ecostatscale (version 1.1)

xt2fun: Unbiased stability paramter estimation

Description

Function for solving for stability paramter values from observed time series. Equivalent to Eq.5 in the main text.

Usage

xt2fun(x0, r, d, d_sd, dt, ndist)

Value

predicted value of x^2 at time t+dt

Arguments

x0

value of x^2 at time t (x(t) in Eq.5)

r

per-capita growth rate (r in Eq.5)

d

mean size of disturbance function (mu in Eq.5)

d_sd

standard deviation of disturbance function (sigma in Eq.5)

dt

time step (i.e. time between x0 and x1) - can be a vector of the same length as x0, or a number if all time steps are of equal length

ndist

number of disturbances in each time step (equivalent to p(t+tau) in Eq.5) - must be same length as x0

Examples

# simulate dynamics, with r=1, d=0, and d_sd=0.1
xtout<-symdyn(r=1, f=1, d=0, d_sd=0.1, sf=0.1, tmax=100)

# abundance in current time step
x0<-xtout$state[1:(nrow(xtout)-1)]
# abundance at t+1
x1<-xtout$state[2:nrow(xtout)]

dt<-diff(xtout$time)
ndist<-xtout$disturbed[-1]

# fit model - note square root transform of response variable,
# and log transform of parameter values

mod<-nls(sqrt(x1^2)~sqrt(xt2fun(x0, r=exp(lr), d=0, d_sd=exp(ld_sd), dt, ndist)),
         start=c(lr=log(1), ld_sd=log(0.1)))
exp(coef(mod)) # model estimates