| Title: | Tools for Working with Connectivity Data |
|---|---|
| Description: | Collects several different methods for analyzing and working with connectivity data in R. Though primarily oriented towards marine larval dispersal, many of the methods are general and useful for terrestrial systems as well. |
| Authors: | David M. Kaplan <[email protected]> [cre,aut], Marco Andrello <[email protected]> [ctb] |
| Maintainer: | David M. Kaplan <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.3.5 |
| Built: | 2025-01-04 05:10:55 UTC |
| Source: | https://github.com/dmkaplan2000/connmattools |
Helper function to compute a set of beta values using formula used in Jacobi et al. (2012).
betasVectorDefault(n, steps = 10, cycles = 3/4, coeff = 0.8, pwr = 3)betasVectorDefault(n, steps = 10, cycles = 3/4, coeff = 0.8, pwr = 3)
n |
numerator of formula from Jacobi et al. (2012). Normally will be
the number of columns in the connectivity matrix if one normalizes the
columns (otherwise, it would typically be |
steps |
number of beta values to return. Defaults to 10. |
cycles |
how many cycles of |
coeff |
coefficient in front of sine function |
pwr |
exponent in denominator |
vector of beta values
David M. Kaplan [email protected]
Jacobi, M. N., Andre, C., Doos, K., and Jonsson, P. R. 2012. Identification of subpopulations from connectivity matrices. Ecography, 35: 1004-1016.
See also optimalSplitConnMat
Calculates recruitment based on the settler-recruit relationship from
Beverton & Holt (1957): slope * settlers / (1+slope*settlers/Rmax)
BevertonHolt(S, slope = 1/0.35, Rmax = 1)BevertonHolt(S, slope = 1/0.35, Rmax = 1)
S |
a vector of settlement values, 1 for each site. |
slope |
slope at the origin of the settler-recruit relationship. Can be
a vector of same length as |
Rmax |
maximum recruitment value. |
slope and Rmax can both either be scalars or vectors of the
same length as S.
A vector of recruitment values.
David M. Kaplan [email protected]
Beverton RJH, Holt SJ (1957) On the dynamics of exploited fish populations. H.M.S.O., London. 533 pp.
Sample connectivity matrix representing potential larval dispersal of loco (Concholepas concholepas) from Chile. The matrix is for 89 sites along the coast of Chile and is derived from a theoretical larval transport model.
A square 89x89 matrix with real, positive elements.
David M. Kaplan [email protected]
Garavelli L, Kaplan DM, Colas F, Stotz W, Yannicelli B, Lett C (2014) Identifying appropriate spatial scales for marine conservation and management using a larval dispersal model: The case of Concholepas concholepas (loco) in Chile. Progress in Oceanography 124:42-53. doi:10.1016/j.pocean.2014.03.011
Tools for Working with Connectivity Data
Collects several different methods for analyzing and working with connectivity data in R. Though primarily oriented towards marine larval dispersal, many of the methods are general and useful for terrestrial systems as well.
| Package: | ConnMatTools |
| Type: | Package |
| Version: | 0.3.5 |
| Date: | 2017-02-02 |
| License: | GPL (>= 2) |
| LazyLoad: | no |
David M. Kaplan [email protected]
Marco Andrello [email protected]
Jacobi, M. N., and Jonsson, P. R. 2011. Optimal networks of nature reserves can be found through eigenvalue perturbation theory of the connectivity matrix. Ecological Applications, 21: 1861-1870.
Jacobi, M. N., Andre, C., Doos, K., and Jonsson, P. R. 2012. Identification of subpopulations from connectivity matrices. Ecography, 35: 1004-1016.
Gruss, A., Kaplan, D. M., and Lett, C. 2012. Estimating local settler-recruit relationship parameters for complex spatially explicit models. Fisheries Research, 127-128: 34-39.
Kaplan, D. M., Botsford, L. W., and Jorgensen, S. 2006. Dispersal per recruit: An efficient method for assessing sustainability in marine reserve networks. Ecological Applications, 16: 2248-2263.
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.
White, J. W. 2010. Adapting the steepness parameter from stock-recruit curves for use in spatially explicit models. Fisheries Research, 102: 330-334.
Gruss A, Kaplan DM, Hart DR (2011) Relative Impacts of Adult Movement, Larval Dispersal and Harvester Movement on the Effectiveness of Reserve Networks. PLoS ONE 6:e19960
Beverton RJH, Holt SJ (1957) On the dynamics of exploited fish populations. H.M.S.O., London. 533 pp.
See optimalSplitConnMat, d.rel.conn.beta.prior
## Not run: optimalSplitConnMat(CM)## Not run: optimalSplitConnMat(CM)
This function returns a probability density function (PDF) for scores for a mix of marked and unmarked individuals with known fraction of marked individuals. The distributions for marked individuals and for unmarked individuals must be known.
d.mix.dists.func(d.unmarked, d.marked)d.mix.dists.func(d.unmarked, d.marked)
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. |
A function representing the PDF of observations drawn from the mixed
distribution of marked and unmarked individuals. The function takes two
arguments: p.marked, the fraction of marked individuals in the
distribution; and obs, a vector of observed score values.
David M. Kaplan [email protected]
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 d.rel.conn.dists.func,
optim.rel.conn.dists.
These functions calculate the probability density function
(d.rel.conn.beta.prior), the probability distribution function (aka
the cumulative distribution function; p.rel.conn.beta.prior) and the
quantile function (q.rel.conn.beta.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 non-uniform prior is
used for the relative connectivity value.
d.rel.conn.beta.prior( phi, p, k, n, prior.shape1 = 0.5, prior.shape2 = prior.shape1, prior.func = function(phi) dbeta(phi, prior.shape1, prior.shape2), ... ) p.rel.conn.beta.prior( phi, p, k, n, prior.shape1 = 0.5, prior.shape2 = prior.shape1, prior.func = function(phi) dbeta(phi, prior.shape1, prior.shape2), ... ) q.rel.conn.beta.prior.func( p, k, n, prior.shape1 = 0.5, prior.shape2 = prior.shape1, prior.func = function(phi) dbeta(phi, prior.shape1, prior.shape2), N = 1000, ... ) q.rel.conn.beta.prior( q, p, k, n, prior.shape1 = 0.5, prior.shape2 = prior.shape1, prior.func = function(phi) dbeta(phi, prior.shape1, prior.shape2), N = 1000, ... )d.rel.conn.beta.prior( phi, p, k, n, prior.shape1 = 0.5, prior.shape2 = prior.shape1, prior.func = function(phi) dbeta(phi, prior.shape1, prior.shape2), ... ) p.rel.conn.beta.prior( phi, p, k, n, prior.shape1 = 0.5, prior.shape2 = prior.shape1, prior.func = function(phi) dbeta(phi, prior.shape1, prior.shape2), ... ) q.rel.conn.beta.prior.func( p, k, n, prior.shape1 = 0.5, prior.shape2 = prior.shape1, prior.func = function(phi) dbeta(phi, prior.shape1, prior.shape2), N = 1000, ... ) q.rel.conn.beta.prior( q, p, k, n, prior.shape1 = 0.5, prior.shape2 = prior.shape1, prior.func = function(phi) dbeta(phi, prior.shape1, prior.shape2), N = 1000, ... )
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 |
prior.shape1 |
First shape parameter for Beta distributed prior. Defaults to 0.5. |
prior.shape2 |
Second shape parameter for Beta distributed prior.
Defaults to being the same as |
prior.func |
Function for prior distribution. Should take one
parameter, |
... |
Extra arguments for the |
N |
Number of points at which to estimate cumulative probability
function for reverse approximation of quantile distribution. Defaults to
|
q |
Vector of quantiles |
The prior distribution for relative connectivity phi defaults to a
Beta distribution with both shape parameters equal to 0.5. This is the
Reference or Jeffreys prior for a binomial distribution parameter. Both
shape parameters equal to 1 corresponds to a uniform prior.
Estimations of the probability distribution are based on numerical
integration using the integrate function, and therefore are
accurate to the level of that function. Some modification of the default
arguments to that function may be necessary to acheive good results for
certain parameter values.
