d.rel.conn.unif.prior {ConnMatTools} R Documentation

## 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

```d.rel.conn.unif.prior(phi, p, k, n, log = FALSE, ...)

p.rel.conn.unif.prior(phi, p, k, n, log = FALSE, ...)

q.rel.conn.unif.prior(q, p, k, n, log = FALSE, ...)
```

### 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 `TRUE`, returns natural logarithm of probabilities, except for `q.rel.conn.unif.prior`, which expects log of probabilities as inputs `...` Extra arguments to Beta distribution functions. See `dbeta` for details. For expert use only. `q` Vector of quantiles

### 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, 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.finite.settlement()`, `d.rel.conn.multinomial.unnorm()`, `d.rel.conn.multiple()`, `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]