ibd_models {island}

Inmigration, birth, death- models

Description

ibd_models simulates population dynamics under three different inmigration, birth and death models.

Usage

ibd_models(n0, beta, delta, mu, K = NULL, time_v, type)

Arguments

n0

Initial number of individuals in the population.

beta

Birth rate, in time^(-1) units.

delta

Death rate, in time^(-1) units.

mu

Inmigration rate, in time^(-1) units.

K

Carrying capacity.

time_v

Vector of times to sample. Must start with 0.

type

Type of inmigration, birth, death- model used to simulate the dynamics. This must be "Kendall", "Alonso" or "Haegeman".

Details

We have included three different stochastic models: Kendall (1948) seminal work, Alonso & McKane (2002) mainland-island model, and Haegeman & Loreau (2010) basic population model with denso-dependent deaths. These models are different formulations of a population dynamics with three basic processes: birth, death and inmigration of individuals. For the specifics, please refer to the original articles.

Value

A data.frame with two columns: one with the time vector and the other with the number of individuals at those times.

Note

Haegeman & Loreau model specification breaks for high values of n0 when the birth rate is lower than the death rate.

References

Kendall, D. G. (1948). On some modes of population growth leading to R. A. Fishers logarithmic series distribution. Biometrika, 35, 6–15.

Haegeman, B. and Loreau, M. (2010). A mathematical synthesis of niche and neutral theories in community ecology. Journal of Theoretical Biology, 269(1), 150–165.

Alonso, D. and McKane, A (2002). Extinction Dynamics in Mainland–Island Metapopulations: An N -patch Stochastic Model. Bulletin of Mathematical Biology, 64, 913–958.

Examples

ibd_models(n0 = 0, beta = 0.4, delta = 0.3, mu = 0.2,
time_v = 0:20, type = "Kendall")
ibd_models(n0 = 0, beta = 0.4, delta = 0.3, mu = 0.1, K = 30,
time_v = 0:20, type = "Alonso")