wf4313/6413-fisheries management · announcements. don't forget that dr. neal is hosting a...
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WF4313/6413-Fisheries Management
Class 16
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Announcements
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Don't forget that Dr. Neal is hosting a fishing day out at the Blackjack Ponds THIS FRIDAY (Nov. 2nd). We will have open fishing, a chance to teach others to fish, a fillet station, and we will be frying fish (so bring an appetite!). If possible, please bring a few extra fishing rods that would be suitable for a novice fisherman, that you wouldn't mind sharing, to help out in case we don't have enough rods.
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AFS Meeting
• Our next meeting is scheduled for Wednesday, Nov. 7th!
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Percina crypta
https://georgiawildlife.com/sites/default/files/wrd/pdf/fact-sheets/halloween_darter-2008.pdf
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Revised Schedule**• October 30 = Group 1 @ Panther Creek• November 6th = Group 2 we’ll do something• November 13th = NO LAB… • Exam II = November 14th
• November 20th = Group 1 will do what group 2 did• November 27th & December 4th ??? ** Contingent on van availability
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Lab 11/6
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Interested in chasing more lamprey?Opportunities to assist on an
undergraduate research project.
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WHERE WE LEFT OFF
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HOW DO MANAGERS DETERMINE HOW MUCH TO HARVEST IN A COMMERCIAL FISHERY? FIRST THEY NEED TO ESTIMATE THE AMOUNT OF FISH OUT THERE!
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What do we need to figure out ho much to harvest?
What is in the biomass dynamics models?1. States: Fish abundance & biomass2. Parameters:
1. Intrinsic growth rate2. Carrying capacity
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Example of Lincoln Peterson Estimator
• Suppose you caught and tagged 948 crappie• Then you caught 421 the next day of which
167 were tagged.
421 948167
(421 1) (948 1)2383 11
2390
67 1
N
N
⋅
+ ⋅ +=
=
+
=
= −
Biased
Unbiased
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>2 Occasions Schnabel Estimator
• For each sample t, the following is determined:– Ct = Total number of individuals caught in sample t– Rt = Number of individuals already marked
(Recaptures) when caught in sample t– Mt = Number of marked animals in the population
just before the sample is taken.• Schnabel treated the multiple samples as a series
of Lincoln-Peterson (L-P) samples and obtained a population estimate as a weighted average of the L-P estimates to estimate N:
N = SUM (Mt*Ct) / ((SUM Rt) + 1)
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Capture-Recapture in practice more than 2 occasions
Suppose you go out 4 times to catch fish and your capture probability is 0.3. If there are 10,000 fish in the population the fish can be:Captured (p=0.3) or not (p=0.7) on occasion 1Captured (p=0.3) or not (p=0.7) on occasion 2Captured (p=0.3) or not (p=0.7) on occasion 3Captured (p=0.3) or not (p=0.7) on occasion 4
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Capture histories of individuals
Capture history (1 is captured and 0 is not)
Never captured
Captured every time
Adds up to 10,000
CaptureHistory Count
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What do we need to figure out ho much to harvest?
What is in the biomass dynamics models?1. States: Fish abundance & biomass2. Parameters:
1. Intrinsic growth rate2. Carrying capacity
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How do we estimate parameters?
We need time series of catch data to fit a model to!
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NOW THAT WE CAN ESTIMATE ABUNDANCE, HOW DO WE ESTIMATE PARAMETERS OF BIOMASS DYNAMIC MODELS?
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Suppose we have data over time
Catch/Effort
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1985 1990 1995 2000
6000
010
0000
1400
0018
0000
Year
Cat
ch (k
g)
Catch data over time
Fit a biomass dynamics model to this data like the Graham Schaeffer, Gompertz, Fox, Pella-Tomlinson.
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CPUE and predicted CPUE
1985 1990 1995 2000
6070
8090
100
110
Year
Cat
ch p
er u
nit e
ffort
Predicted CPUE
Graham-Schaefer Model Fit to data
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Predicted biomass dynamics
1985 1990 1995 2000
4500
0055
0000
6500
0075
0000
Year
Pre
dict
ed b
iom
ass
(kg)
11 1
11 1
( (1 ))
( . ( )0 4111 5
1 )584 1
tt t t
tt t t
BBB r BK
BB BB
−− −
−− −
= ⋅ ⋅ −
= ⋅ ⋅ −
+
+
Graham Schaeffer fit to CPUE data
Biomass in the first year was estimated to be 732259
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Using the fitted model we can predict the effect of varying fishing mortalities• Using the fitted model
• And the estimated catchability 0.0001485687• And CPUE in the previous year was 105• The biomass is estimated as CPUE/q=B• 105/0.0001485687=706743 kg of biomass
11 1 1( (1 ))
11 50.4
584 11 t
t t t tB BB B F B−− − −= ⋅ ⋅ − − ⋅+
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WHAT DO WE DO WITH ABUNDANCE AND PARAMETER ESTIMATES? WE CAN USE THEM TO ESTIMATE SUSTAINED YIELD--- LOTS OF HARVESTED CARP
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Biomass dynamics given 706743 kg of biomass!
