d.rel.conn.finite.settlement {ConnMatTools} R Documentation

## Estimate the probability distribution for the number of settlers originating at a site given a sample from a finite settler pool

### 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 dmkaplan2000@gmail.com

### 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.

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")

```

[Package ConnMatTools version 0.3.5 Index]