makedynamics_general {pttstability}

Simulate general time series

Description

Simulates a time series following a user-defined deterministic function, observation function, process noise function, and colonization function.

Usage

makedynamics_general(
  n = 1000,
  n0 = 0.1,
  pdet = c(log(3), log(1)),
  proc = c(log(1)),
  obs = c(log(1)),
  pcol = c(logit(0.2), log(1)),
  detfun = detfun0,
  procfun = procfun0,
  obsfun = obsfun0,
  colfun = colfun0,
  doplot = FALSE
)

Arguments

n

number of timesteps to simulate

n0

starting population size

pdet

a numeric vector of parameters for the deterministic function

proc

a numeric vector of parameters for the process noise function

obs

a numeric vector of parameters for the observation error function

pcol

a numeric vector of parameters for the colonization function

detfun

A function that simulates deterministic dynamics, which takes in arguments sdet (parameters for deterministic model, taken from pars$proc), and xt, observed abundances at time t. Returns estimated abundances at time t+1 based on deterministic function (either a parametric function or an EDM function). Defaults to detfun0.

procfun

A function that simulates process noise, which takes in arguments sp (parameters for process noise function, taken from pars$proc) and xt (abundances prior to process noise). Returns abundances after process noise has occurred. Defaults to procfun0.

obsfun

An observation function, which takes in up to five variables, including so (a vector of parameter values, inherited from pars$obs), yt (a number, showing observed abundance at time t), xt (predicted abundances), binary value "inverse", and number "N". If inverse = TRUE, then function should simulate N draws from the observation function, centered around value yt. If inverse = FALSE, then function should return log probability denisty of observed value yt given predicted values in xt. Defaults to obsfun0.

colfun

A function simulating colonization events, that takes in two arguments: co, a vector of parameter values taken from pars$pcol, and xt, a number or numeric vector of abundances at time t, before colonization has occurred. Returns predicted abundances after colonization has occurred. Defaults to colful0.

doplot

a logical specifying wether output should be plotted - defaults to FALSE

Value

An n-by-3 dataframe of states, including obs (observed values), truth (true values), and noproc (values without process noise)

Examples

 #run function
 datout<-makedynamics_general(n=2e4, proc = c(-2,log(1.2)))

 #show regression of variance vs. mean for binned data
 datout_ps<-datout[datout$true>0 & datout$noproc>0,]
 #bins
 sq<-seq(0, quantile(datout$true, 0.95), length=50)
 ctd<-cut(datout_ps$noproc, sq)
 #calculate mean and variance by bin
 tdat<-data.frame(mu=(sq[-1]+sq[-length(sq)])/2,
      var=tapply((datout_ps$true-datout_ps$noproc)^2, ctd, mean))
 #plot result
 plot(log(tdat$mu), log(tdat$var), xlab="mu", ylab="var")
 #show regression
 summary(mod<-lm(log(var)~log(mu), tdat)); abline(mod, col=2)