Fit conditioning model to historical data

Bayesian stock reconstruction model of natural and hatchery origin fish population. Maturity and age-1 natural mortality are estimated from coded wire tag catch and escapement at age. A separate series of observed escapement, and hatchery releases reconstructs the population of interest, informed by natural mortality and maturity from CWT (Korman and Walters 2024). The model estimates time-varying maturity rate as well as time-varying ocean survival as a linear model of covariates (separate covariates for age 1 vs. ages 2+). The model can include either a preterminal juvenile fishery, terminal return fishery, or both (see Data and start sections of the documentation).fit_CM() generates the RTMB model from data which can then be passed to sample_CM() to run the MCMC in Stan. Generate a markdown report with report_CM().More information is available on the salmonMSE website

Usage

fit_CM(
  data,
  start = list(),
  map = list(),
  lower = list(),
  upper = list(),
  do_fit = TRUE,
  silent = TRUE,
  control = list(eval.max = 1e+05, iter.max = 1e+05),
  ...
)

sample_CM(fit, ...)

Arguments

data: A list containing data inputs. See details.
start: An optional list containing parameter starting values. See details.
map: An optional list that describes how parameters are fixed in the model. See TMB::MakeADFun().
lower: Named list containing lower bounds for parameters. See details.
upper: Named list containing upper bounds for parameters. See details.
do_fit: Logical, whether to do the fit and estimate the Hessian.
silent: Logical, whether to silence output from RTMB to the console.
control: List, control argument to pass to stats::nlminb().
...: For fit_CM, arguments to RTMB::MakeADFun(). For sample_CM, arguments to rstan::sampling()
fit: List of output from fit_CM()

Value

fit_CM() returns a named list containing the RTMB model (obj), nlminb output (opt), standard errors (SD), and parameter bounds (lower and upper)
sample_CM() returns a stanfit object containing the MCMC chains

Data

Data should passed through a named list with the following entries.

