
lines(propDark ~ dummyDist,lwd=2,col="blue")
propLight <- rep(exp(beta[1])/(1 + exp(beta[1])),length(dummyDist))
lines(propLight ~ dummyDist,lwd=2,col="orange")  
legend(0,0.47,legend=c("Dark Morph","Light Morph"),
  pch=c(22,24),pt.bg=c("blue","orange"),pt.cex=c(2,2),pt.lwd=c(2,2))

detach(case2102)