vcdExtra (version 0.8.7)

CrabSatellites: Horseshoe Crab Mating

Description

Determinants of mating for male satellites to nesting horseshoe crabs. The number of satellites is a natural outcome variable. This dataset is useful for exploring various count data models.

Format

A data frame containing 173 observations on 5 variables.

color

Ordered factor indicating color (light medium, medium, dark medium, dark).

spine

Ordered factor indicating spine condition (both good, one worn or broken, both worn or broken).

width

Carapace width (cm).

weight

Weight (kg).

satellites

Number of satellites.

Details

Brockmann (1996) investigates horseshoe crab mating. The crabs arrive on the beach in pairs to spawn. Furthermore, unattached males also come to the beach, crowd around the nesting couples and compete with attached males for fertilizations. These so-called satellite males form large groups around some couples while ignoring others. Brockmann (1996) shows that the groupings are not driven by environmental factors but by properties of the nesting female crabs. Larger females that are in better condition attract more satellites.

Agresti (2002, 2013) reanalyzes the number of satellites using count models. Explanatory variables are the female crab's color, spine condition, weight, and carapace width. Color and spine condition are ordered factors but are treated as numeric in some analyses.

References

Agresti A (2002). Categorical Data Analysis, 2nd ed., John Wiley & Sons, Hoboken.

Agresti A (2013). Categorical Data Analysis, 3rd ed., John Wiley & Sons, Hoboken. Brockmann HJ (1996). “Satellite Male Groups in Horseshoe Crabs, Limulus polyphemus”, Ethology, 102(1), 1–21.

Examples

## load data, use ordered factors as numeric, and grouped factor version of width
data("CrabSatellites", package = "vcdExtra")
CrabSatellites <- transform(CrabSatellites,
  color = as.numeric(color),
  spine = as.numeric(spine),
  cwidth = cut(width, c(-Inf, seq(23.25, 29.25), Inf))
)

## Agresti, Table 4.4
aggregate(CrabSatellites$satellites,
          list(CrabSatellites$cwidth), function(x)
  round(c(Number = length(x), Sum = sum(x), Mean = mean(x), Var = var(x)), digits = 2))

## Agresti, Figure 4.4
plot(tapply(satellites, cwidth, mean) ~ tapply(width, cwidth, mean),
  data = CrabSatellites,
  ylim = c(0, 6), pch = 19, cex = 1.5,
  xlab = "Mean carapace width (cm)",
  ylab = "Mean number of satellites")

## More examples: ?countreg::CrabSatellites` has examples of other plots and count data models