Estimate the probability distribution of relative connectivity values assuming a uniform prior distribution
Description
These functions calculate the probability density function
(d.rel.conn.unif.prior
), the probability distribution function (aka
the cumulative distribution function; p.rel.conn.unif.prior
) and the
quantile function (q.rel.conn.unif.prior
) for the relative (to all
settlers at the destination site) connectivity value for larval transport
between a source and destination site given a known fraction of marked
individuals (i.e., eggs) in the source population. A uniform prior is used
for the relative connectivity value.
Usage
1 2 3 4 5 
Arguments
phi 
Vector of fractions of individuals (i.e., eggs) from the source population settling at the destination population 
p 
Fraction of individuals (i.e., eggs) marked in the source population 
k 
Number of marked settlers found in sample 
n 
Total number of settlers collected 
log 
If 
q 
Vector of quantiles 
... 
Extra arguments to Beta distribution functions. See

Details
Estimations of the probability distribution are derived from the Beta
distribution (see dbeta
) and should be exact to great
precision.
Value
Vector of probabilities or quantiles.
Functions

d.rel.conn.unif.prior
: Returns the probability density for relative connectivity between a pair of sites 
p.rel.conn.unif.prior
: Returns the cumulative probability distribution for relative connectivity between a paire of sites 
q.rel.conn.unif.prior
: Estimates quantiles for the probability distribution function for relative connectivity between a pair of sites
Author(s)
David M. Kaplan dmkaplan2000@gmail.com
References
Kaplan DM, Cuif M, Fauvelot C, Vigliola L, NguyenHuu T, Tiavouane J and Lett C (in press) Uncertainty in empirical estimates of marine larval connectivity. ICES Journal of Marine Science. doi:10.1093/icesjms/fsw182.
See Also
Other connectivity.estimation: d.rel.conn.beta.prior
,
d.rel.conn.dists.func
,
d.rel.conn.finite.settlement
,
d.rel.conn.multinomial.unnorm
,
d.rel.conn.multiple
,
dual.mark.transmission
,
optim.rel.conn.dists
,
r.marked.egg.fraction
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36  library(ConnMatTools)
k < 10 # Number of marked settlers among sample
n.obs < 87 # Number of settlers in sample
n.settlers < 100 # Total size of settler pool
p < 0.4 # Fraction of eggs that was marked
phi < seq(0,1,length.out=101) # Values for relative connectivity
# Probability distribution assuming infinite settler pool and uniform prior
drc < d.rel.conn.unif.prior(phi,p,k,n.obs)
prc < p.rel.conn.unif.prior(phi,p,k,n.obs)
qrc < q.rel.conn.unif.prior(c(0.025,0.975),p,k,n.obs) # 95% confidence interval
# Test with finite settlement function and large (approx. infinite) settler pool
# Can be a bit slow for large settler pools
dis < d.rel.conn.finite.settlement(0:(7*n.obs),p,k,n.obs,7*n.obs)
# Quantiles
qis < q.rel.conn.finite.settlement(c(0.025,0.975),p,k,n.obs,7*n.obs)
# Finite settler pool
dfs < d.rel.conn.finite.settlement(0:n.settlers,p,k,n.obs,n.settlers)
# Quantiles for the finite settler pool
qfs < q.rel.conn.finite.settlement(c(0.025,0.975),p,k,n.obs,n.settlers)
# Make a plot of different distributions
plot(phi,drc,type="l",main="Probability of relative connectivity values",
xlab=expression(phi),ylab="Probability density")
lines(phi,prc,col="blue")
lines((0:(7*n.obs))/(7*n.obs),dis*(7*n.obs),col="black",lty="dashed")
lines((0:n.settlers)/n.settlers,dfs*n.settlers,col="red",lty="dashed")
abline(v=qrc,col="black")
abline(v=qis/(7*n.obs),col="black",lty="dashed")
abline(v=qfs/n.settlers,col="red",lty="dashed")
