GENERALIZED_LOGISTIC: GENERALISED LOGISTIC MODEL

In antarctic-humpback-2019-assessment/HumpbackSIR: Use Sample-Importance-Resampling to Estimate Southern Humpback Abundance

GENERALISED LOGISTIC MODEL

Description

GENERALIZED_LOGISTIC returns the population projection using a Pella-Tomlison population dynamics model: $$N_t+1 = N_t+N_t*r_max*\left[ 1 - \left( \fracN_tK \right) ^z \right] - C_t$$ where $N$ is the population size at year $t$ or $t+1$, $r_max$ is the maximum net recruitment rate, $K$ is the pre-exploitation population size, $z$ is the parameter that determines the population size where productivity is maximum. For example, a value of 2.39 corresponds to maximum sustainable yield of $0.6K$ and is assumed by the IWC SC, and $C_t$ is the harvest in numbers in year $t$. Population size can be in either numbers or biomass, however, units will have to be the same as the units used for catch, relative abundance, and absolute abundance.

Usage

GENERALIZED_LOGISTIC(r_max, K, N1, z, start_yr, num_Yrs, catches, MVP)

Arguments

r_max	The maximum net recruitment rate ($r_max$).
K	Pre-exploitation population size in numbers or biomass (depending on input).
N1	The population size in numbers or biomass at year 1 (generally assumed to be K).
z	The parameter that determines the population size where productivity is maximum (assumed to be 2.39 by the IWC SC).
start_yr	The first year of the projection (assumed to be the first year in the catch series).
num_Yrs	The number of projection years. Set as the last year in the catch or abundance series, whichever is most recent, minus the start_yr.
catches	The time series of catch in numbers or biomass. Currently does not handle NAs and zeros will have to input a priori for years in which there were no catches.
MVP	The minimum viable population size in numbers or biomass. Computed as 4 * num.haplotypes to compute minimum viable population (from Jackson et al., 2006 and IWC, 2007).

Value

A list of the minimum population size Min.Pop, year of the minimum population size Min.Yr, a indicator of wether the minimum population size is below the MVP, and the predicted population size Pred.N.

Examples

num_Yrs  <-  10
start_yr  <-  1
r_max  <-  0.2
K  <-  1000
N1  <-  K
catches  <-  round(runif(10, min = 0, max = 150 ), 0 )
MVP  <-  0
GENERALIZED_LOGISTIC(r_max, K, N1, z, start_yr, num_Yrs, catches)

antarctic-humpback-2019-assessment/HumpbackSIR documentation built on Nov. 6, 2023, 6:07 p.m.