procfun_ct

Simulates effects of process noise following a Gaussian perturbation.
Note that process noise only influences positive abundances (i.e. process noise cannot contribute to colonization)

noise

process

Includes a collection of functions presented in "Measuring stability in ecological systems without static equilibria" by Clark et al. (2022) <doi:10.1002/ecs2.4328> in Ecosphere.
These can be used to estimate the parameters of a stochastic state space model (i.e. a model where
a time series is observed with error). The goal of this package is to estimate the variability
around a deterministic process, both in terms of observation error - i.e. variability due to
imperfect observations that does not influence system state - and in terms of process noise - i.e.
stochastic variation in the actual state of the process. Unlike classical methods for estimating
variability, this package does not necessarily assume that the deterministic state is fixed (i.e.
a fixed-point equilibrium), meaning that variability around a dynamic trajectory can be estimated
(e.g. stochastic fluctuations during predator-prey dynamics).

Adam Clark

pttstability

Particle-Takens Stability

procfun_ct function

<dl><dt>sp</dt>
<dd>a numeric vector of length two or three, where terms 1-2 specify either the log-transformed standard deviation of the process noise function,
or an intercept and slope for calculating variance of process noise based on a power function of x, of the form var=exp(B0)*x^exp(B1)
The final term in the vector represents the recovery rate - i.e. the continuous time rate at which abundances recover from perturbation</dd>
<dt>xt</dt>
<dd>a number or numeric vector of abundances at time t, before process noise has occurred</dd>
<dt>waiting_time</dt>
<dd>average time between disturbance events: defaults to 1</dd>
<dt>time</dt>
<dd>the timestep - defaults to NULL (i.e. not used)</dd></dl>

Arguments

continuous-time process noise function — procfun_ct

<dl>

<dt>sp</dt>
<dd>a numeric vector of length two or three, where terms 1-2 specify either the log-transformed standard deviation of the process noise function,
or an intercept and slope for calculating variance of process noise based on a power function of x, of the form var=exp(B0)*x^exp(B1)
The final term in the vector represents the recovery rate - i.e. the continuous time rate at which abundances recover from perturbation</dd>


<dt>xt</dt>
<dd>a number or numeric vector of abundances at time t, before process noise has occurred</dd>


<dt>waiting_time</dt>
<dd>average time between disturbance events: defaults to 1</dd>


<dt>time</dt>
<dd>the timestep - defaults to NULL (i.e. not used)</dd>

</dl>

procfun_ct: continuous-time process noise function

Description

Usage

Value

Arguments