README.md

In jasondubois/spopmodel: Methods for and Application of Fish Population Dynamics Model

spopmodel

This R package contains algorithms (i.e., functions & methods) and some data to explore (i.e., model) population dynamics of some fish species. Specifically, this model was designed for San Francisco Estuary-based (SFE) White Sturgeon (Acipenser transmontanus) but could be applied to SFE-based Striped Bass (Morone saxatilis) or other species where pertinent data (see section \<>) are known or available. (The s in spopmodel implies sturgeon or striped bass and is a nod to model developer Shannon B.)

Overview

The collaborative effort between the California Department of Fish and Wildlife (CDFW) and the University of Idaho (College of Natural Resources; UICNR) gave rise to spopmodel. CDFW supplied data and UICNR produced model formulae and R-script. spopmodel facilitates the deployment, application, sharing, and understanding of this population dynamics model.

The model’s primary application will guide management of the SFE-based White Sturgeon fishery. This stochastic age-based model yields population growth rate () over varying exploitation () per set period (e.g., 20 years). spopmodel attempts to make easier the process of exploring different management scenarios and for viewing — among other outcomes — the effects of on .

Though developed using White Sturgeon data, this model (in theory) should[1] be applicable to other datasets having like inputs (see section Data Requirements). However, spopmodel does provide users with functions (or methods) for “every day” analytics (e.g., length-(or age-)frequency; descriptive statistics; growth model given age & length data).

Data Requirements

Model inputs need to be age-based. To yield , one needs per age: frequency[2]; egg count[3]; spawning probability[4]; and survival probability[5].

This model employs a female-based Leslie Matrix with stochasticity (given probability values of input data). Other data not directly inputted to the model are exploitation (; from mark-recapture), length-frequency (adjusted for gear selectivity), male-to-female ratio, and population estimate for the appropriate demographic.

Help documentation is available for the various datasets included herein. Try ?<dataset name> at the R prompt (>).

Other R Packages

Currently, spopmodel imports msm, popbio, & reshape2. From these packages, spopmodel uses the functions listed below. Base-R functions (or methods) are used where needed. Further, spopmodel employs gear selectivity code developed by R. Millar, not available in an R package.

• msm::deltamethod()
• popbio::betaval()
• popbio::stretchbetaval()
• popbio::pop.projection()
• reshape2::dcast()
• reshape2::melt()

Vignettes

Currently, there are three vignettes available: simulations; model_inputs; and bcla_growth. Once you’ve installed and then loaded spopmodel, call each vignette using the code below.

utils::vignette(package = "spopmodel", topic = "<vignette_name>")

Datasets

spopmodel contains six datasets available for use. Each dataset has a help file, as viewed by either help("<dataset_name>") or ?<dataset_name>. To view each dataset, simply type the dataset name at the command prompt (>) or call View(<dataset_name>).

| Dataset Name | Useage | | --------------- | ----------------------------- | | age_dist | model input | | number_eggs | model input | | prob_spawn | model input | | prob_survival | model input | | trammel_catch | growth rate, gear selectivity | | fin_ray_aging | back-calculated length-at-age |

Examples

Herein, we provide some examples for running the model using “built-in” datasets. Please also see vignettes by typing vignette(package = "spopmodel").

Start by loading spopmodel in your current R session. If you have not done so, install this package from GitHub using the code below.

# ********** not run - run only if needed, need to run only once *****
# if (!(require(devtools))) install.packages(pkgs = "devtools")
# devtools::install_github(repo = "jasondubois/spopmodel")
# ********************************************************************

# load library to current session
library(spopmodel)

Growth Rate

Here we demonstrate how to estimate growth rate using von Bertalanffy Growth Model. We need to create some length bins, so let’s see our length range using range(trammel_catch[["FL"]]). We see fork length ranges from 53 to 217, so bins from 50 to 220 by 5 cm will work just fine.

len_breaks <- seq(from = 50, to = 220, by = 5)

Now let’s age the non-aged portion of our trammel net sample. We do this using AgeEach(), which will assign ages to each fish without an age. See ?AgeEach for help file.

Displaying “BinDiagnostics” shows BinCheck (empty length bins [no ages] or where all ages present could not be assigned an age), CountNA (number of ages as NA; i.e., could not be aged), and CountTotal (total sample size).

ages <- AgeEach(
  data = trammel_catch,
  len = FL,
  age = Age,
  lenBreaks = len_breaks
)

ages[["BinDiagnostics"]]
#> $BinCheck
#> [185,190) [190,195) [195,200) [205,210) [210,215) [215,220) 
#>   "empty"  "all NA"   "empty"   "empty"   "empty"  "all NA" 
#> 
#> $CountNA
#> [1] 2
#> 
#> $CountTotal
#> [1] 1000

To run the von Bertalanffy Growth Model (using FitVBGM()), we’ll need to assign the AgeEach() output to a field in trammel_catch. We’ll call this new field AgeAll to maintain (i.e., not overwrite) the Age field. Note: upon running code below, trammel_net will now be in your Global environment with the added field. To see the original (if necessary), run spopmodel::trammel_catch.

trammel_catch$AgeAll <- ages[["Ages"]]

Here we use FitVBGM() to fit the von Bertalanffy Growth Model. FitVBGM() uses stats::nls() and as such requires some starting values. Pass starting values as a list with Linf (asymptotic length), K (growth rate), and t0 (supposed age at zero size). In start_vals, we’ve chosen these values somewhat arbitrarily but are based some on Kohlhorst et al. 1980.

Though we don’t show it here, we could use fit to predict length given age, and then plot predicted values over age \~ length. Note: model fit fails with singular gradient or other errors. I am looking into the problem. For now, below provide an example using data and FitVBGM().

start_vals <- list(Linf = 500, K = 0.3, t0 = -3.638)

fit <- FitVBGM(
  data = trammel_catch,
  len = FL,
  age = AgeAll,
  start = start_vals,
  control = list(warnOnly = TRUE, maxiter = 1000)
)

summary(fit)
#> 
#> Formula: FL ~ Linf * (1 - exp(-K * (AgeAll - t0)))
#> 
#> Parameters:
#>        Estimate Std. Error t value Pr(>|t|)    
#> Linf -115.89571   33.46528  -3.463 0.000557 ***
#> K      -0.03400    0.00502  -6.772 2.16e-11 ***
#> t0     -9.20656    1.22591  -7.510 1.31e-13 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 9.145 on 995 degrees of freedom
#> 
#> Number of iterations to convergence: 10 
#> Achieved convergence tolerance: 5.492e-06
#>   (2 observations deleted due to missingness)

1. emphasized as to date (2019-05-02) model not run on other data

2. where frequency is proportion population estimate

3. along with some measure of error (standard deviation)

4. along with some measure of error (standard deviation)

5. along with some measure of error (standard deviation)

jasondubois/spopmodel documentation built on Dec. 4, 2019, 9:12 p.m.