# logistic3: Two-parameter logistic function In lefko3: Historical and Ahistorical Population Projection Matrix Analysis

 logistic3 R Documentation

## Two-parameter logistic function

### Description

Function logistic3() creates a vector of values produced by the logistic function as applied with a user-specified time lag. The logistic function is given as \phi_{t+1} = \phi_t \lambda (1 - n_t / K). Here, if no separate_N vector is provided, then n_t = \phi_t. If \lambda is not provided, then it defaults to 1.0.

### Usage

logistic3(
start_value,
alpha,
beta = 0,
lambda = 1,
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 carrying capacity K. beta If set to some positive number, then this number is the maximum value of phi to enforce. Otherwise, equals 0 and enforces no limit. lambda The value of the discrete population growth rate to use. Equal to the natural logarithm of the instantaneous growth rate, r. 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 logistic 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 logistic model.

### Value

A numeric vector of values showing values projected under the- logistic function.

### Examples

trial_run1 <- logistic3(1, alpha = 5)
plot(trial_run1)

trial_run2 <- logistic3(1, alpha = 5, beta = 5)
plot(trial_run2)

trial_run3 <- logistic3(1, alpha = 100)
plot(trial_run3)

trial_run4 <- logistic3(1, alpha = 100, beta = 50)
plot(trial_run4)

trial_run5 <- logistic3(1, alpha = 500)
plot(trial_run5)

trial_run6 <- logistic3(1, alpha = 500, beta = 501)
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 <- logistic3(1, alpha = 500, beta = 501, separate_N = used_Ns)
plot(trial_run7)

lefko3 documentation built on May 29, 2024, 6:39 a.m.