Project leader: Professor Nils Chr. Stenseth Post-doc: Dr. Scient. (PhD) Thrond O Haugen

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… Alive and recaptured p Alive f 1-p Alive and not recaptured Marked and released 1-f Dead or emigrated • is apparent survival (open systems) pis probability of recapture

5. f1 f2 f3 f4 f5 ...tocapture historyandsurvival estimats CaptureMark Release Capture occations Time interval p2 p3 p4 p5 p6 Capture history: 100100, with probability: f1(1-p2)f2(1-p3)f3p4c4 c4 is the probability of not being recaptured after 4th capture occation [= (1-f4)+(1-p5)f4(1- p6f5)] Parameters areestimatedby maximum likelihood method

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 q of the vector q containing all identifiable parameters [i.e. maxlnL(q)] ^ ^

7. MLE: an example t1 t2 t3 b3 f1 f2 Para- meters p1 p2 p3 Likelihood: L= (f1p2b3)X111[f1p2(1-b3)]X110[f1 (1-p2)b3]X101 (c1)X100 lnL(f1, p2, b3)= 4ln(f1p2b3)+7ln[f1p2(1-b3)]+2ln[f1 (1-p2)b3]+9ln(c1)

8. Based on log-likelihood-ratio tests (LRT) For nested models only LRT = -2lnL(q0)-(-2lnL(q)) ~c2 with np-rdf 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! Model selection q0= parameter vector for reduced model q = parameter vector for full model

9. Combination fate diagram p Alive and recaptured F Alive and still present 1-p Alive and not recaptured Alive S 1-F Alive and left the system Capture Mark Release r Dead and reported 1-S Dead 1-r Dead and not reported

10. F1 F2 F3 F4 F5 S1 S2 S3 S4 p1 p2 p3 p4 p5 r1 r2 r3 r4 J F M A M J J A S O N D 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 tof 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)

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. J F M A M J J A S O N D Windermere Dead recoveries – natural causes Dead recoveries from gill nets Marking and recaptures Marking and some recaptures by use of traps and seines Dead recoveries from gill nets – Experimental fisheries only Dead recoveries from anglers Dead recoveries – natural causes Dead recoveries from gill nets and anglers Marking and recaptures by use of trap in a fish ladder Mjøsa

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