virtual population analysis - fisheries management
TRANSCRIPT
Virtual Population Analysis
Fish and Fisheries 2014
Dr Magnus Johnson
m
f
N
z
t
Which of these factors do we know?
t-1t-2
If we have 1000 fish and we have a mortality rate of 20% (m = 0.2)How many are left after 1 year?
What figure do you get if mortality is constant throughout the year. Try calculating the same thing but using monthly mortality.
Z
tt eNN
1
Using natural logs we can calculate the number of fish remaining after a year. . . Or 2 years . . Or three years etc
Zt
tt eNN
1Number of fish surviving after 1 year
Zt
tt eNN 1
Number of fish that were around the previous year
3
13
ZeNN A really useful aspect of logs is that we can work out fish surviving after X years simply by multiplying Z
NB! Zt is not the same as Zt !!!!
Z
tttt eNNNNDeaths
1
Z
tt eNNSurvivors
1
Z
t eN 1
Z
t eN 1This number is the number of fish that die due to fishing and natural mortality.
Z = F + MTotal mortality = Fishing mortality + Natural mortality
Z
FProportion of fish dying due to fishing mortality(i.e. Catch)
Z
t eN 1 t
t
Z
F*
Number of fish dying in a year
Proportion due to fishing
Calculate the number of fish from a thousand that would be caught if F = 0.5 and M = 0.1
tC
Z
t eN 1 t
t
Z
F* tC
313
3
33
Ze
Z
F
CN
Assume that M = 0.2, that there is a terminal value of F = 0.6 and that we had a catch of 80 fish in year t
Number of fish that must be around in year 3 in order to yield a particular catch.
8.018.0/6.0
80
e
Nt
= 194 fishThis is the number of fish that must have been around this year to result in a catch of 80 fish.
313
3
33
Ze
Z
F
CN
We now know that 194 fish survived and from that we had a catch of 80 fish this year. We also know that we had a catch of 90 fish the previous year and that M = 0.2.
2
32
ZeNN . .but we don’t know Z2
22 13
2
22
ZZeeN
Z
FC
12
3
2
22
ZeN
Z
FCSimplifies to:
What numbers can we slot into this equation?
212
2
22
ZeN
Z
FC
≡
122 ZZ
ee
12
3
2
22
MFeN
MF
FC
11942.0
902.0
2
2 2
F
eF
F
)(
322 MF
eNN
Z = F + M
What tool in excel can we use to find F?
Now we can use the fact that we know F2
to calculate the population of fish N2
Problems?
• We are using catch figures
• We don’t know M
• We don’t know the terminal F
• We are assuming M to be constant
• We are treating the population as a closed system
• Can we use it to predict anything?