# Creates a function for a specific parameterization of the von Bertalanffy and other common growth functions. Creates a function for a specific parameterizations of the von Bertalanffy, Gompertz, logistic, Richards, Schnute, and Schnute-Richards growth functions. The resulting function can be used to calculate length(s) from age(s) and specific growth function parameters, which is useful for model-fitting and plotting. Equations for each parameterization are shown in [this article](https://fishr-core-team.github.io/FSA/articles/Growth_Function_Parameterizations.html) and with `showGrowthFun`. ```r makeGrowthFun( type = c("von Bertalanffy", "Gompertz", "logistic", "Richards", "Schnute", "Schnute-Richards"), param = 1, pname = NULL, case = NULL, simple = FALSE, msg = FALSE ) ``` ## Arguments - `type`: A single string (i.e., one of von Bertalanffy , Gompertz , logistic , Richards , Schnute , Schnute-Richards ) that indicates the type of growth function to show. - `param`: A single numeric that indicates the specific parameterization of the growth function. Will be ignored if `pname` is non-`NULL`. See details. - `pname`: A single character that indicates the specific parameterization of the growth function. If `NULL` then `param` will be used. See details. - `case`: A numeric that indicates the specific case of the Schnute function to use. - `simple`: A logical that indicates whether the function will accept all parameter values in the first parameter argument (`=FALSE`; DEFAULT) or whether all individual parameters must be specified in separate arguments (`=TRUE`). See examples. - `msg`: A logical that indicates whether a message about the growth function and parameter definitions should be output (`=TRUE`) or not (`=FALSE; DEFAULT`). ## Returns Returns a function that can be used to predict fish size given a vector of ages and values for the growth function parameters and, in some parameterizations, values for constants. The result should be saved to an object that is then the function name. When the resulting function is used, the parameters are ordered as shown when the definitions of the parameters are printed after the function is called (if `msg=TRUE`). If `simple=FALSE` (DEFAULT), then the values for all parameters may be included as a vector in the first parameter argument (but in the same order). Similarly, the values for all constants may be included as a vector in the first constant argument (i.e., `t1`). If `simple=TRUE`, then all parameters and constants must be declared individually. The resulting function is somewhat easier to read when `simple=TRUE`, but is less general for some applications. ## Details Specific parameterizations can be chosen by including a name for the equation in `pname` or a number in `param=` (`param` will be ignored if `pname` is specificied). Specifics equations for the various parameterizations, along with parameter definitions, are in [this article](https://fishr-core-team.github.io/FSA/articles/Growth_Function_Parameterizations.html). See [this article](https://fishr-core-team.github.io/FSA/articles/Fitting_Growth_Functions.html) and examples for how to use this function in the larger context of fitting growth models to data. ## IFAR Chapter 12-Individual Growth. ## Examples ```r #===== Create typical von B function, calc length at single then multiple ages vb <- makeGrowthFun() vb(t=1,Linf=450,K=0.3,t0=-0.5) vb(t=1:5,Linf=450,K=0.3,t0=-0.5) #===== All parameters can be given to first parameter (default), unless simple=TRUE vb(t=1,Linf=c(450,0.3,-0.5)) vbS <- makeGrowthFun(simple=TRUE) ## Not run: vbS(t=1,Linf=c(450,0.3,-0.5)) # will error, parms must be separate