Vector of probabilities or quantiles, or a function in the case of
q.rel.conn.beta.prior.func.
d.rel.conn.beta.prior: Returns the probability density for
relative connectivity between a pair of sites
p.rel.conn.beta.prior: Returns the cumulative probability
distribution for relative connectivity between a paire of sites
q.rel.conn.beta.prior.func: Returns a function to estimate quantiles for
the probability distribution function for relative connectivity between a
pair of sites.
q.rel.conn.beta.prior: Estimates quantiles for the probability
distribution function for relative connectivity between a pair of sites
David M. Kaplan [email protected]
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.dists.func(),
d.rel.conn.finite.settlement(),
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()
library(ConnMatTools) k <- 10 # Number of marked settlers among sample n.obs <- 87 # Number of settlers in sample p <- 0.4 # Fraction of eggs that was marked phi <- seq(0.001,1-0.001,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) qrc <- q.rel.conn.unif.prior(c(0.025,0.975),p,k,n.obs) # 95% confidence interval # Probability distribution assuming infinite settler pool and using reference/Jeffreys prior drp <- d.rel.conn.beta.prior(phi,p,k,n.obs) prp <- p.rel.conn.beta.prior(phi,p,k,n.obs) qrp <- q.rel.conn.beta.prior(c(0.025,0.975),p,k,n.obs) # 95% confidence interval # Make a plot of different distributions # black = Jeffreys prior; red = uniform prior # Jeffreys prior draws distribution slightly towards zero plot(phi,drp,type="l",main="Probability of relative connectivity values", xlab=expression(phi),ylab="Probability density") lines(phi,drc,col="red") abline(v=qrp,col="black",lty="dashed") abline(v=qrc,col="red",lty="dashed")library(ConnMatTools) k <- 10 # Number of marked settlers among sample n.obs <- 87 # Number of settlers in sample p <- 0.4 # Fraction of eggs that was marked phi <- seq(0.001,1-0.001,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) qrc <- q.rel.conn.unif.prior(c(0.025,0.975),p,k,n.obs) # 95% confidence interval # Probability distribution assuming infinite settler pool and using reference/Jeffreys prior drp <- d.rel.conn.beta.prior(phi,p,k,n.obs) prp <- p.rel.conn.beta.prior(phi,p,k,n.obs) qrp <- q.rel.conn.beta.prior(c(0.025,0.975),p,k,n.obs) # 95% confidence interval # Make a plot of different distributions # black = Jeffreys prior; red = uniform prior # Jeffreys prior draws distribution slightly towards zero plot(phi,drp,type="l",main="Probability of relative connectivity values", xlab=expression(phi),ylab="Probability density") lines(phi,drc,col="red") abline(v=qrp,col="black",lty="dashed") abline(v=qrc,col="red",lty="dashed")
These functions return functions that calculate the probability density
function (d.rel.conn.dists.func), the probability distribution
function (aka the cumulative distribution function;
p.rel.conn.dists.func) and the quantile function
(q.rel.conn.dists.func) for relative connectivity given a set of
observed score values, distributions for unmarked and marked individuals, and
an estimate of the fraction of all eggs marked at the source site, p.
d.rel.conn.dists.func( obs, d.unmarked, d.marked, p = 1, N = max(100, min(5000, 2 * length(obs))), prior.shape1 = 0.5, prior.shape2 = prior.shape1, prior.func = function(phi) dbeta(phi, prior.shape1, prior.shape2), ... ) p.rel.conn.dists.func( obs, d.unmarked, d.marked, p = 1, N = max(100, min(5000, 2 * length(obs))), prior.shape1 = 0.5, prior.shape2 = prior.shape1, prior.func = function(phi) dbeta(phi, prior.shape1, prior.shape2), ... ) q.rel.conn.dists.func( obs, d.unmarked, d.marked, p = 1, N = max(100, min(5000, 2 * length(obs))), prior.shape1 = 0.5, prior.shape2 = prior.shape1, prior.func = function(phi) dbeta(phi, prior.shape1, prior.shape2), ... )d.rel.conn.dists.func( obs, d.unmarked, d.marked, p = 1, N = max(100, min(5000, 2 * length(obs))), prior.shape1 = 0.5, prior.shape2 = prior.shape1, prior.func = function(phi) dbeta(phi, prior.shape1, prior.shape2), ... ) p.rel.conn.dists.func( obs, d.unmarked, d.marked, p = 1, N = max(100, min(5000, 2 * length(obs))), prior.shape1 = 0.5, prior.shape2 = prior.shape1, prior.func = function(phi) dbeta(phi, prior.shape1, prior.shape2), ... ) q.rel.conn.dists.func( obs, d.unmarked, d.marked, p = 1, N = max(100, min(5000, 2 * length(obs))), prior.shape1 = 0.5, prior.shape2 = prior.shape1, prior.func = function(phi) dbeta(phi, prior.shape1, prior.shape2), ... )
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. Defaults to 1. |
N |
number of steps between 0 and 1 at which to approximate likelihood
function as input to |
prior.shape1 |
First shape parameter for Beta distributed prior. Defaults to 0.5. |
prior.shape2 |
Second shape parameter for Beta distributed prior.
Defaults to being the same as |
prior.func |
Function for prior distribution. Should take one
parameter, |
... |
Additional arguments for the |
The normalization of the probability distribution is carried out using a
simple, fixed-step trapezoidal integration scheme. By default, the number of
steps between relative connectivity values of 0 and 1 defaults to
2*length(obs) so long as that number is comprised between 100
and 5000.
A function that takes one argument (the relative connectivity for
d.rel.conn.dists.func and p.rel.conn.dists.func; the quantile
for q.rel.conn.dists.func) and returns the probability density,
cumulative probability or score value, respectively. The returned function
accepts both vector and scalar input values.
d.rel.conn.dists.func: Returns a function that is PDF for relative
connectivity
p.rel.conn.dists.func: Returns a function that is cumulative
probability distribution for relative connectivity
q.rel.conn.dists.func: Returns a function that is quantile
function for relative connectivity
David M. Kaplan [email protected]
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.finite.settlement(),
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()
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$real.children, d.unmarked,d.marked,p, prior.shape1=prior.shape1) # Plot it up phi <- seq(0,1,0.001) plot(phi,D(phi),type="l", xlim=c(0,0.1), main="PDF for relative connectivity", xlab=expression(phi), ylab="Probability density") abline(v=phi.mx,col="green",lty="dashed") abline(v=Q(c(0.025,0.975)),col="red",lty="dashed")library(ConnMatTools) data(damselfish.lods) # Histograms of simulated LODs l <- seq(-1,30,0.5) h.in <- hist(damselfish.lods$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")
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.
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)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)
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 |
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 |
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 |
q |
Vector of quantiles |
The relative connectivity between the source and destination sites is
calculated as n.origin/n.settlers.
A vector of probabilities or quantiles.
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).
David M. Kaplan [email protected]
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()
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")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")
This functions calculates the unnormalized probability density function for the relative (to all settlers at the destination site) connectivity value for larval transport between multiple source sites to a destination site. An arbitrary number of source sites can be evaluated.
d.rel.conn.multinomial.unnorm( phis, ps, ks, n.sample, log = FALSE, dirichlet.prior.alphas = 1/(length(phis) + 1) )d.rel.conn.multinomial.unnorm( phis, ps, ks, n.sample, log = FALSE, dirichlet.prior.alphas = 1/(length(phis) + 1) )
phis |
Vector of fractions of individuals (i.e., eggs) from the source populations settling at the destination population |
ps |
Vector of fractions of individuals (i.e., eggs) marked in each of the source populations |
ks |
Vector of numbers of marked settlers from each source population found in the sample |
n.sample |
Vector of total numbers of settlers collected |
log |
Boolean indicating whether or not to return the log probability
density. Defaults to |
dirichlet.prior.alphas |
Parameter value for a Dirichlet prior
distribution for the |
As this function returns the unnormalized probability density, it must be normalized somehow to be produce a true probability density. This can be acheived using a variety of approaches, including brute force integration of the unnormalized probability density and MCMC algorithms.
The unnormalized probability density value. If log=TRUE, then
the logarithm of the probability density value will be returned.
David M. Kaplan [email protected]
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.
