dai: dai

In cboettig/regimeshifts: Models and Data for Ecological Regime Shifts

Description

Growth of yeast population under a serial dilution regime, based on Dai et al 2012 Science paper

Usage

dai(n_t, t = 23, epsilon = rnorm(1, 0, 0.15), theta = c(gamma_high =
  0.439, gamma_low = 0.309, T_lag = 2.97, N_c = 276, K = 176000), DF = 600)

Arguments

n_t	The current population size
t	Number of hours between serial dilutions
epsilon	random shock for dilution. Note: only applied once per dilution (e.g once per function call)
theta	parameters for the model; defaults to estimates from Dai et al; see details
DF	Dilution factor, the environmental variable manipulated to cause the bifurcation

Details

Dai et al model:

$n_t+1 = n_t g(n_t + \epsilon n_t, \theta)$ $g(n_t) = n_t+1 / n_t$

From the supplement of Dai et al (2012), Science: "This model is based on two phases of daily growth: a slow exponential growth phase at low cell densities, followed by a logistic growth phase with a higher per capita growth rate at intermediate cell densities. This model has 5 parameters: T lag is the lag time before yeast cells start to grow after being transferred into new media (the total time for daily growth is 23 hours). In the slow exponential phase, the population grows with a constant per capita growth rate gamma_low . After the population reaches a threshold density N_c , the subsequent logistic growth is determined by gamma_high (gamma_high > gamma_low) and the carrying capacity K"

Value

the population size the next day, after serial dilution and growth

Examples

max_days <- 30
DF <- seq(0, 2000, length=max_days) # schedule for env degredation (increased dilution)
y <- numeric(max_days)

y[1] <- 1.76e5 # initial density

for(day in 1:(max_days-1)){
y[day+1] <- dai(y[day], DF = DF[day])
}

plot(seq_along(y), y)

cboettig/regimeshifts documentation built on July 19, 2019, 1:34 p.m.