vbS(t=1,Linf=450,K=0.3,t0=-0.5) #===== Create original von B, first using param, then using pname vbO <- makeGrowthFun(param=2) vbO2 <- makeGrowthFun(pname="Original") vbO(t=1:5,Linf=450,K=0.3,L0=25) vbO2(t=1:5,Linf=450,K=0.3,L0=25) #===== Create the third parameterization of the logistic growth function # and show some details, and demo calculations logi <- makeGrowthFun(type="logistic",param=3,msg=TRUE) logi(t=1:10,Linf=450,gninf=0.3,L0=25) #===== Simple example of comparing several models vb <- makeGrowthFun(type="von Bertalanffy") gomp <- makeGrowthFun(type="Gompertz",param=2) logi <- makeGrowthFun(type="logistic") ages <- 0:15 vb1 <- vb(ages,Linf=450,K=0.3,t0=-0.5) gomp1 <- gomp(ages,Linf=450,gi=0.3,ti=3) logi1 <- logi(ages,Linf=450,gninf=0.3,ti=3) plot(vb1~ages,type="l",lwd=2,ylim=c(0,450),ylab="Length",xlab="Age") lines(gomp1~ages,lwd=2,col="red") lines(logi1~ages,lwd=2,col="blue") #===== Simple example of four cases of Schnute model (note a,b choices) Schnute1 <- makeGrowthFun(type="Schnute",case=1) Schnute2 <- makeGrowthFun(type="Schnute",case=2) Schnute3 <- makeGrowthFun(type="Schnute",case=3) Schnute4 <- makeGrowthFun(type="Schnute",case=4) ages <- seq(0,15,0.1) s1 <- Schnute1(ages,L1=30,L3=400,a=0.3,b=2,t1=1,t3=15) s2 <- Schnute2(ages,L1=30,L3=400,a=0.3, t1=1,t3=15) s3 <- Schnute3(ages,L1=30,L3=400, b=2,t1=1,t3=15) s4 <- Schnute4(ages,L1=30,L3=400, t1=1,t3=15) plot(s1~ages,type="l",lwd=2,ylim=c(0,450),ylab="Length",xlab="Age") lines(s2~ages,lwd=2,col="red") lines(s3~ages,lwd=2,col="blue") lines(s4~ages,lwd=2,col="green") #===== Fitting the 8th parameterization of the von B growth model to data # make von B function vb8 <- makeGrowthFun(type="von Bertalanffy",param=8,msg=TRUE) # get starting values sv8 <- findGrowthStarts(tl~age,data=SpotVA1,type="von Bertalanffy",param=8, constvals=c(t1=1,t3=5)) # fit function nls8 <- nls(tl~vb8(age,L1,L2,L3,t1=c(t1=1,t3=5)),data=SpotVA1,start=sv8) cbind(Est=coef(nls8),confint(nls8)) plot(tl~age,data=SpotVA1,pch=19,col=col2rgbt("black",0.1)) curve(vb8(x,L1=coef(nls8),t1=c(t1=1,t3=5)),col="blue",lwd=3,add=TRUE) ``` ## References Ogle, D.H. 2016. [Introductory Fisheries Analyses with R](https://fishr-core-team.github.io/fishR/pages/books.html#introductory-fisheries-analyses-with-r). Chapman & Hall/CRC, Boca Raton, FL. Campana, S.E. and C.M. Jones. 1992. Analysis of otolith microstructure data. Pages 73-100 In D.K. Stevenson and S.E. Campana, editors. Otolith microstructure examination and analysis. Canadian Special Publication of Fisheries and Aquatic Sciences 117. [Was (is?) from https://waves-vagues.dfo-mpo.gc.ca/library-bibliotheque/141734.pdf.] Fabens, A. 1965. Properties and fitting of the von Bertalanffy growth curve. Growth 29:265-289. Francis, R.I.C.C. 1988. Are growth parameters estimated from tagging and age-length data comparable? Canadian Journal of Fisheries and Aquatic Sciences, 45:936-942. Gallucci, V.F. and T.J. Quinn II. 1979. Reparameterizing, fitting, and testing a simple growth model. Transactions of the American Fisheries Society, 108:14-25. Garcia-Berthou, E., G. Carmona-Catot, R. Merciai, and D.H. Ogle. A technical note on seasonal growth models. Reviews in Fish Biology and Fisheries 22:635-640. Gompertz, B. 1825. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London. 115:513-583. Haddon, M., C. Mundy, and D. Tarbath. 2008. Using an inverse-logistic model to describe growth increments of blacklip abalone (**Haliotis rubra**) in Tasmania. Fishery Bulletin 106:58-71. [Was (is?) from https://spo.nmfs.noaa.gov/sites/default/files/pdf-content/2008/1061/haddon.pdf.] Karkach, A. S. 2006. Trajectories and models of individual growth. Demographic Research 15:347-400. [Was (is?) from https://www.demographic-research.org/volumes/vol15/12/15-12.pdf.] Katsanevakis, S. and C.D. Maravelias. 