Nothing

```
library(ConnMatTools)
ps <- c(0.7,0.5) # Fraction of eggs "marked" at each source site
ks <- c(4,5) # Number of marked settlers among sample from each source site
n.sample <- 20 # Total sample size. Must be >= sum(ks)
phis0 = runif(3,min=0.05)
phis0 = phis0 / sum(phis0)
phis0 = phis0[1:2] # Don't include relative connectivity of unknown sites
nbatch=1e4
library(mcmc)
ans = metrop(d.rel.conn.multinomial.unnorm,
initial=phis0,nbatch=nbatch,scale=0.1,
log=TRUE,ps=ps,ks=ks,n.sample=n.sample)
# A more serious test would adjust blen and scale to improve results, and would repeat
# multiple times to get results from multiple MCMC chains.
# Plot marginal distribution of relative connectivity from first site
h=hist(ans$batch[,1],xlab="Rel. Conn., Site 1",
main="Relative Connectivity for Source Site 1")
# For comparison, add on curve that would correspond to single site calculation
phi = seq(0,1,length.out=40)
d1 = d.rel.conn.beta.prior(phi,ps[1],ks[1],n.sample)
lines(phi,d1*nbatch*diff(h$breaks)[1],col="red",lwd=5)
# Image plot of bivariate probability density
t=table(cut(ans$batch[,1],phi),cut(ans$batch[,2],phi))
image(t,col=heat.colors(12)[12:1],xlab="Rel. Conn., Site 1",ylab="Rel. Conn., Site 2")
# Add line indicate region above which one can never find results as that would
# lead to a total connectivity great than 1
abline(1,-1,col="black",lty="dashed",lwd=3)
```

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