Berger JO, Bernardo JM, Sun D (2015) Overall Objective Priors. Bayesian Analysis 10:189-221. doi:10.1214/14-BA915
Other connectivity estimation:
d.rel.conn.beta.prior(),
d.rel.conn.dists.func(),
d.rel.conn.finite.settlement(),
d.rel.conn.multiple(),
d.rel.conn.unif.prior(),
dual.mark.transmission(),
optim.rel.conn.dists(),
r.marked.egg.fraction()
library(ConnMatTools) ps <- c(0.7,0.5) # Fraction of eggs "marked" at each source site ks <- c(4,5) # Number of marked settlers among sample from each source site n.sample <- 20 # Total sample size. Must be >= sum(ks) phis0 = runif(3,min=0.05) phis0 = phis0 / sum(phis0) phis0 = phis0[1:2] # Don't include relative connectivity of unknown sites nbatch=1e4 library(mcmc) ans = metrop(d.rel.conn.multinomial.unnorm, initial=phis0,nbatch=nbatch,scale=0.1, log=TRUE,ps=ps,ks=ks,n.sample=n.sample) # A more serious test would adjust blen and scale to improve results, and would repeat # multiple times to get results from multiple MCMC chains. # Plot marginal distribution of relative connectivity from first site h=hist(ans$batch[,1],xlab="Rel. Conn., Site 1", main="Relative Connectivity for Source Site 1") # For comparison, add on curve that would correspond to single site calculation phi = seq(0,1,length.out=40) d1 = d.rel.conn.beta.prior(phi,ps[1],ks[1],n.sample) lines(phi,d1*nbatch*diff(h$breaks)[1],col="red",lwd=5) # Image plot of bivariate probability density t=table(cut(ans$batch[,1],phi),cut(ans$batch[,2],phi)) image(t,col=heat.colors(12)[12:1],xlab="Rel. Conn., Site 1",ylab="Rel. Conn., Site 2") # Add line indicate region above which one can never find results as that would # lead to a total connectivity great than 1 abline(1,-1,col="black",lty="dashed",lwd=3)library(ConnMatTools) ps <- c(0.7,0.5) # Fraction of eggs "marked" at each source site ks <- c(4,5) # Number of marked settlers among sample from each source site n.sample <- 20 # Total sample size. Must be >= sum(ks) phis0 = runif(3,min=0.05) phis0 = phis0 / sum(phis0) phis0 = phis0[1:2] # Don't include relative connectivity of unknown sites nbatch=1e4 library(mcmc) ans = metrop(d.rel.conn.multinomial.unnorm, initial=phis0,nbatch=nbatch,scale=0.1, log=TRUE,ps=ps,ks=ks,n.sample=n.sample) # A more serious test would adjust blen and scale to improve results, and would repeat # multiple times to get results from multiple MCMC chains. # Plot marginal distribution of relative connectivity from first site h=hist(ans$batch[,1],xlab="Rel. Conn., Site 1", main="Relative Connectivity for Source Site 1") # For comparison, add on curve that would correspond to single site calculation phi = seq(0,1,length.out=40) d1 = d.rel.conn.beta.prior(phi,ps[1],ks[1],n.sample) lines(phi,d1*nbatch*diff(h$breaks)[1],col="red",lwd=5) # Image plot of bivariate probability density t=table(cut(ans$batch[,1],phi),cut(ans$batch[,2],phi)) image(t,col=heat.colors(12)[12:1],xlab="Rel. Conn., Site 1",ylab="Rel. Conn., Site 2") # Add line indicate region above which one can never find results as that would # lead to a total connectivity great than 1 abline(1,-1,col="black",lty="dashed",lwd=3)
These functions calculate the probability density function
(d.rel.conn.multiple), the probability distribution function (aka the
cumulative distribution function; p.rel.conn.multiple) and the
quantile function (q.rel.conn.multiple) for the relative (to all
settlers at the destination site) connectivity value for larval transport
between a source and destination site. This version allows one to input
multiple possible fractions of individuals (i.e., eggs) marked at the source
site, multiple possible numbers of settlers collected and multiple possible
marked individuals observed in the sample. This gives one the possibility to
produce ensemble averages over different input parameter values with
different probabilities of being correct.
d.rel.conn.multiple( phi, ps, ks, ns, weights = 1, d.rel.conn = d.rel.conn.beta.prior, ... ) p.rel.conn.multiple( phi, ps, ks, ns, weights = 1, p.rel.conn = p.rel.conn.beta.prior, ... ) q.rel.conn.multiple.func( ps, ks, ns, weights = 1, p.rel.conn = p.rel.conn.beta.prior, N = 1000, ... ) q.rel.conn.multiple( q, ps, ks, ns, weights = 1, p.rel.conn = p.rel.conn.beta.prior, N = 1000, ... )d.rel.conn.multiple( phi, ps, ks, ns, weights = 1, d.rel.conn = d.rel.conn.beta.prior, ... ) p.rel.conn.multiple( phi, ps, ks, ns, weights = 1, p.rel.conn = p.rel.conn.beta.prior, ... ) q.rel.conn.multiple.func( ps, ks, ns, weights = 1, p.rel.conn = p.rel.conn.beta.prior, N = 1000, ... ) q.rel.conn.multiple( q, ps, ks, ns, weights = 1, p.rel.conn = p.rel.conn.beta.prior, N = 1000, ... )
phi |
Vector of fractions of individuals (i.e., eggs) from the source population settling at the destination population |
ps |
Vector of fractions of individuals (i.e., eggs) marked in the source population |
ks |
Vector of numbers of marked settlers found in sample |
ns |
Vector of total numbers of settlers collected |
weights |
Vector of weights for each set of p, k and n values |
d.rel.conn |
Function to use to calculate probability density for
individual combinations of |
... |
Additional arguments for the function |
p.rel.conn |
Function to use to calculate cumulative probability
distribution for individual combinations of |
N |
Number of points at which to estimate cumulative probability
function for reverse approximation of quantile distribution. Defaults to
|
q |
Vector of quantiles |
If ps, ks, ns and weights can be scalars or
vectors of the same length (or lengths divisible into that of the largest
input parameter). weights are normalized to sum to 1 before being
used to sum probabilities from each individual set of input parameters.
Vector of probabilities or quantiles, or a function in the case of
q.rel.conn.multiple.func
d.rel.conn.multiple: Estimates quantiles for the probability
distribution function for relative connectivity between a pair of sites for
multiple possible p, k and n values.
p.rel.conn.multiple: Estimates the cumulative probability
distribution for relative connectivity between a paire of sites for
multiple possible p, k and n values.
q.rel.conn.multiple.func: Returns a function to estimate quantiles for
the probability distribution function for relative connectivity between a
pair of sites for multiple possible p, k and n values.
q.rel.conn.multiple: Estimates quantiles for the probability
distribution function for relative connectivity between a pair of sites for
multiple possible p, k and n values.
David M. Kaplan [email protected]
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.unif.prior(),
dual.mark.transmission(),
optim.rel.conn.dists(),
r.marked.egg.fraction()
library(ConnMatTools) # p values have uniform probability between 0.1 and 0.4 p <- seq(0.1,0.8,length.out=100) # Weights the same for all except first and last, which are halved w <- rep(1,length(p)) w[1]<-0.5 w[length(w)]<-0.5 n <- 20 # Sample size k <- 2 # Marked individuals in sample # phi values to use for plotting distribution phi <- seq(0,1,0.01) prior.shape1 = 1 # Uniform prior # prior.shape1 = 0.5 # Jeffreys prior # Plot distribution plot(phi,d.rel.conn.multiple(phi,p,k,n,w,prior.shape1=prior.shape1), main="Probability density for relative connectivity", xlab=expression(phi), ylab="Probability density", type="l") # Add standard distributions for max and min p values lines(phi,d.rel.conn.beta.prior(phi,min(p),k,n,prior.shape1=prior.shape1), col="red",lty="dashed") lines(phi,d.rel.conn.beta.prior(phi,max(p),k,n,prior.shape1=prior.shape1), col="red",lty="dashed") # Add some quantiles q = q.rel.conn.multiple(c(0.025,0.25,0.5,0.75,0.975), p,k,n,w,prior.shape1=prior.shape1) abline(v=q,col="green")library(ConnMatTools) # p values have uniform probability between 0.1 and 0.4 p <- seq(0.1,0.8,length.out=100) # Weights the same for all except first and last, which are halved w <- rep(1,length(p)) w[1]<-0.5 w[length(w)]<-0.5 n <- 20 # Sample size k <- 2 # Marked individuals in sample # phi values to use for plotting distribution phi <- seq(0,1,0.01) prior.shape1 = 1 # Uniform prior # prior.shape1 = 0.5 # Jeffreys prior # Plot distribution plot(phi,d.rel.conn.multiple(phi,p,k,n,w,prior.shape1=prior.shape1), main="Probability density for relative connectivity", xlab=expression(phi), ylab="Probability density", type="l") # Add standard distributions for max and min p values lines(phi,d.rel.conn.beta.prior(phi,min(p),k,n,prior.shape1=prior.shape1), col="red",lty="dashed") lines(phi,d.rel.conn.beta.prior(phi,max(p),k,n,prior.shape1=prior.shape1), col="red",lty="dashed") # Add some quantiles q = q.rel.conn.multiple(c(0.025,0.25,0.5,0.75,0.975), p,k,n,w,prior.shape1=prior.shape1) abline(v=q,col="green")
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.
