case2202 {Sleuth3}

Characteristics Associated with Salamander Habitat

Description

The Del Norte Salamander (plethodon elongates) is a small (5–7 cm) salamander found among rock rubble, rock outcrops and moss-covered talus in a narrow range of northwest California. To study the habitat characteristics of the species and particularly the tendency of these salamanders to reside in dwindling old-growth forests, researchers selected 47 sites from plausible salamander habitat in national forest and parkland. Randomly chosen grid points were searched for the presence of a site with suitable rocky habitat. At each suitable site, a 7 metre by 7 metre search are was examined for the number of salamanders it contained. This data frame contains the counts of salamanders at the sites, along with the percentage of forest canopy and age of the forest in years.

Usage

case2202

Format

A data frame with 47 observations on the following 4 variables.

Site

Investigated site

Salamanders

Number of salamanders found in 49 m^2 area

PctCover

Percentage of canopy cover

ForestAge

Forest age

Source

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

References

Welsh, H.H. and Lind, A.J. (1995). Journal of Herpetology 29(2): 198–210.

Examples

str(case2202)
attach(case2202)
       
## EXPLORATION AND MODEL BUILDING
logSalamanders <- log(Salamanders + .5)
logForestAge   <- log(ForestAge + .5)
myMatrix       <- cbind(PctCover,logForestAge,logSalamanders)
if (require(car)) { # Use car library
 scatterplotMatrix(myMatrix, diagonal="histogram", reg.line=FALSE, spread=FALSE)
}

myGlm1  <- glm(Salamanders ~ PctCover + logForestAge + PctCover:logForestAge, 
  family=poisson)
summary(myGlm1)   # Backward elimination...
myGlm2 <- update(myGlm1, ~ . - PctCover:logForestAge)
summary(myGlm2)
myGlm3  <- update(myGlm2, ~ . - logForestAge)
summary(myGlm3)   # PctCover is the only explanatory variable remaining

plot(Salamanders ~ PctCover)  # It appears that there are 2 distributions
# of Salamander counts; one for PctCover < 70 and one for PctCover > 70

# See if PctCover is associated Salamanders in each subset
myGlm4 <- glm(Salamanders ~ PctCover, family=poisson,subset=(PctCover > 70))
summary(myGlm4)           # No evidence of an effect for this subset
myGlm5 <- glm(Salamanders ~ PctCover, family=poisson,subset=(PctCover < 70))
summary(myGlm5)           # No evidence on this subset either

## INFERENCE  (2 means)
Group <- ifelse(PctCover > 70,"High","Low")
Group <- factor(Group, levels=c("Low","High") )  # Make "Low Cover" the ref group
myGlm6 <- glm(Salamanders ~ Group, family=poisson)
summary(myGlm6)


## GRAPHICAL DISPLAY FOR PRESENTATION
plot(Salamanders ~ PctCover, ylab="Number of Salamanders",
  xlab="Percentage of Canopy Covered",
  main="Number of Salamanders versus Percent Canopy Cover",
  pch=21,bg="green", cex=2, lwd=2)
beta <- myGlm6$coef
lines(c(0,55),exp(c(beta[1],beta[1])),lwd=2)
text(56,exp(beta[1]),paste("mean= ",round(exp(beta[1]),1)),adj=0)
lines(c(76,93),exp(c(beta[1]+beta[2],beta[1]+beta[2])),lwd=2)
text(56,exp(beta[1]+beta[2]),paste("mean=",round((beta[1]+beta[2]),1)),adj=-1)
    
detach(case2202)