usher3: Two-parameter Usher function

In lefko3: Historical and Ahistorical Population Projection Matrix Analysis

Two-parameter Usher function

Description

Function usher3() creates a vector of values produced by the two- parameter Usher function as applied with a user-specified time lag. The Usher function is given as \phi_{t+1} = \phi_t / (1 + e^{\alpha n_t + \beta}). Here, if no separate_N vector is provided, then n_t = \phi_t.

Usage

usher3(
  start_value,
  alpha,
  beta,
  time_steps = 100L,
  time_lag = 1L,
  pre0_subs = FALSE,
  pre0_value = 0,
  substoch = 0L,
  separate_N = NULL
)

Arguments

start_value	A positive number to start the return vector in time 0.
alpha	The alpha parameter in the two-parameter Usher function.
beta	The beta parameter in the two-parameter Usher function.
time_steps	The number of time steps to run the projection. Must be a positive integer.
time_lag	A positive integer denoting the number of time steps back for the value of phi in the two-parameter Usher function.
pre0_subs	A logical value indicating whether to use a number other than that given in start_value for values of phi lagged from times prior to time 0.
pre0_value	A positive number to use for phi lagged from times prior to time 0. Only used if pre0_subs = TRUE.
substoch	An integer value indicating the kind of substochasticity to use. Values include: 0, no substochasticity enforced (the default); 1, all numbers must be non-negative; and 2, all numbers should be forced to the interval [0, 1].
separate_N	An optional numeric vector with values of N in each time, if phi is to be treated as different from N in the two-parameter model.

Value

A numeric vector of values showing values projected under the two- parameter Usher function.

Examples

trial_run1 <- usher3(1, alpha = -0.5, beta = 0.005)
plot(trial_run1)

trial_run2 <- usher3(1, alpha = 0.5, beta = 0.005)
plot(trial_run2)

trial_run3 <- usher3(1, alpha = -5, beta = 0.005)
plot(trial_run3)

trial_run4 <- usher3(1, alpha = 5, beta = 0.005)
plot(trial_run4)

trial_run5 <- usher3(1, alpha = -25, beta = 0.005)
plot(trial_run5)

trial_run6 <- usher3(1, alpha = 25, beta = 0.005)
plot(trial_run6)

used_Ns <- c(10, 15, 12, 14, 14, 150, 15, 1, 5, 7, 9, 14, 13, 16, 17, 19,
  25, 26)
trial_run7 <- usher3(1, alpha = -0.5, beta = 0.005, separate_N = used_Ns)
plot(trial_run7)

lefko3 documentation built on Oct. 14, 2023, 1:07 a.m.