1. ESTIMATION OF ANIMAL VITAL RATES WITH KNOWN FATE STUDIES ALL MARKED ANIMALS DETECTED

2. KNOWN FATE STUDIES Sample of n animals followed through time and fate can be determined  Radio telemetry studies  Nest success

3. BINOMIAL SURVIVAL MODEL Follow n subjects, and observe y survivors f(y|n,s) = ( ) s y (1-s) n-y L (s|n,y) = s y (1-s) n-y ŝ=y/n; var ̂ (ŝ)=ŝ(1-ŝ)/n  Fate of individual is independent  All detected, and fates are known  No censoring (e.g., no failure of radio) nyny

4. MULE DEER EXAMPLE Number Released AliveDead Treatment571938 Control592138 TreatmentControl ŝ 19/57 = 0.33321/59=0.356 Vâr(ŝ) 0.333(1-0.333)/57=0.0038990.356(1-0.356)/59=0.003886 95%CI0.211 - 0.4580.234 - 0.478  2 =0.058 P>=0.81 example from White and Garrott (1990:209-210) in which 120 mule deer fawns in Colorado were equipped with radio transmitters and followed through winter. Sixty-one fawns were on study area near an oil shale development (“treatment”) and 59 were from areas removed from human activity

5. CONTINUOUS SURVIVAL METHODS (NON-PARAMETRIC APPROACH): KAPLAN-MEIER METHOD S(t) =  ( ) =  (1 - ) S(t) = Probability of surviving t time units from the beginning of the study d = No. of deaths recorded at time j n = No. of animals alive and at risk at time j t = time units since the beginning of the study n j – d j n j djnjdjnj t i=1 t i=1

6. EXAMPLE RADIO-TAGGED BLACK DUCKS Week12345678 Number alive at start4847453934282524 Number dying12254310 Number alive at end47453934282524 Number censored00402000 Ŝ 1 = 47/48 = 0.979 Ŝ 2 = 45/47 = 0.957 Ŝ 3 = 39/41 = 0.951 (note: only 41 because 4 were censored) Ŝ 4 = 34/39 = 0.872 Ŝ 5 = 28/32 = 0.875 (note: only 32 because 2 were censored) Ŝ 6 = 25/28 = 0.893 Ŝ 7 = 24/25 = 0.960 Ŝ 8 = 24/24 = 1.000

7. KM ESTIMATOR Censoring, e.g., transmitter failure  But censoring should be independent of survival  Keep to a minimum (e.g., predator effect on radios) Staggered entry: e.g., animals leave study area (but return)

8. DESIGN CONSIDERATIONS Capture n animals  How many? Use binomial model for sample allocation Must be able to record fates (alive or dead) at the end of each interval  Trade off: study area must be small enough to permit frequent surveys- but too small may lead to more censoring…  Animals not encountered should be censored, and if later resighted should be considered as a new staggered entry  Try to prevent censoring  Censoring must be random and independent of fate

9. NEST STUDIES AND THE MAYFIELD METHOD Hatching rate (prop nest success)  Many nests encountered late in nesting phase  Positive bias in survival (eg., dsr=.99)  “Early” nests have more survival days (s 1 =.99 30 =.74, s 29 =.99 2 =.98)  Chance of failure related to N of days Need to adjust survival rates Basic idea: consider number of days of exposure, rather than number of nests

10. HATCHING SUCCESS-BIAS

11. STUDY DESIGN Nests marked or uniquely identifiable Periodically monitored to determine status Censoring and staggered entry are possible Record monitoring history for each individual: date, time, status

12. MAYFIELD’S ESTIMATOR dsr: daily survival rate dsr ̂ = 1 – d / exposure S ̂ = (dsr ̂ ) t S: probability of survival for study period

13. EXPOSURE Nest No.1 May8 May15 MayExposure days 111114 (2*7) 2103.5 (.5*7) 311010.5 (1*7+.5*7) Total28 Survival histories and exposure via the Mayfield method of three hypothetical nests (1-active nest, 0-nest destroyed)

14. DSR AND SURVIVAL dsr ̂ = 1 – ( d/exposure ) = 1 - 2/28 = 0.9286 var(dsr ̂ ) = {(28-2)x2 / (28) 3 = 0.0023688 S ̂ = dsr ̂ 34 = 0.9286 34 = 0.0806 95% confidence interval: 0.002 – 2.240

15. ASSUMPTIONS Random sampling Rates constant (Accommodate through stratification) Visits recorded Pr(s) not influenced by observer Pr(visit) independent of Pr(survival)

16. MARK MLE DSR MLE in Mark no need for midpoint assumption For details of nesting model in Mark see: http://www.auburn.edu/~grandjb/wildpop/lectures/lect_04.pdf http://www.phidot.org/software/mark/docs/book/pdf/chap17.pdf

17. NEST SURVIVAL MODEL IN MARK Daily nest survival model  Function of nest-, group-, and time-specific explanatory variables (Dinsmore et al. 2002). Allows visitation intervals to vary Requires no assumptions about when nest losses occur. Uses encounter histories of individual nests Likelihood-based procedures Values for time-specific explanatory variables, such as age, date, and precipitation, are allowed to vary daily.

18. INPUT FOR MARK 1.day the nest was found 2.last day the nest was checked when alive 3.last day the nest was checked 4.fate of the nest (0 = successful, 1 = depredated) 5.number (frequency) of nests that had each history (usually 1) nest survival group=1; 1 59 62 1 3; 1 48 48 0 1; 1 37 37 0 1; 1 22 26 1 1; 1 22 24 1 1; 1 12 17 1 1; 1 27 32 1 1; 1 32 32 0 1; 1 45 51 1 1; 1 26 32 1 1;

19. DESIGN ISSUES: NEST SUCCESS Can predict n of samples (nests) needed Trade off between more nests and more visits  Fewer visits & more nests = increased precision  Fewer visits = less information on stage transitions and fledging

20. WHAT YOU SHOULD KNOW Assumptions of the models Random sampling, Rates constant, Visits recorded, Pr(s) not influenced by observer, Pr(visit) independent of Pr(survival) Bias associated with hatching rate  Many nests encountered late in nesting phase  Positive bias in survival  “Early” nests have more survival days, chance of failure related to N of days Use and limitations of censoring and staggered entry  censoring should be independent of survival and kept to a minimum  Animals not encountered should be censored, and if later resighted should be considered as a new staggered entry