1. 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

2. 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)

3. 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)

4. From fate diagrams… Marked and 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

5. ...to capture history and survival estimats Capture Mark Release 11 55 44 33 22 Time interval p2p2 p5p5 p4p4 p3p3 p6p6 Capture history: 100100, with probability:  1 (1-p 2 )  2 (1-p 3 )  3 p 4  4  4 is the probability of not being recaptured after 4 th capture occation [= (1-  4 )+(1-p 5 )  4 (1- p 6  5 )] Parameters are estimated by maximum likelihood method Capture occations

6. 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(  )] ^ ^

7. MLE: an example 33 p1p1 t1t1 t2t2 t3t3 p2p2 p3p3 11 22 Para- meters Likelihood: L= (  1 p 2  3 ) X 111 [  1 p 2 (1-  3 )] X 110 [  1 (1- p 2 )  3 ] X 101 (  1 ) X 100 lnL(  1, p 2,  3 )= 4ln(  1 p 2  3 )+7ln[  1 p 2 (1-  3 )]+2ln[  1 (1- p 2 )  3 ]+9ln(  1 )

8. 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 model  parameter vector for full model

9. Combination fate diagram Capture Mark Release Dead Alive Alive 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

10. MAMJJASONDFJ p1p1 p5p5 p4p4 p3p3 p2p2 F1F1 F5F5 F4F4 F3F3 F2F2 r4r4 r3r3 r2r2 r1r1 S4S4 S3S3 S2S2 S1S1 Joint analysis of dead recoveries and live encounters—non-Brownie parameterisation S t = probability of survival from time t to t+1(survival rate) r t = probability of being found dead and reported during the t to t+1 interval (recovery probability) F t = probability at t of remaining in the sampling area to t+1 | alive at t (fidelity rate) p t = probability of recapture at time t | alive and in sampling area (recapture rate)

11. 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)

12. Windermere MAMJJASONDFJ 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

14. 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?

16. Quarterly survival rates in Windermere pike for 1954–1963 cohorts Tagging cohorts analysed

17. Netting effort in Windermere 1954–1969

18. Proportions captured in south and north basin

19. Late-autumn survival vs rest of the year Tagging cohorts analysed

20. Fishing effort and late-autumn survival

21. Does sex affect survival? Tagging cohorts analysed

22. Does size affect survival?

23. Half-year survival rates for Hunder trout 1966 to 1998

24. Age-structured model combined with annual summer survival for spawning age > 4

25. 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