larkinModel: Generate recruit abundance with Larkin model
In TESA-workshops/TESAsamSim: Closed-loop salmon simulator for 2021 TESA workshop

Description Usage Arguments Value Note Examples

This function calculates recruitment from Larkin model (according to Peterman et al. 2003, modified to take more recent parameter- ization). Uses parameters in log space, like rickerMod, with multivariate normally distributed errors, but cannot incorporate AR1 process error because such models have not been validated.

1	larkinModel(S, Sm1, Sm2, Sm3, a, b, b1, b2, b3, error)

`S`	A numeric vector of spawner abundances.
`Sm1, Sm2, Sm3`	A numeric vector of spawner abundances at 1, 2 and 3 year lags, respectively.
`a`	A numeric vector of alpha values, i.e. productivity at low spawner abundance.
`b`	A numeric vector of beta values, i.e. density dependence para- meter.
`b1, b2, b3`	A numeric vector of delayed density dependent effects at 1, 2, and 3 yera lags, respectively.
`error`	A numeric vector of recruitment deviations, typically generated using `rmvnorm()` and relevant process variance estimates (sigma).

Returns a numeric representing recruit abundance.

the log-normal bias correction has not been fixed for the Larkin model.

#Spawner and recruit values represent millions of fish, parameters
#approximate those of Shuswap CU
larkinModel(S = 1.1, Sm1 = 0.4, Sm2 = 0.2, Sm3 = 0.15, a = 2.2, b = 0.29,
b1 = 0.42, b2 = 0.31, b3 = 0.21, error = 0.3)