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, ...)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, ...)
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 |
... |
Extra arguments to Beta distribution functions. See
|
q |
Vector of quantiles |
Estimations of the probability distribution are derived from the Beta
distribution (see dbeta) and should be exact to great
precision.
Vector of probabilities or quantiles.
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
David M. Kaplan [email protected]
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()
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")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")
This dataset contains both simulated and real 'log of the odds ratio' (LOD) scores for potential parent-child pairs of humbug damselfish (Dascyllus aruanus) from New Caledonia. Data was generated using FaMoz. In all cases, results are for the potential parent with the highest LOD score for a given larval fish (child). Simulated data is based on artificial children generated from either real potential parent-pairs (the 'in' group) or artificial parents generated from observed allelic frequencies (the 'out' group).
A list with 3 elements:
5000 maximum LOD scores for simulated children from random crossing of real potential parents
5000 maximum LOD scores for simulated children from random crossing of artificial potential parents based on observed allelic frequencies
Maximum LOD scores for 200 real juvenile fish
David M. Kaplan [email protected]
Gerber S, Chabrier P, Kremer A (2003) FAMOZ: a software for parentage analysis using dominant, codominant and uniparentally inherited markers. Molecular Ecology Notes 3:479-481. doi:10.1046/j.1471-8286.2003.00439.x
Kaplan et al. (submitted) Uncertainty in marine larval connectivity estimation
See also d.rel.conn.dists.func
This function implements the marine population dynamics model described in Kaplan et al. (2006). This model is most appropriate for examining equilibrium dynamics of age-structured populations or temporal dynamics of semelparous populations.
DispersalPerRecruitModel( LEP, conn.mat, recruits0, timesteps = 10, settler.recruit.func = hockeyStick, ... )DispersalPerRecruitModel( LEP, conn.mat, recruits0, timesteps = 10, settler.recruit.func = hockeyStick, ... )
LEP |
a vector of lifetime-egg-production (LEP; also known as eggs-per-recruit (EPR)) for each site. |
conn.mat |
a square connectivity matrix. |
recruits0 |
a vector of initial recruitment values for each site. |
timesteps |
a vector of timesteps at which to record egg production, settlement and recruitment. |
settler.recruit.func |
a function to calculate recruitment from the
number of settlers at each site. Defaults to |
... |
additional arguments to settler.recruit.func. Typically
|
A list with the following elements:
eggs |
egg production for
the timesteps in |
settlers |
Similar for settlement |
recruits |
Similar for recruitment |
David M. Kaplan [email protected]
Kaplan, D. M., Botsford, L. W., and Jorgensen, S. 2006. Dispersal per recruit: An efficient method for assessing sustainability in marine reserve networks. Ecological Applications, 16: 2248-2263.
See also BevertonHolt, hockeyStick
library(ConnMatTools) data(chile.loco) # Get appropriate collapse slope # critical.FLEP=0.2 is just an example slope <- settlerRecruitSlopeCorrection(chile.loco,critical.FLEP=0.2) # Make the middle 20 sites a reserve # All other sites: scorched earth n <- dim(chile.loco)[2] LEP <- rep(0,n) nn <- round(n/2)-9 LEP[nn:(nn+19)] <- 1 Rmax <- 1 recruits0 <- rep(Rmax,n) # Use DPR model ret <- DispersalPerRecruitModel(LEP,chile.loco,recruits0,1:20,slope=slope,Rmax=Rmax, settler.recruit.func=BevertonHolt) image(1:n,1:20,ret$settlers,xlab="sites",ylab="timesteps", main=c("Settlement","click to proceed")) locator(1) plot(ret$settlers[,20],xlab="sites",ylab="equilibrium settlement", main="click to proceed") locator(1) # Same, but with a uniform Laplacian dispersal matrix and hockeyStick cm <- laplacianConnMat(n,10,0,"circular") ret <- DispersalPerRecruitModel(LEP,cm,recruits0,1:20,slope=1/0.35,Rmax=Rmax) image(1:n,1:20,ret$settlers,xlab="sites",ylab="timesteps", main=c("Settlement","click to proceed")) locator(1) plot(ret$settlers[,20],xlab="sites",ylab="equilibrium settlement")library(ConnMatTools) data(chile.loco) # Get appropriate collapse slope # critical.FLEP=0.2 is just an example slope <- settlerRecruitSlopeCorrection(chile.loco,critical.FLEP=0.2) # Make the middle 20 sites a reserve # All other sites: scorched earth n <- dim(chile.loco)[2] LEP <- rep(0,n) nn <- round(n/2)-9 LEP[nn:(nn+19)] <- 1 Rmax <- 1 recruits0 <- rep(Rmax,n) # Use DPR model ret <- DispersalPerRecruitModel(LEP,chile.loco,recruits0,1:20,slope=slope,Rmax=Rmax, settler.recruit.func=BevertonHolt) image(1:n,1:20,ret$settlers,xlab="sites",ylab="timesteps", main=c("Settlement","click to proceed")) locator(1) plot(ret$settlers[,20],xlab="sites",ylab="equilibrium settlement", main="click to proceed") locator(1) # Same, but with a uniform Laplacian dispersal matrix and hockeyStick cm <- laplacianConnMat(n,10,0,"circular") ret <- DispersalPerRecruitModel(LEP,cm,recruits0,1:20,slope=1/0.35,Rmax=Rmax) image(1:n,1:20,ret$settlers,xlab="sites",ylab="timesteps", main=c("Settlement","click to proceed")) locator(1) plot(ret$settlers[,20],xlab="sites",ylab="equilibrium settlement")
This function implements the marine population dynamics model described in Gruss et al. (2011). The model is an extension of the dispersal-per-recruit model in Kaplan et al. (2006) to include movement in a homerange and a gravity model for fishing effort redistribution.
DPRHomerangeGravity( larval.mat, adult.mat, recruits0, f0, timesteps = 10, settler.recruit.func = hockeyStick, LEP.of.f = function(f) 1 - f, YPR.of.f = function(f) f, gamma = 0, gravity.ts.interval = 1, ... )DPRHomerangeGravity( larval.mat, adult.mat, recruits0, f0, timesteps = 10, settler.recruit.func = hockeyStick, LEP.of.f = function(f) 1 - f, YPR.of.f = function(f) f, gamma = 0, gravity.ts.interval = 1, ... )
larval.mat |
a square larval connectivity matrix. |
adult.mat |
a square adult homerange movement matrix.
|
recruits0 |
a vector of initial recruitment values for each site. |
f0 |
a vector of initial real fishing mortalities for each site. |
timesteps |
a vector of timesteps at which to record egg production, settlement and recruitment. |
settler.recruit.func |
a function to calculate recruitment from the
number of settlers at each site. Defaults to |
LEP.of.f |
a function that returns lifetime-egg-productions given a vector of fishing rates. |
YPR.of.f |
a function that returns yields-per-recruit given a vector of fishing rates. |
gamma |
exponent for the gravity model. Defaults to 0, i.e., no gravity model. |
gravity.ts.interval |
number of timesteps between updates of gravity model. Defaults to 1, i.e., every timestep. |
... |
additional arguments to settler.recruit.func. |
A list with the following elements:
eggs |
egg production for the timesteps in |
settlers |
Similar for settlement |
recruits |
Similar for recruitment |
fishing.mortality |
Real spatial distribution of fishing mortality |
effective.fishing.mortality |
Effective fishing mortality taking into account adult movement |
yield |
Real spatial distribution of yield |
effective.yield |
Effective yield indicating where fish biomass caught originates from |
David M. Kaplan [email protected]
Gruss A, Kaplan DM, Hart DR (2011) Relative Impacts of Adult Movement, Larval Dispersal and Harvester Movement on the Effectiveness of Reserve Networks. PLoS ONE 6:e19960
Kaplan, D. M., Botsford, L. W., and Jorgensen, S. 2006. Dispersal per recruit: An efficient method for assessing sustainability in marine reserve networks. Ecological Applications, 16: 2248-2263.
