Wasp: Wasp Shape of Queens and Workers

In byandell/pda: Practial Data Analysis for Designed Experiments

Description

Scientists studying social insects such as wasps and ants have noted that queen and worker castes can have very different sizes and shapes. For some species, the queens are simply larger, suggesting that they continue to grow with the same basic ‘plan’ as workers. They are just fed for longer. Jeanne, Graf and Yandell (1995) examined a wasp species which does not follow this pattern. They measured 13 responses on 50 workers and 50 queens. The measurements were coded based on body part – head (H), thorax (T), wing (W) or gonadium (G) – and kind of measurement – width (W), height (H) and length (L). The gonadium (also known as gastral tergite) has two length and three width measurements.

Usage

data(Wasp)

Format

Wasp data frame with 100 observations on 14 variables.

[,1]	caste	factor	Queen or Worker
[,2]	TL	numeric	thorax length
[,3]	WL	numeric	wing length
[,4]	HH	numeric	head height
[,5]	HW	numeric	head width
[,6]	TH	numeric	thorax height
[,7]	TW	numeric	thorax width
[,7]	G1L	numeric	gonadium lenght 1
[,7]	G2Wa	numeric	gonadium width 2a
[,7]	G2L	numeric	gonadium length 2
[,4]	HL	numeric	head length
[,7]	G1Wb	numeric	gonadium width 1b
[,7]	G1Wa	numeric	gonadium width 1a
[,7]	G1H	numeric	gonadium height 1

Source

Robert L Jeanne

References

Jeanne RL, Graf CA and Yandell BS (1995) ‘Non-size-based morphological castes in a social insect’, Naturwissenschaften 82, 296-298.

Examples

data( Wasp )

## Multivariate discriminant analysis
library(MASS)
Wasp.lda <- lda( Wasp[,-1], Wasp$caste )
Wasp.lda
Wasp$DA <- predict( Wasp.lda, Wasp[,-1] )$x

## Univariate t statistics
tmp <- Wasp$caste == "Q"
Wasp.t <- apply( Wasp[,-1], 2, function( x ) {
   ( mean( x[tmp] ) - mean( x[!tmp] ) ) /
   sqrt( ( var( x[tmp] ) + var( x[!tmp] ) ) / sum( tmp ) ) } )
rm( tmp )
Wasp.t <- sort( Wasp.t )
Wasp.tmpy <- cor( Wasp[,2:14], Wasp$DA )[ names( Wasp.t[-1] ), 1 ]

## Figure F:18.2 Wasp scatter plots

pairs( Wasp[ , c("HW","TW","G1Wa","DA") ], panel =
   function( x, y, ... ) {
     text( x, y, as.character( Wasp$caste ) ) },
   labels = c("head","thorax","gonadium",
     "discriminant\nanalysis" ) )
title( "Figure F:18.2 Wasp scatter plots" )

## Figure F:18.3 Wasp discriminant analysis

plot( c(1,-1) * Wasp.t["DA"], c(1,-1), type = "n",
   xlab ="t statistics", ylab = "correlation with DA" )
text( c(1,-1) * Wasp.t["DA"], c(1,-1), "DA" )
lines( Wasp.t[-1], Wasp.tmpy )
points( Wasp.t[-1], Wasp.tmpy )
text( Wasp.t[-1] + 5 * sign( Wasp.t[-1] ),
  uncollide(Wasp.tmpy,.05), names( Wasp.t[-1] ) )
abline(h=0,v=0,lty=2)
mtext("queen larger",1,2,adj=1)
mtext("worker larger",1,2,adj=0)
title( "Figure F:18.3 Wasp discriminant analysis" )

# Figure F:18.5 Wasp analysis of covariance

Wasp.cov <- aov( HW ~ G1Wa * caste, Wasp )
anova( Wasp.cov )
Wasp.par <- aov( HW ~ G1Wa + caste, Wasp )
anova( Wasp.par )

print(xyplot(HW ~ G1Wa, Wasp, group = caste, type = "p",
  pch = levels(Wasp$caste), col = 1 + seq(along = levels(Wasp$caste)),
  panel = function(x,y,...) {
    panel.superpose(x,y,...)
    lc = levels(Wasp$caste)
    for(i in seq( along = lc )) {
      ii = lc[i] == Wasp$caste
      panel.lines(Wasp$G1Wa[ii], predict(Wasp.cov)[ii],
        lty = 3, col = i)
      panel.lines(Wasp$G1Wa[ii], predict(Wasp.par)[ii],
        lty = 1, col = i)
    }
  },
  xlab ="(a) gonadium width (G1Wa)",
  ylab = "head width (HW)",
  main = "Figure F:18.5 Wasp" ),
  more = TRUE, split = c(1,1,2,1) )

## residual analysis after removing TW
Wasp.resid <- Wasp[,c("caste","HW","G1Wa","TW")]
Wasp.resid$Hres <- resid( aov( HW ~ TW, Wasp.resid ) )
Wasp.resid$Gres <- resid( aov( G1Wa ~ TW, Wasp.resid ) )
Wasp.covr <- aov( Hres ~ TW + G1Wa + caste, Wasp.resid )
anova( Wasp.covr )
Wasp.covwr <- aov( Hres ~ G1Wa + caste, Wasp.resid )
anova( Wasp.covwr )
Wasp.resid$TW <- rep( mean( Wasp.resid$TW ), nrow( Wasp.resid ) )

print(xyplot(Hres ~ G1Wa, Wasp.resid, group = caste, type = "p",
  pch = levels(Wasp.resid$caste), col = 1 + seq(along = levels(Wasp.resid$caste)),
  panel = function(x,y,...) {
    panel.superpose(x,y,...)
    lc = levels(Wasp.resid$caste)
    for( i in seq(along = lc)) {
      ii = lc[i] == Wasp.resid$caste
      panel.lines(Wasp.resid$G1Wa[ii], predict(Wasp.covr, Wasp.resid)[ii],
        lty = 1, col = i )
      panel.lines(Wasp$G1Wa[ii], predict(Wasp.covwr)[ii],
        lty = 3, col = i )
    }
  },
  xlab ="(b) gonadium width (G1Wa)",
  ylab = "HW residuals on TW",
  main = "Analysis of Covariance" ),
  split = c(2,1,2,1) )

byandell/pda documentation built on May 13, 2019, 9:27 a.m.