Individual Growth Population Biomass Recruitment Natural Mortality Fishing Mortality Immigration Emigration Growth

Length-At-Age Data TL Age Species 24 6 Rainbow 26 8 Rainbow data(TroutBR) rbt <- TroutBR[TroutBR$Species=="Rainbow",] attach(rbt) plot(jitter(TL,1)~jitter(Age,0.5),xlab="Age [jittered]",ylab="Total Length (in) [jittered]") Size At Age

Length-At-Age Models Purposes Main models Summarize growth with a few parameters. Compare growth parameters among populations. Used in key fisheries models, such as Beverton-Holt yield models. Main models Von Bertalanffy Gompertz Schnute Size At Age

Von Bertalanffy Growth Model By far the most prevalent growth model. Developed by Ludwig von Bertalanffy in 1938. Derived from … basic physiological principles of anabolism and catabolism. by assuming rate of growth declines linearly with increasing length. Size At Age

Von Bertalanffy Growth Model Explore parameters with growthModelSim(“vbTypical”) L∞ = asymptotic mean length K = Brody “growth” coefficient not a true measure of the “growth rate” controls how fast L∞ is approached Log(2)/K is time to get halfway between a length and L∞ to = time when mean length is 0 (artifact) Size At Age

Von Bertalanffy Growth Model growmodel.sim("vb",Age,TL,max.len=35) svb <- list(Linf=31.3,K=0.3,to=0.6) vbl1 <- nls(TL~Linf*(1-exp(-K*(Age-to))),start=svb) windows(4,4); par(mar=c(3.5,3.5,1,1),mgp=c(2,0.75,0)) ylmt <- c(-2,32); xlmt<-c(1.5,10) plot(jitter(Age,0.5),jitter(TL,1),xlab="Age",ylab="Total Length (in)",ylim=ylmt,xlim=xlmt,pch=19) x <- data.frame(Age=seq(1.5,10,by=0.1)) y <- predict(vbl1,x) lines(x$Age,y,lwd=1,lty=1,col="red") Linf <- coef(vbl1)[1]; to <- coef(vbl1)[3] lines(c(to,to),c(-5,2),lwd=2,lty=3,col="blue") lines(c(1,2),c(0,0),lwd=2,lty=3,col="blue") points(to,0,col="blue",pch=19,cex=1.25) text(to,-4.5,expression(t[o]),xpd=T,col="blue",cex=1.25) abline(h=Linf,lwd=2,lty=3,col="blue") text(0.8,Linf,expression(L[infinity]),xpd=T,col="blue",cex=1.25) Size At Age

Galucci & Quinn Parameterization New parameter is w=KL∞ a measure of growth rate in the vicinity of t0 “New” model looks like Explore model parameters with growthModelSim(“vbGalucciQuinn”) Size At Age