Year
Biom
ass
(kg)
0
200000
400000
600000
800000
1000000
1200000
0 20 40 60 80 100
F=0
F=0.4
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Equilibrium sustained yield
0.0 0.1 0.2 0.3 0.4 0.5
040
000
8000
012
0000
Fishing mortality
Yie
ld (k
g)
Maximum yield at F=0.21!
Assuming equilibrium!
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Why is this important?
• Most harvest model evaluate equilibrium yield!
• We should harvest 706743*0.21=148416 kg• But it assumes equilibrium which can mess
with dynamics if equilibrium is violated. • Why? Lets explore this!
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Biomass dynamics
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Equilibrium conditions
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Biomass dynamics model assumptions
• Rates are constant• Parameters are constantLets explore these
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Varying carrying capacity
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Variation in carrying capacity
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Varying intrinsic growth rates
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0
20000
40000
60000
80000
100000
120000
140000
160000
180000
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Yiel
d (k
g)
Fishing Mortality
Variable r
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Variable K and r?
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Variable r and K
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Yiel
d (k
g)
Fishing Mortality
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Managing biomass yield of aquatic resources is not easy!
Maximum Sustained
Yield
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Dealing with these issues
• Precautionary approach• Abandon MSY
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Epitaph for MSY
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F0.1
The use of F0.1 has emerged as a useful “rule of thumb” for managing fisheries, but according to Hilborn and Walters (1992) this is an arbitrary, ad hoc strategy with no theoretical basis.
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How do we figure out F0.1
1. Find slope at origin2. Plot line with 10%
of this slope3. Find tangent of
curve at this slope
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0.0 0.1 0.2 0.3 0.4 0.5
040
000
8000
012
0000
Fishing mortality
Yie
ld (k
g)
Slope at origin
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0.0 0.1 0.2 0.3 0.4 0.5
040
000
8000
012
0000
Fishing mortality
Yie
ld (k
g)
10% of slope at origin
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0.0 0.1 0.2 0.3 0.4 0.5
040
000
8000
012
0000
Fishing mortality
Yie
ld (k
g)
10% of slope at origin
F0.1=0.2
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0.0 0.1 0.2 0.3 0.4 0.5
040
000
8000
012
0000
Fishing mortality
Yie
ld (k
g)
10% of slope at origin
F0.1=0.2FMSY=0.21
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F0.1 = 0.2
• Reduces harvest amount• FMSY: 706743*0.21=148416 kg• F0.1: 706743*0.20=141348 kg (~5%
reduction)• Why does F0.1 make sense?
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Continuous harvest?
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Continuous harvest?
Colvin, M.E., Pierce, C.L., Stewart, T.W., 2012. Semidiscretebiomass dynamic modeling: an improved approach for assessing
fish stock responses to pulsed harvest events. Canadian Journal of Fisheries and Aquatic Sciences 69, 1710-1721.
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Traditional biomass models
• Assumes harvest occurs continuously
• Biomass models guide stock management
• Pulsed harvest?
0 2 4 6 8 10
0
50
100
150
200
250
300
Years
Biom
ass
Continuous harvest
Does assuming continuous harvest make a difference?
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Pulsed harvest & biomass dynamics
0 2 4 6 8 10
0
50
100
150
200
250
300
Years
Biom
ass
A Pulsed Harvest System
Pulsed biomass removal
Development of Semi-Discrete Biomass Dynamics Models (BDMs)
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Semi-discrete models• Hybrid class of models that allow pulsed events in
continuous time• Continuous processes
- intrinsic growth rate
• Pulsed harvest
0 2 4 6 8 10
0
50
100
150
200
250
300
Years
Biom
ass
Pulsed harvest
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0 2 4 6 8 10
0
50
100
150
200
250
300
Years
Biom
ass
Can biomass dynamics models be improved by accounting for pulsed
harvests? YES
0 2 4 6 8 10
0
50
00
50
200
250
300
Years
Pulsed harvestContinuous harvest
Better!
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0.00 0.05 0.10 0.15 0.20 0.25 0.30
0
5
10
15
20
25
A: Schaefer
Continuous FMSYSemi-discrete FMSY
ContinousSemi-discrete
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
5
10
15
20
25
30
B: Fox
Continuous FMSYSemi-discrete FMSY
0.00 0.05 0.10 0.15 0.20 0.25 0.30
0
5
10
15
20
C: Pella-Tomlinson
Continuous FMSYSemi-discrete FMSY
Equ
ilbriu
m y
ield
(kg
ha1
)
Fishing mortality (kg ha1yr1)
Equilibrium sustainedyieldsAssuming continuous harvest over estimates MSY!