Ricker reproduction model
Description
Section titled “Description”An implementation of the Ricker reproduction model (Ricker, 1954) with an extension to handle negative reproduction rates.
ricker_reproduction_model(abundance, reproduction_rate, carrying_capacity)
Arguments
Section titled “Arguments”abundance
:<numeric>
vector (or matrix) of abundances.reproduction_rate
:<numeric>
vector (or matrix) of reproduction rates.carrying_capacity
:<numeric>
vector (or matrix) of carrying capacities.
Details
Section titled “Details”Equations:
Section titled “Equations:”If reproduction_rate >= 0
(Ricker, 1954):
N_{t+1} = N_t e^{r (1 - {N_t} / {K})}
If reproduction_rate < 0$:
N_{t+1} = N_t * e^{r}`With:
N_t
= abundance at time tN_{t+1}
= abundance at time t+1r
= reproduction rateK
= carrying capacity
Note that:
abundance
should generally be greater than 0.reproduction_rate
andcarrying_capacity
should either both have the same size as the input abundance or both be of length 1.carrying_capacity
should generally be greater than 0. If it is 0 or less, the abundance will be set to 0.
Important Note:
To optimize performance, the functions modifies the abundance in-place.
This mean the input abundance will be modified (See Examples).
Since the result of this function is usually assigned to the same variable as the input abundance, this is unnoticable in most use cases.
Should you wish to keep the input abundance unchanged, you can rlang::duplicate()
it before passing it to this function.
References
Section titled “References”Ricker, W.E. (1954) Stock and recruitment. Journal of the Fisheries Research Board of Canada, 11, 559—623.
<numeric>
vector (or matrix) of abundances.
Examples
Section titled “Examples”ricker_reproduction_model( abundance = 10, reproduction_rate = 0.25, carrying_capacity = 100)ricker_reproduction_model( abundance = matrix(10, 5, 5), reproduction_rate = 0.25, carrying_capacity = 100)ricker_reproduction_model( abundance = matrix(10, 5, 5), reproduction_rate = matrix(seq(-0.5, 0.5, length.out = 25), 5, 5), carrying_capacity = matrix(100, 5, 5))ricker_reproduction_model( abundance = matrix(10, 5, 5), reproduction_rate = matrix(seq(0, -2, length.out = 25), 5, 5), carrying_capacity = matrix(100, 5, 5))# Note that the input abundance is modified in-placeabu <- 10res <- ricker_reproduction_model( abundance = abu, reproduction_rate = 0.25, carrying_capacity = 100)stopifnot(identical(abu, res))