Nages Integer, number of age classes in the model
Ldyr Integer, number of years in the model
lht Integer, life history type. Should be 1 for now
n_r Integer, number of release strategies for CWT, subset of a hatchery-origin brood year that differ in maturity rate. Default is 1.
cwtrelease Matrix [Ldyr, n_r], coded wire tag (CWT) releases by year and release strategy
cwtesc Array [Ldyr, Nages, n_r]. CWT escapement by brood year, age, and release strategy. Poisson likelhood.
cwtcatPT Array [Ldyr, Nages, n_r]. CWT preterminal catch (juvenile fish), by brood year, age, and release strategy. Poisson likelhood. Set all values to zero to turn off parameters related to the preterminal fishery.
cwtcatT Array [Ldyr, Nages, n_r]. CWT terminal catch (returning, mature fish), by brood year, age, and release strategy. Poisson likelhood. Set all values to zero to turn off parameters related to the terminal fishery.
bvulPT Vector length Nages. Prior mean for the vulnerability at age to the preterminal fishery.
bvulT Vector length Nages. Prior mean for the vulnerability at age to the terminal fishery.
RelRegFPT Vector Ldyr. Trend in relative regional preterminal fishing mortality. Fishing mortality is estimated by estimating a scaling coefficient and annual deviations from this vector. Default is rep(1, d$Ldyr) (no prior trend) if cwtcatPT is provided, otherwise zero.
RelRegFT Vector Ldyr. Trend in relative regional terminal fishing mortality. Default is rep(1, d$Ldyr) (no prior trend) if cwtcatT is provided, otherwise zero.
bmatt Vector length Nages. Proportion maturity at age, base values for calculating the unfished replacement line. Also the prior means if year-specific maturity rates are estimated.
mobase. Vector length Nages. Natural mortality at age, base values for calculating the unfished replacement line and the the equilibrium spawners at age.
covariate1 Optional. Matrix Ldyr, ncov1 of linear covariates that predict natural mortality for age 1.
covariate Optional. Matrix Ldyr, ncov of linear covariates that predict natural mortality for ages 2+.
hatchsurv Numeric, survival of hatchery releases into the smolt life stage. Density-independent. Default is 1. If less than 1, then hatchery origin fish have lower survival to age 2 (after first year of marine life stage) compared to natural origin fish.
gamma Optional. Numeric, the relative spawning success of hatchery origin spawners. Default is 1.
ssum Numeric, proportion of spawners that is female. Can also be a vector Nages
fec Vector length Nages. Fecundity, egg production at age
r_matt Integer, the release strategy for which to use maturity parameter for the natural system. Default is 1.
obsescape Vector length Ldyr, total observed escapement from fisheries, i.e., return to river (all ages and both hatchery/natural fish). Lognormal likelhood.
propwildspawn Vector length Ldyr, proportion of the escapement that spawn (accounts for en-route mortality and broodtake)
obs_pHOS Optional. Vector length Ldyr, observations of proportion of hatchery origin spawners (census) (between 0-1) by brood year. Fitted to model with logistic-normal likelihood.
pHOS_sd Numeric, logistic-normal standard deviation of pHOS observations. Default is 1.
pHOS_init Numeric, initial pHOS for equilibrium abundance in the first year of the model. Default is 0.
s_enroute Numeric, survival of escapement to spawning grounds. Default is 1.
so_mu Numeric, the prior mean for spawners at unfished replacement in logspace. Default is log(3 * max(data$obsescape)).
so_sd Numeric, the prior standard deviation for spawners at unfished replacement in logspace. Default is 0.5.
finitPT Numeric, initial preterminal fishing mortality for calculating the equilibrium juvenile proportions at age in the first year of the model. Default is 0. Set to "estimate" to allow the model to estimate the equilibrium condition.
finitT Numeric, initial terminal fishing mortality for calculating the equilibrium juvenile proportions at age in the first year of the model. Default is 0. Set to "estimate" to allow the model to estimate the equilibrium condition.
spawn_init Numeric, initial spawners to calculate equilibrium abundance in the first year of the model. Default is obsescape[1].
cwtExp Numeric, the CWT expansion factor, typically the reciprocal of the catch sampling rate (higher factors for lower sampling rate). The model scales down the CWT predictions to match the observations. In other words, the model assumes that the CWT catch and escapement are not expanded. For example, cwtExp = 10 divides the CWT predictions by 10 for the likelihood. Default is 1. The Poisson distribution is used for the likelihood of the CWT observations, and the expansion parameter can be used to downweight the CWT likelihood relative to the escapement time series. However it requires adjustments of the CWT catches prior to fitting to ensure the proper population scale. If the expanded catch is 100, then the input CWT catch should be 10 and 50 with cwtExp of 10 and 2, respectively, to maintain the same population scale. The Poisson variance scales with the mean and is higher with cwtExp = 2.
fitness Logical, whether to calculate fitness effects on survival. Default is FALSE.
theta Vector length 2, the optimum phenotype value for the natural and hatchery environments. Default is 100 and 80, respectively. See online article for more information.
rel_loss Vector length 3, the loss in fitness apportioned between the egg, fry (both prior to density-dependence), and smolt (after density-dependence) life stage. The three values should sum to 1.
zbar_start Vector length 2, the mean phenotype of the spawners and broodtake in the natural and hatchery environment, respectively, at the start of the model. Default values of 100 and 100, implying maximum fitness at for the natural environment at the start of the model.
fitness_variance Numeric. The variance (omega-squared) of the fitness function. Assumed identical between the natural and hatchery environments. Default is 100.
phenotype_variance Numeric. The variance (sigma-squared) of the phenotypic trait (with optimum theta). Assumed identical between the natural and hatchery environments. Default is 10.
heritability Numeric. The heritability (h-squared) of the phenotypic trait. Between 0-1. Default is 0.5.
fitness_floor Numeric. The minimum fitness value in the natural and hatchery environments. Default is 0.5.

