# Maximum-likelihood estimate for relative connectivity given two distributions for scores for marked and unmarked individuals

### Description

This function calculates the value for relative connectivity that best fits a
set of observed score values, a pair of distributions for marked and unmarked
individuals and an estimate of the fraction of eggs marked in the source
population, `p`

.

### Usage

1 2 | ```
optim.rel.conn.dists(obs, d.unmarked, d.marked, p = 1, phi0 = 0.5,
method = "Brent", lower = 0, upper = 1, ...)
``` |

### Arguments

`obs` |
Vector of observed score values for potentially marked individuals |

`d.unmarked` |
A function representing the PDF of unmarked individuals. Must be normalized so that it integrates to 1 for the function to work properly. |

`d.marked` |
A function representing the PDF of marked individuals. Must be normalized so that it integrates to 1 for the function to work properly. |

`p` |
Fraction of individuals (i.e., eggs) marked in the source population |

`phi0` |
Initial value for |

`method` |
Method variable for |

`lower` |
Lower limit for search for fraction of marked individuals. Defaults to 0. |

`upper` |
Upper limit for search for fraction of marked individuals. Defaults to 1. |

`...` |
Additional arguments for the |

### Value

A list with results of optimization. Optimal fraction of marked
individuals is in `phi`

field. Negative log-likelihood is in the
`neg.log.prob`

field. See `optim`

for other elements of
list.

### 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.

### 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`

,
`d.rel.conn.unif.prior`

,
`dual.mark.transmission`

,
`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 37 38 39 40 41 42 43 44 45 | ```
library(ConnMatTools)
data(damselfish.lods)
# Histograms of simulated LODs
l <- seq(-1,30,0.5)
h.in <- hist(damselfish.lods$in.group,breaks=l)
h.out <- hist(damselfish.lods$out.group,breaks=l)
# PDFs for marked and unmarked individuals based on simulations
d.marked <- stepfun.hist(h.in)
d.unmarked <- stepfun.hist(h.out)
# Fraction of adults genotyped at source site
p.adults <- 0.25
# prior.shape1=1 # Uniform prior
prior.shape1=0.5 # Jeffreys prior
# Fraction of eggs from one or more genotyped parents
p <- dual.mark.transmission(p.adults)$p
# PDF for relative connectivity
D <- d.rel.conn.dists.func(damselfish.lods$real.children,
d.unmarked,d.marked,p,
prior.shape1=prior.shape1)
# Estimate most probable value for relative connectivity
phi.mx <- optim.rel.conn.dists(damselfish.lods$real.children,
d.unmarked,d.marked,p)$phi
# Estimate 95% confidence interval for relative connectivity
Q <- q.rel.conn.dists.func(damselfish.lods$real.children,
d.unmarked,d.marked,p,
prior.shape1=prior.shape1)
# Plot it up
phi <- seq(0,1,0.001)
plot(phi,D(phi),type="l",
xlim=c(0,0.1),
main="PDF for relative connectivity",
xlab=expression(phi),
ylab="Probability density")
abline(v=phi.mx,col="green",lty="dashed")
abline(v=Q(c(0.025,0.975)),col="red",lty="dashed")
``` |