networksis (version 1.4)

finch: Co-location of Darwin's Finches as a bipartite graph

Description

Data on co-location of finches noted during Charles Darwin's visit to the Galapagos Islands.

Usage

data(finch)

Licenses and Citation

If the source of the data set does not specified otherwise, this data set is protected by the Creative Commons License http://creativecommons.org/licenses/by-nc-nd/2.5/. When publishing results obtained using this data set the original authors should be cited. In addition this package should be cited as noted at http://statnetproject.org/attribution.

Details

Charles Darwin compiled this data for thirteen finch species on a visit to the Galapagos Islands. For each finch type, he recorded on which of seventeen islands that finch could be found. Sanderson (2000) argues that, in examining island biogeography, it is important to condition on the number of islands and species in order to sample from the appropriate null space, so graphs sampled from the null distribution of the observed graph should have the same marginals. Chen, Diaconis, Holmes, and Liu (2005) report the number of graphs matching the marginal constraints of Darwin's finch data to be 67,149,106,137,567,626.

References

Chen Y, Diaconis P, Holmes SP, Liu J (2005) Sequential Monte Carlo Methods for Statistical Analysis of Tables, Journal of the American Statistical Association, 100, 109, V20. Sanderson, J.G. (2000) Testing Ecological Patterns, American Scientist, 88, p.332-339. Besag, J. (2000) Markov Chain Monte Carlo for Statistical Inference, Working Paper #9, Center for Statistics and the Social Sciences, University of Washington http://www.csss.washington.edu/Papers.

See Also

network, sna

Examples

## Darwin's finches example ##
data(finch)
as.sociomatrix(finch)
plot(finch,vertex.col=c(rep(2,13),rep(3,17)),vertex.cex=2.5,displaylabels=FALSE)
## Consider the graph statistic \bar{s}^2 (Roberts and Stone, 1990) ##
prob.vec<-rep(0,500)
s.bar.squared.vec<-rep(0,500)
for(i in 1:500)
{
   sim<-simulate(finch, nsim=1)
   ## Extract new bipartite graph ##
   new.graph<-as.matrix.network(sim)
   ## Calculate custom graph statistic ##
   s.bar.squared<-(sum((new.graph%*%t(new.graph))^2)-
   sum(diag((new.graph%*%t(new.graph))^2)))/(13*12)
   s.bar.squared.vec[i]<-s.bar.squared
   ## Graph probability ##
   prob.vec[i]<-exp(sim %n% "log.prob")
}
## Plot the null distribution of \bar{s}^2 ##
nbreaks<-75
w<-(1/prob.vec)/(sum(1/prob.vec))
intervals<-cut(s.bar.squared.vec, nbreaks, include.lowest=TRUE)
weights<-sapply(split(w, f=intervals), sum)
x<-seq(min(s.bar.squared.vec), max(s.bar.squared.vec), length.out=nbreaks)
plot(x,weights, type="h", xlab="", ylab="Probability Density", lwd=2)
abline(v=53.115)
## Consider graph statistics "coincidences(x)", which measure ##
## the number of finches sharing x islands                    ##
sim<-simulate_sis(finch~coincidences(0:17), nsim=1000)
observed.stats<-summary(finch~coincidences(0:17))
sampled.stats<-sim %n% "samplestatistics"
## Calculate 95\% confidence intervals for coincidences(x) ##
library(Hmisc)
p<-exp(sim %n% "log.prob")
p<-p/sum(p)
maxs<-apply(sampled.stats,2,wtd.quantile,weights=p,probs=0.975,normwt=TRUE)
mins<-apply(sampled.stats,2,wtd.quantile,
weights=p,probs=0.025,normwt=TRUE)
means<-apply(sampled.stats,2,wtd.mean,weights=p)
## Plot distributions for coincidences(x) ##
plot(0:17, means, type="b", ylim=c(0,24.5), lwd=3, lty=3,
xlab="Number of Islands", ylab="Pairs of Finches")

for(i in 1:18)
{
   points(rep(i-1,2), c(maxs[i],mins[i]), type="l", lwd=2)
}
points(0:17, observed.stats, type="b", pch=4, lwd=3)

## Calculate p-value for coincidences(0) ##
r0<-(p%*%sweep(sampled.stats,2,observed.stats,"<"))[1,]
r1<-(p%*%sweep(sampled.stats,2,observed.stats,">"))[1,]
round(apply(cbind(r0,r1),1,min),digits=8)[1]