12 VPA 实际种群分析

250 1101
280 439 310 265
80.88
32.25 19.46
1.18
1.23 1.33
262 0.793
118 0.839 51 1.292
0.692 1.146
0.874 0.959 1.188 1.087
125 2520
70 2010 34 1350
340 47
2875
3.45
M t 2
Assuming growth is described by von-Bertalanfly growth function:
Lt L (1 e
K ( t t 0 )
)
Lt 1 t t 0 ln( 1 ) k L 1 t t1 t 2 K L1 L2 ) ln( 1 ) ln( 1 L L
% error of population number
% error of fishing mortality
30 25 20 15 10 5 0 1 2 3 4 5 6 Age 7 8 9 10 11
References
• • • • John Shepherd http://jgshepherd.com/default.asp David Sampson http://marineresearch.oregonstate.edu/ass ets/page_folders/faculty_page/sampson_h p.htm • Zhan, B. 1995, Fish Stock Assessment, Beijing: China Agriculture Press, pp353, in Chinese.
Linear Interpolation Method
f x
Slope
•
• x2
x1
x2 x1 f ( x1) f ' ( x1)
Βιβλιοθήκη Baidu
Newton Method
From beginning to mid of the year: Mid year：
N Nie
M 2
N N Ci
N y 1,a 1 N y ,a exp( Z y ,a )......... ........( 2) (1) /(2), C y ,a N y 1,a 1 Fy ,a (1 exp( Z y ,a )) Z y ,a exp( Z y ,a ) .........( 3)
Cohort analysis equation is:
N t ( N t 1e
M 2
Ct )e
M 2
From length L to length (L+∆L), assuming the experienced time is ∆t:
N L ( N L L e
M t 2
CL )e
1.09 1.11 1.12 1.15
769 0.214 621 0.235 491 0.252 381 0.374
0.377 0.567 0.426 0.552 0.488 0.516 0.572 0.654
235 1170 212 1800 182 2450
241-270
271-300 301-330 331-360 ∑
1 L L1 ln K L L2
e
M t 2
L L1 L L 2
M t 2
M 2K
XL e

N L ( N L L X L CL ) X L
• Given catch numbers at each length groups (CL),von-Bertalanffy growth parameters (L∞, K), and natural mortality (M), assuming the population number at the largest length group,
Cohort Analysis Equation
N i N i 1 e M 2 Ci e M 2
Assuming M is known, and a starting value of the terminal age N11


N10 N11 e N9
10
N
△t 0.0896
N OS ( N L N LL ) Z
B N OS aL
b
Indian mackerel
Rastrelliger kanagurta
LCA (length based cohort analysis) calculation table of spring season chub mackerel fishery in the northern South China Sea is below:
f x
• f x2
x1
x3
•
f x3
x2
•f x 1
f x1 0, f x2 0 x1 x2 then : x3 2
Bisection Method
f x
•x
2
x1
•x
3
•
x 2 x1 x3 x 2 f ( x 2) f ( x 2) f ( x1)
L (mm)
91-120 121-150 151-180 181-210 211-240
L
(mm)
n
100 67 130 275 160 201 190 75 220 405
CL (105)
4.92 20.20 14.76 5.51 29.75
XL
NL
Z∆t
∆t
Z
Nos B (105) (t)
261 675
Thornback ray
Raja clavata
Atlantic cod
Gadus morhua
Virtual Population Analysis Equations
C y ,a N y ,a Fy , a Z y ,a (1 exp( Z y ,a )).......( 1)
211
1.57
14 1.404
3.4
1.865 0.752
14
744
1135 12700
Starting Value
Goldband Goatfish (Upeneus moluccensis)
EXERCISE
• Goldband Goatfish (Upeneus moluccensis) (RAGAY GULF, 20 January 1980) • Assuming annual yield is ???t, and 200*105 ind., sample size was 671 ind. • Linf=20.0cm, K=0.93y-1, T=28.5oC, M=1.92y-1 • W=0.006*L3.27
Z
F
0.5509 1.0953 0.8492 1.2249 0.8196 0.8443
0.3509 0.8953 0.6492 1.0249 0.6196 0.6443
479
0.2 1.105171
L 7.5 8.5
n 4 22
CL 1.19 6.55
XL 1.0898
NL 456.0
Z△t 0.1879
6
479
Length Based Cohort Analysis
• In the tropical fisheries, if age data are not available, length data can be used to conduct the virtual population analysis using a length based cohort analysis.
• ①Assuming M is known, and a starting value of the terminal age Ny+1,a+1. • ②Given Cy,a, M(Z=Fy,a+M), Ny+1,a+1, Fy,a can be calculated from eq.(3). • ③Given Cy,a, M, Fy,a, Ny,a can be calculated from eq.(1). • ④Given Cy-1,a-1, M, Ny,a, Fy-1,a-1 can be calculated from eq.(3)…….. • ⑤Repeat steps ② to ④, until the youngest age. • ⑥Then population numbers (N) and fishing mortality rate (F) of all the ages are calculated. • N.B. from eq.(3), F can not be solved analytically, iterative numerical methods are needed.
Average annual yield in 1977-1980 was 4132.33t, sample size was 2875 ind., sample weight was 562.86kg, the calculated annual catch was 211.22*105 ind.. • L∞=380mm, K=0.3y-1, M=0.49y-1, • W=5.947*10-6L3.14
N i 1
M N e 2 M 2
From mid to end of the year：
N i 1 N Ci e N i 1 N i e

M 2
Ci e

M 2
Originally it was an approximation to VPA
M 2
C10 e C9 e
e
M 2


M 2
M 2


2
N1 N 2 e M
Z=log(Na/Na+1), F=Z-M
C2 e M

2
Exercise
North Sea cod 1992 data, (M=0.2y-1, exp(M/2)=1.105)
Age 1 2 3 4 5 Catch 27967 32216 8697 4995 1057 Population Z F
• Long-term management: • Maximum Sustainable Yield (MSY), • surplus production model / yield per recruit model • Short-term management: • Total Allowable Catch (TAC), • virtual population analysis, cohort analysis
• THANK YOU FOR YOUR ATTENTION AND QUESTIONS!
Age
1 2 3 4 5 6
M= exp(M/2)=
Catch Population 27967 104422 32216 60188 8697 20127 4995 8609 1057 2529 479 1114
N L ( N L L e
M t 2
C L )e
M t 2
N LL N L N LL N L2L ......
NL Z t ln S ln N L L NL Z ln t N L L
Average population number Average Biomass
ML (cm) 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 16.5
n 4 22 213 105 103 85 68 53 15 3
CL (105)
XL
NL
Z∆t
∆t
Z
Nos (105)
B (t)
20 18 16 14 12 10 8 6 4 2 0 1 2 3 4 5 6 Age 7 8 9 10 11