start

Starting values for parameters can be provided through a named list:

log_cr Numeric, log of the compensation ratio (productivity). Default is 3.
log_so Numeric, unfished spawners in logspace. Default is log(3 * max(data$obsescape)).
moadd Numeric, additive term to base natural mortality rate for age 1 juveniles. Default is zero.
wt Vector Ldyr. Annual deviates in natural mortality during the freshwater life stage (affects egg to smolt survival). Estimated with normal prior with mean zero and standard deviation p$wt_sd. Default is zero.
wto Vector Ldyr. Annual deviates in natural mortality for age 1 juveniles (marine life stage). Estimated with normal prior with mean zero and standard deviation p$wto_sd. Default is zero.
log_FbasePT Numeric, scaling coefficient to estimate preterminal fishing mortality from data$RelRegFPT. Default is log(0.1).
log_FbaseT Numeric, scaling coefficient to estimate preterminal fishing mortality from data$RelRegFT. Default is log(0.1).
log_fanomalyPT Vector Ldyr. Annual lognormal deviates from exp(log_FbasePT) * data$RelRegFPT to estimate preterminal fishing mortality. Estimated with normal prior with mean zero and standard deviation p$fanomaly_sd. Default is zero.
log_fanomalyT Vector Ldyr. Annual lognormal deviates from exp(log_FbaseT) * data$RelRegFT to estimate terminal fishing mortality. Estimated with normal prior with mean zero and standard deviation p$fanomalyPT_sd. Default is zero.
lnE_sd Numeric, lognormal standard deviation of the observed escapement. Estimated with hierarchical gamma(2, 5) prior. Default is 0.1.
wt_sd Numeric, lognormal standard deviation of the egg to smolt (freshwater) natural mortality deviates. Estimated with hierarchical gamma(2, 5) prior. Default is 1.
wto_sd Numeric, lognormal standard deviation of the age 1 (marine) natural mortality deviates. Estimated with hierarchical gamma(2, 5) prior. Default is 1.
fanomalyPT_sd Numeric, lognormal standard deviation of fanomalyPT. Estimated with hierarchical gamma(2, 5) prior. Default is 1.
fanomalyT_sd Numeric, lognormal standard deviation of fanomalyT. Estimated with hierarchical gamma(2, 5) prior. Default is 1.
logit_vulPT Vector Nages-2 of preterminal vulnerability at age in logit space. Fixed to zero and one at age 1 and the maximum age, respectively. Default is qlogis(data$bvul_PT[-c(1, data$Nages)]).
logit_vulT Vector Nages-2 of terminal vulnerability at age in logit space. Fixed to zero and one at age 1 and the maximum age, respectively. Default is qlogis(data$bvul_T[-c(1, data$Nages)]).
logit_matt Matrix Ldyr, Nages-2 maturity by year and age in logit space. Maturity is fixed to zero and one at age 1 and the maximum age, respectively. Default is matrix(qlogis(data$bmatt[-c(1, data$Nages)]), data$Ldyr, data$Nages-2, byrow = TRUE).
sd_matt Vector Nages-2. Logit standard deviation of maturity (logit_matt) by age class. Default is 0.5.
b1 Vector ncov1 of coefficients for linear covariates that predict natural mortality for age 1. Default is zero.
b Vector ncov of coefficients for linear covariates that predict natural mortality for ages 2+. Default is zero.

Bounds

By default, the standard deviation parameters and parameters in normal space (e.g., FbasePT, Fbase_T) have a lower bound of zero. moadd has a lower bound of zero by default, but it is feasible that this parameter can be negative as well. Deviation parameters centred around zero are bounded between -3 to 3. The log_cr parameter has a lower bound of zero.

All other parameters are unbounded.

Covariates on natural mortality

Natural mortality is modeled as the sum of a base value $M^\textrm{base}$, additional scaling factor for age 1 $M^\textrm{add}$, a linear system of covariates $X$ and coefficients $b$:

$$ M_{y,a} = \begin{cases} M^\textrm{base}_a + M^\textrm{add} + \sum_j b^1_j X^1_{y,j} & \quad a = 1\\ M^\textrm{base}_a + \sum_j b_j X_{y,j} & \quad a = 2, \ldots, A \end{cases} $$

References

Korman, J. and Walters, C. 2024. A life cycle model for Chinook salmon population dynamics. Canadian Contractor Report of Hydrography and Ocean Sciences 62: vi + 60 p.

Author

Q. Huynh from Stan code provided by J. Korman and C. Walters