d.rel.conn.finite.settlement: Estimate the probability distribution for the number of...

In dmkaplan2000/ConnMatTools: Tools for Working with Connectivity Data

Description

These functions calculate the probability mass function (d.rel.conn.finite.settlement), the cumulative distribution function (p.rel.conn.finite.settlement) and the quantile function (q.rel.conn.finite.settlement) for the true number of settlers at a site that originated in a particular site given a known fraction of marked eggs among the eggs originating at the source site, a sample of settlers at the destination site, a known fraction of which are marked, and a finite settler pool of known size.

Usage

d.rel.conn.finite.settlement(
  n.origin,
  p,
  k,
  n.obs,
  n.settlers,
  prior.n.origin = 1
)

p.rel.conn.finite.settlement(
  n.origin,
  p,
  k,
  n.obs,
  n.settlers,
  prior.n.origin = 1
)

q.rel.conn.finite.settlement(q, p, k, n.obs, n.settlers, prior.n.origin = 1)

Arguments

n.origin	Vector of integers of possible numbers of settlers in the cohort that originated at the site of marking. All values should be integers <=n.settlers.
p	Fraction of individuals (i.e., eggs) marked in the source population
k	Number of marked settlers in sample
n.obs	Total number of settlers collected
n.settlers	Total number of settlers at the destination site from which the n.obs (<=n.settlers) settlers are collected
prior.n.origin	A prior probability mass function for the number of settlers in the cohort originating at the site of marking. Must be a scalar or a vector of length n.settlers+1. Defaults to 1.
q	Vector of quantiles

Details

The relative connectivity between the source and destination sites is calculated as n.origin/n.settlers.

Value

A vector of probabilities or quantiles.

Functions

• d.rel.conn.finite.settlement: Returns the probability mass function for the numbers of settlers in the cohort that originated at the source site (i.e., site of marking).

• p.rel.conn.finite.settlement: Returns the cumulative distribution function for the numbers of settlers in the cohort that originated at the source site (i.e., site of marking).

• q.rel.conn.finite.settlement: Returns quantiles of the cumulative distribution function for the numbers of settlers in the cohort that originated at the source site (i.e., site of marking).

Author(s)

David M. Kaplan [e-mail]

References

Kaplan DM, Cuif M, Fauvelot C, Vigliola L, Nguyen-Huu 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.multinomial.unnorm(), d.rel.conn.multiple(), d.rel.conn.unif.prior(), dual.mark.transmission(), optim.rel.conn.dists(), r.marked.egg.fraction()

Examples

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")

dmkaplan2000/ConnMatTools documentation built on Feb. 8, 2020, 4:41 p.m.