2008. Modeling fish growth: multi-model inference as a better alternative to a priori using von Bertalanffy equation. Fish and Fisheries 9:178-187. Mooij, W.M., J.M. Van Rooij, and S. Wijnhoven. 1999. Analysis and comparison of fish growth from small samples of length-at-age data: Detection of sexual dimorphism in Eurasian perch as an example. Transactions of the American Fisheries Society 128:483-490. Polacheck, T., J.P. Eveson, and G.M. Laslett. 2004. Increase in growth rates of southern bluefin tuna (**Thunnus maccoyii**) over four decades: 1960 to 2000. Canadian Journal of Fisheries and Aquatic Sciences, 61:307-322. Quinn, T. J. and R. B. Deriso. 1999. Quantitative Fish Dynamics. Oxford University Press, New York, New York. 542 pages. Quist, M.C., M.A. Pegg, and D.R. DeVries. 2012. Age and growth. Chapter 15 in A.V. Zale, D.L Parrish, and T.M. Sutton, editors. Fisheries Techniques, Third Edition. American Fisheries Society, Bethesda, MD. Richards, F. J. 1959. A flexible growth function for empirical use. Journal of Experimental Biology 10:290-300. Ricker, W.E. 1975. Computation and interpretation of biological statistics of fish populations. Technical Report Bulletin 191, Bulletin of the Fisheries Research Board of Canada. [Was (is?) from https://publications.gc.ca/collections/collection_2015/mpo-dfo/Fs94-191-eng.pdf.] Ricker, W.E. 1979. Growth rates and models. Pages 677-743 In W.S. Hoar, D.J. Randall, and J.R. Brett, editors. Fish Physiology, Vol. 8: Bioenergetics and Growth. Academic Press, New York, NY. [Was (is?) from https://books.google.com/books?id=CB1qu2VbKwQC&pg=PA705&lpg=PA705&dq=Gompertz+fish&source=bl&ots=y34lhFP4IU&sig=EM_DGEQMPGIn_DlgTcGIi_wbItE&hl=en&sa=X&ei=QmM4VZK6EpDAgwTt24CABw&ved=0CE8Q6AEwBw#v=onepage&q=Gompertz%20fish&f=false.] Schnute, J. 1981. A versatile growth model with statistically stable parameters. Canadian Journal of Fisheries and Aquatic Sciences, 38:1128-1140. Schnute, J.T. and L.J. Richards. 1990. A unified approach to the analysis of fish growth, maturity, and survivorship data. Canadian Journal of Fisheries and Aquatic Sciences 47:24-40. Somers, I. F. 1988. On a seasonally oscillating growth function. Fishbyte 6(1):8-11. [Was (is?) from https://www.fishbase.us/manual/English/fishbaseSeasonal_Growth.htm.] Tjorve, E. and K. M. C. Tjorve. 2010. A unified approach to the Richards-model family for use in growth analyses: Why we need only two model forms. Journal of Theoretical Biology 267:417-425. [Was (is?) from https://www.researchgate.net/profile/Even_Tjorve/publication/46218377_A_unified_approach_to_the_Richards-model_family_for_use_in_growth_analyses_why_we_need_only_two_model_forms/links/54ba83b80cf29e0cb04bd24e.pdf.] Tjorve, K. M. C. and E. Tjorve. 2017. The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the Unified-Richards family. PLOS One. [Was (is?) from https://doi.org/10.1371/journal.pone.0178691.] Troynikov, V. S., R. W. Day, and A. M. Leorke. Estimation of seasonal growth parameters using a stochastic Gompertz model for tagging data. Journal of Shellfish Research 17:833-838. 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[Was (is?) from https://pmc.ncbi.nlm.nih.gov/articles/PMC1076153/pdf/pnas01729-0009.pdf.] ## See Also `showGrowthFun` to create an expression of the equation and `findGrowthStarts` to develop starting values for a growth function using the same `type` and `pname`/`param` arguments. ## Author(s) Derek H. Ogle, DerekOgle51@gmail.com , thanks to Gabor Grothendieck for a hint about using `get()`.

makeGrowthFun function