xt2fun: Unbiased stability paramter estimation

In ecostatscale: Statistical Scaling Functions for Ecological Systems

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)

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

Value

predicted value of x^2 at time t+dt

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

ecostatscale documentation built on Oct. 23, 2023, 1:06 a.m.