漁業(yè)生存率和死亡率評(píng)估)

1、3-6 MortalityName: Zhu Shunli(Fisheries Biology, Assessment and Management)ContentsMortality1. Catch curves2. Age-based catch curves3. Length-based catch curves4. Beverton & Holt equations5. Wetherall plots6. Virtual Population Analysis7. Mark-recapture data8. Natural moralityMortality definitio

2、n: the death rate of a population of fishesThe life history is a serious of time intervals through which an individual survives several risks,Being eaten(Predation)Starving(Starvation)Being harvested(fishing)Dying from disease MoralityAn individual fish survives into a defined life-stage Survival cu

3、rves illustrate three fundamentally different mortality patterns.Type 1: survival high unit sentences(human)Type 2:constant survival rate throughout life(birds)Type 3 :survival very low early in life, rate constant during adulthood(fish)Glossary of symbolsDiscrete rates Instantaneous ratesA =total m

4、ortality rate Z =total mortality rateS=Total survival rate u= fishing mortality rate F =fishing mortality rate v=natural mortality rate M =natural mortality rateTotal mortality=harvest mortality + natural mortalityIn discrete time A=u+vIn continuous time Z=F+M Let N=number of fish, the rate of chang

5、e of fish over time is described most simply by the equation The survival rate(S) for unit time(when the time interval is 1 year) is: S=exp-ZInstantaneous rates may be converted to percentages as: survival(%)=100exp-Z And, as mortality is the complementary value of survival: mortality(%)=100(1-exp-Z

6、)The total morality rate(Z):Z=F+MIn an exploited fish stock,: Nt =N0exp-(M+F) Nt =N0exp-(M+F)Number surviving (Nt):This equation can be rearranged to give the linear equation:lnNt=lnN0-ZtAge-based catch curves The abundance of individuals in each different age classAge composition dataCatch per unit

7、 effort(CPUE) Infer age compositionAge composition dataCPUE dataLength-frequency data Length-based catch curvesIn the catch curve equation, The equation becomes:A length-converted catch curve is a plot of ln(F/t) against t, where F is the number of individuals in each age class and t is relative age

8、. The von Bertalanffy growth equationAssume that the rate of the growth of an organism declines with size so that the rate of change in length ,l, may be describe by:Where t is time,l is length(or some other measure of size)K is the growth rateL ， termed L infinity in fisheries science, is the asymp

9、totic length at which growth is zero. The von Bertalanffy growth equationIntegrating this becomes:3 parameters(L ,k and t0) The lower limit of he length class: the inverse of the von Bertalanffy equation with t0=0 as only relative age is required, with K=0.39, and L =121mm. That is:The value,dt, is

10、estimated as the age at L2(tL2) minus the age at L1(tL1).Mean ages are ages at the mid-point of each length class,(L1+L2)/2. l Beverton & Holt equation l Beverton & Holt equationBerverton & Holt suggested the following relationship between total morality,Z,and mean length:Where is the me

11、an length of fish L is the lower limit of the first length interval of fish which is fully vulnerable to the fishing gear. L , is the asymptotic length at which growth is zero.L l Beverton & Holt equationThe following version of the Bevertom&Holt equation may be used:Where Lc is the mean len

12、gth at the first capture. is the mean length of the fish in the catch.L , is the asymptotic length at which growth is zero.L ccL l Wetherall plotsA modified version of the Beverton & Holt Z-formula suggests that values 0f can be plotted against a series points, L, as a straight line:As before, i

13、s the mean length of all fish. Is the lower limits for the length intervals of fully vulnerable fish. -LL-L =a+bLLLL l Wetherall plots l Wetherall plots The mean length, , above the lower limit of the length interval is estimated as (F*L)/n,where L is the mid-point of the length interval . and n is

14、the number of fish above L.LL l Wetherall plots l Wetherall plots l Wetherall plots From the regression line, the value of Z/K is estimated from the slope , b, as:Z/K=-(1+b)/b=-(1-0.265)/(-0.265)=2.8L may be estimated from the intercept , a, with the X-axis as:L =-a/b=-63.49/-0.265As the value of th

15、e growth coefficient was estimated as K=1.2 from modal progression analysis, then:Z=2.8*1.2=3.4 l Virtual Population Analysisthe number of fish surviving from one year(Nt) to next year(Nt+1) is given by:Nt+1=Nt exp-(Ft +M) (1)The catch (Ct) is the proportion dying owing to fishing, and may be estima

16、ted from the catch equation:Ct=Ft/ZNt(1-exp-(F+M) (2)Divide equation(1) by equation(1) produce Gulland equation:Nt+1/Ct=(Ft+M)exp-(Ft+M)/Ft(1-exp-(Ft+M) (3) l Virtual Population Analysis l Virtual Population Analysis l Virtual Population AnalysisFrom Equation:Nt+1=NTexp-(M+F)Ft=-ln(Nt+1 /Nt)-M l Mar

17、k-recapture dataIf N0 is the number of fish initially tagged, then the number of tagged fish , Nr, at the beginning of any time interval r, would be:Nt=N0exp-Zt (1)The catch equation , the number of tagged fish catch(Cr) during time interval r is:Cr=Nr(F/Z)(1-exp-Zt) (2)Substitude equation 1 in equation 2 gives:Cr=No exp-Zt(F/Z)(1-exp-Zt) l Mark-recapture dataTaking natural logs of both sides of the equation, this becomes:LnCr=ln(N0F/Z)+ln(1-exp