DispersalPerRecruitModel: Population dynamics model based on lifetime-egg-production

In dmkaplan2000/ConnMatTools: Tools for Working with Connectivity Data

Description

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.

Usage

DispersalPerRecruitModel(
  LEP,
  conn.mat,
  recruits0,
  timesteps = 10,
  settler.recruit.func = hockeyStick,
  ...
)

Arguments

LEP	a vector of lifetime-egg-production (LEP; also known as eggs-per-recruit (EPR)) for each site.
conn.mat	a square connectivity matrix. dim(conn.mat) = rep(length(LEP),2)
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 hockeyStick.
...	additional arguments to settler.recruit.func. Typically Rmax and slope.

Value

A list with the following elements:

eggs	egg production for the timesteps in timesteps
settlers	Similar for settlement
recruits	Similar for recruitment

Author(s)

David M. Kaplan [e-mail]

References

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

See also BevertonHolt, hockeyStick

Examples

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")

dmkaplan2000/ConnMatTools documentation built on Feb. 8, 2020, 4:41 p.m.