ejosymart / gtransition

Stochastic growth expressed through a transition matrix for the growth variability as probability of shift from one length class to another during a time period.

Gtransition

Estimate a Stochastic Growth Matrix Based on Length Structure Data This package describes a theoretical model expressing the variability observed in the individual growth, such that each individual in the population exhibits a growth pattern with a nonlinear trend toward an expected value. Thus, the growth is represented by the proportion of individuals in the length class $l$ during a time interval. The proportion of individuals that grow from length class $l$ to all length classes $l^{'}$ is represented by a probabilistic density function, usually gamma distribution or normal distribution; therefore the growth pattern depends of their parameters, where the mean value indicates the average growth increment, and the variance explains the individual variability in growth, consequently both parameters determine the proportion of individuals going from one length class to another.

Installation

Install the CRAN version:

install.packages("Gtransition")

Or install de development version:

# install.packages("devtools")
devtools::install_github("ejosymart/Gtransition")

After, that call the package:

library("Gtransition")

Examples

This is a basic example which shows you how to calculate the transition growth matrix:

Mean growth increment (based on von Bertalanffy equation)

output <- mgi(lowerL = 78, upperL = 202, classL = 4, 
              Linf = 197.42, k = 0.1938, method = "vonB")

output
#> $delta
#>  [1] 20.6867442 19.9820348 19.2773254 18.5726160 17.8679066 17.1631972
#>  [7] 16.4584878 15.7537784 15.0490690 14.3443596 13.6396503 12.9349409
#> [13] 12.2302315 11.5255221 10.8208127 10.1161033  9.4113939  8.7066845
#> [19]  8.0019751  7.2972657  6.5925564  5.8878470  5.1831376  4.4784282
#> [25]  3.7737188  3.0690094  2.3643000  1.6595906  0.9548812  0.2501718
#> [31]  0.0000000
#> 
#> $Laverage
#>  [1]  80  84  88  92  96 100 104 108 112 116 120 124 128 132 136 140 144 148 152
#> [20] 156 160 164 168 172 176 180 184 188 192 196 200
#> 
#> attr(,"class")
#> [1] "Gincrement" "list"
delta    <- output$delta
Laverage <- output$Laverage

Transition growth matrix

Gmat <- transitionM(lowerL = 78, upperL = 202, classL = 4, 
                   distribution = "gamma", 
                   delta = delta, beta = 0.105, sigma = NULL)

Plots

plot(Gmat)

plot(Gmat, xlab = "XLAB", ylab = "YLAB", adjY = -25,
     col = "grey40", sizeAxis1 = 0.5, sizeAxis2 = 0.5,
     filename = "myplot", 
     savePDF = TRUE, widthPDF = 3, heightPDF = 10, 
     savePNG = TRUE, widthPNG = 300, heightPNG = 1000, resPNG = 110)

References

Luquin-Covarrubias M., Morales-Bojorquez E. (2020). Effects of stochastic growth on population dynamics and management quantities estimated from an integrated catch-at-length assessment model: Panopea globosa as case study. Ecologial Modeling 440, 109384. https://doi.org/10.1016/j.ecolmodel.2020.109384

Sullivan P.J., Lai H., Galluci V.F. (1990). A Catch-at-Length analysis that incorporates a stochastic model of growth. Can. J. Fish. Aquat. Sci. 47: 184-198.