# optim.rel.conn.dists: Maximum-likelihood estimate for relative connectivity given... In ConnMatTools: Tools for Working with Connectivity Data

## 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 3 4 5 6 7 8 9 10 11``` ```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 φ, the fraction of settlers at the destination population that originated at the source population, for `optim` function. Defaults to 0.5. `method` Method variable for `optim` function. Defaults to `"Brent"`. `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 `optim` function.

## 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.

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()`
 ``` 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") ```