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