See also BevertonHolt, hockeyStick,
DispersalPerRecruitModel
Estimates the fraction of eggs produced at the source site that are the result of crossing parents, one or both of which have been genotyped. Based on the assumption that probability of breeding between pairs of individuals is completely independent of whether or not one or more of those individuals was genotyped.
dual.mark.transmission(p.female, p.male = p.female)dual.mark.transmission(p.female, p.male = p.female)
p.female |
Fraction of all adult females genotyped in the source population |
p.male |
Fraction of all adult males genotyped in the source
population. Defaults to be equal to |
A list with the following elements:
2x2 matrix with probabilities for producing offspring with male or female known or unknown parents
fraction of all eggs produced at source site that will come from at least one genotyped parent
Fraction of eggs with a single known female parent among all eggs that have one or more known parents
Fraction of eggs with a single known male parent among all eggs that have one or more known parents
Fraction of eggs with two known parents among all eggs that have one or more known parents
David M. Kaplan [email protected]
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(),
optim.rel.conn.dists(),
r.marked.egg.fraction()
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$real.children, d.unmarked,d.marked,p, prior.shape1=prior.shape1) # Plot it up phi <- seq(0,1,0.001) plot(phi,D(phi),type="l", xlim=c(0,0.1), main="PDF for relative connectivity", xlab=expression(phi), ylab="Probability density") abline(v=phi.mx,col="green",lty="dashed") abline(v=Q(c(0.025,0.975)),col="red",lty="dashed")library(ConnMatTools) data(damselfish.lods) # Histograms of simulated LODs l <- seq(-1,30,0.5) h.in <- hist(damselfish.lods$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")
This function computes a limited number of eigenvalues and eigenvectors of a
matrix. It uses arpack function from the
igraph package. If this package is not available, it will use
the standard eigen function to do the calculation, but will
issue a warning.
eigs( M, nev = min(dim(M)[1] - 1, 1), sym = sum(abs(M - t(M)))/sum(abs(M)) < 1e-10, which = "LM", use.arpack = TRUE, options.arpack = NULL )eigs( M, nev = min(dim(M)[1] - 1, 1), sym = sum(abs(M - t(M)))/sum(abs(M)) < 1e-10, which = "LM", use.arpack = TRUE, options.arpack = NULL )
M |
a matrix. |
nev |
number of eigenvalues and eigenvectors to return |
sym |
A boolean indicating if matrix is symmetric or not. Defaults to checking if this is the case or not. |
which |
A character string indicating which eigenvalues to return.
Defaults to "LM", meaning largest magnitude eigenvalues. If not using
|
use.arpack |
Boolean determining if calculation is to be done with
|
options.arpack |
Additional options for |
A list with at least the following two items:
values |
A set of eigenvalues |
vectors |
A matrix of eigenvectors |
David M. Kaplan [email protected]
See also arpack
Calculates shape and scale parameters for a gamma distribution from the mean
and standard deviation of the distribution, or vice-versa. One supplies
either mean and sd or shape and scale and the
function returns a list with all four parameter values.
gammaParamsConvert(...)gammaParamsConvert(...)
... |
This function can be run either supplying |
A list with mean, sd, shape and scale
parameters of the corresponding gamma distribution.
David M. Kaplan [email protected]
library(ConnMatTools) mn <- 1 sd <- 0.4 l <- gammaParamsConvert(mean=mn,sd=sd) x <- seq(0,2,length.out=50) # Plot gamma and normal distributions - for sd << mean, the two should be very close plot(x,dgamma(x,l$shape,scale=l$scale), main="Normal versus Gamma distributions",type="l") lines(x,dnorm(x,l$mean,l$sd),col="red")library(ConnMatTools) mn <- 1 sd <- 0.4 l <- gammaParamsConvert(mean=mn,sd=sd) x <- seq(0,2,length.out=50) # Plot gamma and normal distributions - for sd << mean, the two should be very close plot(x,dgamma(x,l$shape,scale=l$scale), main="Normal versus Gamma distributions",type="l") lines(x,dnorm(x,l$mean,l$sd),col="red")
Calculates recruitment based on a settler-recruit relationship that increases linearly until it reaches a maximum values.
hockeyStick(S, slope = 1/0.35, Rmax = 1)hockeyStick(S, slope = 1/0.35, Rmax = 1)
S |
a vector of settlement values, 1 for each site. |
slope |
slope at the origin of the settler-recruit relationship. Can be
a vector of same length as |
Rmax |
maximum recruitment value. |
slope and Rmax can both either be scalars or vectors of the
same length as S.
A vector of recruitment values.
David M. Kaplan [email protected]
Kaplan, D. M., Botsford, L. W., and Jorgensen, S. 2006. Dispersal per recruit: An efficient method for assessing sustainability in marine reserve networks. Ecological Applications, 16: 2248-2263.
This function generates a connectivity matrix that is governed by a Laplacian
distribution: D[i,j]=exp(abs(x[i]-y[i]-shift)/disp.dist)/2/disp.dist
laplacianConnMat(num.sites, disp.dist, shift = 0, boundaries = "nothing")laplacianConnMat(num.sites, disp.dist, shift = 0, boundaries = "nothing")
num.sites |
number of sites. Sites are assumed to be aligned on a linear coastline. |
disp.dist |
dispersal distance in "site" units (i.e., 1 site = 1 unit of distance) |
shift |
advection distance in "site" units. Defaults to 0. |
boundaries |
string indicating what to do at boundaries. Defaults to "nothing". Possible values include: "nothing", "conservative" and "circular" |
The boundary argument can have the following different values:
"nothing" meaning do nothing special with boundaries; "conservative" meaning force
columns of matrix to sum to 1; and "circular" meaning wrap edges.
A square connectivity matrix
David M. Kaplan [email protected]
Kaplan, D. M., Botsford, L. W., and Jorgensen, S. 2006. Dispersal per recruit: An efficient method for assessing sustainability in marine reserve networks. Ecological Applications, 16: 2248-2263.
See also DispersalPerRecruitModel
library(ConnMatTools) cm <- laplacianConnMat(100,10,15,"circular") image(cm)library(ConnMatTools) cm <- laplacianConnMat(100,10,15,"circular") image(cm)
Local retention is defined as the diagonal elements of the connectivity matrix.
localRetention(conn.mat)localRetention(conn.mat)
conn.mat |
A square connectivity matrix. |
David M. Kaplan [email protected]
library(ConnMatTools) data(chile.loco) sr <- selfRecruitment(chile.loco) lr <- localRetention(chile.loco) rlr <- relativeLocalRetention(chile.loco)library(ConnMatTools) data(chile.loco) sr <- selfRecruitment(chile.loco) lr <- localRetention(chile.loco) rlr <- relativeLocalRetention(chile.loco)
This function tries to merge random subopoulations, checking if the result is a better soluton to the minimization problem.
mergeSubpops(subpops.lst, conn.mat, beta)mergeSubpops(subpops.lst, conn.mat, beta)
subpops.lst |
A list whose elements are vectors of indices for each subpopulation. See |
conn.mat |
A square connectivity matrix. This matrix has typically been normalized and made symmetric prior to using this function. |
beta |
Controls degree of splitting of connectivity matrix, with larger values generating more subpopulations. |
List of the same format as subpops.lst, but with potentially fewer subpopulations.
