population dynamics of aquatic top predators: effects of harvesting regimes and environmental...
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Population dynamics of aquatic top predators: effects of harvesting regimes and
environmental factors
Project leader: Professor Nils Chr. Stenseth
Post-doc: Dr. Scient. (PhD) Thrond O Haugen
Who is involved?
• Centre for Ecology and Hydrology– PhD Ian Winfield
• University of Oslo– Professor Leif Asbjørn Vøllestad– PhD Per Aass (at the Zoological Museum)
• Mangement institutions– Tore Qvenild (fishery manager, Hedmark county)– MSc Ola Hegge (fishery manger Oppland county)
• Norwegian Institute of Water Research (NIVA)
Project objectives• Increase knowledge on population dynamics of
aquatic top predators• How is population dynamics affected by
changes in:– Abiotic conditions (temperature and eutrophication)– Biotic conditions (prey abundance, density)– Harvesting regimes (qualitative and quantitative)
• Reliable estimates of demographic rates:– Survival (age, stage, sex specific, environment-
specific, density-specific, basin specific)– Recruitment (population growth rate)
From fate diagrams…
Markedand
released Dead or emigrated
Alive
1-p
p
1-
Alive and recaptured
Alive and not recaptured
is apparent survival (open systems)
p is probability of recapture
...to capture history and survival estimats
Capture Mark
Release
1 5432
Time interval
p2 p5p4p3 p6
Capture history: 100100,
with probability: 1(1-p2)2(1-p3)3p44
4 is the probability of not being recaptured after 4th capture occation [= (1-4)+(1-p5)4(1- p65)]
Parameters are estimated by maximum likelihood method
Capture occations
Maximum log-likelihood estimation(MLE)
• Under the assumption of mutually exclusive capture histories probabilities of unique capture histories may be estimated– independence of fates and identity of rates among individuals
• Statistical likelihood of a data set is the product of capture histories over all capture histories observed
• Maximizes the log-likelihood for the estimator of the vector containing all identifiable parameters [i.e. maxlnL()]
^^
MLE: an example
X111=4 R 11p 23
X110=7 R 11p 2(1-3)
X101=2 R 11(1-p 2)3
X100=9 R 1[1-1p 2-1(1-p 2)3]
Captured 3rd occation
Expected numbers 3rd occation
R 1=22X11
X10
Numbers released
Captured 2nd occation
3p1
t1 t2 t3
p2 p3
1 2Para-meters
Likelihood: L= (1p23)X111[1p2(1-3)]X110[1 (1- p2)3]X101 (1)X100
lnL(1, p2, 3)= 4ln(1p23)+7ln[1p2(1-3)]+2ln[1 (1- p2)3]+9ln(1)
Model selection• Based on log-likelihood-ratio tests (LRT)
– For nested models only• LRT = -2lnL()-(-2lnL()) ~2 with np-r df• Problems with multiple testing
• Akaike Information Criterion (AIC)– No testing involved– AIC = -2lnL + 2*np (choose the lowest)– May not converge to one model only
• Biological a priori knowledge should guide the formation of hypotheses and the selection of models!
parameter vector for reduced modelparameter vector for full model
Combination fate diagram
CaptureMark
Release
Dead
AliveAlive and not recaptured
Alive and recaptured
Dead and reported
Dead and not reported
p
1-p
1-r
r
1-F
F
1-S
S
Alive and still present
Alive and left the system
M A M J J A S O N DFJ
p1 p5p4p3p2
F1 F5F4F3F2
r4r3r2r1
S4S3S2S1
Joint analysis of dead recoveries and live encounters—non-Brownie parameterisation
St = probability of survival from time t to t+1(survival rate)
rt = probability of being found dead and reported during the t to t+1 interval (recovery probability)
Ft= probability at t of remaining in the sampling area to t+1 | alive at t (fidelity rate)
pt = probability of recapture at time t | alive and in sampling area (recapture rate)
The data series• Trout from Mjøsa (n = 7002; 1966–2001); pike from
Windermere (n = 5560; 1949–2001)• Combined data
– Recoveries (dead) and recaptures– Continous and experimental recaptures
• Good environmental data (covariates)– Eutrophication, temperature, prey abundance– Fishing effort
• Multiple recaptures– 57.9 % of the pike have been recaptured once or more – 38.1 % for Mjøsa trout
• Constraints:– Allmost exclusively mature fish (all for the trout)
Windermere
M A M J J A S O N DFJ
Mjøsa
Dead recoveries from gill nets –Experimental fisheries only
Dead recoveries from gill nets
Marking and recaptures
Marking and recaptures by use of trap in a fish ladder
Dead recoveries from gill nets and anglers
Dead recoveries from anglers
Marking and some recaptures by use of
traps and seines
Dead recoveries – natural causes
Dead recoveries – natural causes
Frequency of recaptures
0.090
0.014
0.004
0.381
0.041
0.006
0.579
0.000
7
0.000
0.001
0.010
0.100
1.000
Once ormore
Twice ormore
Three timesor more
Four timesor more
Five times
Prop
ortio
n
WindermereMjøsa
Addressed questions
• Are there temporal inter- and intra-annual trends in survival rates?
• Does gill netting affect the survival rates?• What is the relative contribution from anglers and
gill netting to the total mortality?• Does size at marking affect the survival rates?• Does age affect survival rates?• Does sex affect the survival rates?
0 %
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 %
100 %
North basin South basin
MigratingNot migrating
Quarterly survival rates in Windermere pike for 1954–1963 cohorts
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
S
Tagging cohorts analysed
Netting effort in Windermere 1954–1969
0
500
1000
1500
2000
2500
3000
3500
4000
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
Net
ting
effo
rt (3
0 yd
net
day
s)
TotalNorth basinSouth basin
0 %
20 %
40 %
60 %
80 %
100 %
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
South basinNorth basin
Proportions captured in south and north basin
Late-autumn survival vs rest of the year
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
S
Tagging cohorts analysed
Fishing effort and late-autumn survival
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0 500 1000 1500 2000 2500 3000 3500
Gillnet effort for the south basin
Ear
ly w
inte
r sur
viva
l
Does sex affect survival?
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
S
Males
Females
Tagging cohorts analysed
Does size affect survival?
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965
S
Not size adjustedSize-adjusted
Size-adjusted survival estimates (standardized to 55.1 cm)
Half-year survival rates for Hunder trout 1966 to 1998
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
S
Pooled estimates for summer/autumn survival during spawning run and for first winter following first spawning
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
para
met
er e
stim
ate
Spr
Summer survival for spawning age > 4pooled half-year survival for spawning age 1-4
Age-structured model combined with annual summer survival for spawning age > 4
Challenges to come
• How sensitive are the parameter estimates to changes in the discretisation policy
• GOF must be performed!• Estimating c-hat• Do the entire time series for Windermere
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