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

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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.

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

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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")

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