David M. Kaplan [email protected]
Jacobi, M. N., Andre, C., Doos, K., and Jonsson, P. R. 2012. Identification of subpopulations from connectivity matrices. Ecography, 35: 1004-1016.
See also optimalSplitConnMat,
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.
optim.rel.conn.dists( obs, d.unmarked, d.marked, p = 1, phi0 = 0.5, method = "Brent", lower = 0, upper = 1, ... )optim.rel.conn.dists( obs, d.unmarked, d.marked, p = 1, phi0 = 0.5, method = "Brent", lower = 0, upper = 1, ... )
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 |
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.
David M. Kaplan [email protected]
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()
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$real.children, d.unmarked,d.marked,p, prior.shape1=prior.shape1) # Plot it up phi <- seq(0,1,0.001) plot(phi,D(phi),type="l", xlim=c(0,0.1), main="PDF for relative connectivity", xlab=expression(phi), ylab="Probability density") abline(v=phi.mx,col="green",lty="dashed") abline(v=Q(c(0.025,0.975)),col="red",lty="dashed")library(ConnMatTools) data(damselfish.lods) # Histograms of simulated LODs l <- seq(-1,30,0.5) h.in <- hist(damselfish.lods$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")
Algorithm for iteratively determining subpopulations of highly-connected sites. Uses an iterative method described in Jacobi et al. (2012)
optimalSplitConnMat( conn.mat, normalize.cols = TRUE, make.symmetric = "mean", remove.diagonal = FALSE, cycles = 2, betas = betasVectorDefault(ifelse(normalize.cols, dim(conn.mat)[2], prod(dim(conn.mat))/sum(conn.mat)), steps), steps = 10, ... )optimalSplitConnMat( conn.mat, normalize.cols = TRUE, make.symmetric = "mean", remove.diagonal = FALSE, cycles = 2, betas = betasVectorDefault(ifelse(normalize.cols, dim(conn.mat)[2], prod(dim(conn.mat))/sum(conn.mat)), steps), steps = 10, ... )
conn.mat |
A square connectivity matrix. |
normalize.cols |
A boolean indicating if columns of conn.mat should be normalized by the sum of all elements in the column. Defaults to TRUE. |
make.symmetric |
A string indicating how to force conn.mat to be symmetric. "mean" (the default) will replace C_ij by (C_ij + C_ji)/2. "max" will replace C_ij by the maximum of C_ij and C_ji. |
remove.diagonal |
A boolean indicating if the diagonal elements of conn.mat should be removed before determining the subpopulations. Defaults to FALSE. |
cycles |
Number of times to pass over values in betas. |
betas |
Vector of beta values to try. If not given, will
default to |
steps |
Number of beta values to produce using betasVectorDefault. Ignored if betas argument is explicitly given. |
... |
further arguments to be passed to |
A list with the following elements:
betas |
Vector of all beta values tested |
num.subpops |
Vector of number of subpopulations found for each value of beta |
qualities |
Vector of the quality statistic for each subpopulation division |
subpops |
A matrix with dimensions dim(conn.mat)[2] X length(betas) indicating which subpopulation each site belongs to |
best.splits |
A list indicating for each number of
subpopulations, which column of subpops contains the division with
the lowest quality statistic. E.g.,
|
In Jacobi et al. (2012) paper, the connectivity matrix is
oriented so that is dispersal from i to j, whereas in this R
package, the connectivity matrix is oriented so that is
dispersal from j to i. This choice of orientation is arbitrary,
but one must always be consistent. From j to i is more common in
population dynamics because it works well with matrix
multiplication (e.g., settlers = conn.mat %*% eggs).
David M. Kaplan [email protected]
Jacobi, M. N., Andre, C., Doos, K., and Jonsson, P. R. 2012. Identification of subpopulations from connectivity matrices. Ecography, 35: 1004-1016.
See also splitConnMat,
recSplitConnMat, mergeSubpops,
qualitySubpops
library(ConnMatTools) data(chile.loco) num <- prod(dim(chile.loco)) / sum(chile.loco) betas <- betasVectorDefault(n=num,steps=4) chile.loco.split <- optimalSplitConnMat(chile.loco,normalize.cols=FALSE, betas=betas) # Extra 3rd division print(paste("Examining split with",names(chile.loco.split$best.splits)[1], "subpopulations.")) pops <- subpopsVectorToList(chile.loco.split$subpops[,chile.loco.split$best.splits[[1]]$index]) reduce.loco <- reducedConnMat(pops,chile.loco) sr <- selfRecruitment(reduce.loco) lr <- localRetention(reduce.loco) rlr <- relativeLocalRetention(reduce.loco)library(ConnMatTools) data(chile.loco) num <- prod(dim(chile.loco)) / sum(chile.loco) betas <- betasVectorDefault(n=num,steps=4) chile.loco.split <- optimalSplitConnMat(chile.loco,normalize.cols=FALSE, betas=betas) # Extra 3rd division print(paste("Examining split with",names(chile.loco.split$best.splits)[1], "subpopulations.")) pops <- subpopsVectorToList(chile.loco.split$subpops[,chile.loco.split$best.splits[[1]]$index]) reduce.loco <- reducedConnMat(pops,chile.loco) sr <- selfRecruitment(reduce.loco) lr <- localRetention(reduce.loco) rlr <- relativeLocalRetention(reduce.loco)
This function returns the probability each of a set of observations corresponds to a marked individual given the distribution of scores for unmarked and marked individuals and the fraction of individuals that are marked.
prob.marked(obs, d.unmarked, d.marked, phi = 0.5, p = 1)prob.marked(obs, d.unmarked, d.marked, phi = 0.5, p = 1)
obs |
A vector of score values for a random sample of (marked and unmarked) individuals from the population |
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. |
phi |
The fraction of settlers at the destination population that originated at the source population. Defaults to 0.5, which would correspond to an even sample of marked and unmarked individuals. |
p |
Fraction of individuals (i.e., eggs) marked in the source population. Defaults to 1. |
A vector of the same size as obs containing the probability
that each individual is marked
David M. Kaplan [email protected]
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 d.rel.conn.dists.func,
optim.rel.conn.dists.
This function finds the optimal network of protected areas based on connectivity using the eigenvalue perturbation approach described in Nilsson Jacobi & Jonsson (2011).
protectedAreaSelection( conn.mat, nev = dim(conn.mat)[1], delta = 0.1, theta = 0.05, M = 20, epsilon.lambda = 1e-04, epsilon.uv = 0.05, only.list = T, ... )protectedAreaSelection( conn.mat, nev = dim(conn.mat)[1], delta = 0.1, theta = 0.05, M = 20, epsilon.lambda = 1e-04, epsilon.uv = 0.05, only.list = T, ... )
conn.mat |
a square connectivity matrix. |
nev |
number of eigenvalues and associated eigenvectors to be calculated. |
delta |
the effect of protecting site i (e.g. increase in survival or fecundity in protected areas relative to unprotected areas). Now a single value, in future it will be possible to specify site-specific values. The perturbation theory used in the construction of the algorithm assumes delta to be small (e.g. delta=0.1). However, higher values give also good results. |
theta |
the threshold of donor times recipient value that a site must have to be selected. |
M |
the maximal number of sites selected from each subpopulation even if there are more sites above the threshold theta |
epsilon.lambda |
Threshold for removing complex eigenvalues. |
epsilon.uv |
Threshold for removing eigenvectors with elements of opposite signs of comparable magnitude. |
only.list |
Logical, whether the function return only the list of selected sites or also the predicted impact of each selected site on the eigenvalues |
... |
Additional arguments for the |
If only.list is TRUE, just returns the list of selected sites.
If FALSE, then result will be a list containing selected sites and
predicted impact of each selected site on the eigenvalues.
Marco Andrello [email protected]
Jacobi, M. N., and Jonsson, P. R. 2011. Optimal networks of nature reserves can be found through eigenvalue perturbation theory of the connectivity matrix. Ecological Applications, 21: 1861-1870.
A measure of the leakage between subpopulations for a given division of the
connectivity matrix into subpopulations. This statistic is equal to 1 -
mean(RLR) of the reduced connectivity matrix, where RLR=relative local
retention (relativeLocalRetention), i.e., the fraction of
settling individuals that originated at their site of settlement.
qualitySubpops(subpops.lst, conn.mat)qualitySubpops(subpops.lst, conn.mat)
subpops.lst |
A list whose elements are vectors of indices for each
subpopulation. If a vector of integers is given, then
|
conn.mat |
A square connectivity matrix. |
The quality statistic.
A smaller value of the quality statistic indicates less leakage.
David M. Kaplan [email protected]
Jacobi, M. N., Andre, C., Doos, K., and Jonsson, P. R. 2012. Identification of subpopulations from connectivity matrices. Ecography, 35: 1004-1016.
See also optimalSplitConnMat,
subpopsVectorToList, relativeLocalRetention
This function estimates the fraction of eggs "marked" at a site (where the "mark" could be micro-chemical or genetic) taking into account uncertainty in female (and potentially male in the case of dual genetic mark transmission) reproductive output. It generates a set of potential values for the fraction of eggs marked assuming that reproductive output of each marked or unmarked mature individual is given by a random variable drawn from a single probability distribution with known mean and standard deviation (or equivalently coefficient of variation) and that the numbers of marked and unmarked individuals are large enough that the central limit theorem applies and, therefore, their collective reproductive outputs are reasonably well described by a gamma distribution whose mean and standard deviation are appropriately scaled based on the number of individual reproducers. The function also returns the total egg production corresponding to each fraction of marked eggs, needed for estimating absolute connectivity values (i.e., elements of the connectivity matrix needed for assessing population persistence).
r.marked.egg.fraction( n, n.females, n.marked.females = round(n.females * p.marked.females), mean.female = 1, cv.female, dual = FALSE, male.uncert = FALSE, n.males = n.females, n.marked.males = tryCatch(round(n.males * p.marked.males), error = function(e) n.marked.females), mean.male = mean.female, cv.male = cv.female, p.marked.females, p.marked.males = p.marked.females )r.marked.egg.fraction( n, n.females, n.marked.females = round(n.females * p.marked.females), mean.female = 1, cv.female, dual = FALSE, male.uncert = FALSE, n.males = n.females, n.marked.males = tryCatch(round(n.males * p.marked.males), error = function(e) n.marked.females), mean.male = mean.female, cv.male = cv.female, p.marked.females, p.marked.males = p.marked.females )
n |
Number of random values to estimates |
n.females |
Total number of mature females in the population |
n.marked.females |
Number of marked females in population |
mean.female |
Mean egg production of each mature female. Defaults to 1. |
cv.female |
Coefficient of variation of reproductive output of an individual mature female |
dual |
Logical variable. If |
male.uncert |
Logical variable. If |
n.males |
Total number of mature males in the population. Only used if
|
n.marked.males |
Number of marked males in population. Only used if
|
mean.male |
Mean sperm production of each mature male. Only used if
|
cv.male |
Coefficient of variation of reproductive output of an
individual mature male. Only used if |
p.marked.females |
Fraction of marked females in population. Can be
supplied instead of |
p.marked.males |
Fraction of marked males in population. Can be supplied
instead of |
A list with the following elements:
Vector of
length n with estimates for fraction of marked
eggs
Vector of length n with estimates for total egg
production
Vector of length n with estimates for
total number of marked eggs produced
Only returned if
dual=TRUE. If male.uncert=FALSE, then a scalar equal to
n.males. Otherwise, a vector of length n with estimates for
total sperm production
Only returned if
dual=TRUE. If male.uncert=FALSE, then a scalar equal to
n.marked.males. Otherwise, a vector of length n with
estimates for total marked sperm production
David M. Kaplan [email protected]
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(),
optim.rel.conn.dists()
library(ConnMatTools) n.females <- 500 n.marked.females <- 100 p.marked.females <- n.marked.females/n.females mn <- 1 cv <- 1 # Numbers of males and marked males and variance in male sperm production # assumed the same as values for females # Random values from distribution of pure female mark transmission F=r.marked.egg.fraction(1000,n.females=n.females,n.marked.females=n.marked.females, mean.female=mn,cv.female=cv) # Random values from distribution of dual female-male mark transmission, but # fraction of marked eggs only depends on fraction of marked males Fm=r.marked.egg.fraction(1000,n.females=n.females,n.marked.females=n.marked.females, mean.female=mn,cv.female=cv,dual=TRUE,male.uncert=FALSE) # Random values from distribution of dual female-male mark transmission, with # fraction of marked eggs depending on absolute marked and unmarked sperm output FM=r.marked.egg.fraction(1000,n.females=n.females,n.marked.females=n.marked.females, mean.female=mn,cv.female=cv,dual=TRUE,male.uncert=TRUE) # Plot of pure female mark transmission hist(F$p,50,main="Female mark transmission", xlab="Fraction of marked eggs", ylab="Frequency") # Female+male mark transmission, but no variability in male mark transmission h <- hist(Fm$p,50,main="Female+male mark transmission, no male uncert.", xlab="Fraction of marked eggs", ylab="Frequency") hh <- hist((1-p.marked.females)*F$p + p.marked.females, breaks=c(-Inf,h$breaks,Inf),plot=FALSE) lines(hh$mids,hh$counts,col="red") # Plot of pure female mark transmission h <- hist(FM$p,50,plot=FALSE) hh <- hist(Fm$p, breaks=c(-Inf,h$breaks,Inf),plot=FALSE) plot(h,ylim=c(0,1.1*max(hh$counts,h$counts)), main="Female+Male mark transmission, male uncert.", xlab="Fraction of marked eggs", ylab="Frequency") lines(hh$mids,hh$counts,col="red")library(ConnMatTools) n.females <- 500 n.marked.females <- 100 p.marked.females <- n.marked.females/n.females mn <- 1 cv <- 1 # Numbers of males and marked males and variance in male sperm production # assumed the same as values for females # Random values from distribution of pure female mark transmission F=r.marked.egg.fraction(1000,n.females=n.females,n.marked.females=n.marked.females, mean.female=mn,cv.female=cv) # Random values from distribution of dual female-male mark transmission, but # fraction of marked eggs only depends on fraction of marked males Fm=r.marked.egg.fraction(1000,n.females=n.females,n.marked.females=n.marked.females, mean.female=mn,cv.female=cv,dual=TRUE,male.uncert=FALSE) # Random values from distribution of dual female-male mark transmission, with # fraction of marked eggs depending on absolute marked and unmarked sperm output FM=r.marked.egg.fraction(1000,n.females=n.females,n.marked.females=n.marked.females, mean.female=mn,cv.female=cv,dual=TRUE,male.uncert=TRUE) # Plot of pure female mark transmission hist(F$p,50,main="Female mark transmission", xlab="Fraction of marked eggs", ylab="Frequency") # Female+male mark transmission, but no variability in male mark transmission h <- hist(Fm$p,50,main="Female+male mark transmission, no male uncert.", xlab="Fraction of marked eggs", ylab="Frequency") hh <- hist((1-p.marked.females)*F$p + p.marked.females, breaks=c(-Inf,h$breaks,Inf),plot=FALSE) lines(hh$mids,hh$counts,col="red") # Plot of pure female mark transmission h <- hist(FM$p,50,plot=FALSE) hh <- hist(Fm$p, breaks=c(-Inf,h$breaks,Inf),plot=FALSE) plot(h,ylim=c(0,1.1*max(hh$counts,h$counts)), main="Female+Male mark transmission, male uncert.", xlab="Fraction of marked eggs", ylab="Frequency") lines(hh$mids,hh$counts,col="red")
This funtion recursively splits each subpopulation of a list of subpopulations until none of the subpopulations can be split further to improve the minimization.
recSplitConnMat(subpops.lst, conn.mat, beta, ...)recSplitConnMat(subpops.lst, conn.mat, beta, ...)
subpops.lst |
A list whose elements are vectors of indices for each subpopulation. See |
conn.mat |
A square connectivity matrix. This matrix has typically been normalized and made symmetric prior to using this function. |
beta |
Controls degree of splitting of connectivity matrix, with larger values generating more subpopulations. |
... |
further arguments to be passed to |
David M. Kaplan [email protected]
Jacobi, M. N., Andre, C., Doos, K., and Jonsson, P. R. 2012. Identification of subpopulations from connectivity matrices. Ecography, 35: 1004-1016.
See also optimalSplitConnMat,
splitConnMat,
subpopsVectorToList
Reduces a connectivity matrix based on a set of subpopulations. If there are
N subpopulations, then the reduced matrix will have dimensions NxN. The
reduced matrix will be ordered according to the order of subpopulations in
subpops.lst.
reducedConnMat(subpops.lst, conn.mat)reducedConnMat(subpops.lst, conn.mat)
subpops.lst |
A list whose elements are vectors of indices for each
subpopulation. If a vector of integers is given, then
|
conn.mat |
A square connectivity matrix. |
A reduced connectivity matrix. The sum of all elements of this reduced connectivity matrix will be equal to the sum of all elements of the original connectivity matrix.
David M. Kaplan [email protected]
Jacobi, M. N., Andre, C., Doos, K., and Jonsson, P. R. 2012. Identification of subpopulations from connectivity matrices. Ecography, 35: 1004-1016.
See also qualitySubpops
library(ConnMatTools) data(chile.loco) num <- prod(dim(chile.loco)) / sum(chile.loco) betas <- betasVectorDefault(n=num,steps=4) chile.loco.split <- optimalSplitConnMat(chile.loco,normalize.cols=FALSE, betas=betas) # Extra 3rd division print(paste("Examining split with",names(chile.loco.split$best.splits)[1], "subpopulations.")) pops <- subpopsVectorToList(chile.loco.split$subpops[,chile.loco.split$best.splits[[1]]$index]) reduce.loco <- reducedConnMat(pops,chile.loco) sr <- selfRecruitment(reduce.loco) lr <- localRetention(reduce.loco) rlr <- relativeLocalRetention(reduce.loco)library(ConnMatTools) data(chile.loco) num <- prod(dim(chile.loco)) / sum(chile.loco) betas <- betasVectorDefault(n=num,steps=4) chile.loco.split <- optimalSplitConnMat(chile.loco,normalize.cols=FALSE, betas=betas) # Extra 3rd division print(paste("Examining split with",names(chile.loco.split$best.splits)[1], "subpopulations.")) pops <- subpopsVectorToList(chile.loco.split$subpops[,chile.loco.split$best.splits[[1]]$index]) reduce.loco <- reducedConnMat(pops,chile.loco) sr <- selfRecruitment(reduce.loco) lr <- localRetention(reduce.loco) rlr <- relativeLocalRetention(reduce.loco)
Relative local retention is defined as the diagonal elements of the connectivity matrix divided by the sum of the corresponding column of the connectivity matrix.
relativeLocalRetention(conn.mat)relativeLocalRetention(conn.mat)
conn.mat |
A square connectivity matrix. |
David M. Kaplan [email protected]
library(ConnMatTools) data(chile.loco) sr <- selfRecruitment(chile.loco) lr <- localRetention(chile.loco) rlr <- relativeLocalRetention(chile.loco)library(ConnMatTools) data(chile.loco) sr <- selfRecruitment(chile.loco) lr <- localRetention(chile.loco) rlr <- relativeLocalRetention(chile.loco)
If egg production is uniform over sites, then self recruitment is defined as the diagonal elements of the connectivity matrix divided by the sum of the corresponding row of the connectivity matrix. If not, then the elements of the dispersal matrix must be weighted by the number of eggs produced.
selfRecruitment(conn.mat, eggs = NULL)selfRecruitment(conn.mat, eggs = NULL)
conn.mat |
A square connectivity matrix. |
eggs |
A vector of egg production values for each site. Defaults to
|
David M. Kaplan [email protected]
library(ConnMatTools) data(chile.loco) sr <- selfRecruitment(chile.loco) lr <- localRetention(chile.loco) rlr <- relativeLocalRetention(chile.loco)library(ConnMatTools) data(chile.loco) sr <- selfRecruitment(chile.loco) lr <- localRetention(chile.loco) rlr <- relativeLocalRetention(chile.loco)
This function corrects the slope of the settler-recruit curve so that the collapse point of the spatially-explicit population model corresponding to the connectivity matrix agrees with that of the global non-spatially-explicit model. Uses the method in White (2010).
settlerRecruitSlopeCorrection( conn.mat, slope = 1, natural.LEP = 1, critical.FLEP = 0.35, use.arpack = TRUE )settlerRecruitSlopeCorrection( conn.mat, slope = 1, natural.LEP = 1, critical.FLEP = 0.35, use.arpack = TRUE )
conn.mat |
a square connectivity matrix. |
slope |
slope at the origin of the settler-recruit relationship. Only
interesting to fix this argument if it is a vector of length =
|
natural.LEP |
value of lifetime-egg-production (LEP), also known as
eggs-per-recruit, in the absence of fishing. Can be a vector of length =
|
critical.FLEP |
Fraction of natural.LEP at which collapse occurs. Defaults to 0.35. |
use.arpack |
Boolean determining if calculation is to be done with
|
The slope argument corrected so that collapse happens when LEP is critical.FLEP * natural.LEP.
David M. Kaplan [email protected]
White, J. W. 2010. Adapting the steepness parameter from stock-recruit curves for use in spatially explicit models. Fisheries Research, 102: 330-334.
This function tries to optimally split a given subpopulation into two smaller subpopulations.
splitConnMat( indices, conn.mat, beta, tries = 5, threshold = 1e-10, alpha = 0.1, maxit = 500 )splitConnMat( indices, conn.mat, beta, tries = 5, threshold = 1e-10, alpha = 0.1, maxit = 500 )
indices |
vector of indices of sites in a subpopulation |
conn.mat |
a square connectivity matrix. This matrix has typically been normalized and made symmetric prior to using this function. |
beta |
controls degree of splitting of connectivity matrix, with larger values generating more subpopulations. |
tries |
how many times to restart the optimization algorithm. Defaults to 5. |
threshold |
controls when to stop each "try". Defaults to 1e-10. |
alpha |
controls rate of convergence to solution |
maxit |
Maximum number of iterations to perform per "try". |
List with one or two elements, each containing a vector of indices of sites in a subpopulations
David M. Kaplan [email protected]
Jacobi, M. N., Andre, C., Doos, K., and Jonsson, P. R. 2012. Identification of subpopulations from connectivity matrices. Ecography, 35: 1004-1016.
See also optimalSplitConnMat,
recSplitConnMat,
subpopsVectorToList
This function creates a step function from the bars in a histogram
object. By default, the step function will be normalized so that it
integrates to 1.
stepfun.hist(h, ..., normalize = TRUE)stepfun.hist(h, ..., normalize = TRUE)
h |
an object of type |
... |
Additional arguments for the default |
normalize |
Boolean indicating whether or not to normalize the output
stepfun so that it integrates to 1. Defaults to |
A function of class stepfun. The height of the steps will be
divided by the distance between breaks and possibly the total count.
David M. Kaplan [email protected]
See also d.rel.conn.dists.func,
optim.rel.conn.dists.
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$real.children, d.unmarked,d.marked,p, prior.shape1=prior.shape1) # Plot it up phi <- seq(0,1,0.001) plot(phi,D(phi),type="l", xlim=c(0,0.1), main="PDF for relative connectivity", xlab=expression(phi), ylab="Probability density") abline(v=phi.mx,col="green",lty="dashed") abline(v=Q(c(0.025,0.975)),col="red",lty="dashed")library(ConnMatTools) data(damselfish.lods) # Histograms of simulated LODs l <- seq(-1,30,0.5) h.in <- hist(damselfish.lods$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")
A helper function to convert a vector of subpopulation identifications into a
list appropriate for recSplitConnMat,
qualitySubpops, etc.
subpopsVectorToList(x)subpopsVectorToList(x)
x |
vector of subpopulation identifications |
Note that subpopulations list will be ordered according to the numerical order of the subpopulation indices in the original matrix, which will not necessarily be that of the spatial order of sites in the original connectivity matrix.
A list where each element is a vector of indices for a given subpopulation.
David M. Kaplan [email protected]
See also recSplitConnMat, qualitySubpops